TSTP Solution File: GEO205+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:54:48 EDT 2022
% Result : Theorem 48.92s 49.14s
% Output : Refutation 48.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 14 unt; 26 nHn; 21 RR)
% Number of literals : 98 ( 0 equ; 15 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 : 56 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO205+2.p',unknown),
[] ).
cnf(2,axiom,
~ distinct_lines(A,A),
file('GEO205+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO205+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ distinct_lines(A,B)
| distinct_lines(A,C)
| distinct_lines(B,C) ),
file('GEO205+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO205+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,A)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO205+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,B)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO205+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('GEO205+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ apart_point_and_line(A,B)
| distinct_lines(B,C)
| apart_point_and_line(A,C) ),
file('GEO205+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(A,B) ),
file('GEO205+2.p',unknown),
[] ).
cnf(15,axiom,
~ distinct_lines(dollar_c2,dollar_c1),
file('GEO205+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ convergent_lines(dollar_c3,dollar_c1)
| distinct_points(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)) ),
file('GEO205+2.p',unknown),
[] ).
cnf(17,axiom,
convergent_lines(dollar_c3,dollar_c2),
file('GEO205+2.p',unknown),
[] ).
cnf(18,plain,
distinct_lines(dollar_c3,dollar_c2),
inference(hyper,[status(thm)],[17,14]),
[iquote('hyper,17,14')] ).
cnf(19,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[17,6]),
[iquote('hyper,17,6')] ).
cnf(20,plain,
( distinct_lines(dollar_c3,A)
| distinct_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[18,5]),
[iquote('hyper,18,5')] ).
cnf(23,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[19,6]),
[iquote('hyper,19,6')] ).
cnf(25,plain,
( convergent_lines(dollar_c3,A)
| distinct_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[19,14]),
[iquote('hyper,19,14')] ).
cnf(29,plain,
distinct_lines(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[20,15]),
[iquote('hyper,20,15')] ).
cnf(31,plain,
( distinct_lines(dollar_c3,A)
| distinct_lines(dollar_c1,A) ),
inference(hyper,[status(thm)],[29,5]),
[iquote('hyper,29,5')] ).
cnf(33,plain,
convergent_lines(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[25,15]),
[iquote('hyper,25,15')] ).
cnf(35,plain,
distinct_points(intersection_point(dollar_c3,dollar_c2),intersection_point(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[33,16]),
[iquote('hyper,33,16')] ).
cnf(36,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c1,A) ),
inference(hyper,[status(thm)],[33,6]),
[iquote('hyper,33,6')] ).
cnf(38,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(B,A)
| convergent_lines(dollar_c2,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[23,6]),
[iquote('hyper,23,6')] ).
cnf(41,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[23,3]),
[iquote('hyper,23,3')] ).
cnf(46,plain,
distinct_lines(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[31,2]),
[iquote('hyper,31,2')] ).
cnf(49,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[36,6]),
[iquote('hyper,36,6')] ).
cnf(58,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c2,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[41,6]),
[iquote('hyper,41,6')] ).
cnf(89,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(hyper,[status(thm)],[35,11,46]),
[iquote('hyper,35,11,46')] ).
cnf(114,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c2,B)
| convergent_lines(C,B)
| convergent_lines(C,D)
| convergent_lines(A,D) ),
inference(hyper,[status(thm)],[38,6]),
[iquote('hyper,38,6')] ).
cnf(144,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[49,3]),
[iquote('hyper,49,3')] ).
cnf(146,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[49,6]),
[iquote('hyper,49,6')] ).
cnf(147,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[146]),3]),
[iquote('factor,146.1.3,unit_del,3')] ).
cnf(149,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c1,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[144,6]),
[iquote('hyper,144,6')] ).
cnf(174,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c2) ),
inference(hyper,[status(thm)],[58,3]),
[iquote('hyper,58,3')] ).
cnf(260,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[149,3]),
[iquote('hyper,149,3')] ).
cnf(658,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[89,9,174]),1,3]),
[iquote('hyper,89,9,174,unit_del,1,3')] ).
cnf(4877,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[658,10,147]),1,3]),
[iquote('hyper,658,10,147,unit_del,1,3')] ).
cnf(4905,plain,
apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4877,9,260]),1,3]),
[iquote('hyper,4877,9,260,unit_del,1,3')] ).
cnf(4906,plain,
( distinct_lines(dollar_c1,A)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),A) ),
inference(hyper,[status(thm)],[4905,13]),
[iquote('hyper,4905,13')] ).
cnf(4926,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c2),A)
| distinct_lines(dollar_c1,B)
| distinct_lines(A,B) ),
inference(hyper,[status(thm)],[4906,5]),
[iquote('hyper,4906,5')] ).
cnf(4937,plain,
apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4926,15]),2]),
[iquote('hyper,4926,15,unit_del,2')] ).
cnf(4968,plain,
convergent_lines(dollar_c2,A),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4937,10,114]),1])])])]),
[iquote('hyper,4937,10,114,unit_del,1,factor_simp,factor_simp,factor_simp')] ).
cnf(4969,plain,
$false,
inference(binary,[status(thm)],[4968,3]),
[iquote('binary,4968.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 07:32:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox on n028.cluster.edu,
% 1.67/1.88 Wed Jul 27 07:32:49 2022
% 1.67/1.88 The command was "./otter". The process ID is 27515.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 formula_list(usable).
