%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO178+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:54:37 EDT 2022
% Result : Theorem 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 13 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,A) ),
file('GEO178+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| distinct_points(C,B) ),
file('GEO178+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ distinct_points(dollar_c1,dollar_c3)
| ~ distinct_points(dollar_c1,dollar_c2) ),
file('GEO178+2.p',unknown),
[] ).
cnf(16,axiom,
distinct_points(dollar_c3,dollar_c2),
file('GEO178+2.p',unknown),
[] ).
cnf(17,axiom,
apart_point_and_line(dollar_c1,line_connecting(dollar_c3,dollar_c2)),
file('GEO178+2.p',unknown),
[] ).
cnf(21,plain,
distinct_points(dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[17,8,16]),
[iquote('hyper,17,8,16')] ).
cnf(22,plain,
distinct_points(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[17,7,16]),
[iquote('hyper,17,7,16')] ).
cnf(24,plain,
$false,
inference(hyper,[status(thm)],[22,15,21]),
[iquote('hyper,22,15,21')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO178+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 07:19:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox on n019.cluster.edu,
% 1.69/1.90 Wed Jul 27 07:19:37 2022
% 1.69/1.90 The command was "./otter". The process ID is 2468.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 formula_list(usable).
% 1.69/1.90 all X (-distinct_points(X,X)).
% 1.69/1.90 all X (-distinct_lines(X,X)).
% 1.69/1.90 all X (-convergent_lines(X,X)).
% 1.69/1.90 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.69/1.90 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.69/1.90 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.69/1.90 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))).
% 1.69/1.90 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)))).
% 1.69/1.90 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)).
% 1.69/1.90 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.69/1.90 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.69/1.90 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.69/1.90 -(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))).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 -------> usable clausifies to:
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] -distinct_points(X,X).
% 1.69/1.90 0 [] -distinct_lines(X,X).
% 1.69/1.90 0 [] -convergent_lines(X,X).
% 1.69/1.90 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.69/1.90 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.69/1.90 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.69/1.90 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.69/1.90 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.69/1.90 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.69/1.90 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.69/1.90 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).
% 1.69/1.90 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.69/1.90 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.69/1.90 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.69/1.90 0 [] distinct_points($c3,$c2).
% 1.69/1.90 0 [] apart_point_and_line($c1,line_connecting($c3,$c2)).
% 1.69/1.90 0 [] -distinct_points($c1,$c3)| -distinct_points($c1,$c2).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.69/1.90
% 1.69/1.90 This is a non-Horn set without equality. The strategy will
% 1.69/1.90 be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.90 satellites in sos and with nuclei in usable.
% 1.69/1.90
% 1.69/1.90 dependent: set(hyper_res).
% 1.69/1.90 dependent: set(factor).
% 1.69/1.90 dependent: set(unit_deletion).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.69/1.90 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.69/1.90 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.69/1.90 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.69/1.90 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.69/1.90 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.69/1.90 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.69/1.90 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.69/1.90 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.69/1.90 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.69/1.90 ** 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).
% 1.69/1.90 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.69/1.90 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.69/1.90 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.69/1.90 ** KEPT (pick-wt=6): 15 [] -distinct_points($c1,$c3)| -distinct_points($c1,$c2).
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 16 [] distinct_points($c3,$c2).
% 1.69/1.90 ** KEPT (pick-wt=5): 17 [] apart_point_and_line($c1,line_connecting($c3,$c2)).
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 -----> EMPTY CLAUSE at 0.00 sec ----> 24 [hyper,22,15,21] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 2. Level of proof is 1.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Theorem
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 4
% 1.69/1.90 clauses generated 16
% 1.69/1.90 clauses kept 23
% 1.69/1.90 clauses forward subsumed 9
% 1.69/1.90 clauses back subsumed 0
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 2468 finished Wed Jul 27 07:19:38 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------