TSTP Solution File: GEO226+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:54:56 EDT 2022
% Result : Theorem 1.93s 2.12s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 3 unt; 1 nHn; 5 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(intersection_point(A,B),A) ),
file('GEO226+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(intersection_point(A,B),B) ),
file('GEO226+1.p',unknown),
[] ).
cnf(21,axiom,
convergent_lines(dollar_c2,dollar_c1),
file('GEO226+1.p',unknown),
[] ).
cnf(23,axiom,
( apart_point_and_line(A,dollar_c2)
| apart_point_and_line(A,dollar_c1) ),
file('GEO226+1.p',unknown),
[] ).
cnf(34,plain,
apart_point_and_line(intersection_point(dollar_c2,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[23,9,21]),
[iquote('hyper,23,9,21')] ).
cnf(48,plain,
$false,
inference(hyper,[status(thm)],[34,10,21]),
[iquote('hyper,34,10,21')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 07:37:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.12 ----- Otter 3.3f, August 2004 -----
% 1.93/2.12 The process was started by sandbox on n023.cluster.edu,
% 1.93/2.12 Wed Jul 27 07:37:33 2022
% 1.93/2.12 The command was "./otter". The process ID is 32653.
% 1.93/2.12
% 1.93/2.12 set(prolog_style_variables).
% 1.93/2.12 set(auto).
% 1.93/2.12 dependent: set(auto1).
% 1.93/2.12 dependent: set(process_input).
% 1.93/2.12 dependent: clear(print_kept).
% 1.93/2.12 dependent: clear(print_new_demod).
% 1.93/2.12 dependent: clear(print_back_demod).
% 1.93/2.12 dependent: clear(print_back_sub).
% 1.93/2.12 dependent: set(control_memory).
% 1.93/2.12 dependent: assign(max_mem, 12000).
% 1.93/2.12 dependent: assign(pick_given_ratio, 4).
% 1.93/2.12 dependent: assign(stats_level, 1).
% 1.93/2.12 dependent: assign(max_seconds, 10800).
% 1.93/2.12 clear(print_given).
% 1.93/2.12
% 1.93/2.12 formula_list(usable).
% 1.93/2.12 all X (-distinct_points(X,X)).
% 1.93/2.12 all X (-distinct_lines(X,X)).
% 1.93/2.12 all X (-convergent_lines(X,X)).
% 1.93/2.12 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.93/2.12 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.93/2.12 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.93/2.12 all X Y (distinct_points(X,Y)-> -apart_point_and_line(X,line_connecting(X,Y))).
% 1.93/2.12 all X Y (distinct_points(X,Y)-> -apart_point_and_line(Y,line_connecting(X,Y))).
% 1.93/2.12 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),X)).
% 1.93/2.12 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),Y)).
% 1.93/2.12 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)).
% 1.93/2.12 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.93/2.12 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.93/2.12 all X Y Z (convergent_lines(X,Y)->distinct_lines(Y,Z)|convergent_lines(X,Z)).
% 1.93/2.12 all A B (point(A)&point(B)&distinct_points(A,B)->line(line_connecting(A,B))).
% 1.93/2.12 all L M (line(L)&line(M)&convergent_lines(L,M)->point(intersection_point(L,M))).
% 1.93/2.12 all L A (line(L)&point(A)->line(parallel_through_point(L,A))).
% 1.93/2.12 all L A (line(L)&point(A)->line(orthogonal_through_point(L,A))).
% 1.93/2.12 -(all L M (line(L)&line(M)&convergent_lines(L,M)-> (exists X (point(X)-> -apart_point_and_line(X,L)& -apart_point_and_line(X,M))))).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 -------> usable clausifies to:
% 1.93/2.12
% 1.93/2.12 list(usable).
% 1.93/2.12 0 [] -distinct_points(X,X).
% 1.93/2.12 0 [] -distinct_lines(X,X).
% 1.93/2.12 0 [] -convergent_lines(X,X).
% 1.93/2.12 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.93/2.12 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.93/2.12 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.93/2.12 0 [] -distinct_points(X,Y)| -apart_point_and_line(X,line_connecting(X,Y)).
% 1.93/2.12 0 [] -distinct_points(X,Y)| -apart_point_and_line(Y,line_connecting(X,Y)).
% 1.93/2.12 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),X).
% 1.93/2.12 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),Y).
% 1.93/2.12 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).
% 1.93/2.12 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.93/2.12 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.93/2.12 0 [] -convergent_lines(X,Y)|distinct_lines(Y,Z)|convergent_lines(X,Z).
