TSTP Solution File: SET586+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:13:44 EDT 2022
% Result : Theorem 2.06s 2.26s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 11 unt; 1 nHn; 15 RR)
% Number of literals : 25 ( 1 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('SET586+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET586+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET586+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET586+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET586+3.p',unknown),
[] ).
cnf(9,axiom,
~ subset(intersection(dollar_c3,dollar_c1),intersection(dollar_c2,dollar_c1)),
file('SET586+3.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET586+3.p',unknown),
[] ).
cnf(14,axiom,
intersection(A,B) = intersection(B,A),
file('SET586+3.p',unknown),
[] ).
cnf(17,axiom,
subset(dollar_c3,dollar_c2),
file('SET586+3.p',unknown),
[] ).
cnf(21,plain,
~ subset(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),
inference(para_from,[status(thm),theory(equality)],[14,9]),
[iquote('para_from,14.1.1,9.1.2')] ).
cnf(30,plain,
member(dollar_f1(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),intersection(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[13,21]),
[iquote('hyper,13,21')] ).
cnf(50,plain,
member(dollar_f1(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),dollar_c1),
inference(hyper,[status(thm)],[30,2]),
[iquote('hyper,30,2')] ).
cnf(51,plain,
member(dollar_f1(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),dollar_c3),
inference(hyper,[status(thm)],[30,1]),
[iquote('hyper,30,1')] ).
cnf(249,plain,
member(dollar_f1(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),dollar_c2),
inference(hyper,[status(thm)],[51,4,17]),
[iquote('hyper,51,4,17')] ).
cnf(579,plain,
member(dollar_f1(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),intersection(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[249,3,50]),
[iquote('hyper,249,3,50')] ).
cnf(2376,plain,
subset(intersection(dollar_c3,dollar_c1),intersection(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[579,5]),
[iquote('hyper,579,5')] ).
cnf(2377,plain,
$false,
inference(binary,[status(thm)],[2376,21]),
[iquote('binary,2376.1,21.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:37:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.06/2.26 ----- Otter 3.3f, August 2004 -----
% 2.06/2.26 The process was started by sandbox2 on n007.cluster.edu,
% 2.06/2.26 Wed Jul 27 10:37:46 2022
% 2.06/2.26 The command was "./otter". The process ID is 6205.
% 2.06/2.26
% 2.06/2.26 set(prolog_style_variables).
% 2.06/2.26 set(auto).
% 2.06/2.26 dependent: set(auto1).
% 2.06/2.26 dependent: set(process_input).
% 2.06/2.26 dependent: clear(print_kept).
% 2.06/2.26 dependent: clear(print_new_demod).
% 2.06/2.26 dependent: clear(print_back_demod).
% 2.06/2.26 dependent: clear(print_back_sub).
% 2.06/2.26 dependent: set(control_memory).
% 2.06/2.26 dependent: assign(max_mem, 12000).
% 2.06/2.26 dependent: assign(pick_given_ratio, 4).
% 2.06/2.26 dependent: assign(stats_level, 1).
% 2.06/2.26 dependent: assign(max_seconds, 10800).
% 2.06/2.26 clear(print_given).
% 2.06/2.26
% 2.06/2.26 formula_list(usable).
% 2.06/2.26 all A (A=A).
% 2.06/2.26 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 2.06/2.26 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 2.06/2.26 all B C (intersection(B,C)=intersection(C,B)).
% 2.06/2.26 all B subset(B,B).
% 2.06/2.26 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 2.06/2.26 -(all B C D (subset(B,C)->subset(intersection(B,D),intersection(C,D)))).
% 2.06/2.26 end_of_list.
% 2.06/2.26
% 2.06/2.26 -------> usable clausifies to:
% 2.06/2.26
% 2.06/2.26 list(usable).
% 2.06/2.26 0 [] A=A.
% 2.06/2.26 0 [] -member(D,intersection(B,C))|member(D,B).
% 2.06/2.26 0 [] -member(D,intersection(B,C))|member(D,C).
% 2.06/2.26 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 2.06/2.26 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 2.06/2.26 0 [] subset(B,C)|member($f1(B,C),B).
% 2.06/2.26 0 [] subset(B,C)| -member($f1(B,C),C).
% 2.06/2.26 0 [] intersection(B,C)=intersection(C,B).
% 2.06/2.26 0 [] subset(B,B).
% 2.06/2.26 0 [] B!=C| -member(D,B)|member(D,C).
% 2.06/2.26 0 [] B!=C|member(D,B)| -member(D,C).
% 2.06/2.26 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 2.06/2.26 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 2.06/2.26 0 [] subset($c3,$c2).
