TSTP Solution File: SET095+4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:13:05 EDT 2022
% Result : Theorem 2.10s 2.26s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 1 nHn; 7 RR)
% Number of literals : 11 ( 2 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET095+4.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(A,singleton(B))
| A = B ),
file('SET095+4.p',unknown),
[] ).
cnf(28,axiom,
~ subset(singleton(dollar_c1),dollar_c2),
file('SET095+4.p',unknown),
[] ).
cnf(35,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET095+4.p',unknown),
[] ).
cnf(37,axiom,
member(dollar_c1,dollar_c2),
file('SET095+4.p',unknown),
[] ).
cnf(104,plain,
member(dollar_f1(singleton(dollar_c1),dollar_c2),singleton(dollar_c1)),
inference(hyper,[status(thm)],[35,28]),
[iquote('hyper,35,28')] ).
cnf(979,plain,
dollar_f1(singleton(dollar_c1),dollar_c2) = dollar_c1,
inference(hyper,[status(thm)],[104,18]),
[iquote('hyper,104,18')] ).
cnf(982,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[979,2]),28,37]),
[iquote('para_from,979.1.1,2.2.1,unit_del,28,37')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 10:50:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.17 ----- Otter 3.3f, August 2004 -----
% 2.00/2.17 The process was started by sandbox2 on n020.cluster.edu,
% 2.00/2.17 Wed Jul 27 10:50:08 2022
% 2.00/2.17 The command was "./otter". The process ID is 26924.
% 2.00/2.17
% 2.00/2.17 set(prolog_style_variables).
% 2.00/2.17 set(auto).
% 2.00/2.17 dependent: set(auto1).
% 2.00/2.17 dependent: set(process_input).
% 2.00/2.17 dependent: clear(print_kept).
% 2.00/2.17 dependent: clear(print_new_demod).
% 2.00/2.17 dependent: clear(print_back_demod).
% 2.00/2.17 dependent: clear(print_back_sub).
% 2.00/2.17 dependent: set(control_memory).
% 2.00/2.17 dependent: assign(max_mem, 12000).
% 2.00/2.17 dependent: assign(pick_given_ratio, 4).
% 2.00/2.17 dependent: assign(stats_level, 1).
% 2.00/2.17 dependent: assign(max_seconds, 10800).
% 2.00/2.17 clear(print_given).
% 2.00/2.17
% 2.00/2.17 formula_list(usable).
% 2.00/2.17 all A (A=A).
% 2.00/2.17 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 2.00/2.17 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 2.00/2.17 all X A (member(X,power_set(A))<->subset(X,A)).
% 2.00/2.17 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 2.00/2.17 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 2.00/2.17 all X (-member(X,empty_set)).
% 2.00/2.17 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 2.00/2.17 all X A (member(X,singleton(A))<->X=A).
% 2.00/2.17 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 2.00/2.17 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 2.00/2.17 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 2.00/2.17 -(all A X (member(X,A)->subset(singleton(X),A))).
% 2.00/2.17 end_of_list.
% 2.00/2.17
% 2.00/2.17 -------> usable clausifies to:
% 2.00/2.17
% 2.00/2.17 list(usable).
% 2.00/2.17 0 [] A=A.
% 2.00/2.17 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 2.00/2.17 0 [] subset(A,B)|member($f1(A,B),A).
% 2.00/2.17 0 [] subset(A,B)| -member($f1(A,B),B).
% 2.00/2.17 0 [] -e_qual_set(A,B)|subset(A,B).
% 2.00/2.17 0 [] -e_qual_set(A,B)|subset(B,A).
% 2.00/2.17 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.00/2.17 0 [] -member(X,power_set(A))|subset(X,A).
% 2.00/2.17 0 [] member(X,power_set(A))| -subset(X,A).
% 2.00/2.17 0 [] -member(X,intersection(A,B))|member(X,A).
% 2.00/2.17 0 [] -member(X,intersection(A,B))|member(X,B).
% 2.00/2.17 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 2.00/2.17 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 2.00/2.17 0 [] member(X,union(A,B))| -member(X,A).
