TSTP Solution File: GEO180+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO180+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 12:54:38 EDT 2022
% Result : Theorem 2.16s 2.34s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 9 unt; 21 nHn; 11 RR)
% Number of literals : 81 ( 0 equ; 11 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO180+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
file('GEO180+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(A,line_connecting(A,B)) ),
file('GEO180+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ distinct_points(A,B)
| ~ apart_point_and_line(B,line_connecting(A,B)) ),
file('GEO180+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ 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) ),
file('GEO180+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ apart_point_and_line(A,B)
| distinct_points(A,C)
| apart_point_and_line(C,B) ),
file('GEO180+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ apart_point_and_line(A,B)
| distinct_lines(B,C)
| apart_point_and_line(A,C) ),
file('GEO180+1.p',unknown),
[] ).
cnf(15,axiom,
~ apart_point_and_line(dollar_c3,line_connecting(dollar_c1,dollar_c2)),
file('GEO180+1.p',unknown),
[] ).
cnf(16,axiom,
distinct_points(dollar_c3,dollar_c2),
file('GEO180+1.p',unknown),
[] ).
cnf(17,axiom,
apart_point_and_line(dollar_c1,line_connecting(dollar_c3,dollar_c2)),
file('GEO180+1.p',unknown),
[] ).
cnf(18,plain,
( distinct_points(dollar_c3,A)
| distinct_points(dollar_c2,A) ),
inference(hyper,[status(thm)],[16,4]),
[iquote('hyper,16,4')] ).
cnf(19,plain,
( distinct_lines(line_connecting(dollar_c3,dollar_c2),A)
| apart_point_and_line(dollar_c1,A) ),
inference(hyper,[status(thm)],[17,13]),
[iquote('hyper,17,13')] ).
cnf(20,plain,
( distinct_points(dollar_c1,A)
| apart_point_and_line(A,line_connecting(dollar_c3,dollar_c2)) ),
inference(hyper,[status(thm)],[17,12]),
[iquote('hyper,17,12')] ).
cnf(21,plain,
( distinct_points(dollar_c2,A)
| distinct_points(dollar_c3,B)
| distinct_points(A,B) ),
inference(hyper,[status(thm)],[18,4]),
[iquote('hyper,18,4')] ).
cnf(22,plain,
distinct_points(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[18,1]),
[iquote('hyper,18,1')] ).
cnf(24,plain,
( apart_point_and_line(dollar_c1,A)
| apart_point_and_line(dollar_c2,line_connecting(dollar_c3,dollar_c2))
| apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,line_connecting(dollar_c3,dollar_c2))
| apart_point_and_line(dollar_c3,A) ),
inference(hyper,[status(thm)],[19,11,22]),
[iquote('hyper,19,11,22')] ).
cnf(33,plain,
( distinct_points(dollar_c2,A)
| distinct_points(A,dollar_c3) ),
inference(hyper,[status(thm)],[21,1]),
[iquote('hyper,21,1')] ).
cnf(35,plain,
( distinct_points(dollar_c2,A)
| distinct_points(dollar_c3,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(hyper,[status(thm)],[21,4]),
[iquote('hyper,21,4')] ).
cnf(36,plain,
( distinct_points(dollar_c3,A)
| distinct_points(A,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[35]),1]),
[iquote('factor,35.1.3,unit_del,1')] ).
cnf(38,plain,
( distinct_points(A,dollar_c3)
| distinct_points(dollar_c2,B)
| distinct_points(A,B) ),
inference(hyper,[status(thm)],[33,4]),
[iquote('hyper,33,4')] ).
cnf(59,plain,
( apart_point_and_line(dollar_c1,A)
| apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,line_connecting(dollar_c3,dollar_c2))
| apart_point_and_line(dollar_c3,A) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,8,36]),1]),
[iquote('hyper,24,8,36,unit_del,1')] ).
cnf(88,plain,
( distinct_points(A,dollar_c3)
| distinct_points(A,B)
| distinct_points(dollar_c2,C)
| distinct_points(B,C) ),
inference(hyper,[status(thm)],[38,4]),
[iquote('hyper,38,4')] ).
cnf(206,plain,
( distinct_points(A,dollar_c3)
| distinct_points(A,B)
| distinct_points(B,dollar_c2) ),
inference(hyper,[status(thm)],[88,1]),
[iquote('hyper,88,1')] ).
