%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:54:51 EDT 2022
% Result : Theorem 2.05s 2.24s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 28 ( 10 unt; 18 nHn; 10 RR)
% Number of literals : 60 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ distinct_lines(A,A),
file('GEO213+1.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO213+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ distinct_lines(A,B)
| distinct_lines(A,C)
| distinct_lines(B,C) ),
file('GEO213+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO213+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(B,C)
| convergent_lines(A,C) ),
file('GEO213+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ convergent_lines(A,B)
| ~ unorthogonal_lines(A,B)
| convergent_lines(A,C)
| unorthogonal_lines(B,C) ),
file('GEO213+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ convergent_lines(A,B)
| ~ unorthogonal_lines(A,B)
| unorthogonal_lines(A,C)
| convergent_lines(B,C) ),
file('GEO213+1.p',unknown),
[] ).
cnf(24,axiom,
~ distinct_lines(dollar_c3,dollar_c1),
file('GEO213+1.p',unknown),
[] ).
cnf(25,axiom,
~ unorthogonal_lines(dollar_c2,dollar_c1),
file('GEO213+1.p',unknown),
[] ).
cnf(26,axiom,
( convergent_lines(A,B)
| unorthogonal_lines(A,B) ),
file('GEO213+1.p',unknown),
[] ).
cnf(27,axiom,
unorthogonal_lines(dollar_c3,dollar_c2),
file('GEO213+1.p',unknown),
[] ).
cnf(28,plain,
convergent_lines(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[26,25]),
[iquote('hyper,26,25')] ).
cnf(30,plain,
( distinct_lines(dollar_c1,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[28,14]),
[iquote('hyper,28,14')] ).
cnf(31,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c1,A) ),
inference(hyper,[status(thm)],[28,6]),
[iquote('hyper,28,6')] ).
cnf(35,plain,
( convergent_lines(dollar_c2,A)
| distinct_lines(dollar_c1,B)
| distinct_lines(A,B) ),
inference(hyper,[status(thm)],[30,5]),
[iquote('hyper,30,5')] ).
cnf(37,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c2,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[31,6]),
[iquote('hyper,31,6')] ).
cnf(119,plain,
convergent_lines(dollar_c2,dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[35,24]),2]),
[iquote('hyper,35,24,unit_del,2')] ).
cnf(130,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,A) ),
inference(hyper,[status(thm)],[119,6]),
[iquote('hyper,119,6')] ).
cnf(152,plain,
( convergent_lines(dollar_c1,A)
| convergent_lines(dollar_c2,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
inference(hyper,[status(thm)],[37,6]),
[iquote('hyper,37,6')] ).
cnf(157,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[152]),3]),
[iquote('factor,152.1.3,unit_del,3')] ).
cnf(167,plain,
( convergent_lines(dollar_c3,A)
| unorthogonal_lines(dollar_c2,A) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[130,18,27]),3]),
[iquote('hyper,130,18,27,unit_del,3')] ).
cnf(255,plain,
( convergent_lines(dollar_c3,A)
| unorthogonal_lines(dollar_c2,B)
| convergent_lines(A,B)
| convergent_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[167,19,157]),
[iquote('hyper,167,19,157')] ).
cnf(260,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[255]),25]),
[iquote('factor,255.3.4,unit_del,25')] ).
cnf(356,plain,
( convergent_lines(dollar_c3,A)
| distinct_lines(dollar_c1,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[260,14]),
[iquote('hyper,260,14')] ).
cnf(358,plain,
distinct_lines(dollar_c1,dollar_c3),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[356]),3]),
[iquote('factor,356.1.3,unit_del,3')] ).
cnf(360,plain,
( distinct_lines(dollar_c1,A)
| distinct_lines(dollar_c3,A) ),
inference(hyper,[status(thm)],[358,5]),
[iquote('hyper,358,5')] ).
cnf(620,plain,
distinct_lines(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[360,2]),
[iquote('hyper,360,2')] ).
cnf(621,plain,
$false,
inference(binary,[status(thm)],[620,24]),
[iquote('binary,620.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 06:58:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.95 ----- Otter 3.3f, August 2004 -----
% 1.75/1.95 The process was started by sandbox2 on n004.cluster.edu,
% 1.75/1.95 Wed Jul 27 06:58:51 2022
% 1.75/1.95 The command was "./otter". The process ID is 19537.
