TSTP Solution File: GEO198+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 5.14s 5.37s
% Output : Refutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 11 unt; 16 nHn; 17 RR)
% Number of literals : 63 ( 0 equ; 11 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 : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO198+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO198+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO198+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,A)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO198+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,B)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO198+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('GEO198+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(A,B) ),
file('GEO198+2.p',unknown),
[] ).
cnf(15,axiom,
~ apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c1),
file('GEO198+2.p',unknown),
[] ).
cnf(16,axiom,
convergent_lines(dollar_c3,dollar_c2),
file('GEO198+2.p',unknown),
[] ).
cnf(18,axiom,
convergent_lines(dollar_c3,dollar_c1),
file('GEO198+2.p',unknown),
[] ).
cnf(19,axiom,
apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c2),
file('GEO198+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(25,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c1,A) ),
inference(hyper,[status(thm)],[18,6]),
[iquote('hyper,18,6')] ).
cnf(31,plain,
distinct_points(intersection_point(dollar_c3,dollar_c1),intersection_point(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[19,10,16]),
[iquote('hyper,19,10,16')] ).
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(50,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[25,6]),
[iquote('hyper,25,6')] ).
cnf(51,plain,
convergent_lines(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[25,3]),
[iquote('hyper,25,3')] ).
cnf(54,plain,
distinct_lines(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[51,14]),
[iquote('hyper,51,14')] ).
cnf(84,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,11,54]),15]),
[iquote('hyper,31,11,54,unit_del,15')] ).
cnf(105,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[34,3]),
[iquote('hyper,34,3')] ).
cnf(111,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(192,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[50,3]),
[iquote('hyper,50,3')] ).
cnf(194,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[50,6]),
[iquote('hyper,50,6')] ).
cnf(195,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[194]),3]),
[iquote('factor,194.1.3,unit_del,3')] ).
cnf(201,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(dollar_c1,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[192,6]),
[iquote('hyper,192,6')] ).
cnf(479,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c2) ),
inference(hyper,[status(thm)],[111,3]),
[iquote('hyper,111,3')] ).
cnf(749,plain,
( convergent_lines(A,dollar_c3)
| convergent_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[201,3]),
[iquote('hyper,201,3')] ).
cnf(1185,plain,
( apart_point_and_line(intersection_point(dollar_c3,dollar_c1),dollar_c3)
| apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[84,10,195]),1,3]),
[iquote('hyper,84,10,195,unit_del,1,3')] ).
cnf(2104,plain,
apart_point_and_line(intersection_point(dollar_c3,dollar_c2),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1185,9,749]),1,3]),
[iquote('hyper,1185,9,749,unit_del,1,3')] ).
cnf(2130,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2104,9,479]),1,3]),
[iquote('hyper,2104,9,479,unit_del,1,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 07:06:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.73/1.91 ----- Otter 3.3f, August 2004 -----
% 1.73/1.91 The process was started by sandbox2 on n010.cluster.edu,
% 1.73/1.91 Wed Jul 27 07:06:10 2022
% 1.73/1.91 The command was "./otter". The process ID is 1295.
% 1.73/1.91
% 1.73/1.91 set(prolog_style_variables).
% 1.73/1.91 set(auto).
% 1.73/1.91 dependent: set(auto1).
% 1.73/1.91 dependent: set(process_input).
% 1.73/1.91 dependent: clear(print_kept).
% 1.73/1.91 dependent: clear(print_new_demod).
% 1.73/1.91 dependent: clear(print_back_demod).
% 1.73/1.91 dependent: clear(print_back_sub).
% 1.73/1.91 dependent: set(control_memory).
% 1.73/1.91 dependent: assign(max_mem, 12000).
% 1.73/1.91 dependent: assign(pick_given_ratio, 4).
% 1.73/1.91 dependent: assign(stats_level, 1).
% 1.73/1.91 dependent: assign(max_seconds, 10800).
% 1.73/1.91 clear(print_given).
% 1.73/1.91
% 1.73/1.91 formula_list(usable).
% 1.73/1.91 all X (-distinct_points(X,X)).
% 1.73/1.91 all X (-distinct_lines(X,X)).
% 1.73/1.91 all X (-convergent_lines(X,X)).
% 1.73/1.91 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.73/1.91 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.73/1.91 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.73/1.91 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))).
% 1.73/1.91 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)))).
% 1.73/1.91 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)).
% 1.73/1.91 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.73/1.91 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.73/1.91 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.73/1.91 -(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(X,Z),Y))).
% 1.73/1.91 end_of_list.
