TSTP Solution File: GEO199+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO199+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 12:54:46 EDT 2022
% Result : Theorem 28.89s 29.09s
% Output : Refutation 28.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 10 unt; 17 nHn; 14 RR)
% Number of literals : 71 ( 0 equ; 12 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO199+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO199+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO199+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,A)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO199+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,B)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO199+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('GEO199+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ apart_point_and_line(A,B)
| distinct_points(A,C)
| apart_point_and_line(C,B) ),
file('GEO199+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(A,B) ),
file('GEO199+2.p',unknown),
[] ).
cnf(15,axiom,
~ apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1),
file('GEO199+2.p',unknown),
[] ).
cnf(16,axiom,
convergent_lines(dollar_c3,dollar_c2),
file('GEO199+2.p',unknown),
[] ).
cnf(19,axiom,
apart_point_and_line(intersection_point(dollar_c2,dollar_c3),dollar_c1),
file('GEO199+2.p',unknown),
[] ).
cnf(21,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[16,6]),
[iquote('hyper,16,6')] ).
cnf(29,plain,
( distinct_points(intersection_point(dollar_c2,dollar_c3),A)
| apart_point_and_line(A,dollar_c1) ),
inference(hyper,[status(thm)],[19,12]),
[iquote('hyper,19,12')] ).
cnf(34,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[21,6]),
[iquote('hyper,21,6')] ).
cnf(35,plain,
convergent_lines(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[21,3]),
[iquote('hyper,21,3')] ).
cnf(38,plain,
distinct_lines(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[35,14]),
[iquote('hyper,35,14')] ).
cnf(70,plain,
( apart_point_and_line(A,dollar_c1)
| apart_point_and_line(intersection_point(dollar_c2,dollar_c3),dollar_c2)
| apart_point_and_line(intersection_point(dollar_c2,dollar_c3),dollar_c3)
| apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c3) ),
inference(hyper,[status(thm)],[29,11,38]),
[iquote('hyper,29,11,38')] ).
cnf(105,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[34,3]),
[iquote('hyper,34,3')] ).
cnf(107,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[34,6]),
[iquote('hyper,34,6')] ).
cnf(108,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(A,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[107]),3]),
[iquote('factor,107.1.3,unit_del,3')] ).
cnf(110,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c2,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[105,6]),
[iquote('hyper,105,6')] ).
cnf(432,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,B)
| convergent_lines(dollar_c2,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[110,6]),
[iquote('hyper,110,6')] ).
cnf(433,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c2) ),
inference(hyper,[status(thm)],[110,3]),
[iquote('hyper,110,3')] ).
cnf(506,plain,
( apart_point_and_line(A,dollar_c1)
| apart_point_and_line(intersection_point(dollar_c2,dollar_c3),dollar_c3)
| apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[70,9,433]),1,3]),
[iquote('hyper,70,9,433,unit_del,1,3')] ).
cnf(4083,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,B)
| convergent_lines(B,dollar_c2) ),
inference(hyper,[status(thm)],[432,3]),
[iquote('hyper,432,3')] ).
cnf(5341,plain,
( apart_point_and_line(A,dollar_c1)
| apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[506,10,105]),1,3]),
[iquote('hyper,506,10,105,unit_del,1,3')] ).
cnf(5342,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c2)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3) ),
inference(hyper,[status(thm)],[5341,15]),
[iquote('hyper,5341,15')] ).
cnf(5408,plain,
apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5342,10,108]),1,3]),
[iquote('hyper,5342,10,108,unit_del,1,3')] ).
cnf(5455,plain,
convergent_lines(A,dollar_c3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5408,9,4083]),1])]),
[iquote('hyper,5408,9,4083,unit_del,1,factor_simp')] ).
cnf(5456,plain,
$false,
inference(binary,[status(thm)],[5455,3]),
[iquote('binary,5455.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO199+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 07:09:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.93 ----- Otter 3.3f, August 2004 -----
% 1.71/1.93 The process was started by sandbox on n024.cluster.edu,
% 1.71/1.93 Wed Jul 27 07:09:10 2022
% 1.71/1.93 The command was "./otter". The process ID is 2816.
% 1.71/1.93
% 1.71/1.93 set(prolog_style_variables).
% 1.71/1.93 set(auto).
% 1.71/1.93 dependent: set(auto1).
% 1.71/1.93 dependent: set(process_input).
% 1.71/1.93 dependent: clear(print_kept).
% 1.71/1.93 dependent: clear(print_new_demod).
% 1.71/1.93 dependent: clear(print_back_demod).
% 1.71/1.93 dependent: clear(print_back_sub).
% 1.71/1.93 dependent: set(control_memory).
% 1.71/1.93 dependent: assign(max_mem, 12000).
% 1.71/1.93 dependent: assign(pick_given_ratio, 4).
% 1.71/1.93 dependent: assign(stats_level, 1).
% 1.71/1.93 dependent: assign(max_seconds, 10800).
% 1.71/1.93 clear(print_given).
% 1.71/1.93
% 1.71/1.93 formula_list(usable).
% 1.71/1.93 all X (-distinct_points(X,X)).
% 1.71/1.93 all X (-distinct_lines(X,X)).
% 1.71/1.93 all X (-convergent_lines(X,X)).
% 1.71/1.93 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.71/1.93 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.71/1.93 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.71/1.93 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))).
