TSTP Solution File: GEO187+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 93.44s 93.62s
% Output : Refutation 93.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 10 unt; 21 nHn; 16 RR)
% Number of literals : 92 ( 0 equ; 11 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO187+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
file('GEO187+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,A) ),
file('GEO187+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,B) ),
file('GEO187+2.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('GEO187+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ apart_point_and_line(A,B)
| distinct_lines(B,C)
| apart_point_and_line(A,C) ),
file('GEO187+2.p',unknown),
[] ).
cnf(15,axiom,
~ apart_point_and_line(dollar_c4,line_connecting(dollar_c2,dollar_c1)),
file('GEO187+2.p',unknown),
[] ).
cnf(16,axiom,
~ apart_point_and_line(dollar_c3,line_connecting(dollar_c2,dollar_c1)),
file('GEO187+2.p',unknown),
[] ).
cnf(17,axiom,
distinct_points(dollar_c4,dollar_c3),
file('GEO187+2.p',unknown),
[] ).
cnf(18,axiom,
distinct_points(dollar_c2,dollar_c1),
file('GEO187+2.p',unknown),
[] ).
cnf(19,axiom,
( apart_point_and_line(dollar_c2,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3)) ),
file('GEO187+2.p',unknown),
[] ).
cnf(20,plain,
( distinct_points(dollar_c4,A)
| distinct_points(dollar_c3,A) ),
inference(hyper,[status(thm)],[17,4]),
[iquote('hyper,17,4')] ).
cnf(22,plain,
( distinct_points(dollar_c3,A)
| distinct_points(dollar_c4,B)
| distinct_points(A,B) ),
inference(hyper,[status(thm)],[20,4]),
[iquote('hyper,20,4')] ).
cnf(23,plain,
distinct_points(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[20,1]),
[iquote('hyper,20,1')] ).
cnf(28,plain,
( apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3))
| distinct_lines(line_connecting(dollar_c4,dollar_c3),A)
| apart_point_and_line(dollar_c2,A) ),
inference(hyper,[status(thm)],[19,13]),
[iquote('hyper,19,13')] ).
cnf(41,plain,
( distinct_points(dollar_c3,A)
| distinct_points(A,dollar_c4) ),
inference(hyper,[status(thm)],[22,1]),
[iquote('hyper,22,1')] ).
cnf(44,plain,
( distinct_points(A,dollar_c4)
| distinct_points(dollar_c3,B)
| distinct_points(A,B) ),
inference(hyper,[status(thm)],[41,4]),
[iquote('hyper,41,4')] ).
cnf(56,plain,
( distinct_points(A,dollar_c4)
| distinct_points(A,B)
| distinct_points(dollar_c3,C)
| distinct_points(B,C) ),
inference(hyper,[status(thm)],[44,4]),
[iquote('hyper,44,4')] ).
cnf(71,plain,
( apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c3,A)
| apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c4,A) ),
inference(hyper,[status(thm)],[28,11,23]),
[iquote('hyper,28,11,23')] ).
cnf(257,plain,
( distinct_points(A,dollar_c4)
| distinct_points(A,B)
| distinct_points(B,C)
| distinct_points(dollar_c3,D)
| distinct_points(C,D) ),
inference(hyper,[status(thm)],[56,4]),
[iquote('hyper,56,4')] ).
cnf(258,plain,
( distinct_points(A,dollar_c4)
| distinct_points(A,B)
| distinct_points(B,dollar_c3) ),
inference(hyper,[status(thm)],[56,1]),
[iquote('hyper,56,1')] ).
cnf(710,plain,
( apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c3,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,7,18]),16,15,1]),
[iquote('hyper,71,7,18,unit_del,16,15,1')] ).
cnf(1339,plain,
( distinct_points(A,dollar_c4)
| distinct_points(A,B)
| distinct_points(B,C)
| distinct_points(C,D)
| distinct_points(dollar_c3,E)
| distinct_points(D,E) ),
inference(hyper,[status(thm)],[257,4]),
[iquote('hyper,257,4')] ).
cnf(1881,plain,
( apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[710,8,258]),1,1,1]),
[iquote('hyper,710,8,258,unit_del,1,1,1')] ).
