TSTP Solution File: SET014-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:12:47 EDT 2022
% Result : Unsatisfiable 2.91s 3.07s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 9 unt; 7 nHn; 14 RR)
% Number of literals : 31 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,B)
| ~ subset(B,C)
| member(A,C) ),
file('SET014-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET014-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
file('SET014-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(A,union(B,C))
| member(A,B)
| member(A,C) ),
file('SET014-2.p',unknown),
[] ).
cnf(18,axiom,
~ subset(union(as,bs),cs),
file('SET014-2.p',unknown),
[] ).
cnf(22,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET014-2.p',unknown),
[] ).
cnf(23,axiom,
( member(A,B)
| member(A,complement(B)) ),
file('SET014-2.p',unknown),
[] ).
cnf(26,axiom,
subset(as,cs),
file('SET014-2.p',unknown),
[] ).
cnf(27,axiom,
subset(bs,cs),
file('SET014-2.p',unknown),
[] ).
cnf(28,plain,
member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)),
inference(hyper,[status(thm)],[22,18]),
[iquote('hyper,22,18')] ).
cnf(46,plain,
( member(member_of_1_not_of_2(A,B),complement(B))
| subset(A,B) ),
inference(hyper,[status(thm)],[23,3]),
[iquote('hyper,23,3')] ).
cnf(47,plain,
( member(A,complement(bs))
| member(A,cs) ),
inference(hyper,[status(thm)],[23,2,27]),
[iquote('hyper,23,2,27')] ).
cnf(48,plain,
( member(A,complement(as))
| member(A,cs) ),
inference(hyper,[status(thm)],[23,2,26]),
[iquote('hyper,23,2,26')] ).
cnf(91,plain,
( member(member_of_1_not_of_2(union(as,bs),cs),as)
| member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
inference(hyper,[status(thm)],[28,7]),
[iquote('hyper,28,7')] ).
cnf(2914,plain,
member(member_of_1_not_of_2(union(as,bs),cs),complement(cs)),
inference(hyper,[status(thm)],[46,18]),
[iquote('hyper,46,18')] ).
cnf(3212,plain,
member(member_of_1_not_of_2(union(as,bs),cs),complement(as)),
inference(hyper,[status(thm)],[2914,4,48]),
[iquote('hyper,2914,4,48')] ).
cnf(3291,plain,
member(member_of_1_not_of_2(union(as,bs),cs),bs),
inference(hyper,[status(thm)],[3212,4,91]),
[iquote('hyper,3212,4,91')] ).
cnf(3296,plain,
member(member_of_1_not_of_2(union(as,bs),cs),cs),
inference(hyper,[status(thm)],[3291,4,47]),
[iquote('hyper,3291,4,47')] ).
cnf(3325,plain,
$false,
inference(hyper,[status(thm)],[3296,4,2914]),
[iquote('hyper,3296,4,2914')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 10:56:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.91/3.07 ----- Otter 3.3f, August 2004 -----
% 2.91/3.07 The process was started by sandbox on n014.cluster.edu,
% 2.91/3.07 Wed Jul 27 10:56:09 2022
% 2.91/3.07 The command was "./otter". The process ID is 32297.
% 2.91/3.07
% 2.91/3.07 set(prolog_style_variables).
% 2.91/3.07 set(auto).
% 2.91/3.07 dependent: set(auto1).
% 2.91/3.07 dependent: set(process_input).
% 2.91/3.07 dependent: clear(print_kept).
% 2.91/3.07 dependent: clear(print_new_demod).
% 2.91/3.07 dependent: clear(print_back_demod).
% 2.91/3.07 dependent: clear(print_back_sub).
% 2.91/3.07 dependent: set(control_memory).
% 2.91/3.07 dependent: assign(max_mem, 12000).
% 2.91/3.07 dependent: assign(pick_given_ratio, 4).
% 2.91/3.07 dependent: assign(stats_level, 1).
% 2.91/3.07 dependent: assign(max_seconds, 10800).
% 2.91/3.07 clear(print_given).
% 2.91/3.07
% 2.91/3.07 list(usable).
% 2.91/3.07 0 [] -member(X,empty_set).
% 2.91/3.07 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 2.91/3.07 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 2.91/3.07 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 2.91/3.07 0 [] member(X,Xs)|member(X,complement(Xs)).
% 2.91/3.07 0 [] -member(X,Xs)| -member(X,complement(Xs)).
% 2.91/3.07 0 [] -member(X,Xs)|member(X,union(Xs,Ys)).
% 2.91/3.07 0 [] -member(X,Ys)|member(X,union(Xs,Ys)).
% 2.91/3.07 0 [] -member(X,union(Xs,Ys))|member(X,Xs)|member(X,Ys).
% 2.91/3.07 0 [] -member(X,Xs)| -member(X,Ys)|member(X,intersection(Xs,Ys)).
% 2.91/3.07 0 [] -member(X,intersection(Xs,Ys))|member(X,Xs).
% 2.91/3.07 0 [] -member(X,intersection(Xs,Ys))|member(X,Ys).
% 2.91/3.07 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 2.91/3.07 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 2.91/3.07 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 2.91/3.07 0 [] e_qual_sets(Xs,Xs).
% 2.91/3.07 0 [] -e_qual_sets(Xs,Ys)|e_qual_sets(Ys,Xs).
% 2.91/3.07 0 [] -e_qual_sets(Xs,Ys)| -e_qual_sets(Ys,Zs)|e_qual_sets(Xs,Zs).
% 2.91/3.07 0 [] e_qual_elements(X,X).
% 2.91/3.07 0 [] -e_qual_elements(X,Y)|e_qual_elements(Y,X).
% 2.91/3.07 0 [] -e_qual_elements(X,Y)| -e_qual_elements(Y,Z)|e_qual_elements(X,Z).
