%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO209+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 12:54:50 EDT 2022
% Result : Theorem 1.77s 1.99s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 7 unt; 5 nHn; 7 RR)
% Number of literals : 23 ( 0 equ; 6 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO209+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ distinct_lines(A,B)
| apart_point_and_line(C,A)
| apart_point_and_line(C,B)
| convergent_lines(A,B) ),
file('GEO209+2.p',unknown),
[] ).
cnf(18,axiom,
~ apart_point_and_line(dollar_c4,dollar_c2),
file('GEO209+2.p',unknown),
[] ).
cnf(19,axiom,
~ apart_point_and_line(dollar_c4,dollar_c1),
file('GEO209+2.p',unknown),
[] ).
cnf(20,axiom,
~ convergent_lines(dollar_c2,dollar_c3),
file('GEO209+2.p',unknown),
[] ).
cnf(21,axiom,
~ convergent_lines(dollar_c1,dollar_c3),
file('GEO209+2.p',unknown),
[] ).
cnf(23,axiom,
distinct_lines(dollar_c2,dollar_c1),
file('GEO209+2.p',unknown),
[] ).
cnf(26,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c1)
| convergent_lines(dollar_c2,dollar_c1) ),
inference(hyper,[status(thm)],[23,17]),
[iquote('hyper,23,17')] ).
cnf(39,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c1)
| convergent_lines(dollar_c2,B)
| convergent_lines(dollar_c1,B) ),
inference(hyper,[status(thm)],[26,6]),
[iquote('hyper,26,6')] ).
cnf(150,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[39,20]),21]),
[iquote('hyper,39,20,unit_del,21')] ).
cnf(153,plain,
apart_point_and_line(dollar_c4,dollar_c1),
inference(hyper,[status(thm)],[150,18]),
[iquote('hyper,150,18')] ).
cnf(154,plain,
$false,
inference(binary,[status(thm)],[153,19]),
[iquote('binary,153.1,19.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO209+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:58:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.77/1.97 ----- Otter 3.3f, August 2004 -----
% 1.77/1.97 The process was started by sandbox on n019.cluster.edu,
% 1.77/1.97 Wed Jul 27 06:58:37 2022
% 1.77/1.97 The command was "./otter". The process ID is 11584.
% 1.77/1.97
% 1.77/1.97 set(prolog_style_variables).
% 1.77/1.97 set(auto).
% 1.77/1.97 dependent: set(auto1).
% 1.77/1.97 dependent: set(process_input).
% 1.77/1.97 dependent: clear(print_kept).
% 1.77/1.97 dependent: clear(print_new_demod).
% 1.77/1.97 dependent: clear(print_back_demod).
% 1.77/1.97 dependent: clear(print_back_sub).
% 1.77/1.97 dependent: set(control_memory).
% 1.77/1.97 dependent: assign(max_mem, 12000).
% 1.77/1.97 dependent: assign(pick_given_ratio, 4).
% 1.77/1.97 dependent: assign(stats_level, 1).
% 1.77/1.97 dependent: assign(max_seconds, 10800).
% 1.77/1.97 clear(print_given).
% 1.77/1.97
% 1.77/1.97 formula_list(usable).
% 1.77/1.97 all X (-distinct_points(X,X)).
% 1.77/1.97 all X (-distinct_lines(X,X)).
% 1.77/1.97 all X (-convergent_lines(X,X)).
% 1.77/1.97 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.77/1.97 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.77/1.97 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.77/1.97 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))).
% 1.77/1.97 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)))).
% 1.77/1.97 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)).
% 1.77/1.97 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.77/1.97 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.77/1.97 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.77/1.97 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.77/1.97 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.77/1.97 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.77/1.97 -(all A L M N (apart_point_and_line(A,L)& -apart_point_and_line(A,M)& -apart_point_and_line(A,N)& -convergent_lines(M,L)& -convergent_lines(N,L)-> -distinct_lines(M,N))).
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 -------> usable clausifies to:
% 1.77/1.97
% 1.77/1.97 list(usable).
% 1.77/1.97 0 [] -distinct_points(X,X).
% 1.77/1.97 0 [] -distinct_lines(X,X).
