%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:54:54 EDT 2022
% Result : Theorem 1.86s 2.08s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 2 nHn; 5 RR)
% Number of literals : 10 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
( unorthogonal_lines(A,B)
| unorthogonal_lines(A,C)
| ~ convergent_lines(B,C) ),
file('GEO220+2.p',unknown),
[] ).
cnf(20,axiom,
~ unorthogonal_lines(dollar_c3,dollar_c2),
file('GEO220+2.p',unknown),
[] ).
cnf(21,axiom,
~ unorthogonal_lines(dollar_c3,dollar_c1),
file('GEO220+2.p',unknown),
[] ).
cnf(23,axiom,
convergent_lines(dollar_c2,dollar_c1),
file('GEO220+2.p',unknown),
[] ).
cnf(26,plain,
( unorthogonal_lines(A,dollar_c2)
| unorthogonal_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[23,19]),
[iquote('hyper,23,19')] ).
cnf(36,plain,
unorthogonal_lines(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[26,20]),
[iquote('hyper,26,20')] ).
cnf(37,plain,
$false,
inference(binary,[status(thm)],[36,21]),
[iquote('binary,36.1,21.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 07:13:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.08 ----- Otter 3.3f, August 2004 -----
% 1.86/2.08 The process was started by sandbox2 on n011.cluster.edu,
% 1.86/2.08 Wed Jul 27 07:13:55 2022
% 1.86/2.08 The command was "./otter". The process ID is 13677.
% 1.86/2.08
% 1.86/2.08 set(prolog_style_variables).
% 1.86/2.08 set(auto).
% 1.86/2.08 dependent: set(auto1).
% 1.86/2.08 dependent: set(process_input).
% 1.86/2.08 dependent: clear(print_kept).
% 1.86/2.08 dependent: clear(print_new_demod).
% 1.86/2.08 dependent: clear(print_back_demod).
% 1.86/2.08 dependent: clear(print_back_sub).
% 1.86/2.08 dependent: set(control_memory).
% 1.86/2.08 dependent: assign(max_mem, 12000).
% 1.86/2.08 dependent: assign(pick_given_ratio, 4).
% 1.86/2.08 dependent: assign(stats_level, 1).
% 1.86/2.08 dependent: assign(max_seconds, 10800).
% 1.86/2.08 clear(print_given).
% 1.86/2.08
% 1.86/2.08 formula_list(usable).
% 1.86/2.08 all X (-distinct_points(X,X)).
% 1.86/2.08 all X (-distinct_lines(X,X)).
% 1.86/2.08 all X (-convergent_lines(X,X)).
% 1.86/2.08 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.86/2.08 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.86/2.08 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.86/2.08 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))).
% 1.86/2.08 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)))).
% 1.86/2.08 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)).
% 1.86/2.08 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.86/2.08 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.86/2.08 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.86/2.08 all L M (-(-convergent_lines(L,M)& -unorthogonal_lines(L,M))).
% 1.86/2.08 all L M N ((-convergent_lines(L,M)| -unorthogonal_lines(L,M))& (-convergent_lines(L,N)| -unorthogonal_lines(L,N))-> -convergent_lines(M,N)| -unorthogonal_lines(M,N)).
% 1.86/2.08 all L M N (-unorthogonal_lines(L,M)& -unorthogonal_lines(L,N)-> -convergent_lines(M,N)).
% 1.86/2.08 -(all L M N (-unorthogonal_lines(L,M)& -unorthogonal_lines(L,N)-> -convergent_lines(M,N))).
% 1.86/2.08 end_of_list.
% 1.86/2.08
% 1.86/2.08 -------> usable clausifies to:
% 1.86/2.08
% 1.86/2.08 list(usable).
% 1.86/2.08 0 [] -distinct_points(X,X).
% 1.86/2.08 0 [] -distinct_lines(X,X).
% 1.86/2.08 0 [] -convergent_lines(X,X).