cnf(214,plain,
( distinct_points(A,dollar_c3)
| distinct_points(B,dollar_c2)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(hyper,[status(thm)],[206,4]),
[iquote('hyper,206,4')] ).
cnf(384,plain,
( apart_point_and_line(dollar_c1,A)
| apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,A) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,7,206]),1,1]),
[iquote('hyper,59,7,206,unit_del,1,1')] ).
cnf(441,plain,
( apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,A)
| distinct_points(dollar_c1,B)
| apart_point_and_line(B,A) ),
inference(hyper,[status(thm)],[384,12]),
[iquote('hyper,384,12')] ).
cnf(613,plain,
( apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,A)
| distinct_points(dollar_c1,dollar_c2) ),
inference(factor,[status(thm)],[441]),
[iquote('factor,441.1.4')] ).
cnf(627,plain,
( apart_point_and_line(dollar_c2,A)
| apart_point_and_line(dollar_c3,A)
| apart_point_and_line(dollar_c2,line_connecting(dollar_c1,dollar_c2)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[613,7,384]),15]),
[iquote('hyper,613,7,384,unit_del,15')] ).
cnf(629,plain,
apart_point_and_line(dollar_c2,line_connecting(dollar_c1,dollar_c2)),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[627]),15]),
[iquote('factor,627.1.3,unit_del,15')] ).
cnf(645,plain,
apart_point_and_line(dollar_c2,line_connecting(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[629,8,20]),
[iquote('hyper,629,8,20')] ).
cnf(650,plain,
distinct_points(A,dollar_c2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[645,8,214]),1])]),
[iquote('hyper,645,8,214,unit_del,1,factor_simp')] ).
cnf(651,plain,
$false,
inference(binary,[status(thm)],[650,1]),
[iquote('binary,650.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO180+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:10:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox on n024.cluster.edu,
% 1.69/1.89 Wed Jul 27 07:10:25 2022
% 1.69/1.89 The command was "./otter". The process ID is 5470.
% 1.69/1.89
% 1.69/1.89 set(prolog_style_variables).
% 1.69/1.89 set(auto).
% 1.69/1.89 dependent: set(auto1).
% 1.69/1.89 dependent: set(process_input).
% 1.69/1.89 dependent: clear(print_kept).
% 1.69/1.89 dependent: clear(print_new_demod).
% 1.69/1.89 dependent: clear(print_back_demod).
% 1.69/1.89 dependent: clear(print_back_sub).
% 1.69/1.89 dependent: set(control_memory).
% 1.69/1.89 dependent: assign(max_mem, 12000).
% 1.69/1.89 dependent: assign(pick_given_ratio, 4).
% 1.69/1.89 dependent: assign(stats_level, 1).
% 1.69/1.89 dependent: assign(max_seconds, 10800).
% 1.69/1.89 clear(print_given).
% 1.69/1.89
% 1.69/1.89 formula_list(usable).
% 1.69/1.89 all X (-distinct_points(X,X)).
% 1.69/1.89 all X (-distinct_lines(X,X)).
% 1.69/1.89 all X (-convergent_lines(X,X)).
% 1.69/1.89 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.69/1.89 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.69/1.89 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.69/1.89 all X Y (distinct_points(X,Y)-> -apart_point_and_line(X,line_connecting(X,Y))).
% 1.69/1.89 all X Y (distinct_points(X,Y)-> -apart_point_and_line(Y,line_connecting(X,Y))).
% 1.69/1.89 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),X)).
% 1.69/1.89 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),Y)).
% 1.69/1.89 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)).
% 1.69/1.89 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.69/1.89 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.69/1.89 all X Y Z (convergent_lines(X,Y)->distinct_lines(Y,Z)|convergent_lines(X,Z)).
% 1.69/1.89 -(all X Y Z (distinct_points(X,Y)-> (apart_point_and_line(Z,line_connecting(X,Y))->apart_point_and_line(X,line_connecting(Z,Y))))).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 -------> usable clausifies to:
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] -distinct_points(X,X).
% 1.69/1.89 0 [] -distinct_lines(X,X).
% 1.69/1.89 0 [] -convergent_lines(X,X).
