%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO206+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 1.72s 1.97s
% Output : Refutation 1.72s
% 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 : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO206+2.p',unknown),
[] ).
cnf(15,axiom,
~ convergent_lines(parallel_through_point(A,B),A),
file('GEO206+2.p',unknown),
[] ).
cnf(16,axiom,
~ apart_point_and_line(A,parallel_through_point(B,A)),
file('GEO206+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('GEO206+2.p',unknown),
[] ).
cnf(18,axiom,
~ apart_point_and_line(dollar_c3,dollar_c2),
file('GEO206+2.p',unknown),
[] ).
cnf(19,axiom,
~ convergent_lines(dollar_c2,dollar_c1),
file('GEO206+2.p',unknown),
[] ).
cnf(20,axiom,
distinct_lines(dollar_c2,parallel_through_point(dollar_c1,dollar_c3)),
file('GEO206+2.p',unknown),
[] ).
cnf(21,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,parallel_through_point(dollar_c1,dollar_c3))
| convergent_lines(dollar_c2,parallel_through_point(dollar_c1,dollar_c3)) ),
inference(hyper,[status(thm)],[20,17]),
[iquote('hyper,20,17')] ).
cnf(40,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,parallel_through_point(dollar_c1,dollar_c3))
| convergent_lines(dollar_c2,B)
| convergent_lines(parallel_through_point(dollar_c1,dollar_c3),B) ),
inference(hyper,[status(thm)],[21,6]),
[iquote('hyper,21,6')] ).
cnf(158,plain,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,parallel_through_point(dollar_c1,dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,19]),15]),
[iquote('hyper,40,19,unit_del,15')] ).
cnf(159,plain,
apart_point_and_line(dollar_c3,parallel_through_point(dollar_c1,dollar_c3)),
inference(hyper,[status(thm)],[158,18]),
[iquote('hyper,158,18')] ).
cnf(160,plain,
$false,
inference(binary,[status(thm)],[159,16]),
[iquote('binary,159.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO206+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 06:55:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.94 ----- Otter 3.3f, August 2004 -----
% 1.72/1.94 The process was started by sandbox2 on n012.cluster.edu,
% 1.72/1.94 Wed Jul 27 06:55:20 2022
% 1.72/1.94 The command was "./otter". The process ID is 23197.
% 1.72/1.94
% 1.72/1.94 set(prolog_style_variables).
% 1.72/1.94 set(auto).
% 1.72/1.94 dependent: set(auto1).
% 1.72/1.94 dependent: set(process_input).
% 1.72/1.94 dependent: clear(print_kept).
% 1.72/1.94 dependent: clear(print_new_demod).
% 1.72/1.94 dependent: clear(print_back_demod).
% 1.72/1.94 dependent: clear(print_back_sub).
% 1.72/1.94 dependent: set(control_memory).
% 1.72/1.94 dependent: assign(max_mem, 12000).
% 1.72/1.94 dependent: assign(pick_given_ratio, 4).
% 1.72/1.94 dependent: assign(stats_level, 1).
% 1.72/1.94 dependent: assign(max_seconds, 10800).
% 1.72/1.94 clear(print_given).
% 1.72/1.94
% 1.72/1.94 formula_list(usable).
% 1.72/1.94 all X (-distinct_points(X,X)).
% 1.72/1.94 all X (-distinct_lines(X,X)).
% 1.72/1.94 all X (-convergent_lines(X,X)).
% 1.72/1.94 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.72/1.94 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.72/1.94 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.72/1.94 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))).
% 1.72/1.94 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)))).
% 1.72/1.94 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)).
% 1.72/1.94 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.72/1.94 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.72/1.94 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.72/1.94 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.72/1.94 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.72/1.94 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.72/1.94 -(all X Y Z (-apart_point_and_line(X,Y)& -convergent_lines(Y,Z)-> -distinct_lines(Y,parallel_through_point(Z,X)))).
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 -------> usable clausifies to:
% 1.72/1.94
% 1.72/1.94 list(usable).
