TSTP Solution File: GEO215+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO215+2 : 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 12:54:52 EDT 2022
% Result : Theorem 1.82s 2.03s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 9 unt; 8 nHn; 12 RR)
% Number of literals : 40 ( 0 equ; 11 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO215+2.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO215+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO215+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,A)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO215+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(C,B)
| distinct_points(C,intersection_point(A,B)) ),
file('GEO215+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(A,B) ),
file('GEO215+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ distinct_lines(A,B)
| apart_point_and_line(C,A)
| apart_point_and_line(C,B)
| unorthogonal_lines(A,D)
| unorthogonal_lines(B,D) ),
file('GEO215+2.p',unknown),
[] ).
cnf(24,axiom,
~ unorthogonal_lines(dollar_c3,dollar_c1),
file('GEO215+2.p',unknown),
[] ).
cnf(25,axiom,
~ unorthogonal_lines(dollar_c2,dollar_c1),
file('GEO215+2.p',unknown),
[] ).
cnf(27,axiom,
convergent_lines(dollar_c3,dollar_c2),
file('GEO215+2.p',unknown),
[] ).
cnf(31,plain,
distinct_lines(dollar_c3,dollar_c2),
inference(hyper,[status(thm)],[27,14]),
[iquote('hyper,27,14')] ).
cnf(32,plain,
( convergent_lines(dollar_c3,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[27,6]),
[iquote('hyper,27,6')] ).
cnf(37,plain,
( apart_point_and_line(A,dollar_c3)
| apart_point_and_line(A,dollar_c2)
| unorthogonal_lines(dollar_c3,B)
| unorthogonal_lines(dollar_c2,B) ),
inference(hyper,[status(thm)],[31,23]),
[iquote('hyper,31,23')] ).
cnf(48,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(dollar_c3,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[32,6]),
[iquote('hyper,32,6')] ).
cnf(49,plain,
convergent_lines(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[32,3]),
[iquote('hyper,32,3')] ).
cnf(73,plain,
( apart_point_and_line(A,dollar_c3)
| apart_point_and_line(A,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[37,24]),25]),
[iquote('hyper,37,24,unit_del,25')] ).
cnf(127,plain,
( apart_point_and_line(A,dollar_c2)
| distinct_points(A,intersection_point(dollar_c2,dollar_c3)) ),
inference(hyper,[status(thm)],[73,10,49]),
[iquote('hyper,73,10,49')] ).
cnf(337,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c3) ),
inference(hyper,[status(thm)],[48,3]),
[iquote('hyper,48,3')] ).
cnf(905,plain,
apart_point_and_line(intersection_point(dollar_c2,dollar_c3),dollar_c2),
inference(hyper,[status(thm)],[127,1]),
[iquote('hyper,127,1')] ).
cnf(920,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[905,9,337]),1,3]),
[iquote('hyper,905,9,337,unit_del,1,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO215+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % 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 07:17:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.87 ----- Otter 3.3f, August 2004 -----
% 1.67/1.87 The process was started by sandbox on n004.cluster.edu,
% 1.67/1.87 Wed Jul 27 07:17:36 2022
% 1.67/1.87 The command was "./otter". The process ID is 5862.
% 1.67/1.87
% 1.67/1.87 set(prolog_style_variables).
% 1.67/1.87 set(auto).
% 1.67/1.87 dependent: set(auto1).
% 1.67/1.87 dependent: set(process_input).
% 1.67/1.87 dependent: clear(print_kept).
% 1.67/1.87 dependent: clear(print_new_demod).
% 1.67/1.87 dependent: clear(print_back_demod).
% 1.67/1.87 dependent: clear(print_back_sub).
% 1.67/1.87 dependent: set(control_memory).
% 1.67/1.87 dependent: assign(max_mem, 12000).
% 1.67/1.87 dependent: assign(pick_given_ratio, 4).
% 1.67/1.87 dependent: assign(stats_level, 1).
% 1.67/1.87 dependent: assign(max_seconds, 10800).
% 1.67/1.87 clear(print_given).
% 1.67/1.87
% 1.67/1.87 formula_list(usable).
% 1.67/1.87 all X (-distinct_points(X,X)).
% 1.67/1.87 all X (-distinct_lines(X,X)).
% 1.67/1.87 all X (-convergent_lines(X,X)).
% 1.67/1.87 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.67/1.87 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.67/1.87 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.67/1.87 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))).
% 1.67/1.87 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)))).
% 1.67/1.87 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)).
% 1.67/1.87 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.67/1.87 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.67/1.87 all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.67/1.87 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.67/1.87 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.67/1.87 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.67/1.87 all L M (convergent_lines(L,M)|unorthogonal_lines(L,M)).
% 1.67/1.87 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)).
% 1.67/1.87 all A L (-unorthogonal_lines(orthogonal_through_point(L,A),L)).
% 1.67/1.87 all A L (-apart_point_and_line(A,orthogonal_through_point(L,A))).