% 1.69/1.89 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.69/1.89 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.69/1.89 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.69/1.89 0 [] -distinct_points(X,Y)| -apart_point_and_line(X,line_connecting(X,Y)).
% 1.69/1.89 0 [] -distinct_points(X,Y)| -apart_point_and_line(Y,line_connecting(X,Y)).
% 1.69/1.89 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),X).
% 1.69/1.89 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),Y).
% 1.69/1.89 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).
% 1.69/1.89 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.69/1.89 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.69/1.89 0 [] -convergent_lines(X,Y)|distinct_lines(Y,Z)|convergent_lines(X,Z).
% 1.69/1.89 0 [] distinct_points($c3,$c2).
% 1.69/1.89 0 [] apart_point_and_line($c1,line_connecting($c3,$c2)).
% 1.69/1.89 0 [] -apart_point_and_line($c3,line_connecting($c1,$c2)).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.69/1.89
% 1.69/1.89 This is a non-Horn set without equality. The strategy will
% 1.69/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.89 satellites in sos and with nuclei in usable.
% 1.69/1.89
% 1.69/1.89 dependent: set(hyper_res).
% 1.69/1.89 dependent: set(factor).
% 1.69/1.89 dependent: set(unit_deletion).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.69/1.89 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.69/1.89 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.69/1.89 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.69/1.89 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.69/1.89 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.69/1.89 ** KEPT (pick-wt=8): 7 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 1.69/1.89 ** KEPT (pick-wt=8): 8 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 1.69/1.89 ** KEPT (pick-wt=8): 9 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),A).
% 2.16/2.34 ** KEPT (pick-wt=8): 10 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),B).
% 2.16/2.34 ** 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).
% 2.16/2.34 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 2.16/2.34 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 2.16/2.34 ** KEPT (pick-wt=9): 14 [] -convergent_lines(A,B)|distinct_lines(B,C)|convergent_lines(A,C).
% 2.16/2.34 ** KEPT (pick-wt=5): 15 [] -apart_point_and_line($c3,line_connecting($c1,$c2)).
% 2.16/2.34
% 2.16/2.34 ------------> process sos:
% 2.16/2.34 ** KEPT (pick-wt=3): 16 [] distinct_points($c3,$c2).
% 2.16/2.34 ** KEPT (pick-wt=5): 17 [] apart_point_and_line($c1,line_connecting($c3,$c2)).
% 2.16/2.34
% 2.16/2.34 ======= end of input processing =======
% 2.16/2.34
% 2.16/2.34 =========== start of search ===========
% 2.16/2.34
% 2.16/2.34 -------- PROOF --------
% 2.16/2.34
% 2.16/2.34 ----> UNIT CONFLICT at 0.46 sec ----> 651 [binary,650.1,1.1] $F.
% 2.16/2.34
% 2.16/2.34 Length of proof is 21. Level of proof is 13.
% 2.16/2.34
% 2.16/2.34 ---------------- PROOF ----------------
% 2.16/2.34 % SZS status Theorem
% 2.16/2.34 % SZS output start Refutation
% See solution above
% 2.16/2.34 ------------ end of proof -------------
% 2.16/2.34
% 2.16/2.34
% 2.16/2.34 Search stopped by max_proofs option.
% 2.16/2.34
% 2.16/2.34
% 2.16/2.34 Search stopped by max_proofs option.
% 2.16/2.34
% 2.16/2.34 ============ end of search ============
% 2.16/2.34
% 2.16/2.34 -------------- statistics -------------
% 2.16/2.34 clauses given 49
% 2.16/2.34 clauses generated 5104
% 2.16/2.34 clauses kept 650
% 2.16/2.34 clauses forward subsumed 4471
% 2.16/2.34 clauses back subsumed 388
% 2.16/2.34 Kbytes malloced 976
% 2.16/2.34
% 2.16/2.34 ----------- times (seconds) -----------
% 2.16/2.34 user CPU time 0.46 (0 hr, 0 min, 0 sec)
% 2.16/2.34 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.16/2.34 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.16/2.34
% 2.16/2.34 That finishes the proof of the theorem.
% 2.16/2.34
% 2.16/2.34 Process 5470 finished Wed Jul 27 07:10:27 2022
% 2.16/2.34 Otter interrupted
% 2.16/2.34 PROOF FOUND
%------------------------------------------------------------------------------