TSTP Solution File: SET012-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET012-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:12:46 EDT 2022
% Result : Unsatisfiable 83.16s 83.37s
% Output : Refutation 83.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 15 unt; 10 nHn; 22 RR)
% Number of literals : 51 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,B)
| ~ subset(B,C)
| member(A,C) ),
file('SET012-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET012-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
file('SET012-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ e_qual_sets(A,B)
| subset(A,B) ),
file('SET012-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ e_qual_sets(A,B)
| subset(B,A) ),
file('SET012-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(A,B)
| ~ subset(B,A)
| e_qual_sets(B,A) ),
file('SET012-2.p',unknown),
[] ).
cnf(18,axiom,
~ e_qual_sets(a,c),
file('SET012-2.p',unknown),
[] ).
cnf(22,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET012-2.p',unknown),
[] ).
cnf(23,axiom,
( member(A,B)
| member(A,complement(B)) ),
file('SET012-2.p',unknown),
[] ).
cnf(26,axiom,
e_qual_sets(complement(a),b),
file('SET012-2.p',unknown),
[] ).
cnf(27,axiom,
e_qual_sets(complement(b),c),
file('SET012-2.p',unknown),
[] ).
cnf(28,plain,
( member(member_of_1_not_of_2(A,B),A)
| e_qual_sets(A,B)
| member(member_of_1_not_of_2(B,A),B) ),
inference(hyper,[status(thm)],[22,13,22]),
[iquote('hyper,22,13,22')] ).
cnf(31,plain,
subset(b,complement(a)),
inference(hyper,[status(thm)],[26,12]),
[iquote('hyper,26,12')] ).
cnf(32,plain,
subset(complement(a),b),
inference(hyper,[status(thm)],[26,11]),
[iquote('hyper,26,11')] ).
cnf(58,plain,
subset(c,complement(b)),
inference(hyper,[status(thm)],[27,12]),
[iquote('hyper,27,12')] ).
cnf(59,plain,
subset(complement(b),c),
inference(hyper,[status(thm)],[27,11]),
[iquote('hyper,27,11')] ).
cnf(61,plain,
( member(A,b)
| member(A,a) ),
inference(hyper,[status(thm)],[32,2,23]),
[iquote('hyper,32,2,23')] ).
cnf(114,plain,
( member(A,complement(b))
| member(A,complement(c)) ),
inference(hyper,[status(thm)],[58,2,23]),
[iquote('hyper,58,2,23')] ).
cnf(117,plain,
( member(A,c)
| member(A,b) ),
inference(hyper,[status(thm)],[59,2,23]),
[iquote('hyper,59,2,23')] ).
cnf(471,plain,
( member(A,c)
| member(A,complement(a)) ),
inference(hyper,[status(thm)],[117,2,31]),
[iquote('hyper,117,2,31')] ).
cnf(1701,plain,
( member(member_of_1_not_of_2(a,A),c)
| e_qual_sets(a,A)
| member(member_of_1_not_of_2(A,a),A) ),
inference(hyper,[status(thm)],[471,4,28]),
[iquote('hyper,471,4,28')] ).
cnf(4670,plain,
( member(A,complement(c))
| member(A,a) ),
inference(hyper,[status(thm)],[114,4,61]),
[iquote('hyper,114,4,61')] ).
cnf(6281,plain,
( member(member_of_1_not_of_2(c,a),c)
| subset(a,c) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1701,3]),18]),
[iquote('hyper,1701,3,unit_del,18')] ).
cnf(6282,plain,
member(member_of_1_not_of_2(c,a),c),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[6281,13,22]),18])]),
[iquote('hyper,6281,13,22,unit_del,18,factor_simp')] ).
cnf(6300,plain,
member(member_of_1_not_of_2(c,a),a),
inference(hyper,[status(thm)],[6282,4,4670]),
[iquote('hyper,6282,4,4670')] ).
cnf(6592,plain,
subset(c,a),
inference(hyper,[status(thm)],[6300,3]),
[iquote('hyper,6300,3')] ).
cnf(6603,plain,
member(member_of_1_not_of_2(a,c),a),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[6592,13,22]),18]),
[iquote('hyper,6592,13,22,unit_del,18')] ).
cnf(6685,plain,
member(member_of_1_not_of_2(a,c),c),
inference(hyper,[status(thm)],[6603,4,471]),
[iquote('hyper,6603,4,471')] ).
cnf(6715,plain,
subset(a,c),
inference(hyper,[status(thm)],[6685,3]),
[iquote('hyper,6685,3')] ).
cnf(6716,plain,
e_qual_sets(a,c),
inference(hyper,[status(thm)],[6715,13,6592]),
[iquote('hyper,6715,13,6592')] ).
cnf(6717,plain,
$false,
inference(binary,[status(thm)],[6716,18]),
[iquote('binary,6716.1,18.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET012-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.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 10:56:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.71/6.94 ----- Otter 3.3f, August 2004 -----
% 6.71/6.94 The process was started by sandbox on n008.cluster.edu,
% 6.71/6.94 Wed Jul 27 10:56:08 2022
% 6.71/6.94 The command was "./otter". The process ID is 19103.
