TSTP Solution File: GEO216+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:54:52 EDT 2022
% Result : Theorem 2.02s 2.18s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 1 nHn; 4 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO216+2.p',unknown),
[] ).
cnf(20,axiom,
~ unorthogonal_lines(dollar_c1,dollar_c1),
file('GEO216+2.p',unknown),
[] ).
cnf(21,axiom,
( convergent_lines(A,B)
| unorthogonal_lines(A,B) ),
file('GEO216+2.p',unknown),
[] ).
cnf(22,plain,
convergent_lines(dollar_c1,dollar_c1),
inference(hyper,[status(thm)],[21,20]),
[iquote('hyper,21,20')] ).
cnf(23,plain,
$false,
inference(binary,[status(thm)],[22,3]),
[iquote('binary,22.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 07:16:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.02/2.18 ----- Otter 3.3f, August 2004 -----
% 2.02/2.18 The process was started by sandbox on n025.cluster.edu,
% 2.02/2.18 Wed Jul 27 07:16:45 2022
% 2.02/2.18 The command was "./otter". The process ID is 30495.
% 2.02/2.18
% 2.02/2.18 set(prolog_style_variables).
% 2.02/2.18 set(auto).
% 2.02/2.18 dependent: set(auto1).
% 2.02/2.18 dependent: set(process_input).
% 2.02/2.18 dependent: clear(print_kept).
% 2.02/2.18 dependent: clear(print_new_demod).
% 2.02/2.18 dependent: clear(print_back_demod).
% 2.02/2.18 dependent: clear(print_back_sub).
% 2.02/2.18 dependent: set(control_memory).
% 2.02/2.18 dependent: assign(max_mem, 12000).
% 2.02/2.18 dependent: assign(pick_given_ratio, 4).
% 2.02/2.18 dependent: assign(stats_level, 1).
% 2.02/2.18 dependent: assign(max_seconds, 10800).
% 2.02/2.18 clear(print_given).
% 2.02/2.18
% 2.02/2.18 formula_list(usable).
% 2.02/2.18 all X (-distinct_points(X,X)).
% 2.02/2.18 all X (-distinct_lines(X,X)).
% 2.02/2.18 all X (-convergent_lines(X,X)).
% 2.02/2.18 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 2.02/2.18 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 2.02/2.18 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 2.02/2.18 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))).
% 2.02/2.18 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)))).
% 2.02/2.18 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)).
% 2.02/2.18 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 2.02/2.18 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 2.02/2.18 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 2.02/2.18 all L M (-(-convergent_lines(L,M)& -unorthogonal_lines(L,M))).
% 2.02/2.18 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)).
% 2.02/2.18 all L M N (-unorthogonal_lines(L,M)& -unorthogonal_lines(L,N)-> -convergent_lines(M,N)).
% 2.02/2.18 -(all L (-(-unorthogonal_lines(L,L)))).
% 2.02/2.18 end_of_list.
% 2.02/2.18
% 2.02/2.18 -------> usable clausifies to:
% 2.02/2.18
% 2.02/2.18 list(usable).
% 2.02/2.18 0 [] -distinct_points(X,X).
% 2.02/2.18 0 [] -distinct_lines(X,X).
% 2.02/2.18 0 [] -convergent_lines(X,X).
% 2.02/2.18 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 2.02/2.18 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 2.02/2.18 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 2.02/2.18 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 2.02/2.18 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 2.02/2.18 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 2.02/2.18 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 2.02/2.18 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).
% 2.02/2.18 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 2.02/2.18 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 2.02/2.18 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 2.02/2.18 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 2.02/2.18 0 [] convergent_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 2.02/2.18 0 [] convergent_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 2.02/2.18 0 [] unorthogonal_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 2.02/2.18 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 2.02/2.18 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N).
% 2.02/2.18 0 [] -unorthogonal_lines($c1,$c1).
% 2.02/2.18 end_of_list.
% 2.02/2.18
% 2.02/2.18 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 2.02/2.18
% 2.02/2.18 This is a non-Horn set without equality. The strategy will
% 2.02/2.18 be ordered hyper_res, unit deletion, and factoring, with
% 2.02/2.18 satellites in sos and with nuclei in usable.
% 2.02/2.18
% 2.02/2.18 dependent: set(hyper_res).
% 2.02/2.18 dependent: set(factor).
% 2.02/2.18 dependent: set(unit_deletion).
% 2.02/2.18
% 2.02/2.18 ------------> process usable:
% 2.02/2.18 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 2.02/2.18 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 2.02/2.18 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 2.02/2.18 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 2.02/2.18 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 2.02/2.18 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 2.02/2.18 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 2.02/2.18 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 2.02/2.18 ** 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).
% 2.02/2.18 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 2.02/2.18 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 2.02/2.18 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 2.02/2.18 ** KEPT (pick-wt=12): 15 [] convergent_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=12): 16 [] convergent_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=12): 17 [] unorthogonal_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=12): 18 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=9): 19 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C).
% 2.02/2.18 ** KEPT (pick-wt=3): 20 [] -unorthogonal_lines($c1,$c1).
% 2.02/2.18 19 back subsumes 18.
% 2.02/2.18
% 2.02/2.18 ------------> process sos:
% 2.02/2.18 ** KEPT (pick-wt=6): 21 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 2.02/2.18
% 2.02/2.18 ======= end of input processing =======
% 2.02/2.18
% 2.02/2.18 =========== start of search ===========
% 2.02/2.18
% 2.02/2.18 -------- PROOF --------
% 2.02/2.18
% 2.02/2.18 ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,3.1] $F.
% 2.02/2.18
% 2.02/2.18 Length of proof is 1. Level of proof is 1.
% 2.02/2.18
% 2.02/2.18 ---------------- PROOF ----------------
% 2.02/2.18 % SZS status Theorem
% 2.02/2.18 % SZS output start Refutation
% See solution above
% 2.02/2.18 ------------ end of proof -------------
% 2.02/2.18
% 2.02/2.18
% 2.02/2.18 Search stopped by max_proofs option.
% 2.02/2.18
% 2.02/2.18
% 2.02/2.18 Search stopped by max_proofs option.
% 2.02/2.18
% 2.02/2.18 ============ end of search ============
% 2.02/2.18
% 2.02/2.18 -------------- statistics -------------
% 2.02/2.18 clauses given 1
% 2.02/2.18 clauses generated 13
% 2.02/2.18 clauses kept 22
% 2.02/2.18 clauses forward subsumed 12
% 2.02/2.18 clauses back subsumed 1
% 2.02/2.18 Kbytes malloced 976
% 2.02/2.18
% 2.02/2.18 ----------- times (seconds) -----------
% 2.02/2.18 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.18
% 2.02/2.18 That finishes the proof of the theorem.
% 2.02/2.18
% 2.02/2.18 Process 30495 finished Wed Jul 27 07:16:47 2022
% 2.02/2.18 Otter interrupted
% 2.02/2.18 PROOF FOUND
%------------------------------------------------------------------------------