% 1.93/2.12 0 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.93/2.12 0 [] -line(L)| -line(M)| -convergent_lines(L,M)|point(intersection_point(L,M)).
% 1.93/2.12 0 [] -line(L)| -point(A)|line(parallel_through_point(L,A)).
% 1.93/2.12 0 [] -line(L)| -point(A)|line(orthogonal_through_point(L,A)).
% 1.93/2.12 0 [] line($c2).
% 1.93/2.12 0 [] line($c1).
% 1.93/2.12 0 [] convergent_lines($c2,$c1).
% 1.93/2.12 0 [] point(X).
% 1.93/2.12 0 [] apart_point_and_line(X,$c2)|apart_point_and_line(X,$c1).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.93/2.12
% 1.93/2.12 This is a non-Horn set without equality. The strategy will
% 1.93/2.12 be ordered hyper_res, unit deletion, and factoring, with
% 1.93/2.12 satellites in sos and with nuclei in usable.
% 1.93/2.12
% 1.93/2.12 dependent: set(hyper_res).
% 1.93/2.12 dependent: set(factor).
% 1.93/2.12 dependent: set(unit_deletion).
% 1.93/2.12
% 1.93/2.12 ------------> process usable:
% 1.93/2.12 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.93/2.12 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.93/2.12 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.93/2.12 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.93/2.12 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.93/2.12 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.93/2.12 ** KEPT (pick-wt=8): 7 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=8): 8 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=8): 9 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),A).
% 1.93/2.12 ** KEPT (pick-wt=8): 10 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),B).
% 1.93/2.12 ** 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).
% 1.93/2.12 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.93/2.12 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.93/2.12 ** KEPT (pick-wt=9): 14 [] -convergent_lines(A,B)|distinct_lines(B,C)|convergent_lines(A,C).
% 1.93/2.12 ** KEPT (pick-wt=11): 15 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=11): 16 [] -line(A)| -line(B)| -convergent_lines(A,B)|point(intersection_point(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=8): 17 [] -line(A)| -point(B)|line(parallel_through_point(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=8): 18 [] -line(A)| -point(B)|line(orthogonal_through_point(A,B)).
% 1.93/2.12
% 1.93/2.12 ------------> process sos:
% 1.93/2.12 ** KEPT (pick-wt=2): 19 [] line($c2).
% 1.93/2.12 ** KEPT (pick-wt=2): 20 [] line($c1).
% 1.93/2.12 ** KEPT (pick-wt=3): 21 [] convergent_lines($c2,$c1).
% 1.93/2.12 ** KEPT (pick-wt=2): 22 [] point(A).
% 1.93/2.12 ** KEPT (pick-wt=6): 23 [] apart_point_and_line(A,$c2)|apart_point_and_line(A,$c1).
% 1.93/2.12 22 back subsumes 16.
% 1.93/2.12
% 1.93/2.12 ======= end of input processing =======
% 1.93/2.12
% 1.93/2.12 =========== start of search ===========
% 1.93/2.12
% 1.93/2.12 -------- PROOF --------
% 1.93/2.12
% 1.93/2.12 -----> EMPTY CLAUSE at 0.00 sec ----> 48 [hyper,34,10,21] $F.
% 1.93/2.12
% 1.93/2.12 Length of proof is 1. Level of proof is 1.
% 1.93/2.12
% 1.93/2.12 ---------------- PROOF ----------------
% 1.93/2.12 % SZS status Theorem
% 1.93/2.12 % SZS output start Refutation
% See solution above
% 1.93/2.12 ------------ end of proof -------------
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12 ============ end of search ============
% 1.93/2.12
% 1.93/2.12 -------------- statistics -------------
% 1.93/2.12 clauses given 10
% 1.93/2.12 clauses generated 36
% 1.93/2.12 clauses kept 47
% 1.93/2.12 clauses forward subsumed 11
% 1.93/2.12 clauses back subsumed 1
% 1.93/2.12 Kbytes malloced 976
% 1.93/2.12
% 1.93/2.12 ----------- times (seconds) -----------
% 1.93/2.12 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.12
% 1.93/2.12 That finishes the proof of the theorem.
% 1.93/2.12
% 1.93/2.12 Process 32653 finished Wed Jul 27 07:37:35 2022
% 1.98/2.12 Otter interrupted
% 1.98/2.12 PROOF FOUND
%------------------------------------------------------------------------------