%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:54:55 EDT 2022
% Result : Theorem 161.16s 161.40s
% Output : Refutation 161.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 9 unt; 13 nHn; 8 RR)
% Number of literals : 51 ( 0 equ; 9 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO223+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO223+1.p',unknown),
[] ).
cnf(15,axiom,
~ convergent_lines(parallel_through_point(A,B),A),
file('GEO223+1.p',unknown),
[] ).
cnf(16,axiom,
~ apart_point_and_line(A,parallel_through_point(B,A)),
file('GEO223+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ convergent_lines(A,B)
| ~ unorthogonal_lines(A,B)
| convergent_lines(A,C)
| unorthogonal_lines(B,C) ),
file('GEO223+1.p',unknown),
[] ).
cnf(21,axiom,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
file('GEO223+1.p',unknown),
[] ).
cnf(22,axiom,
~ apart_point_and_line(A,orthogonal_through_point(B,A)),
file('GEO223+1.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('GEO223+1.p',unknown),
[] ).
cnf(24,axiom,
( convergent_lines(A,B)
| unorthogonal_lines(A,B) ),
file('GEO223+1.p',unknown),
[] ).
cnf(25,axiom,
distinct_lines(parallel_through_point(dollar_c1,dollar_c2),orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2)),
file('GEO223+1.p',unknown),
[] ).
cnf(26,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(hyper,[status(thm)],[24,21]),
[iquote('hyper,24,21')] ).
cnf(28,plain,
( convergent_lines(orthogonal_through_point(A,B),C)
| convergent_lines(A,C) ),
inference(hyper,[status(thm)],[26,6]),
[iquote('hyper,26,6')] ).
cnf(32,plain,
( convergent_lines(A,B)
| convergent_lines(orthogonal_through_point(A,C),D)
| convergent_lines(B,D) ),
inference(hyper,[status(thm)],[28,6]),
[iquote('hyper,28,6')] ).
cnf(38,plain,
( apart_point_and_line(A,parallel_through_point(dollar_c1,dollar_c2))
| apart_point_and_line(A,orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2))
| unorthogonal_lines(parallel_through_point(dollar_c1,dollar_c2),B)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2),B) ),
inference(hyper,[status(thm)],[25,23]),
[iquote('hyper,25,23')] ).
cnf(152,plain,
( convergent_lines(A,B)
| convergent_lines(B,orthogonal_through_point(A,C)) ),
inference(hyper,[status(thm)],[32,3]),
[iquote('hyper,32,3')] ).
cnf(188,plain,
( convergent_lines(A,orthogonal_through_point(B,C))
| convergent_lines(B,D)
| convergent_lines(A,D) ),
inference(hyper,[status(thm)],[152,6]),
[iquote('hyper,152,6')] ).
cnf(954,plain,
( convergent_lines(A,orthogonal_through_point(B,C))
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[188,3]),
[iquote('hyper,188,3')] ).
cnf(1025,plain,
( convergent_lines(parallel_through_point(dollar_c1,dollar_c2),A)
| convergent_lines(parallel_through_point(dollar_c1,dollar_c2),B)
| unorthogonal_lines(orthogonal_through_point(A,C),B)
| apart_point_and_line(D,parallel_through_point(dollar_c1,dollar_c2))
| apart_point_and_line(D,orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2),orthogonal_through_point(A,C)) ),
inference(hyper,[status(thm)],[954,18,38]),
[iquote('hyper,954,18,38')] ).
cnf(1052,plain,
( convergent_lines(parallel_through_point(dollar_c1,dollar_c2),A)
| apart_point_and_line(B,parallel_through_point(dollar_c1,dollar_c2))
| apart_point_and_line(B,orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2),orthogonal_through_point(A,C)) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[1025]),21]),
[iquote('factor,1025.1.2,unit_del,21')] ).
cnf(5437,plain,
( apart_point_and_line(A,parallel_through_point(dollar_c1,dollar_c2))
| apart_point_and_line(A,orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1052,21]),15]),
[iquote('hyper,1052,21,unit_del,15')] ).
cnf(5438,plain,
apart_point_and_line(dollar_c2,orthogonal_through_point(orthogonal_through_point(dollar_c1,dollar_c2),dollar_c2)),
inference(hyper,[status(thm)],[5437,16]),
[iquote('hyper,5437,16')] ).
cnf(5439,plain,
$false,
inference(binary,[status(thm)],[5438,22]),
[iquote('binary,5438.1,22.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 07:18:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox2 on n012.cluster.edu,
% 1.74/1.94 Wed Jul 27 07:18:35 2022
% 1.74/1.94 The command was "./otter". The process ID is 11818.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 formula_list(usable).