% 2.91/3.07 0 [] subset(as,cs).
% 2.91/3.07 0 [] subset(bs,cs).
% 2.91/3.07 0 [] -subset(union(as,bs),cs).
% 2.91/3.07 end_of_list.
% 2.91/3.07
% 2.91/3.07 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 2.91/3.07
% 2.91/3.07 This is a non-Horn set without equality. The strategy will
% 2.91/3.07 be ordered hyper_res, unit deletion, and factoring, with
% 2.91/3.07 satellites in sos and with nuclei in usable.
% 2.91/3.07
% 2.91/3.07 dependent: set(hyper_res).
% 2.91/3.07 dependent: set(factor).
% 2.91/3.07 dependent: set(unit_deletion).
% 2.91/3.07
% 2.91/3.07 ------------> process usable:
% 2.91/3.07 ** KEPT (pick-wt=3): 1 [] -member(A,empty_set).
% 2.91/3.07 ** KEPT (pick-wt=9): 2 [] -member(A,B)| -subset(B,C)|member(A,C).
% 2.91/3.07 ** KEPT (pick-wt=8): 3 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 2.91/3.07 ** KEPT (pick-wt=7): 4 [] -member(A,B)| -member(A,complement(B)).
% 2.91/3.07 ** KEPT (pick-wt=8): 5 [] -member(A,B)|member(A,union(B,C)).
% 2.91/3.07 ** KEPT (pick-wt=8): 6 [] -member(A,B)|member(A,union(C,B)).
% 2.91/3.07 ** KEPT (pick-wt=11): 7 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.91/3.07 ** KEPT (pick-wt=11): 8 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 2.91/3.07 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,B).
% 2.91/3.07 ** KEPT (pick-wt=8): 10 [] -member(A,intersection(B,C))|member(A,C).
% 2.91/3.07 ** KEPT (pick-wt=6): 11 [] -e_qual_sets(A,B)|subset(A,B).
% 2.91/3.07 ** KEPT (pick-wt=6): 12 [] -e_qual_sets(A,B)|subset(B,A).
% 2.91/3.07 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 2.91/3.07 ** KEPT (pick-wt=6): 14 [] -e_qual_sets(A,B)|e_qual_sets(B,A).
% 2.91/3.07 ** KEPT (pick-wt=9): 15 [] -e_qual_sets(A,B)| -e_qual_sets(B,C)|e_qual_sets(A,C).
% 2.91/3.07 ** KEPT (pick-wt=6): 16 [] -e_qual_elements(A,B)|e_qual_elements(B,A).
% 2.91/3.07 ** KEPT (pick-wt=9): 17 [] -e_qual_elements(A,B)| -e_qual_elements(B,C)|e_qual_elements(A,C).
% 2.91/3.07 ** KEPT (pick-wt=5): 18 [] -subset(union(as,bs),cs).
% 2.91/3.07
% 2.91/3.07 ------------> process sos:
% 2.91/3.07 ** KEPT (pick-wt=8): 22 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 2.91/3.07 ** KEPT (pick-wt=7): 23 [] member(A,B)|member(A,complement(B)).
% 2.91/3.07 ** KEPT (pick-wt=3): 24 [] e_qual_sets(A,A).
% 2.91/3.07 ** KEPT (pick-wt=3): 25 [] e_qual_elements(A,A).
% 2.91/3.07 ** KEPT (pick-wt=3): 26 [] subset(as,cs).
% 2.91/3.07 ** KEPT (pick-wt=3): 27 [] subset(bs,cs).
% 2.91/3.07 24 back subsumes 21.
% 2.91/3.07
% 2.91/3.07 ======= end of input processing =======
% 2.91/3.07
% 2.91/3.07 =========== start of search ===========
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Resetting weight limit to 10.
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Resetting weight limit to 10.
% 2.91/3.07
% 2.91/3.07 sos_size=2703
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Resetting weight limit to 9.
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Resetting weight limit to 9.
% 2.91/3.07
% 2.91/3.07 sos_size=2766
% 2.91/3.07
% 2.91/3.07 -------- PROOF --------
% 2.91/3.07
% 2.91/3.07 -----> EMPTY CLAUSE at 1.13 sec ----> 3325 [hyper,3296,4,2914] $F.
% 2.91/3.07
% 2.91/3.07 Length of proof is 9. Level of proof is 5.
% 2.91/3.07
% 2.91/3.07 ---------------- PROOF ----------------
% 2.91/3.07 % SZS status Unsatisfiable
% 2.91/3.07 % SZS output start Refutation
% See solution above
% 2.91/3.07 ------------ end of proof -------------
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Search stopped by max_proofs option.
% 2.91/3.07
% 2.91/3.07
% 2.91/3.07 Search stopped by max_proofs option.
% 2.91/3.07
% 2.91/3.07 ============ end of search ============
% 2.91/3.07
% 2.91/3.07 -------------- statistics -------------
% 2.91/3.07 clauses given 335
% 2.91/3.07 clauses generated 54598
% 2.91/3.07 clauses kept 3324
% 2.91/3.07 clauses forward subsumed 6550
% 2.91/3.07 clauses back subsumed 35
% 2.91/3.07 Kbytes malloced 5859
% 2.91/3.07
% 2.91/3.07 ----------- times (seconds) -----------
% 2.91/3.07 user CPU time 1.13 (0 hr, 0 min, 1 sec)
% 2.91/3.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.91/3.07 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.91/3.07
% 2.91/3.07 That finishes the proof of the theorem.
% 2.91/3.07
% 2.91/3.07 Process 32297 finished Wed Jul 27 10:56:12 2022
% 2.91/3.07 Otter interrupted
% 2.91/3.07 PROOF FOUND
%------------------------------------------------------------------------------