cnf(1953,plain,
apart_point_and_line(dollar_c1,line_connecting(dollar_c4,dollar_c3)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1881,7,258]),1,1,1]),
[iquote('hyper,1881,7,258,unit_del,1,1,1')] ).
cnf(1954,plain,
( distinct_lines(line_connecting(dollar_c4,dollar_c3),A)
| apart_point_and_line(dollar_c1,A) ),
inference(hyper,[status(thm)],[1953,13]),
[iquote('hyper,1953,13')] ).
cnf(2156,plain,
( apart_point_and_line(dollar_c1,A)
| apart_point_and_line(dollar_c3,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c3,A)
| apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c4,A) ),
inference(hyper,[status(thm)],[1954,11,23]),
[iquote('hyper,1954,11,23')] ).
cnf(4450,plain,
( distinct_points(A,dollar_c4)
| distinct_points(A,B)
| distinct_points(B,C)
| distinct_points(C,D)
| distinct_points(D,dollar_c3) ),
inference(hyper,[status(thm)],[1339,1]),
[iquote('hyper,1339,1')] ).
cnf(4451,plain,
( distinct_points(A,dollar_c4)
| distinct_points(B,C)
| distinct_points(C,D)
| distinct_points(D,dollar_c3)
| distinct_points(A,E)
| distinct_points(B,E) ),
inference(hyper,[status(thm)],[4450,4]),
[iquote('hyper,4450,4')] ).
cnf(4486,plain,
( apart_point_and_line(dollar_c3,line_connecting(dollar_c4,dollar_c3))
| apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2156,8,18]),16,15,1]),
[iquote('hyper,2156,8,18,unit_del,16,15,1')] ).
cnf(4519,plain,
apart_point_and_line(dollar_c4,line_connecting(dollar_c4,dollar_c3)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4486,8,258]),1,1,1]),
[iquote('hyper,4486,8,258,unit_del,1,1,1')] ).
cnf(4552,plain,
distinct_points(A,dollar_c4),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4519,7,4451]),1,1])])])]),
[iquote('hyper,4519,7,4451,unit_del,1,1,factor_simp,factor_simp,factor_simp')] ).
cnf(4553,plain,
$false,
inference(binary,[status(thm)],[4552,1]),
[iquote('binary,4552.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:22:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox2 on n009.cluster.edu,
% 1.71/1.91 Wed Jul 27 07:22:51 2022
% 1.71/1.91 The command was "./otter". The process ID is 27734.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 formula_list(usable).
% 1.71/1.91 all X (-distinct_points(X,X)).
% 1.71/1.91 all X (-distinct_lines(X,X)).
% 1.71/1.91 all X (-convergent_lines(X,X)).
% 1.71/1.91 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.71/1.91 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.71/1.91 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.71/1.91 all X Y Z (distinct_points(X,Y)-> (apart_point_and_line(Z,line_connecting(X,Y))->distinct_points(Z,X)&distinct_points(Z,Y))).
% 1.71/1.91 all X Y Z (convergent_lines(X,Y)-> (apart_point_and_line(Z,X)|apart_point_and_line(Z,Y)->distinct_points(Z,intersection_point(X,Y)))).
% 1.71/1.91 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)).
% 1.71/1.91 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.71/1.91 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.71/1.91 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.71/1.91 -(all X Y U V (distinct_points(X,Y)&distinct_points(U,V)& -apart_point_and_line(X,line_connecting(U,V))& -apart_point_and_line(Y,line_connecting(U,V))-> -apart_point_and_line(U,line_connecting(X,Y))& -apart_point_and_line(V,line_connecting(X,Y)))).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 -------> usable clausifies to:
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] -distinct_points(X,X).
% 1.71/1.91 0 [] -distinct_lines(X,X).
% 1.71/1.91 0 [] -convergent_lines(X,X).
% 1.71/1.91 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.71/1.91 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.71/1.91 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.71/1.91 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.71/1.91 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.71/1.91 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.71/1.91 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.71/1.91 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).
% 1.71/1.91 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.71/1.91 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.71/1.91 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.71/1.91 0 [] distinct_points($c4,$c3).
% 1.71/1.91 0 [] distinct_points($c2,$c1).