% 1.86/2.08 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.86/2.08 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.86/2.08 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.86/2.08 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.86/2.08 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.86/2.08 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.86/2.08 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.86/2.08 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).
% 1.86/2.08 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.86/2.08 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.86/2.08 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.86/2.08 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.86/2.08 0 [] convergent_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.86/2.08 0 [] convergent_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.86/2.08 0 [] unorthogonal_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.86/2.08 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.86/2.08 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N).
% 1.86/2.08 0 [] -unorthogonal_lines($c3,$c2).
% 1.86/2.08 0 [] -unorthogonal_lines($c3,$c1).
% 1.86/2.08 0 [] convergent_lines($c2,$c1).
% 1.86/2.08 end_of_list.
% 1.86/2.08
% 1.86/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.86/2.08
% 1.86/2.08 This is a non-Horn set without equality. The strategy will
% 1.86/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.86/2.08 satellites in sos and with nuclei in usable.
% 1.86/2.08
% 1.86/2.08 dependent: set(hyper_res).
% 1.86/2.08 dependent: set(factor).
% 1.86/2.08 dependent: set(unit_deletion).
% 1.86/2.08
% 1.86/2.08 ------------> process usable:
% 1.86/2.08 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.86/2.08 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.86/2.08 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.86/2.08 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.86/2.08 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.86/2.08 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.86/2.08 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.86/2.08 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.86/2.08 ** 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).
% 1.86/2.08 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.86/2.08 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.86/2.08 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.86/2.08 ** KEPT (pick-wt=12): 15 [] convergent_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=12): 16 [] convergent_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=12): 17 [] unorthogonal_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=12): 18 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=9): 19 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C).
% 1.86/2.08 ** KEPT (pick-wt=3): 20 [] -unorthogonal_lines($c3,$c2).
% 1.86/2.08 ** KEPT (pick-wt=3): 21 [] -unorthogonal_lines($c3,$c1).
% 1.86/2.08 19 back subsumes 18.
% 1.86/2.08
% 1.86/2.08 ------------> process sos:
% 1.86/2.08 ** KEPT (pick-wt=6): 22 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 1.86/2.08 ** KEPT (pick-wt=3): 23 [] convergent_lines($c2,$c1).
% 1.86/2.08
% 1.86/2.08 ======= end of input processing =======
% 1.86/2.08
% 1.86/2.08 =========== start of search ===========
% 1.86/2.08
% 1.86/2.08 -------- PROOF --------
% 1.86/2.08
% 1.86/2.08 ----> UNIT CONFLICT at 0.00 sec ----> 37 [binary,36.1,21.1] $F.
% 1.86/2.08
% 1.86/2.08 Length of proof is 2. Level of proof is 2.
% 1.86/2.08
% 1.86/2.08 ---------------- PROOF ----------------
% 1.86/2.08 % SZS status Theorem
% 1.86/2.08 % SZS output start Refutation
% See solution above
% 1.86/2.08 ------------ end of proof -------------
% 1.86/2.08
% 1.86/2.08
% 1.86/2.08 Search stopped by max_proofs option.
% 1.86/2.08
% 1.86/2.08
% 1.86/2.08 Search stopped by max_proofs option.
% 1.86/2.08
% 1.86/2.08 ============ end of search ============
% 1.86/2.08
% 1.86/2.08 -------------- statistics -------------
% 1.86/2.08 clauses given 6
% 1.86/2.08 clauses generated 34
% 1.86/2.08 clauses kept 36
% 1.86/2.08 clauses forward subsumed 21
% 1.86/2.08 clauses back subsumed 1
% 1.86/2.08 Kbytes malloced 976
% 1.86/2.08
% 1.86/2.08 ----------- times (seconds) -----------
% 1.86/2.08 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.86/2.08
% 1.86/2.08 That finishes the proof of the theorem.
% 1.86/2.08
% 1.86/2.08 Process 13677 finished Wed Jul 27 07:13:57 2022
% 1.86/2.08 Otter interrupted
% 1.86/2.08 PROOF FOUND
%------------------------------------------------------------------------------