% 6.71/6.94
% 6.71/6.94 set(prolog_style_variables).
% 6.71/6.94 set(auto).
% 6.71/6.94 dependent: set(auto1).
% 6.71/6.94 dependent: set(process_input).
% 6.71/6.94 dependent: clear(print_kept).
% 6.71/6.94 dependent: clear(print_new_demod).
% 6.71/6.94 dependent: clear(print_back_demod).
% 6.71/6.94 dependent: clear(print_back_sub).
% 6.71/6.94 dependent: set(control_memory).
% 6.71/6.94 dependent: assign(max_mem, 12000).
% 6.71/6.94 dependent: assign(pick_given_ratio, 4).
% 6.71/6.94 dependent: assign(stats_level, 1).
% 6.71/6.94 dependent: assign(max_seconds, 10800).
% 6.71/6.94 clear(print_given).
% 6.71/6.94
% 6.71/6.94 list(usable).
% 6.71/6.94 0 [] -member(X,empty_set).
% 6.71/6.94 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 6.71/6.94 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 6.71/6.94 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 6.71/6.94 0 [] member(X,Xs)|member(X,complement(Xs)).
% 6.71/6.94 0 [] -member(X,Xs)| -member(X,complement(Xs)).
% 6.71/6.94 0 [] -member(X,Xs)|member(X,union(Xs,Ys)).
% 6.71/6.94 0 [] -member(X,Ys)|member(X,union(Xs,Ys)).
% 6.71/6.94 0 [] -member(X,union(Xs,Ys))|member(X,Xs)|member(X,Ys).
% 6.71/6.94 0 [] -member(X,Xs)| -member(X,Ys)|member(X,intersection(Xs,Ys)).
% 6.71/6.94 0 [] -member(X,intersection(Xs,Ys))|member(X,Xs).
% 6.71/6.94 0 [] -member(X,intersection(Xs,Ys))|member(X,Ys).
% 6.71/6.94 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 6.71/6.94 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 6.71/6.94 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 6.71/6.94 0 [] e_qual_sets(Xs,Xs).
% 6.71/6.94 0 [] -e_qual_sets(Xs,Ys)|e_qual_sets(Ys,Xs).
% 6.71/6.94 0 [] -e_qual_sets(Xs,Ys)| -e_qual_sets(Ys,Zs)|e_qual_sets(Xs,Zs).
% 6.71/6.94 0 [] e_qual_elements(X,X).
% 6.71/6.94 0 [] -e_qual_elements(X,Y)|e_qual_elements(Y,X).
% 6.71/6.94 0 [] -e_qual_elements(X,Y)| -e_qual_elements(Y,Z)|e_qual_elements(X,Z).
% 6.71/6.94 0 [] e_qual_sets(complement(a),b).
% 6.71/6.94 0 [] e_qual_sets(complement(b),c).
% 6.71/6.94 0 [] -e_qual_sets(a,c).
% 6.71/6.94 end_of_list.
% 6.71/6.94
% 6.71/6.94 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 6.71/6.94
% 6.71/6.94 This is a non-Horn set without equality. The strategy will
% 6.71/6.94 be ordered hyper_res, unit deletion, and factoring, with
% 6.71/6.94 satellites in sos and with nuclei in usable.
% 6.71/6.94
% 6.71/6.94 dependent: set(hyper_res).
% 6.71/6.94 dependent: set(factor).
% 6.71/6.94 dependent: set(unit_deletion).
% 6.71/6.94
% 6.71/6.94 ------------> process usable:
% 6.71/6.94 ** KEPT (pick-wt=3): 1 [] -member(A,empty_set).
% 6.71/6.94 ** KEPT (pick-wt=9): 2 [] -member(A,B)| -subset(B,C)|member(A,C).
% 6.71/6.94 ** KEPT (pick-wt=8): 3 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 6.71/6.94 ** KEPT (pick-wt=7): 4 [] -member(A,B)| -member(A,complement(B)).
% 6.71/6.94 ** KEPT (pick-wt=8): 5 [] -member(A,B)|member(A,union(B,C)).
% 6.71/6.94 ** KEPT (pick-wt=8): 6 [] -member(A,B)|member(A,union(C,B)).