% 1.67/1.87 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)).
% 1.67/1.87 -(all L M N (convergent_lines(L,M)->unorthogonal_lines(L,N)|unorthogonal_lines(M,N))).
% 1.67/1.87 end_of_list.
% 1.67/1.87
% 1.67/1.87 -------> usable clausifies to:
% 1.67/1.87
% 1.67/1.87 list(usable).
% 1.67/1.87 0 [] -distinct_points(X,X).
% 1.67/1.87 0 [] -distinct_lines(X,X).
% 1.67/1.87 0 [] -convergent_lines(X,X).
% 1.67/1.87 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.67/1.87 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.67/1.87 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.67/1.87 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.67/1.87 0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.67/1.87 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.87 0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.87 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).
% 1.67/1.87 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.67/1.87 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.67/1.87 0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.67/1.87 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.67/1.87 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.67/1.87 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.67/1.87 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.67/1.87 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|convergent_lines(M,N).
% 1.67/1.87 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|unorthogonal_lines(M,N).
% 1.67/1.87 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|convergent_lines(M,N).
% 1.82/2.03 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 1.82/2.03 0 [] -unorthogonal_lines(orthogonal_through_point(L,A),L).
% 1.82/2.03 0 [] -apart_point_and_line(A,orthogonal_through_point(L,A)).
% 1.82/2.03 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).
% 1.82/2.03 0 [] convergent_lines($c3,$c2).
% 1.82/2.03 0 [] -unorthogonal_lines($c3,$c1).
% 1.82/2.03 0 [] -unorthogonal_lines($c2,$c1).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.82/2.03
% 1.82/2.03 This is a non-Horn set without equality. The strategy will
% 1.82/2.03 be ordered hyper_res, unit deletion, and factoring, with
% 1.82/2.03 satellites in sos and with nuclei in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: set(factor).
% 1.82/2.03 dependent: set(unit_deletion).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.82/2.03 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.82/2.03 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.82/2.03 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.82/2.03 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.82/2.03 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.82/2.03 ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.82/2.03 ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.82/2.03 ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.82/2.03 ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.82/2.03 ** 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).
% 1.82/2.03 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.82/2.03 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.82/2.03 ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.82/2.03 ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 1.82/2.03 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.82/2.03 ** 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).
% 1.82/2.03 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).
% 1.82/2.03 ** KEPT (pick-wt=12): 18 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|unorthogonal_lines(B,C).
% 1.82/2.03 ** KEPT (pick-wt=12): 19 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|convergent_lines(B,C).
% 1.82/2.03 ** KEPT (pick-wt=12): 20 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|unorthogonal_lines(B,C).
% 1.82/2.03 ** KEPT (pick-wt=5): 21 [] -unorthogonal_lines(orthogonal_through_point(A,B),A).
% 1.82/2.03 ** KEPT (pick-wt=5): 22 [] -apart_point_and_line(A,orthogonal_through_point(B,A)).
% 1.82/2.03 ** 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).
% 1.82/2.03 ** KEPT (pick-wt=3): 24 [] -unorthogonal_lines($c3,$c1).
% 1.82/2.03 ** KEPT (pick-wt=3): 25 [] -unorthogonal_lines($c2,$c1).
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=6): 26 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 1.82/2.03 ** KEPT (pick-wt=3): 27 [] convergent_lines($c3,$c2).
% 1.82/2.03
% 1.82/2.03 ======= end of input processing =======
% 1.82/2.03
% 1.82/2.03 =========== start of search ===========
% 1.82/2.03
% 1.82/2.03 -------- PROOF --------
% 1.82/2.03
% 1.82/2.03 -----> EMPTY CLAUSE at 0.16 sec ----> 920 [hyper,905,9,337,unit_del,1,3] $F.
% 1.82/2.03
% 1.82/2.03 Length of proof is 9. Level of proof is 5.
% 1.82/2.03
% 1.82/2.03 ---------------- PROOF ----------------
% 1.82/2.03 % SZS status Theorem
% 1.82/2.03 % SZS output start Refutation
% See solution above
% 1.82/2.03 ------------ end of proof -------------
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03 ============ end of search ============
% 1.82/2.03
% 1.82/2.03 -------------- statistics -------------
% 1.82/2.03 clauses given 89
% 1.82/2.03 clauses generated 3165
% 1.82/2.03 clauses kept 919
% 1.82/2.03 clauses forward subsumed 2273
% 1.82/2.03 clauses back subsumed 50
% 1.82/2.03 Kbytes malloced 1953
% 1.82/2.03
% 1.82/2.03 ----------- times (seconds) -----------
% 1.82/2.03 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 1.82/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.03
% 1.82/2.03 That finishes the proof of the theorem.
% 1.82/2.03
% 1.82/2.03 Process 5862 finished Wed Jul 27 07:17:38 2022
% 1.82/2.03 Otter interrupted
% 1.82/2.03 PROOF FOUND
%------------------------------------------------------------------------------