TSTP Solution File: SET347+4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:13:25 EDT 2022
% Result : Theorem 4.16s 4.33s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 18 unt; 9 nHn; 15 RR)
% Number of literals : 64 ( 7 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET347+4.p',unknown),
[] ).
cnf(5,axiom,
( e_qual_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET347+4.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(A,power_set(B))
| subset(A,B) ),
file('SET347+4.p',unknown),
[] ).
cnf(7,axiom,
( member(A,power_set(B))
| ~ subset(A,B) ),
file('SET347+4.p',unknown),
[] ).
cnf(14,axiom,
~ member(A,empty_set),
file('SET347+4.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET347+4.p',unknown),
[] ).
cnf(17,axiom,
( member(A,difference(B,C))
| ~ member(A,B)
| member(A,C) ),
file('SET347+4.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(A,singleton(B))
| A = B ),
file('SET347+4.p',unknown),
[] ).
cnf(19,axiom,
( member(A,singleton(B))
| A != B ),
file('SET347+4.p',unknown),
[] ).
cnf(21,axiom,
( member(A,unordered_pair(B,C))
| A != B ),
file('SET347+4.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(A,sum(B))
| member(dollar_f2(A,B),B) ),
file('SET347+4.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(A,product(B))
| ~ member(C,B)
| member(A,C) ),
file('SET347+4.p',unknown),
[] ).
cnf(28,axiom,
~ e_qual_set(sum(empty_set),empty_set),
file('SET347+4.p',unknown),
[] ).
cnf(34,axiom,
A = A,
file('SET347+4.p',unknown),
[] ).
cnf(35,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET347+4.p',unknown),
[] ).
cnf(36,axiom,
( member(A,product(B))
| member(dollar_f3(A,B),B) ),
file('SET347+4.p',unknown),
[] ).
cnf(38,plain,
member(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[34,21]),
[iquote('hyper,34,21')] ).
cnf(39,plain,
member(A,singleton(A)),
inference(hyper,[status(thm)],[34,19]),
[iquote('hyper,34,19')] ).
cnf(42,plain,
( member(A,difference(singleton(A),B))
| member(A,B) ),
inference(hyper,[status(thm)],[39,17]),
[iquote('hyper,39,17')] ).
cnf(69,plain,
( member(A,difference(unordered_pair(A,B),C))
| member(A,C) ),
inference(hyper,[status(thm)],[38,17]),
[iquote('hyper,38,17')] ).
cnf(113,plain,
( member(dollar_f1(A,B),A)
| member(A,power_set(B)) ),
inference(hyper,[status(thm)],[35,7]),
[iquote('hyper,35,7')] ).
cnf(116,plain,
( member(dollar_f1(singleton(A),B),singleton(A))
| member(A,B) ),
inference(hyper,[status(thm)],[35,1,39]),
[iquote('hyper,35,1,39')] ).
cnf(289,plain,
( member(dollar_f3(A,singleton(B)),singleton(B))
| member(A,B) ),
inference(hyper,[status(thm)],[36,26,39]),
[iquote('hyper,36,26,39')] ).
cnf(627,plain,
( member(A,difference(singleton(A),sum(B)))
| member(dollar_f2(A,B),B) ),
inference(hyper,[status(thm)],[42,23]),
[iquote('hyper,42,23')] ).
cnf(646,plain,
member(A,difference(singleton(A),empty_set)),
inference(hyper,[status(thm)],[42,14]),
[iquote('hyper,42,14')] ).
cnf(821,plain,
member(A,difference(unordered_pair(A,B),empty_set)),
inference(hyper,[status(thm)],[69,16,646]),
[iquote('hyper,69,16,646')] ).
cnf(888,plain,
member(empty_set,power_set(A)),
inference(hyper,[status(thm)],[113,16,821]),
[iquote('hyper,113,16,821')] ).
cnf(907,plain,
subset(empty_set,A),
inference(hyper,[status(thm)],[888,6]),
[iquote('hyper,888,6')] ).
cnf(921,plain,
member(dollar_f1(singleton(A),empty_set),singleton(A)),
inference(hyper,[status(thm)],[116,16,821]),
[iquote('hyper,116,16,821')] ).
cnf(933,plain,
dollar_f1(singleton(A),empty_set) = A,
inference(hyper,[status(thm)],[921,18]),
[iquote('hyper,921,18')] ).
cnf(934,plain,
( A = B
| ~ member(B,singleton(A)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[933,18]),933]),
[iquote('para_into,932.1.1,18.2.1,demod,933')] ).
cnf(937,plain,
( ~ member(A,B)
| ~ member(B,singleton(empty_set)) ),
inference(para_from,[status(thm),theory(equality)],[934,14]),
[iquote('para_from,934.1.1,14.1.2')] ).