% 1.75/1.95
% 1.75/1.95 set(prolog_style_variables).
% 1.75/1.95 set(auto).
% 1.75/1.95 dependent: set(auto1).
% 1.75/1.95 dependent: set(process_input).
% 1.75/1.95 dependent: clear(print_kept).
% 1.75/1.95 dependent: clear(print_new_demod).
% 1.75/1.95 dependent: clear(print_back_demod).
% 1.75/1.95 dependent: clear(print_back_sub).
% 1.75/1.95 dependent: set(control_memory).
% 1.75/1.95 dependent: assign(max_mem, 12000).
% 1.75/1.95 dependent: assign(pick_given_ratio, 4).
% 1.75/1.95 dependent: assign(stats_level, 1).
% 1.75/1.95 dependent: assign(max_seconds, 10800).
% 1.75/1.95 clear(print_given).
% 1.75/1.95
% 1.75/1.95 formula_list(usable).
% 1.75/1.95 all X (-distinct_points(X,X)).
% 1.75/1.95 all X (-distinct_lines(X,X)).
% 1.75/1.95 all X (-convergent_lines(X,X)).
% 1.75/1.95 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.75/1.95 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.75/1.95 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.75/1.95 all X Y (distinct_points(X,Y)-> -apart_point_and_line(X,line_connecting(X,Y))).
% 1.75/1.95 all X Y (distinct_points(X,Y)-> -apart_point_and_line(Y,line_connecting(X,Y))).
% 1.75/1.95 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),X)).
% 1.75/1.95 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),Y)).
% 1.75/1.95 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)).
% 1.75/1.95 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.75/1.95 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.75/1.95 all X Y Z (convergent_lines(X,Y)->distinct_lines(Y,Z)|convergent_lines(X,Z)).
% 1.75/1.95 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.75/1.95 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.75/1.95 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.75/1.95 all L M (convergent_lines(L,M)|unorthogonal_lines(L,M)).
% 1.75/1.95 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)).
% 1.75/1.95 all A L (-unorthogonal_lines(orthogonal_through_point(L,A),L)).
% 1.75/1.95 all A L (-apart_point_and_line(A,orthogonal_through_point(L,A))).
% 1.75/1.95 all A L M N (distinct_lines(L,M)->apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N)).
% 1.75/1.95 -(all L M N (unorthogonal_lines(L,M)->distinct_lines(L,N)|unorthogonal_lines(M,N))).
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 -------> usable clausifies to:
% 1.75/1.95
% 1.75/1.95 list(usable).
% 1.75/1.95 0 [] -distinct_points(X,X).
% 1.75/1.95 0 [] -distinct_lines(X,X).
% 1.75/1.95 0 [] -convergent_lines(X,X).
% 1.75/1.95 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.75/1.95 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.75/1.95 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.75/1.95 0 [] -distinct_points(X,Y)| -apart_point_and_line(X,line_connecting(X,Y)).
% 1.75/1.95 0 [] -distinct_points(X,Y)| -apart_point_and_line(Y,line_connecting(X,Y)).
% 1.75/1.95 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),X).
% 1.75/1.95 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),Y).
% 1.75/1.95 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).
% 1.75/1.95 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.75/1.95 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.75/1.95 0 [] -convergent_lines(X,Y)|distinct_lines(Y,Z)|convergent_lines(X,Z).
% 1.75/1.95 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.75/1.95 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.75/1.95 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.75/1.95 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.75/1.95 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|convergent_lines(M,N).
% 1.75/1.95 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|unorthogonal_lines(M,N).
% 1.75/1.95 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|convergent_lines(M,N).
% 2.05/2.24 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 2.05/2.24 0 [] -unorthogonal_lines(orthogonal_through_point(L,A),L).
% 2.05/2.24 0 [] -apart_point_and_line(A,orthogonal_through_point(L,A)).
% 2.05/2.24 0 [] -distinct_lines(L,M)|apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 2.05/2.24 0 [] unorthogonal_lines($c3,$c2).
% 2.05/2.24 0 [] -distinct_lines($c3,$c1).
% 2.05/2.24 0 [] -unorthogonal_lines($c2,$c1).
% 2.05/2.24 end_of_list.
