TSTP Solution File: GEO203+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:54:47 EDT 2022
% Result : Theorem 53.61s 53.82s
% Output : Refutation 53.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 8 unt; 20 nHn; 15 RR)
% Number of literals : 73 ( 0 equ; 12 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO203+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO203+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
file('GEO203+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO203+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,A) ),
file('GEO203+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,B) ),
file('GEO203+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,A)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO203+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('GEO203+2.p',unknown),
[] ).
cnf(15,axiom,
convergent_lines(dollar_c3,dollar_c2),
file('GEO203+2.p',unknown),
[] ).
cnf(16,axiom,
convergent_lines(dollar_c3,dollar_c1),
file('GEO203+2.p',unknown),
[] ).
cnf(17,axiom,
distinct_points(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)),
file('GEO203+2.p',unknown),
[] ).
cnf(18,axiom,
distinct_lines(line_connecting(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)),dollar_c3),
file('GEO203+2.p',unknown),
[] ).
cnf(20,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[15,6]),
[iquote('hyper,15,6')] ).
cnf(22,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c1,A) ),
inference(hyper,[status(thm)],[16,6]),
[iquote('hyper,16,6')] ).
cnf(26,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[20,6]),
[iquote('hyper,20,6')] ).
cnf(32,plain,
( distinct_points(intersection_point(dollar_c3,dollar_c2),A)
| distinct_points(intersection_point(dollar_c3,dollar_c1),A) ),
inference(hyper,[status(thm)],[17,4]),
[iquote('hyper,17,4')] ).
cnf(35,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[22,6]),
[iquote('hyper,22,6')] ).
cnf(40,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),line_connecting(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)))
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),line_connecting(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)))
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(hyper,[status(thm)],[18,11,17]),
[iquote('hyper,18,11,17')] ).
cnf(56,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[26,3]),
[iquote('hyper,26,3')] ).
cnf(67,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c2,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[56,6]),
[iquote('hyper,56,6')] ).
cnf(118,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[35,3]),
[iquote('hyper,35,3')] ).
cnf(123,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c1,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[118,6]),
[iquote('hyper,118,6')] ).
cnf(178,plain,
( distinct_points(intersection_point(dollar_c3,dollar_c1),A)
| distinct_points(intersection_point(dollar_c3,dollar_c2),B)
| distinct_points(A,B) ),
inference(hyper,[status(thm)],[32,4]),
[iquote('hyper,32,4')] ).
cnf(248,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),line_connecting(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)))
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,7,32]),1,1]),
[iquote('hyper,40,7,32,unit_del,1,1')] ).
cnf(391,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c2) ),
inference(hyper,[status(thm)],[67,3]),
[iquote('hyper,67,3')] ).
cnf(440,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[123,3]),
[iquote('hyper,123,3')] ).
cnf(2889,plain,
( distinct_points(intersection_point(dollar_c3,dollar_c1),A)
| distinct_points(intersection_point(dollar_c3,dollar_c2),B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(hyper,[status(thm)],[178,4]),
[iquote('hyper,178,4')] ).
cnf(2890,plain,
( distinct_points(intersection_point(dollar_c3,dollar_c2),A)
| distinct_points(A,intersection_point(dollar_c3,dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2889]),1]),
[iquote('factor,2889.1.3,unit_del,1')] ).
cnf(4568,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[248,8,2890]),1,1]),
[iquote('hyper,248,8,2890,unit_del,1,1')] ).
cnf(4583,plain,
apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4568,9,391]),1,3]),
[iquote('hyper,4568,9,391,unit_del,1,3')] ).
cnf(4616,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4583,9,440]),1,3]),
[iquote('hyper,4583,9,440,unit_del,1,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 06:55:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.57/1.78 ----- Otter 3.3f, August 2004 -----
% 1.57/1.78 The process was started by sandbox2 on n003.cluster.edu,
% 1.57/1.78 Wed Jul 27 06:55:41 2022
% 1.57/1.78 The command was "./otter". The process ID is 4811.
% 1.57/1.78
% 1.57/1.78 set(prolog_style_variables).
% 1.57/1.78 set(auto).
% 1.57/1.78 dependent: set(auto1).
% 1.57/1.78 dependent: set(process_input).
% 1.57/1.78 dependent: clear(print_kept).
% 1.57/1.78 dependent: clear(print_new_demod).
% 1.57/1.78 dependent: clear(print_back_demod).
% 1.57/1.78 dependent: clear(print_back_sub).
% 1.57/1.78 dependent: set(control_memory).
% 1.57/1.78 dependent: assign(max_mem, 12000).
% 1.57/1.78 dependent: assign(pick_given_ratio, 4).
% 1.57/1.78 dependent: assign(stats_level, 1).
% 1.57/1.78 dependent: assign(max_seconds, 10800).
% 1.57/1.78 clear(print_given).
% 1.57/1.78
% 1.57/1.78 formula_list(usable).
% 1.57/1.78 all X (-distinct_points(X,X)).
% 1.57/1.78 all X (-distinct_lines(X,X)).
% 1.57/1.78 all X (-convergent_lines(X,X)).
% 1.57/1.78 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.57/1.78 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.57/1.78 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.57/1.78 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))).
% 1.57/1.78 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)))).