% 1.77/1.97 0 [] -convergent_lines(X,X).
% 1.77/1.97 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.77/1.97 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.77/1.97 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.77/1.97 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.77/1.97 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.77/1.97 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.77/1.97 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.77/1.97 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).
% 1.77/1.97 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.77/1.97 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.77/1.97 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.77/1.97 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.77/1.97 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.77/1.97 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.77/1.97 0 [] apart_point_and_line($c4,$c3).
% 1.77/1.97 0 [] -apart_point_and_line($c4,$c2).
% 1.77/1.97 0 [] -apart_point_and_line($c4,$c1).
% 1.77/1.97 0 [] -convergent_lines($c2,$c3).
% 1.77/1.97 0 [] -convergent_lines($c1,$c3).
% 1.77/1.97 0 [] distinct_lines($c2,$c1).
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.77/1.97
% 1.77/1.97 This is a non-Horn set without equality. The strategy will
% 1.77/1.97 be ordered hyper_res, unit deletion, and factoring, with
% 1.77/1.97 satellites in sos and with nuclei in usable.
% 1.77/1.97
% 1.77/1.97 dependent: set(hyper_res).
% 1.77/1.97 dependent: set(factor).
% 1.77/1.97 dependent: set(unit_deletion).
% 1.77/1.97
% 1.77/1.97 ------------> process usable:
% 1.77/1.97 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.77/1.97 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.77/1.97 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.77/1.97 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.77/1.99 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.77/1.99 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.77/1.99 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.77/1.99 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.77/1.99 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.77/1.99 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.77/1.99 ** 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).
% 1.77/1.99 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.77/1.99 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.77/1.99 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.77/1.99 ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 1.77/1.99 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.77/1.99 ** KEPT (pick-wt=12): 17 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|convergent_lines(A,B).
% 1.77/1.99 ** KEPT (pick-wt=3): 18 [] -apart_point_and_line($c4,$c2).
% 1.77/1.99 ** KEPT (pick-wt=3): 19 [] -apart_point_and_line($c4,$c1).
% 1.77/1.99 ** KEPT (pick-wt=3): 20 [] -convergent_lines($c2,$c3).
% 1.77/1.99 ** KEPT (pick-wt=3): 21 [] -convergent_lines($c1,$c3).
% 1.77/1.99
% 1.77/1.99 ------------> process sos:
% 1.77/1.99 ** KEPT (pick-wt=3): 22 [] apart_point_and_line($c4,$c3).
% 1.77/1.99 ** KEPT (pick-wt=3): 23 [] distinct_lines($c2,$c1).
% 1.77/1.99
% 1.77/1.99 ======= end of input processing =======
% 1.77/1.99
% 1.77/1.99 =========== start of search ===========
% 1.77/1.99
% 1.77/1.99 -------- PROOF --------
% 1.77/1.99
% 1.77/1.99 ----> UNIT CONFLICT at 0.02 sec ----> 154 [binary,153.1,19.1] $F.
% 1.77/1.99
% 1.77/1.99 Length of proof is 4. Level of proof is 4.
% 1.77/1.99
% 1.77/1.99 ---------------- PROOF ----------------
% 1.77/1.99 % SZS status Theorem
% 1.77/1.99 % SZS output start Refutation
% See solution above
% 1.77/1.99 ------------ end of proof -------------
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99 ============ end of search ============
% 1.77/1.99
% 1.77/1.99 -------------- statistics -------------
% 1.77/1.99 clauses given 28
% 1.77/1.99 clauses generated 746
% 1.77/1.99 clauses kept 153
% 1.77/1.99 clauses forward subsumed 616
% 1.77/1.99 clauses back subsumed 28
% 1.77/1.99 Kbytes malloced 976
% 1.77/1.99
% 1.77/1.99 ----------- times (seconds) -----------
% 1.77/1.99 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.77/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.99
% 1.77/1.99 That finishes the proof of the theorem.
% 1.77/1.99
% 1.77/1.99 Process 11584 finished Wed Jul 27 06:58:38 2022
% 1.84/1.99 Otter interrupted
% 1.84/1.99 PROOF FOUND
%------------------------------------------------------------------------------