% 2.05/2.24
% 2.05/2.24 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 2.05/2.24
% 2.05/2.24 This is a non-Horn set without equality. The strategy will
% 2.05/2.24 be ordered hyper_res, unit deletion, and factoring, with
% 2.05/2.24 satellites in sos and with nuclei in usable.
% 2.05/2.24
% 2.05/2.24 dependent: set(hyper_res).
% 2.05/2.24 dependent: set(factor).
% 2.05/2.24 dependent: set(unit_deletion).
% 2.05/2.24
% 2.05/2.24 ------------> process usable:
% 2.05/2.24 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 2.05/2.24 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 2.05/2.24 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 2.05/2.24 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 2.05/2.24 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=8): 7 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 2.05/2.24 ** KEPT (pick-wt=8): 8 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 2.05/2.24 ** KEPT (pick-wt=8): 9 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),A).
% 2.05/2.24 ** KEPT (pick-wt=8): 10 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),B).
% 2.05/2.24 ** 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).
% 2.05/2.24 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 2.05/2.24 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 2.05/2.24 ** KEPT (pick-wt=9): 14 [] -convergent_lines(A,B)|distinct_lines(B,C)|convergent_lines(A,C).
% 2.05/2.24 ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 2.05/2.24 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 2.05/2.24 ** 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).
% 2.05/2.24 Following clause subsumed by 6 during input processing: 0 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=12): 18 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|unorthogonal_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=12): 19 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|convergent_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=12): 20 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|unorthogonal_lines(B,C).
% 2.05/2.24 ** KEPT (pick-wt=5): 21 [] -unorthogonal_lines(orthogonal_through_point(A,B),A).
% 2.05/2.24 ** KEPT (pick-wt=5): 22 [] -apart_point_and_line(A,orthogonal_through_point(B,A)).
% 2.05/2.24 ** KEPT (pick-wt=15): 23 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|unorthogonal_lines(A,D)|unorthogonal_lines(B,D).
% 2.05/2.24 ** KEPT (pick-wt=3): 24 [] -distinct_lines($c3,$c1).
% 2.05/2.24 ** KEPT (pick-wt=3): 25 [] -unorthogonal_lines($c2,$c1).
% 2.05/2.24
% 2.05/2.24 ------------> process sos:
% 2.05/2.24 ** KEPT (pick-wt=6): 26 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 2.05/2.24 ** KEPT (pick-wt=3): 27 [] unorthogonal_lines($c3,$c2).
% 2.05/2.24
% 2.05/2.24 ======= end of input processing =======
% 2.05/2.24
% 2.05/2.24 =========== start of search ===========
% 2.05/2.24
% 2.05/2.24 -------- PROOF --------
% 2.05/2.24
% 2.05/2.24 ----> UNIT CONFLICT at 0.29 sec ----> 621 [binary,620.1,24.1] $F.
% 2.05/2.24
% 2.05/2.24 Length of proof is 16. Level of proof is 12.
% 2.05/2.24
% 2.05/2.24 ---------------- PROOF ----------------
% 2.05/2.24 % SZS status Theorem
% 2.05/2.24 % SZS output start Refutation
% See solution above
% 2.05/2.24 ------------ end of proof -------------
% 2.05/2.24
% 2.05/2.24
% 2.05/2.24 Search stopped by max_proofs option.
% 2.05/2.24
% 2.05/2.24
% 2.05/2.24 Search stopped by max_proofs option.
% 2.05/2.24
% 2.05/2.24 ============ end of search ============
% 2.05/2.24
% 2.05/2.24 -------------- statistics -------------
% 2.05/2.24 clauses given 62
% 2.05/2.24 clauses generated 2598
% 2.05/2.24 clauses kept 620
% 2.05/2.24 clauses forward subsumed 2006
% 2.05/2.24 clauses back subsumed 82
% 2.05/2.24 Kbytes malloced 976
% 2.05/2.24
% 2.05/2.24 ----------- times (seconds) -----------
% 2.05/2.24 user CPU time 0.29 (0 hr, 0 min, 0 sec)
% 2.05/2.24 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.05/2.24 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.05/2.24
% 2.05/2.24 That finishes the proof of the theorem.
% 2.05/2.24
% 2.05/2.24 Process 19537 finished Wed Jul 27 06:58:53 2022
% 2.05/2.24 Otter interrupted
% 2.05/2.24 PROOF FOUND
%------------------------------------------------------------------------------