% 2.06/2.26 0 [] -subset(intersection($c3,$c1),intersection($c2,$c1)).
% 2.06/2.26 end_of_list.
% 2.06/2.26
% 2.06/2.26 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.06/2.26
% 2.06/2.26 This ia a non-Horn set with equality. The strategy will be
% 2.06/2.26 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.06/2.26 deletion, with positive clauses in sos and nonpositive
% 2.06/2.26 clauses in usable.
% 2.06/2.26
% 2.06/2.26 dependent: set(knuth_bendix).
% 2.06/2.26 dependent: set(anl_eq).
% 2.06/2.26 dependent: set(para_from).
% 2.06/2.26 dependent: set(para_into).
% 2.06/2.26 dependent: clear(para_from_right).
% 2.06/2.26 dependent: clear(para_into_right).
% 2.06/2.26 dependent: set(para_from_vars).
% 2.06/2.26 dependent: set(eq_units_both_ways).
% 2.06/2.26 dependent: set(dynamic_demod_all).
% 2.06/2.26 dependent: set(dynamic_demod).
% 2.06/2.26 dependent: set(order_eq).
% 2.06/2.26 dependent: set(back_demod).
% 2.06/2.26 dependent: set(lrpo).
% 2.06/2.26 dependent: set(hyper_res).
% 2.06/2.26 dependent: set(unit_deletion).
% 2.06/2.26 dependent: set(factor).
% 2.06/2.26
% 2.06/2.26 ------------> process usable:
% 2.06/2.26 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 2.06/2.26 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 2.06/2.26 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.06/2.26 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.06/2.26 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 2.06/2.26 ** KEPT (pick-wt=9): 6 [] A!=B| -member(C,A)|member(C,B).
% 2.06/2.26 ** KEPT (pick-wt=9): 7 [] A!=B|member(C,A)| -member(C,B).
% 2.06/2.26 ** KEPT (pick-wt=13): 8 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 2.06/2.26 ** KEPT (pick-wt=7): 9 [] -subset(intersection($c3,$c1),intersection($c2,$c1)).
% 2.06/2.26
% 2.06/2.26 ------------> process sos:
% 2.06/2.26 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.06/2.26 ** KEPT (pick-wt=8): 13 [] subset(A,B)|member($f1(A,B),A).
% 2.06/2.26 ** KEPT (pick-wt=7): 14 [] intersection(A,B)=intersection(B,A).
% 2.06/2.26 ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 2.06/2.26 ** KEPT (pick-wt=13): 16 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 2.06/2.26 ** KEPT (pick-wt=3): 17 [] subset($c3,$c2).
% 2.06/2.26 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.06/2.26 12 back subsumes 11.
% 2.06/2.26 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] intersection(A,B)=intersection(B,A).
% 2.06/2.26
% 2.06/2.26 ======= end of input processing =======
% 2.06/2.26
% 2.06/2.26 =========== start of search ===========
% 2.06/2.26
% 2.06/2.26 -------- PROOF --------
% 2.06/2.26
% 2.06/2.26 ----> UNIT CONFLICT at 0.27 sec ----> 2377 [binary,2376.1,21.1] $F.
% 2.06/2.26
% 2.06/2.26 Length of proof is 7. Level of proof is 6.
% 2.06/2.26
% 2.06/2.26 ---------------- PROOF ----------------
% 2.06/2.26 % SZS status Theorem
% 2.06/2.26 % SZS output start Refutation
% See solution above
% 2.06/2.26 ------------ end of proof -------------
% 2.06/2.26
% 2.06/2.26
% 2.06/2.26 Search stopped by max_proofs option.
% 2.06/2.26
% 2.06/2.26
% 2.06/2.26 Search stopped by max_proofs option.
% 2.06/2.26
% 2.06/2.26 ============ end of search ============
% 2.06/2.26
% 2.06/2.26 -------------- statistics -------------
% 2.06/2.26 clauses given 78
% 2.06/2.26 clauses generated 5176
% 2.06/2.26 clauses kept 2376
% 2.06/2.26 clauses forward subsumed 2776
% 2.06/2.26 clauses back subsumed 66
% 2.06/2.26 Kbytes malloced 2929
% 2.06/2.26
% 2.06/2.26 ----------- times (seconds) -----------
% 2.06/2.26 user CPU time 0.27 (0 hr, 0 min, 0 sec)
% 2.06/2.26 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.06/2.26 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.06/2.26
% 2.06/2.26 That finishes the proof of the theorem.
% 2.06/2.26
% 2.06/2.26 Process 6205 finished Wed Jul 27 10:37:48 2022
% 2.06/2.26 Otter interrupted
% 2.06/2.26 PROOF FOUND
%------------------------------------------------------------------------------