% 1.74/1.94 all X (-distinct_points(X,X)).
% 1.74/1.94 all X (-distinct_lines(X,X)).
% 1.74/1.94 all X (-convergent_lines(X,X)).
% 1.74/1.94 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.74/1.94 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.74/1.94 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.74/1.94 all X Y (distinct_points(X,Y)-> -apart_point_and_line(X,line_connecting(X,Y))).
% 1.74/1.94 all X Y (distinct_points(X,Y)-> -apart_point_and_line(Y,line_connecting(X,Y))).
% 1.74/1.94 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),X)).
% 1.74/1.94 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),Y)).
% 1.74/1.94 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)).
% 1.74/1.94 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.74/1.94 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.74/1.94 all X Y Z (convergent_lines(X,Y)->distinct_lines(Y,Z)|convergent_lines(X,Z)).
% 1.74/1.94 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.74/1.94 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.74/1.94 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.74/1.94 all L M (convergent_lines(L,M)|unorthogonal_lines(L,M)).
% 1.74/1.94 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)).
% 1.74/1.94 all A L (-unorthogonal_lines(orthogonal_through_point(L,A),L)).
% 1.74/1.94 all A L (-apart_point_and_line(A,orthogonal_through_point(L,A))).
% 1.74/1.94 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)).
% 1.74/1.94 -(all A L (-distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)))).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 -------> usable clausifies to:
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] -distinct_points(X,X).
% 1.74/1.94 0 [] -distinct_lines(X,X).
% 1.74/1.94 0 [] -convergent_lines(X,X).
% 1.74/1.94 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.74/1.94 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.74/1.94 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.74/1.94 0 [] -distinct_points(X,Y)| -apart_point_and_line(X,line_connecting(X,Y)).
% 1.74/1.94 0 [] -distinct_points(X,Y)| -apart_point_and_line(Y,line_connecting(X,Y)).
% 1.74/1.94 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),X).
% 1.74/1.94 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),Y).
% 1.74/1.94 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).
% 1.74/1.94 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.74/1.94 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.74/1.94 0 [] -convergent_lines(X,Y)|distinct_lines(Y,Z)|convergent_lines(X,Z).
% 1.74/1.94 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.74/1.94 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.74/1.94 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.74/1.94 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.74/1.94 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|convergent_lines(M,N).
% 1.74/1.94 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|unorthogonal_lines(M,N).
% 1.74/1.94 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|convergent_lines(M,N).
% 161.16/161.40 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 161.16/161.40 0 [] -unorthogonal_lines(orthogonal_through_point(L,A),L).
% 161.16/161.40 0 [] -apart_point_and_line(A,orthogonal_through_point(L,A)).
% 161.16/161.40 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).
% 161.16/161.40 0 [] distinct_lines(parallel_through_point($c1,$c2),orthogonal_through_point(orthogonal_through_point($c1,$c2),$c2)).
% 161.16/161.40 end_of_list.
% 161.16/161.40
% 161.16/161.40 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 161.16/161.40
% 161.16/161.40 This is a non-Horn set without equality. The strategy will
% 161.16/161.40 be ordered hyper_res, unit deletion, and factoring, with
% 161.16/161.40 satellites in sos and with nuclei in usable.
% 161.16/161.40
% 161.16/161.40 dependent: set(hyper_res).
% 161.16/161.40 dependent: set(factor).
% 161.16/161.40 dependent: set(unit_deletion).
