TSTP Solution File: SET632+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:13:56 EDT 2022
% Result : Theorem 1.65s 1.89s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of clauses : 30 ( 12 unt; 11 nHn; 17 RR)
% Number of literals : 52 ( 5 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET632+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ intersect(A,B)
| member(dollar_f2(A,B),B) ),
file('SET632+3.p',unknown),
[] ).
cnf(5,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET632+3.p',unknown),
[] ).
cnf(6,axiom,
~ member(A,empty_set),
file('SET632+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ disjoint(A,B)
| ~ intersect(A,B) ),
file('SET632+3.p',unknown),
[] ).
cnf(10,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET632+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ intersect(A,B)
| intersect(B,A) ),
file('SET632+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ empty(A)
| ~ member(B,A) ),
file('SET632+3.p',unknown),
[] ).
cnf(13,axiom,
dollar_c3 != empty_set,
file('SET632+3.p',unknown),
[] ).
cnf(14,plain,
empty_set != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(18,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET632+3.p',unknown),
[] ).
cnf(19,axiom,
( disjoint(A,B)
| intersect(A,B) ),
file('SET632+3.p',unknown),
[] ).
cnf(21,axiom,
( empty(A)
| member(dollar_f3(A),A) ),
file('SET632+3.p',unknown),
[] ).
cnf(22,axiom,
subset(dollar_c3,dollar_c2),
file('SET632+3.p',unknown),
[] ).
cnf(23,axiom,
subset(dollar_c3,dollar_c1),
file('SET632+3.p',unknown),
[] ).
cnf(24,axiom,
disjoint(dollar_c2,dollar_c1),
file('SET632+3.p',unknown),
[] ).
cnf(33,plain,
( member(dollar_f1(A,B),A)
| B = A
| member(dollar_f1(B,A),B) ),
inference(hyper,[status(thm)],[18,10,18]),
[iquote('hyper,18,10,18')] ).
cnf(35,plain,
( disjoint(A,B)
| intersect(B,A) ),
inference(hyper,[status(thm)],[19,11]),
[iquote('hyper,19,11')] ).
cnf(36,plain,
( disjoint(A,B)
| member(dollar_f2(A,B),B) ),
inference(hyper,[status(thm)],[19,4]),
[iquote('hyper,19,4')] ).
cnf(39,plain,
disjoint(dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[35,7,24]),
[iquote('hyper,35,7,24')] ).
cnf(152,plain,
( disjoint(A,B)
| member(dollar_f3(B),B) ),
inference(hyper,[status(thm)],[36,12,21]),
[iquote('hyper,36,12,21')] ).
cnf(166,plain,
( disjoint(A,dollar_c3)
| member(dollar_f3(dollar_c3),dollar_c1) ),
inference(hyper,[status(thm)],[152,1,23]),
[iquote('hyper,152,1,23')] ).
cnf(167,plain,
( disjoint(A,dollar_c3)
| member(dollar_f3(dollar_c3),dollar_c2) ),
inference(hyper,[status(thm)],[152,1,22]),
[iquote('hyper,152,1,22')] ).
cnf(218,plain,
( disjoint(A,dollar_c3)
| intersect(dollar_c1,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[167,5,166])]),
[iquote('hyper,167,5,166,factor_simp')] ).
cnf(241,plain,
disjoint(A,dollar_c3),
inference(hyper,[status(thm)],[218,7,39]),
[iquote('hyper,218,7,39')] ).
cnf(242,plain,
disjoint(dollar_c3,A),
inference(hyper,[status(thm)],[241,7,35]),
[iquote('hyper,241,7,35')] ).
cnf(255,plain,
( A = empty_set
| member(dollar_f1(A,empty_set),A) ),
inference(hyper,[status(thm)],[33,6]),
[iquote('hyper,33,6')] ).
cnf(546,plain,
member(dollar_f1(dollar_c3,empty_set),dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[255,1,23]),14]),
[iquote('hyper,255,1,23,unit_del,14')] ).
cnf(636,plain,
intersect(dollar_c3,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[546,5,255]),14]),
[iquote('hyper,546,5,255,unit_del,14')] ).
cnf(698,plain,
$false,
inference(hyper,[status(thm)],[636,7,242]),
[iquote('hyper,636,7,242')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:42:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.65/1.89 ----- Otter 3.3f, August 2004 -----
% 1.65/1.89 The process was started by sandbox2 on n022.cluster.edu,
% 1.65/1.89 Wed Jul 27 10:42:05 2022
% 1.65/1.89 The command was "./otter". The process ID is 22857.