cnf(956,plain,
member(dollar_f3(A,singleton(empty_set)),singleton(empty_set)),
inference(hyper,[status(thm)],[289,937,39]),
[iquote('hyper,289,937,39')] ).
cnf(961,plain,
dollar_f3(A,singleton(empty_set)) = empty_set,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[956,934])]),
[iquote('hyper,956,934,flip.1')] ).
cnf(980,plain,
member(A,difference(singleton(A),sum(empty_set))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[627,937,289]),961]),14]),
[iquote('hyper,627,937,289,demod,961,unit_del,14')] ).
cnf(986,plain,
member(sum(empty_set),power_set(A)),
inference(hyper,[status(thm)],[980,16,113]),
[iquote('hyper,980,16,113')] ).
cnf(992,plain,
subset(sum(empty_set),A),
inference(hyper,[status(thm)],[986,6]),
[iquote('hyper,986,6')] ).
cnf(1006,plain,
e_qual_set(sum(empty_set),empty_set),
inference(hyper,[status(thm)],[992,5,907]),
[iquote('hyper,992,5,907')] ).
cnf(1007,plain,
$false,
inference(binary,[status(thm)],[1006,28]),
[iquote('binary,1006.1,28.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:45:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.72/1.90 ----- Otter 3.3f, August 2004 -----
% 1.72/1.90 The process was started by sandbox on n021.cluster.edu,
% 1.72/1.90 Wed Jul 27 10:45:53 2022
% 1.72/1.90 The command was "./otter". The process ID is 18823.
% 1.72/1.90
% 1.72/1.90 set(prolog_style_variables).
% 1.72/1.90 set(auto).
% 1.72/1.90 dependent: set(auto1).
% 1.72/1.90 dependent: set(process_input).
% 1.72/1.90 dependent: clear(print_kept).
% 1.72/1.90 dependent: clear(print_new_demod).
% 1.72/1.90 dependent: clear(print_back_demod).
% 1.72/1.90 dependent: clear(print_back_sub).
% 1.72/1.90 dependent: set(control_memory).
% 1.72/1.90 dependent: assign(max_mem, 12000).
% 1.72/1.90 dependent: assign(pick_given_ratio, 4).
% 1.72/1.90 dependent: assign(stats_level, 1).
% 1.72/1.90 dependent: assign(max_seconds, 10800).
% 1.72/1.90 clear(print_given).
% 1.72/1.90
% 1.72/1.90 formula_list(usable).
% 1.72/1.90 all A (A=A).
% 1.72/1.90 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 1.72/1.90 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 1.72/1.90 all X A (member(X,power_set(A))<->subset(X,A)).
% 1.72/1.90 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 1.72/1.90 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 1.72/1.90 all X (-member(X,empty_set)).
% 1.72/1.90 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 1.72/1.90 all X A (member(X,singleton(A))<->X=A).
% 1.72/1.90 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 1.72/1.90 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 1.72/1.90 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 1.72/1.90 -e_qual_set(sum(empty_set),empty_set).
% 1.72/1.90 end_of_list.
% 1.72/1.90
% 1.72/1.90 -------> usable clausifies to:
% 1.72/1.90
% 1.72/1.90 list(usable).
% 1.72/1.90 0 [] A=A.
% 1.72/1.90 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 1.72/1.90 0 [] subset(A,B)|member($f1(A,B),A).
% 1.72/1.90 0 [] subset(A,B)| -member($f1(A,B),B).
% 1.72/1.90 0 [] -e_qual_set(A,B)|subset(A,B).
% 1.72/1.90 0 [] -e_qual_set(A,B)|subset(B,A).
% 1.72/1.90 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.72/1.90 0 [] -member(X,power_set(A))|subset(X,A).
% 1.72/1.90 0 [] member(X,power_set(A))| -subset(X,A).
% 1.72/1.90 0 [] -member(X,intersection(A,B))|member(X,A).
% 1.72/1.90 0 [] -member(X,intersection(A,B))|member(X,B).
% 1.72/1.90 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 1.72/1.90 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 1.72/1.90 0 [] member(X,union(A,B))| -member(X,A).
% 1.72/1.90 0 [] member(X,union(A,B))| -member(X,B).
% 1.72/1.90 0 [] -member(X,empty_set).
% 1.72/1.90 0 [] -member(B,difference(E,A))|member(B,E).
% 1.72/1.90 0 [] -member(B,difference(E,A))| -member(B,A).
% 1.72/1.90 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 1.72/1.90 0 [] -member(X,singleton(A))|X=A.
% 1.72/1.90 0 [] member(X,singleton(A))|X!=A.
% 1.72/1.90 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 1.72/1.90 0 [] member(X,unordered_pair(A,B))|X!=A.
% 1.72/1.90 0 [] member(X,unordered_pair(A,B))|X!=B.