% 1.72/1.94 0 [] -distinct_points(X,X).
% 1.72/1.94 0 [] -distinct_lines(X,X).
% 1.72/1.94 0 [] -convergent_lines(X,X).
% 1.72/1.94 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.72/1.94 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.72/1.94 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.72/1.94 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.72/1.94 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.72/1.94 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.72/1.94 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.72/1.94 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).
% 1.72/1.94 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.72/1.94 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.72/1.94 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.72/1.94 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.72/1.94 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.72/1.94 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.72/1.94 0 [] -apart_point_and_line($c3,$c2).
% 1.72/1.94 0 [] -convergent_lines($c2,$c1).
% 1.72/1.94 0 [] distinct_lines($c2,parallel_through_point($c1,$c3)).
% 1.72/1.94 end_of_list.
% 1.72/1.94
% 1.72/1.94 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.72/1.94
% 1.72/1.94 This is a non-Horn set without equality. The strategy will
% 1.72/1.94 be ordered hyper_res, unit deletion, and factoring, with
% 1.72/1.94 satellites in sos and with nuclei in usable.
% 1.72/1.94
% 1.72/1.94 dependent: set(hyper_res).
% 1.72/1.94 dependent: set(factor).
% 1.72/1.94 dependent: set(unit_deletion).
% 1.72/1.94
% 1.72/1.94 ------------> process usable:
% 1.72/1.94 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.72/1.94 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.72/1.94 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.72/1.94 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.72/1.94 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.72/1.97 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.72/1.97 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.72/1.97 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.72/1.97 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.72/1.97 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.72/1.97 ** 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).
% 1.72/1.97 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.72/1.97 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.72/1.97 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.72/1.97 ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 1.72/1.97 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.72/1.97 ** 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).
% 1.72/1.97 ** KEPT (pick-wt=3): 18 [] -apart_point_and_line($c3,$c2).
% 1.72/1.97 ** KEPT (pick-wt=3): 19 [] -convergent_lines($c2,$c1).
% 1.72/1.97
% 1.72/1.97 ------------> process sos:
% 1.72/1.97 ** KEPT (pick-wt=5): 20 [] distinct_lines($c2,parallel_through_point($c1,$c3)).
% 1.72/1.97
% 1.72/1.97 ======= end of input processing =======
% 1.72/1.97
% 1.72/1.97 =========== start of search ===========
% 1.72/1.97
% 1.72/1.97 -------- PROOF --------
% 1.72/1.97
% 1.72/1.97 ----> UNIT CONFLICT at 0.04 sec ----> 160 [binary,159.1,16.1] $F.
% 1.72/1.97
% 1.72/1.97 Length of proof is 4. Level of proof is 4.
% 1.72/1.97
% 1.72/1.97 ---------------- PROOF ----------------
% 1.72/1.97 % SZS status Theorem
% 1.72/1.97 % SZS output start Refutation
% See solution above
% 1.72/1.97 ------------ end of proof -------------
% 1.72/1.97
% 1.72/1.97
% 1.72/1.97 Search stopped by max_proofs option.
% 1.72/1.97
% 1.72/1.97
% 1.72/1.97 Search stopped by max_proofs option.
% 1.72/1.97
% 1.72/1.97 ============ end of search ============
% 1.72/1.97
% 1.72/1.97 -------------- statistics -------------
% 1.72/1.97 clauses given 38
% 1.72/1.97 clauses generated 853
% 1.72/1.97 clauses kept 159
% 1.72/1.97 clauses forward subsumed 714
% 1.72/1.97 clauses back subsumed 6
% 1.72/1.97 Kbytes malloced 976
% 1.72/1.97
% 1.72/1.97 ----------- times (seconds) -----------
% 1.72/1.97 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.72/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.97
% 1.72/1.97 That finishes the proof of the theorem.
% 1.72/1.97
% 1.72/1.97 Process 23197 finished Wed Jul 27 06:55:22 2022
% 1.72/1.97 Otter interrupted
% 1.72/1.97 PROOF FOUND
%------------------------------------------------------------------------------