TSTP Solution File: TOP001-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:26:47 EDT 2022
% Result : Unsatisfiable 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 23 ( 13 unt; 1 nHn; 22 RR)
% Number of literals : 37 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element_of_set(A,union_of_members(B))
| element_of_set(A,f1(B,A)) ),
file('TOP001-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ element_of_set(A,union_of_members(B))
| element_of_collection(f1(B,A),B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(3,axiom,
( element_of_set(A,union_of_members(B))
| ~ element_of_set(A,C)
| ~ element_of_collection(C,B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ basis(A,B)
| e_qual_sets(union_of_members(B),A) ),
file('TOP001-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ element_of_collection(A,top_of_basis(B))
| ~ element_of_set(C,A)
| element_of_set(C,f10(B,A,C)) ),
file('TOP001-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ element_of_collection(A,top_of_basis(B))
| ~ element_of_set(C,A)
| element_of_collection(f10(B,A,C),B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset_sets(A,B)
| ~ element_of_set(C,A)
| element_of_set(C,B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ e_qual_sets(A,B)
| subset_sets(A,B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(9,axiom,
( subset_sets(A,B)
| ~ element_of_set(in_1st_set(A,B),B) ),
file('TOP001-2.p',unknown),
[] ).
cnf(10,axiom,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file('TOP001-2.p',unknown),
[] ).
cnf(12,axiom,
( subset_sets(A,B)
| element_of_set(in_1st_set(A,B),A) ),
file('TOP001-2.p',unknown),
[] ).
cnf(13,axiom,
basis(cx,f),
file('TOP001-2.p',unknown),
[] ).
cnf(14,plain,
e_qual_sets(union_of_members(f),cx),
inference(hyper,[status(thm)],[13,4]),
[iquote('hyper,13,4')] ).
cnf(15,plain,
subset_sets(union_of_members(f),cx),
inference(hyper,[status(thm)],[14,8]),
[iquote('hyper,14,8')] ).
cnf(16,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),union_of_members(top_of_basis(f))),
inference(hyper,[status(thm)],[12,10]),
[iquote('hyper,12,10')] ).
cnf(18,plain,
element_of_collection(f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),top_of_basis(f)),
inference(hyper,[status(thm)],[16,2]),
[iquote('hyper,16,2')] ).
cnf(19,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx))),
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(21,plain,
element_of_collection(f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),in_1st_set(union_of_members(top_of_basis(f)),cx)),f),
inference(hyper,[status(thm)],[19,6,18]),
[iquote('hyper,19,6,18')] ).
cnf(22,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),f10(f,f1(top_of_basis(f),in_1st_set(union_of_members(top_of_basis(f)),cx)),in_1st_set(union_of_members(top_of_basis(f)),cx))),
inference(hyper,[status(thm)],[19,5,18]),
[iquote('hyper,19,5,18')] ).
cnf(56,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),union_of_members(f)),
inference(hyper,[status(thm)],[22,3,21]),
[iquote('hyper,22,3,21')] ).
cnf(57,plain,
element_of_set(in_1st_set(union_of_members(top_of_basis(f)),cx),cx),
inference(hyper,[status(thm)],[56,7,15]),
[iquote('hyper,56,7,15')] ).
cnf(61,plain,
subset_sets(union_of_members(top_of_basis(f)),cx),
inference(hyper,[status(thm)],[57,9]),
[iquote('hyper,57,9')] ).
cnf(62,plain,
$false,
inference(binary,[status(thm)],[61,10]),
[iquote('binary,61.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 01:55:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox on n003.cluster.edu,
% 1.67/1.89 Wed Jul 27 01:55:11 2022
% 1.67/1.89 The command was "./otter". The process ID is 21017.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] -element_of_set(U,union_of_members(Vf))|element_of_set(U,f1(Vf,U)).
% 1.67/1.89 0 [] -element_of_set(U,union_of_members(Vf))|element_of_collection(f1(Vf,U),Vf).
% 1.67/1.89 0 [] element_of_set(U,union_of_members(Vf))| -element_of_set(U,Uu1)| -element_of_collection(Uu1,Vf).
% 1.67/1.89 0 [] -basis(X,Vf)|e_qual_sets(union_of_members(Vf),X).
% 1.67/1.89 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_set(X,f10(Vf,U,X)).
% 1.67/1.89 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_collection(f10(Vf,U,X),Vf).
% 1.67/1.89 0 [] subset_sets(X,X).
% 1.67/1.89 0 [] -subset_sets(X,Y)| -element_of_set(U,X)|element_of_set(U,Y).
% 1.67/1.89 0 [] -e_qual_sets(X,Y)|subset_sets(X,Y).
% 1.67/1.89 0 [] subset_sets(X,Y)|element_of_set(in_1st_set(X,Y),X).
% 1.67/1.89 0 [] subset_sets(X,Y)| -element_of_set(in_1st_set(X,Y),Y).
% 1.67/1.89 0 [] basis(cx,f).
% 1.67/1.89 0 [] -subset_sets(union_of_members(top_of_basis(f)),cx).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.67/1.89
% 1.67/1.89 This is a non-Horn set without equality. The strategy will
% 1.67/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.89 satellites in sos and with nuclei in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89 dependent: set(unit_deletion).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=9): 1 [] -element_of_set(A,union_of_members(B))|element_of_set(A,f1(B,A)).
% 1.67/1.89 ** KEPT (pick-wt=9): 2 [] -element_of_set(A,union_of_members(B))|element_of_collection(f1(B,A),B).
% 1.67/1.89 ** KEPT (pick-wt=10): 3 [] element_of_set(A,union_of_members(B))| -element_of_set(A,C)| -element_of_collection(C,B).
% 1.67/1.89 ** KEPT (pick-wt=7): 4 [] -basis(A,B)|e_qual_sets(union_of_members(B),A).
% 1.67/1.89 ** KEPT (pick-wt=13): 5 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_set(C,f10(B,A,C)).
% 1.67/1.89 ** KEPT (pick-wt=13): 6 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_collection(f10(B,A,C),B).
% 1.67/1.89 ** KEPT (pick-wt=9): 7 [] -subset_sets(A,B)| -element_of_set(C,A)|element_of_set(C,B).
% 1.67/1.89 ** KEPT (pick-wt=6): 8 [] -e_qual_sets(A,B)|subset_sets(A,B).
% 1.67/1.89 ** KEPT (pick-wt=8): 9 [] subset_sets(A,B)| -element_of_set(in_1st_set(A,B),B).
% 1.67/1.89 ** KEPT (pick-wt=5): 10 [] -subset_sets(union_of_members(top_of_basis(f)),cx).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 11 [] subset_sets(A,A).
% 1.67/1.89 ** KEPT (pick-wt=8): 12 [] subset_sets(A,B)|element_of_set(in_1st_set(A,B),A).
% 1.67/1.89 ** KEPT (pick-wt=3): 13 [] basis(cx,f).
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 62 [binary,61.1,10.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 10. Level of proof is 6.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Unsatisfiable
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 18
% 1.67/1.89 clauses generated 81
% 1.67/1.89 clauses kept 61
% 1.67/1.89 clauses forward subsumed 33
% 1.67/1.89 clauses back subsumed 7
% 1.67/1.89 Kbytes malloced 976
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 21017 finished Wed Jul 27 01:55:13 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------