% 1.73/1.91
% 1.73/1.91 -------> usable clausifies to:
% 1.73/1.91
% 1.73/1.91 list(usable).
% 1.73/1.91 0 [] -distinct_points(X,X).
% 1.73/1.91 0 [] -distinct_lines(X,X).
% 1.73/1.91 0 [] -convergent_lines(X,X).
% 1.73/1.91 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.73/1.91 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.73/1.91 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.73/1.91 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.73/1.91 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.73/1.91 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.73/1.91 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.73/1.91 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).
% 1.73/1.91 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.73/1.91 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.73/1.91 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.73/1.91 0 [] convergent_lines($c3,$c2).
% 1.73/1.91 0 [] convergent_lines($c1,$c2).
% 1.73/1.91 0 [] convergent_lines($c3,$c1).
% 1.73/1.91 0 [] -apart_point_and_line(intersection_point($c3,$c2),$c1).
% 1.73/1.91 0 [] apart_point_and_line(intersection_point($c3,$c1),$c2).
% 1.73/1.91 end_of_list.
% 1.73/1.91
% 1.73/1.91 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.73/1.91
% 1.73/1.91 This is a non-Horn set without equality. The strategy will
% 1.73/1.91 be ordered hyper_res, unit deletion, and factoring, with
% 1.73/1.91 satellites in sos and with nuclei in usable.
% 1.73/1.91
% 1.73/1.91 dependent: set(hyper_res).
% 1.73/1.91 dependent: set(factor).
% 1.73/1.91 dependent: set(unit_deletion).
% 1.73/1.91
% 1.73/1.91 ------------> process usable:
% 1.73/1.91 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.73/1.91 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.73/1.91 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.73/1.91 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.73/1.91 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.73/1.91 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.73/1.91 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.73/1.91 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 5.14/5.37 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 5.14/5.37 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 5.14/5.37 ** 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).
% 5.14/5.37 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 5.14/5.37 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 5.14/5.37 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 5.14/5.37 ** KEPT (pick-wt=5): 15 [] -apart_point_and_line(intersection_point($c3,$c2),$c1).
% 5.14/5.37
% 5.14/5.37 ------------> process sos:
% 5.14/5.37 ** KEPT (pick-wt=3): 16 [] convergent_lines($c3,$c2).
% 5.14/5.37 ** KEPT (pick-wt=3): 17 [] convergent_lines($c1,$c2).
% 5.14/5.37 ** KEPT (pick-wt=3): 18 [] convergent_lines($c3,$c1).
% 5.14/5.37 ** KEPT (pick-wt=5): 19 [] apart_point_and_line(intersection_point($c3,$c1),$c2).
% 5.14/5.37
% 5.14/5.37 ======= end of input processing =======
% 5.14/5.37
% 5.14/5.37 =========== start of search ===========
% 5.14/5.37
% 5.14/5.37 -------- PROOF --------
% 5.14/5.37
% 5.14/5.37 -----> EMPTY CLAUSE at 3.46 sec ----> 2130 [hyper,2104,9,479,unit_del,1,3] $F.
% 5.14/5.37
% 5.14/5.37 Length of proof is 18. Level of proof is 6.
% 5.14/5.37
% 5.14/5.37 ---------------- PROOF ----------------
% 5.14/5.37 % SZS status Theorem
% 5.14/5.37 % SZS output start Refutation
% See solution above
% 5.14/5.37 ------------ end of proof -------------
% 5.14/5.37
% 5.14/5.37
% 5.14/5.37 Search stopped by max_proofs option.
% 5.14/5.37
% 5.14/5.37
% 5.14/5.37 Search stopped by max_proofs option.
% 5.14/5.37
% 5.14/5.37 ============ end of search ============
% 5.14/5.37
% 5.14/5.37 -------------- statistics -------------
% 5.14/5.37 clauses given 179
% 5.14/5.37 clauses generated 15674
% 5.14/5.37 clauses kept 2129
% 5.14/5.37 clauses forward subsumed 13563
% 5.14/5.37 clauses back subsumed 639
% 5.14/5.37 Kbytes malloced 1953
% 5.14/5.37
% 5.14/5.37 ----------- times (seconds) -----------
% 5.14/5.37 user CPU time 3.46 (0 hr, 0 min, 3 sec)
% 5.14/5.37 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 5.14/5.37 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.14/5.37
% 5.14/5.37 That finishes the proof of the theorem.
% 5.14/5.37
% 5.14/5.37 Process 1295 finished Wed Jul 27 07:06:15 2022
% 5.14/5.37 Otter interrupted
% 5.14/5.37 PROOF FOUND
%------------------------------------------------------------------------------