% 6.71/6.94 ** KEPT (pick-wt=11): 7 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 6.71/6.94 ** KEPT (pick-wt=11): 8 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 6.71/6.94 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,B).
% 6.71/6.94 ** KEPT (pick-wt=8): 10 [] -member(A,intersection(B,C))|member(A,C).
% 6.71/6.94 ** KEPT (pick-wt=6): 11 [] -e_qual_sets(A,B)|subset(A,B).
% 6.71/6.94 ** KEPT (pick-wt=6): 12 [] -e_qual_sets(A,B)|subset(B,A).
% 6.71/6.94 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 6.71/6.94 ** KEPT (pick-wt=6): 14 [] -e_qual_sets(A,B)|e_qual_sets(B,A).
% 6.71/6.94 ** KEPT (pick-wt=9): 15 [] -e_qual_sets(A,B)| -e_qual_sets(B,C)|e_qual_sets(A,C).
% 6.71/6.94 ** KEPT (pick-wt=6): 16 [] -e_qual_elements(A,B)|e_qual_elements(B,A).
% 6.71/6.94 ** KEPT (pick-wt=9): 17 [] -e_qual_elements(A,B)| -e_qual_elements(B,C)|e_qual_elements(A,C).
% 6.71/6.94 ** KEPT (pick-wt=3): 18 [] -e_qual_sets(a,c).
% 6.71/6.94
% 6.71/6.94 ------------> process sos:
% 6.71/6.94 ** KEPT (pick-wt=8): 22 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 6.71/6.94 ** KEPT (pick-wt=7): 23 [] member(A,B)|member(A,complement(B)).
% 6.71/6.94 ** KEPT (pick-wt=3): 24 [] e_qual_sets(A,A).
% 6.71/6.94 ** KEPT (pick-wt=3): 25 [] e_qual_elements(A,A).
% 6.71/6.94 ** KEPT (pick-wt=4): 26 [] e_qual_sets(complement(a),b).
% 6.71/6.94 ** KEPT (pick-wt=4): 27 [] e_qual_sets(complement(b),c).
% 6.71/6.94 24 back subsumes 21.
% 6.71/6.94
% 6.71/6.94 ======= end of input processing =======
% 6.71/6.94
% 6.71/6.94 =========== start of search ===========
% 6.71/6.94
% 6.71/6.94
% 6.71/6.94 Resetting weight limit to 10.
% 6.71/6.94
% 6.71/6.94
% 6.71/6.94 Resetting weight limit to 10.
% 6.71/6.94
% 6.71/6.94 sos_size=4296
% 6.71/6.94
% 6.71/6.94
% 6.71/6.94 Resetting weight limit to 9.
% 6.71/6.94
% 6.71/6.94
% 6.71/6.94 Resetting weight limit to 9.
% 6.71/6.94
% 6.71/6.94 sos_size=4484
% 83.16/83.37
% 83.16/83.37 -- HEY sandbox, WE HAVE A PROOF!! --
% 83.16/83.37
% 83.16/83.37 ----> UNIT CONFLICT at 81.45 sec ----> 6717 [binary,6716.1,18.1] $F.
% 83.16/83.37
% 83.16/83.37 Length of proof is 19. Level of proof is 12.
% 83.16/83.37
% 83.16/83.37 ---------------- PROOF ----------------
% 83.16/83.37 % SZS status Unsatisfiable
% 83.16/83.37 % SZS output start Refutation
% See solution above
% 83.16/83.37 ------------ end of proof -------------
% 83.16/83.37
% 83.16/83.37
% 83.16/83.37 Search stopped by max_proofs option.
% 83.16/83.37
% 83.16/83.37
% 83.16/83.37 Search stopped by max_proofs option.
% 83.16/83.37
% 83.16/83.37 ============ end of search ============
% 83.16/83.37
% 83.16/83.37 -------------- statistics -------------
% 83.16/83.37 clauses given 2988
% 83.16/83.37 clauses generated 11283760
% 83.16/83.37 clauses kept 6716
% 83.16/83.37 clauses forward subsumed 114357
% 83.16/83.37 clauses back subsumed 221
% 83.16/83.37 Kbytes malloced 10742
% 83.16/83.37
% 83.16/83.37 ----------- times (seconds) -----------
% 83.16/83.37 user CPU time 81.45 (0 hr, 1 min, 21 sec)
% 83.16/83.37 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 83.16/83.37 wall-clock time 83 (0 hr, 1 min, 23 sec)
% 83.16/83.37
% 83.16/83.37 That finishes the proof of the theorem.
% 83.16/83.37
% 83.16/83.37 Process 19103 finished Wed Jul 27 10:57:31 2022
% 83.16/83.37 Otter interrupted
% 83.16/83.37 PROOF FOUND
%------------------------------------------------------------------------------