TSTP Solution File: SET027+4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET027+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:12:51 EDT 2022
% Result : Theorem 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 10 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET027+4.p',unknown),
[] ).
cnf(2,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET027+4.p',unknown),
[] ).
cnf(28,axiom,
~ subset(dollar_c3,dollar_c1),
file('SET027+4.p',unknown),
[] ).
cnf(35,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET027+4.p',unknown),
[] ).
cnf(37,axiom,
subset(dollar_c3,dollar_c2),
file('SET027+4.p',unknown),
[] ).
cnf(38,axiom,
subset(dollar_c2,dollar_c1),
file('SET027+4.p',unknown),
[] ).
cnf(89,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c3),
inference(hyper,[status(thm)],[35,28]),
[iquote('hyper,35,28')] ).
cnf(182,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c2),
inference(hyper,[status(thm)],[89,1,37]),
[iquote('hyper,89,1,37')] ).
cnf(363,plain,
member(dollar_f1(dollar_c3,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[182,1,38]),
[iquote('hyper,182,1,38')] ).
cnf(531,plain,
subset(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[363,2]),
[iquote('hyper,363,2')] ).
cnf(532,plain,
$false,
inference(binary,[status(thm)],[531,28]),
[iquote('binary,531.1,28.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET027+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:34:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox on n009.cluster.edu,
% 1.74/1.94 Wed Jul 27 10:34:51 2022
% 1.74/1.94 The command was "./otter". The process ID is 26996.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 formula_list(usable).
% 1.74/1.94 all A (A=A).
% 1.74/1.94 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 1.74/1.94 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 1.74/1.94 all X A (member(X,power_set(A))<->subset(X,A)).
% 1.74/1.94 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 1.74/1.94 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 1.74/1.94 all X (-member(X,empty_set)).
% 1.74/1.94 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 1.74/1.94 all X A (member(X,singleton(A))<->X=A).
% 1.74/1.94 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 1.74/1.94 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 1.74/1.94 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 1.74/1.94 -(all A B C (subset(A,B)&subset(B,C)->subset(A,C))).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 -------> usable clausifies to:
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 1.74/1.94 0 [] subset(A,B)|member($f1(A,B),A).
% 1.74/1.94 0 [] subset(A,B)| -member($f1(A,B),B).
% 1.74/1.94 0 [] -e_qual_set(A,B)|subset(A,B).
% 1.74/1.94 0 [] -e_qual_set(A,B)|subset(B,A).
% 1.74/1.94 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.74/1.94 0 [] -member(X,power_set(A))|subset(X,A).
% 1.74/1.94 0 [] member(X,power_set(A))| -subset(X,A).
% 1.74/1.94 0 [] -member(X,intersection(A,B))|member(X,A).
% 1.74/1.94 0 [] -member(X,intersection(A,B))|member(X,B).
% 1.74/1.94 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 1.74/1.94 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 1.74/1.94 0 [] member(X,union(A,B))| -member(X,A).
% 1.74/1.94 0 [] member(X,union(A,B))| -member(X,B).
% 1.74/1.94 0 [] -member(X,empty_set).
% 1.74/1.94 0 [] -member(B,difference(E,A))|member(B,E).
% 1.74/1.94 0 [] -member(B,difference(E,A))| -member(B,A).
% 1.74/1.94 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 1.74/1.94 0 [] -member(X,singleton(A))|X=A.
% 1.74/1.94 0 [] member(X,singleton(A))|X!=A.
% 1.74/1.94 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 1.74/1.94 0 [] member(X,unordered_pair(A,B))|X!=A.
% 1.74/1.94 0 [] member(X,unordered_pair(A,B))|X!=B.
% 1.74/1.94 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 1.74/1.94 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 1.74/1.94 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 1.74/1.94 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 1.74/1.94 0 [] member(X,product(A))|member($f3(X,A),A).
% 1.74/1.94 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 1.74/1.94 0 [] subset($c3,$c2).
% 1.74/1.94 0 [] subset($c2,$c1).
% 1.74/1.94 0 [] -subset($c3,$c1).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.74/1.94
% 1.74/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.94 deletion, with positive clauses in sos and nonpositive
% 1.74/1.94 clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: set(unit_deletion).
% 1.74/1.94 dependent: set(factor).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.74/1.94 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.74/1.94 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 1.74/1.94 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 1.74/1.94 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.74/1.94 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 1.74/1.94 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 1.74/1.94 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 1.74/1.94 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 1.74/1.95 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 1.74/1.95 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 1.74/1.95 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 1.74/1.95 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 1.74/1.95 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.74/1.95 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 1.74/1.95 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 1.74/1.95 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 1.74/1.95 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 1.74/1.95 ** KEPT (pick-wt=3): 28 [] -subset($c3,$c1).
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 34 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=8): 35 [] subset(A,B)|member($f1(A,B),A).
% 1.74/1.95 ** KEPT (pick-wt=9): 36 [] member(A,product(B))|member($f3(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=3): 37 [] subset($c3,$c2).
% 1.74/1.95 ** KEPT (pick-wt=3): 38 [] subset($c2,$c1).
% 1.74/1.95 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 1.74/1.95
% 1.74/1.95 ======= end of input processing =======
% 1.74/1.95
% 1.74/1.95 =========== start of search ===========
% 1.74/1.95
% 1.74/1.95 -------- PROOF --------
% 1.74/1.95
% 1.74/1.95 ----> UNIT CONFLICT at 0.02 sec ----> 532 [binary,531.1,28.1] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 4. Level of proof is 4.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Theorem
% 1.74/1.95 % SZS output start Refutation
% See solution above
% 1.74/1.95 ------------ end of proof -------------
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95 ============ end of search ============
% 1.74/1.95
% 1.74/1.95 -------------- statistics -------------
% 1.74/1.95 clauses given 19
% 1.74/1.95 clauses generated 619
% 1.74/1.95 clauses kept 531
% 1.74/1.95 clauses forward subsumed 122
% 1.74/1.95 clauses back subsumed 5
% 1.74/1.95 Kbytes malloced 2929
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.74/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.95
% 1.74/1.95 That finishes the proof of the theorem.
% 1.74/1.95
% 1.74/1.95 Process 26996 finished Wed Jul 27 10:34:52 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
%------------------------------------------------------------------------------