% 1.72/1.90 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 1.72/1.90 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 1.72/1.90 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 1.72/1.90 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 1.72/1.90 0 [] member(X,product(A))|member($f3(X,A),A).
% 1.72/1.90 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 1.72/1.90 0 [] -e_qual_set(sum(empty_set),empty_set).
% 1.72/1.90 end_of_list.
% 1.72/1.90
% 1.72/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.90
% 1.72/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.90 deletion, with positive clauses in sos and nonpositive
% 1.72/1.90 clauses in usable.
% 1.72/1.90
% 1.72/1.90 dependent: set(knuth_bendix).
% 1.72/1.90 dependent: set(anl_eq).
% 1.72/1.90 dependent: set(para_from).
% 1.72/1.90 dependent: set(para_into).
% 1.72/1.90 dependent: clear(para_from_right).
% 1.72/1.90 dependent: clear(para_into_right).
% 1.72/1.90 dependent: set(para_from_vars).
% 1.72/1.90 dependent: set(eq_units_both_ways).
% 1.72/1.90 dependent: set(dynamic_demod_all).
% 1.72/1.90 dependent: set(dynamic_demod).
% 1.72/1.90 dependent: set(order_eq).
% 1.72/1.90 dependent: set(back_demod).
% 1.72/1.90 dependent: set(lrpo).
% 1.72/1.90 dependent: set(hyper_res).
% 1.72/1.90 dependent: set(unit_deletion).
% 1.72/1.90 dependent: set(factor).
% 1.72/1.90
% 1.72/1.90 ------------> process usable:
% 1.72/1.90 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.72/1.90 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.72/1.90 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 1.72/1.90 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 1.72/1.90 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.72/1.90 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 1.72/1.90 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 1.72/1.90 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 1.72/1.90 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 4.16/4.33 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 4.16/4.33 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 4.16/4.33 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 4.16/4.33 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 4.16/4.33 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 4.16/4.33 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 4.16/4.33 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 4.16/4.33 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 4.16/4.33 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 4.16/4.33 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 4.16/4.33 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 4.16/4.33 ** KEPT (pick-wt=4): 28 [] -e_qual_set(sum(empty_set),empty_set).
% 4.16/4.33
% 4.16/4.33 ------------> process sos:
% 4.16/4.33 ** KEPT (pick-wt=3): 34 [] A=A.
% 4.16/4.33 ** KEPT (pick-wt=8): 35 [] subset(A,B)|member($f1(A,B),A).
% 4.16/4.33 ** KEPT (pick-wt=9): 36 [] member(A,product(B))|member($f3(A,B),B).
% 4.16/4.33 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 4.16/4.33
% 4.16/4.33 ======= end of input processing =======
% 4.16/4.33
% 4.16/4.33 =========== start of search ===========
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Resetting weight limit to 8.
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Resetting weight limit to 8.
% 4.16/4.33
% 4.16/4.33 sos_size=648
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Resetting weight limit to 7.
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Resetting weight limit to 7.
% 4.16/4.33
% 4.16/4.33 sos_size=698
% 4.16/4.33
% 4.16/4.33 -------- PROOF --------
% 4.16/4.33
% 4.16/4.33 ----> UNIT CONFLICT at 2.43 sec ----> 1007 [binary,1006.1,28.1] $F.
% 4.16/4.33
% 4.16/4.33 Length of proof is 22. Level of proof is 14.
% 4.16/4.33
% 4.16/4.33 ---------------- PROOF ----------------
% 4.16/4.33 % SZS status Theorem
% 4.16/4.33 % SZS output start Refutation
% See solution above
% 4.16/4.33 ------------ end of proof -------------
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Search stopped by max_proofs option.
% 4.16/4.33
% 4.16/4.33
% 4.16/4.33 Search stopped by max_proofs option.
% 4.16/4.33
% 4.16/4.33 ============ end of search ============
% 4.16/4.33
% 4.16/4.33 -------------- statistics -------------
% 4.16/4.33 clauses given 668
% 4.16/4.33 clauses generated 651853
% 4.16/4.33 clauses kept 1004
% 4.16/4.33 clauses forward subsumed 26970
% 4.16/4.33 clauses back subsumed 47
% 4.16/4.33 Kbytes malloced 10742
% 4.16/4.33
% 4.16/4.33 ----------- times (seconds) -----------
% 4.16/4.33 user CPU time 2.43 (0 hr, 0 min, 2 sec)
% 4.16/4.33 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.16/4.33 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.16/4.33
% 4.16/4.33 That finishes the proof of the theorem.
% 4.16/4.33
% 4.16/4.33 Process 18823 finished Wed Jul 27 10:45:57 2022
% 4.16/4.33 Otter interrupted
% 4.16/4.33 PROOF FOUND
%------------------------------------------------------------------------------