% 1.65/1.89
% 1.65/1.89 set(prolog_style_variables).
% 1.65/1.89 set(auto).
% 1.65/1.89 dependent: set(auto1).
% 1.65/1.89 dependent: set(process_input).
% 1.65/1.89 dependent: clear(print_kept).
% 1.65/1.89 dependent: clear(print_new_demod).
% 1.65/1.89 dependent: clear(print_back_demod).
% 1.65/1.89 dependent: clear(print_back_sub).
% 1.65/1.89 dependent: set(control_memory).
% 1.65/1.89 dependent: assign(max_mem, 12000).
% 1.65/1.89 dependent: assign(pick_given_ratio, 4).
% 1.65/1.89 dependent: assign(stats_level, 1).
% 1.65/1.89 dependent: assign(max_seconds, 10800).
% 1.65/1.89 clear(print_given).
% 1.65/1.89
% 1.65/1.89 formula_list(usable).
% 1.65/1.89 all A (A=A).
% 1.65/1.89 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.65/1.89 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.65/1.89 all B (-member(B,empty_set)).
% 1.65/1.89 all B C (disjoint(B,C)<-> -intersect(B,C)).
% 1.65/1.89 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.65/1.89 all B C (intersect(B,C)->intersect(C,B)).
% 1.65/1.89 all B subset(B,B).
% 1.65/1.89 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.65/1.89 -(all B C D (subset(B,C)&subset(B,D)&disjoint(C,D)->B=empty_set)).
% 1.65/1.89 end_of_list.
% 1.65/1.89
% 1.65/1.89 -------> usable clausifies to:
% 1.65/1.89
% 1.65/1.89 list(usable).
% 1.65/1.89 0 [] A=A.
% 1.65/1.89 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.65/1.89 0 [] subset(B,C)|member($f1(B,C),B).
% 1.65/1.89 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.65/1.89 0 [] -intersect(B,C)|member($f2(B,C),B).
% 1.65/1.89 0 [] -intersect(B,C)|member($f2(B,C),C).
% 1.65/1.89 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.65/1.89 0 [] -member(B,empty_set).
% 1.65/1.89 0 [] -disjoint(B,C)| -intersect(B,C).
% 1.65/1.89 0 [] disjoint(B,C)|intersect(B,C).
% 1.65/1.89 0 [] B!=C|subset(B,C).
% 1.65/1.89 0 [] B!=C|subset(C,B).
% 1.65/1.89 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.65/1.89 0 [] -intersect(B,C)|intersect(C,B).
% 1.65/1.89 0 [] subset(B,B).
% 1.65/1.89 0 [] -empty(B)| -member(C,B).
% 1.65/1.89 0 [] empty(B)|member($f3(B),B).
% 1.65/1.89 0 [] subset($c3,$c2).
% 1.65/1.89 0 [] subset($c3,$c1).
% 1.65/1.89 0 [] disjoint($c2,$c1).
% 1.65/1.89 0 [] $c3!=empty_set.
% 1.65/1.89 end_of_list.
% 1.65/1.89
% 1.65/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.65/1.89
% 1.65/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.89 deletion, with positive clauses in sos and nonpositive
% 1.65/1.89 clauses in usable.
% 1.65/1.89
% 1.65/1.89 dependent: set(knuth_bendix).
% 1.65/1.89 dependent: set(anl_eq).
% 1.65/1.89 dependent: set(para_from).
% 1.65/1.89 dependent: set(para_into).
% 1.65/1.89 dependent: clear(para_from_right).
% 1.65/1.89 dependent: clear(para_into_right).
% 1.65/1.89 dependent: set(para_from_vars).
% 1.65/1.89 dependent: set(eq_units_both_ways).
% 1.65/1.89 dependent: set(dynamic_demod_all).
% 1.65/1.89 dependent: set(dynamic_demod).
% 1.65/1.89 dependent: set(order_eq).
% 1.65/1.89 dependent: set(back_demod).
% 1.65/1.89 dependent: set(lrpo).