% 1.71/1.91 0 [] -apart_point_and_line($c4,line_connecting($c2,$c1)).
% 1.71/1.91 0 [] -apart_point_and_line($c3,line_connecting($c2,$c1)).
% 1.71/1.91 0 [] apart_point_and_line($c2,line_connecting($c4,$c3))|apart_point_and_line($c1,line_connecting($c4,$c3)).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.71/1.91
% 1.71/1.91 This is a non-Horn set without equality. The strategy will
% 1.71/1.91 be ordered hyper_res, unit deletion, and factoring, with
% 1.71/1.91 satellites in sos and with nuclei in usable.
% 1.71/1.91
% 1.71/1.91 dependent: set(hyper_res).
% 1.71/1.91 dependent: set(factor).
% 1.71/1.91 dependent: set(unit_deletion).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.71/1.91 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.71/1.91 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.71/1.91 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.71/1.91 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.71/1.91 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.71/1.91 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 93.44/93.62 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 93.44/93.62 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 93.44/93.62 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 93.44/93.62 ** 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).
% 93.44/93.62 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 93.44/93.62 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 93.44/93.62 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 93.44/93.62 ** KEPT (pick-wt=5): 15 [] -apart_point_and_line($c4,line_connecting($c2,$c1)).
% 93.44/93.62 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line($c3,line_connecting($c2,$c1)).
% 93.44/93.62
% 93.44/93.62 ------------> process sos:
% 93.44/93.62 ** KEPT (pick-wt=3): 17 [] distinct_points($c4,$c3).
% 93.44/93.62 ** KEPT (pick-wt=3): 18 [] distinct_points($c2,$c1).
% 93.44/93.62 ** KEPT (pick-wt=10): 19 [] apart_point_and_line($c2,line_connecting($c4,$c3))|apart_point_and_line($c1,line_connecting($c4,$c3)).
% 93.44/93.62
% 93.44/93.62 ======= end of input processing =======
% 93.44/93.62
% 93.44/93.62 =========== start of search ===========
% 93.44/93.62
% 93.44/93.62
% 93.44/93.62 Resetting weight limit to 18.
% 93.44/93.62
% 93.44/93.62
% 93.44/93.62 Resetting weight limit to 18.
% 93.44/93.62
% 93.44/93.62 sos_size=2265
% 93.44/93.62
% 93.44/93.62 -- HEY sandbox2, WE HAVE A PROOF!! --
% 93.44/93.62
% 93.44/93.62 ----> UNIT CONFLICT at 91.71 sec ----> 4553 [binary,4552.1,1.1] $F.
% 93.44/93.62
% 93.44/93.62 Length of proof is 21. Level of proof is 13.
% 93.44/93.62
% 93.44/93.62 ---------------- PROOF ----------------
% 93.44/93.62 % SZS status Theorem
% 93.44/93.62 % SZS output start Refutation
% See solution above
% 93.44/93.62 ------------ end of proof -------------
% 93.44/93.62
% 93.44/93.62
% 93.44/93.62 Search stopped by max_proofs option.
% 93.44/93.62
% 93.44/93.62
% 93.44/93.62 Search stopped by max_proofs option.
% 93.44/93.62
% 93.44/93.62 ============ end of search ============
% 93.44/93.62
% 93.44/93.62 -------------- statistics -------------
% 93.44/93.62 clauses given 655
% 93.44/93.62 clauses generated 316020
% 93.44/93.62 clauses kept 4552
% 93.44/93.62 clauses forward subsumed 83561
% 93.44/93.62 clauses back subsumed 2438
% 93.44/93.62 Kbytes malloced 4882
% 93.44/93.62
% 93.44/93.62 ----------- times (seconds) -----------
% 93.44/93.62 user CPU time 91.71 (0 hr, 1 min, 31 sec)
% 93.44/93.62 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 93.44/93.62 wall-clock time 93 (0 hr, 1 min, 33 sec)
% 93.44/93.62
% 93.44/93.62 That finishes the proof of the theorem.
% 93.44/93.62
% 93.44/93.62 Process 27734 finished Wed Jul 27 07:24:24 2022
% 93.44/93.62 Otter interrupted
% 93.44/93.62 PROOF FOUND
%------------------------------------------------------------------------------