% 1.57/1.78 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)).
% 1.57/1.78 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.57/1.78 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.57/1.78 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.57/1.78 -(all X Y Z (convergent_lines(X,Y)&convergent_lines(X,Z)&distinct_points(intersection_point(X,Y),intersection_point(X,Z))-> -distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X))).
% 1.57/1.78 end_of_list.
% 1.57/1.78
% 1.57/1.78 -------> usable clausifies to:
% 1.57/1.78
% 1.57/1.78 list(usable).
% 1.57/1.78 0 [] -distinct_points(X,X).
% 1.57/1.78 0 [] -distinct_lines(X,X).
% 1.57/1.78 0 [] -convergent_lines(X,X).
% 1.57/1.78 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.57/1.78 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.57/1.78 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.57/1.78 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.57/1.78 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.57/1.78 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.57/1.78 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.57/1.78 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).
% 1.57/1.78 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.57/1.78 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.57/1.78 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.57/1.78 0 [] convergent_lines($c3,$c2).
% 1.57/1.78 0 [] convergent_lines($c3,$c1).
% 1.57/1.78 0 [] distinct_points(intersection_point($c3,$c2),intersection_point($c3,$c1)).
% 1.57/1.78 0 [] distinct_lines(line_connecting(intersection_point($c3,$c2),intersection_point($c3,$c1)),$c3).
% 1.57/1.78 end_of_list.
% 1.57/1.78
% 1.57/1.78 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.57/1.78
% 1.57/1.78 This is a non-Horn set without equality. The strategy will
% 1.57/1.78 be ordered hyper_res, unit deletion, and factoring, with
% 1.57/1.78 satellites in sos and with nuclei in usable.
% 1.57/1.78
% 1.57/1.78 dependent: set(hyper_res).
% 1.57/1.78 dependent: set(factor).
% 1.57/1.78 dependent: set(unit_deletion).
% 1.57/1.78
% 1.57/1.78 ------------> process usable:
% 1.57/1.78 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.57/1.78 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.57/1.78 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.57/1.78 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.57/1.78 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.57/1.78 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.57/1.78 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.57/1.78 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 53.61/53.82 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 53.61/53.82 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 53.61/53.82 ** 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).
% 53.61/53.82 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 53.61/53.82 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 53.61/53.82 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 53.61/53.82
% 53.61/53.82 ------------> process sos:
% 53.61/53.82 ** KEPT (pick-wt=3): 15 [] convergent_lines($c3,$c2).
% 53.61/53.82 ** KEPT (pick-wt=3): 16 [] convergent_lines($c3,$c1).
% 53.61/53.82 ** KEPT (pick-wt=7): 17 [] distinct_points(intersection_point($c3,$c2),intersection_point($c3,$c1)).
% 53.61/53.82 ** KEPT (pick-wt=9): 18 [] distinct_lines(line_connecting(intersection_point($c3,$c2),intersection_point($c3,$c1)),$c3).
% 53.61/53.82
% 53.61/53.82 ======= end of input processing =======
% 53.61/53.82
% 53.61/53.82 =========== start of search ===========
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Resetting weight limit to 16.
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Resetting weight limit to 16.
% 53.61/53.82
% 53.61/53.82 sos_size=3733
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Resetting weight limit to 15.
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Resetting weight limit to 15.
% 53.61/53.82
% 53.61/53.82 sos_size=3763
% 53.61/53.82
% 53.61/53.82 -- HEY sandbox2, WE HAVE A PROOF!! --
% 53.61/53.82
% 53.61/53.82 -----> EMPTY CLAUSE at 52.03 sec ----> 4616 [hyper,4583,9,440,unit_del,1,3] $F.
% 53.61/53.82
% 53.61/53.82 Length of proof is 18. Level of proof is 6.
% 53.61/53.82
% 53.61/53.82 ---------------- PROOF ----------------
% 53.61/53.82 % SZS status Theorem
% 53.61/53.82 % SZS output start Refutation
% See solution above
% 53.61/53.82 ------------ end of proof -------------
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Search stopped by max_proofs option.
% 53.61/53.82
% 53.61/53.82
% 53.61/53.82 Search stopped by max_proofs option.
% 53.61/53.82
% 53.61/53.82 ============ end of search ============
% 53.61/53.82
% 53.61/53.82 -------------- statistics -------------
% 53.61/53.82 clauses given 239
% 53.61/53.82 clauses generated 54528
% 53.61/53.82 clauses kept 4615
% 53.61/53.82 clauses forward subsumed 45427
% 53.61/53.82 clauses back subsumed 2341
% 53.61/53.82 Kbytes malloced 4882
% 53.61/53.82
% 53.61/53.82 ----------- times (seconds) -----------
% 53.61/53.82 user CPU time 52.04 (0 hr, 0 min, 52 sec)
% 53.61/53.82 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 53.61/53.82 wall-clock time 54 (0 hr, 0 min, 54 sec)
% 53.61/53.82
% 53.61/53.82 That finishes the proof of the theorem.
% 53.61/53.82
% 53.61/53.82 Process 4811 finished Wed Jul 27 06:56:35 2022
% 53.61/53.82 Otter interrupted
% 53.61/53.82 PROOF FOUND
%------------------------------------------------------------------------------