% 1.65/1.89 dependent: set(hyper_res).
% 1.65/1.89 dependent: set(unit_deletion).
% 1.65/1.89 dependent: set(factor).
% 1.65/1.89
% 1.65/1.89 ------------> process usable:
% 1.65/1.89 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.65/1.89 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.65/1.89 ** KEPT (pick-wt=8): 3 [] -intersect(A,B)|member($f2(A,B),A).
% 1.65/1.89 ** KEPT (pick-wt=8): 4 [] -intersect(A,B)|member($f2(A,B),B).
% 1.65/1.89 ** KEPT (pick-wt=9): 5 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.65/1.89 ** KEPT (pick-wt=3): 6 [] -member(A,empty_set).
% 1.65/1.89 ** KEPT (pick-wt=6): 7 [] -disjoint(A,B)| -intersect(A,B).
% 1.65/1.89 ** KEPT (pick-wt=6): 8 [] A!=B|subset(A,B).
% 1.65/1.89 ** KEPT (pick-wt=6): 9 [] A!=B|subset(B,A).
% 1.65/1.89 ** KEPT (pick-wt=9): 10 [] A=B| -subset(A,B)| -subset(B,A).
% 1.65/1.89 ** KEPT (pick-wt=6): 11 [] -intersect(A,B)|intersect(B,A).
% 1.65/1.89 ** KEPT (pick-wt=5): 12 [] -empty(A)| -member(B,A).
% 1.65/1.89 ** KEPT (pick-wt=3): 14 [copy,13,flip.1] empty_set!=$c3.
% 1.65/1.89
% 1.65/1.89 ------------> process sos:
% 1.65/1.89 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.65/1.89 ** KEPT (pick-wt=8): 18 [] subset(A,B)|member($f1(A,B),A).
% 1.65/1.89 ** KEPT (pick-wt=6): 19 [] disjoint(A,B)|intersect(A,B).
% 1.65/1.89 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 1.65/1.89 ** KEPT (pick-wt=6): 21 [] empty(A)|member($f3(A),A).
% 1.65/1.89 ** KEPT (pick-wt=3): 22 [] subset($c3,$c2).
% 1.65/1.89 ** KEPT (pick-wt=3): 23 [] subset($c3,$c1).
% 1.65/1.89 ** KEPT (pick-wt=3): 24 [] disjoint($c2,$c1).
% 1.65/1.89 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.65/1.89 17 back subsumes 16.
% 1.65/1.89
% 1.65/1.89 ======= end of input processing =======
% 1.65/1.89
% 1.65/1.89 =========== start of search ===========
% 1.65/1.89
% 1.65/1.89 -------- PROOF --------
% 1.65/1.89
% 1.65/1.89 -----> EMPTY CLAUSE at 0.06 sec ----> 698 [hyper,636,7,242] $F.
% 1.65/1.89
% 1.65/1.89 Length of proof is 14. Level of proof is 6.
% 1.65/1.89
% 1.65/1.89 ---------------- PROOF ----------------
% 1.65/1.89 % SZS status Theorem
% 1.65/1.89 % SZS output start Refutation
% See solution above
% 1.65/1.89 ------------ end of proof -------------
% 1.65/1.89
% 1.65/1.89
% 1.65/1.89 Search stopped by max_proofs option.
% 1.65/1.89
% 1.65/1.89
% 1.65/1.89 Search stopped by max_proofs option.
% 1.65/1.89
% 1.65/1.89 ============ end of search ============
% 1.65/1.89
% 1.65/1.89 -------------- statistics -------------
% 1.65/1.89 clauses given 68
% 1.65/1.89 clauses generated 2076
% 1.65/1.89 clauses kept 696
% 1.65/1.89 clauses forward subsumed 1381
% 1.65/1.89 clauses back subsumed 189
% 1.65/1.89 Kbytes malloced 1953
% 1.65/1.89
% 1.65/1.89 ----------- times (seconds) -----------
% 1.65/1.89 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.65/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.89
% 1.65/1.89 That finishes the proof of the theorem.
% 1.65/1.89
% 1.65/1.89 Process 22857 finished Wed Jul 27 10:42:07 2022
% 1.65/1.89 Otter interrupted
% 1.65/1.89 PROOF FOUND
%------------------------------------------------------------------------------