% 161.16/161.40
% 161.16/161.40 ------------> process usable:
% 161.16/161.40 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 161.16/161.40 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 161.16/161.40 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 161.16/161.40 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 161.16/161.40 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 161.16/161.40 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 161.16/161.40 ** KEPT (pick-wt=8): 7 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 161.16/161.40 ** KEPT (pick-wt=8): 8 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 161.16/161.40 ** KEPT (pick-wt=8): 9 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),A).
% 161.16/161.40 ** KEPT (pick-wt=8): 10 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),B).
% 161.16/161.40 ** 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).
% 161.16/161.40 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 161.16/161.40 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 161.16/161.40 ** KEPT (pick-wt=9): 14 [] -convergent_lines(A,B)|distinct_lines(B,C)|convergent_lines(A,C).
% 161.16/161.40 ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 161.16/161.40 ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 161.16/161.40 ** 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).
% 161.16/161.40 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).
% 161.16/161.40 ** KEPT (pick-wt=12): 18 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|unorthogonal_lines(B,C).
% 161.16/161.40 ** KEPT (pick-wt=12): 19 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|convergent_lines(B,C).
% 161.16/161.40 ** KEPT (pick-wt=12): 20 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|unorthogonal_lines(B,C).
% 161.16/161.40 ** KEPT (pick-wt=5): 21 [] -unorthogonal_lines(orthogonal_through_point(A,B),A).
% 161.16/161.40 ** KEPT (pick-wt=5): 22 [] -apart_point_and_line(A,orthogonal_through_point(B,A)).
% 161.16/161.40 ** 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).
% 161.16/161.40
% 161.16/161.40 ------------> process sos:
% 161.16/161.40 ** KEPT (pick-wt=6): 24 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 161.16/161.40 ** KEPT (pick-wt=9): 25 [] distinct_lines(parallel_through_point($c1,$c2),orthogonal_through_point(orthogonal_through_point($c1,$c2),$c2)).
% 161.16/161.40
% 161.16/161.40 ======= end of input processing =======
% 161.16/161.40
% 161.16/161.40 =========== start of search ===========
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 21.
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 21.
% 161.16/161.40
% 161.16/161.40 sos_size=3718
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 20.
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 20.
% 161.16/161.40
% 161.16/161.40 sos_size=3734
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 17.
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 17.
% 161.16/161.40
% 161.16/161.40 sos_size=3744
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 16.
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Resetting weight limit to 16.
% 161.16/161.40
% 161.16/161.40 sos_size=3754
% 161.16/161.40
% 161.16/161.40 -- HEY sandbox2, WE HAVE A PROOF!! --
% 161.16/161.40
% 161.16/161.40 ----> UNIT CONFLICT at 159.46 sec ----> 5439 [binary,5438.1,22.1] $F.
% 161.16/161.40
% 161.16/161.40 Length of proof is 11. Level of proof is 10.
% 161.16/161.40
% 161.16/161.40 ---------------- PROOF ----------------
% 161.16/161.40 % SZS status Theorem
% 161.16/161.40 % SZS output start Refutation
% See solution above
% 161.16/161.40 ------------ end of proof -------------
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Search stopped by max_proofs option.
% 161.16/161.40
% 161.16/161.40
% 161.16/161.40 Search stopped by max_proofs option.
% 161.16/161.40
% 161.16/161.40 ============ end of search ============
% 161.16/161.40
% 161.16/161.40 -------------- statistics -------------
% 161.16/161.40 clauses given 2099
% 161.16/161.40 clauses generated 4819609
% 161.16/161.40 clauses kept 5438
% 161.16/161.40 clauses forward subsumed 20812
% 161.16/161.40 clauses back subsumed 781
% 161.16/161.40 Kbytes malloced 5859
% 161.16/161.40
% 161.16/161.40 ----------- times (seconds) -----------
% 161.16/161.40 user CPU time 159.46 (0 hr, 2 min, 39 sec)
% 161.16/161.40 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 161.16/161.40 wall-clock time 161 (0 hr, 2 min, 41 sec)
% 161.16/161.40
% 161.16/161.40 That finishes the proof of the theorem.
% 161.16/161.40
% 161.16/161.40 Process 11818 finished Wed Jul 27 07:21:16 2022
% 161.16/161.40 Otter interrupted
% 161.16/161.40 PROOF FOUND
%------------------------------------------------------------------------------