% 1.67/1.88 all X (-distinct_points(X,X)).
% 1.67/1.88 all X (-distinct_lines(X,X)).
% 1.67/1.88 all X (-convergent_lines(X,X)).
% 1.67/1.88 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.67/1.88 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.67/1.88 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.67/1.88 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))).
% 1.67/1.88 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)))).
% 1.67/1.88 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)).
% 1.67/1.88 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.67/1.88 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.67/1.88 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.67/1.88 -(all X Y Z (convergent_lines(X,Y)& -distinct_lines(Y,Z)->convergent_lines(X,Z)& -distinct_points(intersection_point(X,Y),intersection_point(X,Z)))).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 -------> usable clausifies to:
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] -distinct_points(X,X).
% 1.67/1.88 0 [] -distinct_lines(X,X).
% 1.67/1.88 0 [] -convergent_lines(X,X).
% 1.67/1.88 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.67/1.88 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.67/1.88 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.67/1.88 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.67/1.88 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.67/1.88 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.88 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.88 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).
% 1.67/1.88 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.67/1.88 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.67/1.88 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.67/1.88 0 [] convergent_lines($c3,$c2).
% 1.67/1.88 0 [] -distinct_lines($c2,$c1).
% 1.67/1.88 0 [] -convergent_lines($c3,$c1)|distinct_points(intersection_point($c3,$c2),intersection_point($c3,$c1)).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.67/1.88
% 1.67/1.88 This is a non-Horn set without equality. The strategy will
% 1.67/1.88 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.88 satellites in sos and with nuclei in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: set(factor).
% 1.67/1.88 dependent: set(unit_deletion).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.67/1.88 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.67/1.88 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.67/1.88 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.67/1.88 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.67/1.88 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.67/1.88 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.67/1.88 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.67/1.88 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 48.92/49.14 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 48.92/49.14 ** 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).
% 48.92/49.14 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 48.92/49.14 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 48.92/49.14 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 48.92/49.14 ** KEPT (pick-wt=3): 15 [] -distinct_lines($c2,$c1).
% 48.92/49.14 ** KEPT (pick-wt=10): 16 [] -convergent_lines($c3,$c1)|distinct_points(intersection_point($c3,$c2),intersection_point($c3,$c1)).
% 48.92/49.14
% 48.92/49.14 ------------> process sos:
% 48.92/49.14 ** KEPT (pick-wt=3): 17 [] convergent_lines($c3,$c2).
% 48.92/49.14
% 48.92/49.14 ======= end of input processing =======
% 48.92/49.14
% 48.92/49.14 =========== start of search ===========
% 48.92/49.14
% 48.92/49.14
% 48.92/49.14 Resetting weight limit to 15.
% 48.92/49.14
% 48.92/49.14
% 48.92/49.14 Resetting weight limit to 15.
% 48.92/49.14
% 48.92/49.14 sos_size=4252
% 48.92/49.14
% 48.92/49.14 -- HEY sandbox, WE HAVE A PROOF!! --
% 48.92/49.14
% 48.92/49.14 ----> UNIT CONFLICT at 47.26 sec ----> 4969 [binary,4968.1,3.1] $F.
% 48.92/49.14
% 48.92/49.14 Length of proof is 30. Level of proof is 13.
% 48.92/49.14
% 48.92/49.14 ---------------- PROOF ----------------
% 48.92/49.14 % SZS status Theorem
% 48.92/49.14 % SZS output start Refutation
% See solution above
% 48.92/49.14 ------------ end of proof -------------
% 48.92/49.14
% 48.92/49.14
% 48.92/49.14 Search stopped by max_proofs option.
% 48.92/49.14
% 48.92/49.14
% 48.92/49.14 Search stopped by max_proofs option.
% 48.92/49.14
% 48.92/49.14 ============ end of search ============
% 48.92/49.14
% 48.92/49.14 -------------- statistics -------------
% 48.92/49.14 clauses given 500
% 48.92/49.14 clauses generated 68331
% 48.92/49.14 clauses kept 4968
% 48.92/49.14 clauses forward subsumed 45536
% 48.92/49.14 clauses back subsumed 1129
% 48.92/49.14 Kbytes malloced 4882
% 48.92/49.14
% 48.92/49.14 ----------- times (seconds) -----------
% 48.92/49.14 user CPU time 47.26 (0 hr, 0 min, 47 sec)
% 48.92/49.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 48.92/49.14 wall-clock time 48 (0 hr, 0 min, 48 sec)
% 48.92/49.14
% 48.92/49.14 That finishes the proof of the theorem.
% 48.92/49.14
% 48.92/49.14 Process 27515 finished Wed Jul 27 07:33:37 2022
% 48.92/49.14 Otter interrupted
% 48.92/49.14 PROOF FOUND
%------------------------------------------------------------------------------