% 1.71/1.93 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)))).
% 1.71/1.93 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)).
% 1.71/1.93 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.71/1.93 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.71/1.93 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.71/1.93 -(all X Y Z (convergent_lines(X,Y)&convergent_lines(Z,Y)&convergent_lines(X,Z)& -apart_point_and_line(intersection_point(X,Y),Z)-> -apart_point_and_line(intersection_point(Y,X),Z))).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 -------> usable clausifies to:
% 1.71/1.93
% 1.71/1.93 list(usable).
% 1.71/1.93 0 [] -distinct_points(X,X).
% 1.71/1.93 0 [] -distinct_lines(X,X).
% 1.71/1.93 0 [] -convergent_lines(X,X).
% 1.71/1.93 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.71/1.93 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.71/1.93 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.71/1.93 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.71/1.93 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.71/1.93 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.71/1.93 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.71/1.93 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).
% 1.71/1.93 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.71/1.93 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.71/1.93 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.71/1.93 0 [] convergent_lines($c3,$c2).
% 1.71/1.93 0 [] convergent_lines($c1,$c2).
% 1.71/1.93 0 [] convergent_lines($c3,$c1).
% 1.71/1.93 0 [] -apart_point_and_line(intersection_point($c3,$c2),$c1).
% 1.71/1.93 0 [] apart_point_and_line(intersection_point($c2,$c3),$c1).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.71/1.93
% 1.71/1.93 This is a non-Horn set without equality. The strategy will
% 1.71/1.93 be ordered hyper_res, unit deletion, and factoring, with
% 1.71/1.93 satellites in sos and with nuclei in usable.
% 1.71/1.93
% 1.71/1.93 dependent: set(hyper_res).
% 1.71/1.93 dependent: set(factor).
% 1.71/1.93 dependent: set(unit_deletion).
% 1.71/1.93
% 1.71/1.93 ------------> process usable:
% 1.71/1.93 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.71/1.93 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.71/1.93 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.71/1.93 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.71/1.93 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.71/1.93 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.71/1.93 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.71/1.93 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 28.89/29.09 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 28.89/29.09 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 28.89/29.09 ** 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).
% 28.89/29.09 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 28.89/29.09 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 28.89/29.09 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 28.89/29.09 ** KEPT (pick-wt=5): 15 [] -apart_point_and_line(intersection_point($c3,$c2),$c1).
% 28.89/29.09
% 28.89/29.09 ------------> process sos:
% 28.89/29.09 ** KEPT (pick-wt=3): 16 [] convergent_lines($c3,$c2).
% 28.89/29.09 ** KEPT (pick-wt=3): 17 [] convergent_lines($c1,$c2).
% 28.89/29.09 ** KEPT (pick-wt=3): 18 [] convergent_lines($c3,$c1).
% 28.89/29.09 ** KEPT (pick-wt=5): 19 [] apart_point_and_line(intersection_point($c2,$c3),$c1).
% 28.89/29.09
% 28.89/29.09 ======= end of input processing =======
% 28.89/29.09
% 28.89/29.09 =========== start of search ===========
% 28.89/29.09
% 28.89/29.09
% 28.89/29.09 Resetting weight limit to 15.
% 28.89/29.09
% 28.89/29.09
% 28.89/29.09 Resetting weight limit to 15.
% 28.89/29.09
% 28.89/29.09 sos_size=4336
% 28.89/29.09
% 28.89/29.09 -- HEY sandbox, WE HAVE A PROOF!! --
% 28.89/29.09
% 28.89/29.09 ----> UNIT CONFLICT at 27.17 sec ----> 5456 [binary,5455.1,3.1] $F.
% 28.89/29.09
% 28.89/29.09 Length of proof is 18. Level of proof is 10.
% 28.89/29.09
% 28.89/29.09 ---------------- PROOF ----------------
% 28.89/29.09 % SZS status Theorem
% 28.89/29.09 % SZS output start Refutation
% See solution above
% 28.89/29.09 ------------ end of proof -------------
% 28.89/29.09
% 28.89/29.09
% 28.89/29.09 Search stopped by max_proofs option.
% 28.89/29.09
% 28.89/29.09
% 28.89/29.09 Search stopped by max_proofs option.
% 28.89/29.09
% 28.89/29.09 ============ end of search ============
% 28.89/29.09
% 28.89/29.09 -------------- statistics -------------
% 28.89/29.09 clauses given 727
% 28.89/29.09 clauses generated 159573
% 28.89/29.09 clauses kept 5455
% 28.89/29.09 clauses forward subsumed 37138
% 28.89/29.09 clauses back subsumed 524
% 28.89/29.09 Kbytes malloced 4882
% 28.89/29.09
% 28.89/29.09 ----------- times (seconds) -----------
% 28.89/29.09 user CPU time 27.17 (0 hr, 0 min, 27 sec)
% 28.89/29.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 28.89/29.09 wall-clock time 29 (0 hr, 0 min, 29 sec)
% 28.89/29.09
% 28.89/29.09 That finishes the proof of the theorem.
% 28.89/29.09
% 28.89/29.09 Process 2816 finished Wed Jul 27 07:09:39 2022
% 28.89/29.09 Otter interrupted
% 28.89/29.10 PROOF FOUND
%------------------------------------------------------------------------------