% 2.00/2.17 0 [] member(X,union(A,B))| -member(X,B).
% 2.00/2.17 0 [] -member(X,empty_set).
% 2.00/2.17 0 [] -member(B,difference(E,A))|member(B,E).
% 2.00/2.17 0 [] -member(B,difference(E,A))| -member(B,A).
% 2.00/2.17 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 2.00/2.17 0 [] -member(X,singleton(A))|X=A.
% 2.00/2.17 0 [] member(X,singleton(A))|X!=A.
% 2.00/2.17 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 2.00/2.17 0 [] member(X,unordered_pair(A,B))|X!=A.
% 2.00/2.17 0 [] member(X,unordered_pair(A,B))|X!=B.
% 2.00/2.17 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 2.00/2.17 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 2.00/2.17 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 2.00/2.17 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 2.00/2.17 0 [] member(X,product(A))|member($f3(X,A),A).
% 2.00/2.17 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 2.00/2.17 0 [] member($c1,$c2).
% 2.00/2.17 0 [] -subset(singleton($c1),$c2).
% 2.00/2.17 end_of_list.
% 2.00/2.17
% 2.00/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.00/2.17
% 2.00/2.17 This ia a non-Horn set with equality. The strategy will be
% 2.00/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.00/2.17 deletion, with positive clauses in sos and nonpositive
% 2.00/2.17 clauses in usable.
% 2.00/2.17
% 2.00/2.17 dependent: set(knuth_bendix).
% 2.00/2.17 dependent: set(anl_eq).
% 2.00/2.17 dependent: set(para_from).
% 2.00/2.17 dependent: set(para_into).
% 2.00/2.17 dependent: clear(para_from_right).
% 2.00/2.17 dependent: clear(para_into_right).
% 2.00/2.17 dependent: set(para_from_vars).
% 2.00/2.17 dependent: set(eq_units_both_ways).
% 2.00/2.17 dependent: set(dynamic_demod_all).
% 2.00/2.17 dependent: set(dynamic_demod).
% 2.00/2.17 dependent: set(order_eq).
% 2.00/2.17 dependent: set(back_demod).
% 2.00/2.17 dependent: set(lrpo).
% 2.00/2.17 dependent: set(hyper_res).
% 2.00/2.17 dependent: set(unit_deletion).
% 2.00/2.17 dependent: set(factor).
% 2.00/2.17
% 2.00/2.17 ------------> process usable:
% 2.00/2.17 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.00/2.17 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 2.00/2.17 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 2.00/2.17 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 2.00/2.17 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.00/2.17 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 2.00/2.17 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 2.00/2.17 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 2.00/2.17 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 2.10/2.26 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 2.10/2.26 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 2.10/2.26 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 2.10/2.26 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 2.10/2.26 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.10/2.26 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 2.10/2.26 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 2.10/2.26 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 2.10/2.26 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 2.10/2.26 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 2.10/2.26 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 2.10/2.26 ** KEPT (pick-wt=4): 28 [] -subset(singleton($c1),$c2).
% 2.10/2.26
% 2.10/2.26 ------------> process sos:
% 2.10/2.26 ** KEPT (pick-wt=3): 34 [] A=A.
% 2.10/2.26 ** KEPT (pick-wt=8): 35 [] subset(A,B)|member($f1(A,B),A).
% 2.10/2.26 ** KEPT (pick-wt=9): 36 [] member(A,product(B))|member($f3(A,B),B).
% 2.10/2.26 ** KEPT (pick-wt=3): 37 [] member($c1,$c2).
% 2.10/2.26 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 2.10/2.26
% 2.10/2.26 ======= end of input processing =======
% 2.10/2.26
% 2.10/2.26 =========== start of search ===========
% 2.10/2.26
% 2.10/2.26
% 2.10/2.26 Resetting weight limit to 7.
% 2.10/2.26
% 2.10/2.26
% 2.10/2.26 Resetting weight limit to 7.
% 2.10/2.26
% 2.10/2.26 sos_size=867
% 2.10/2.26
% 2.10/2.26 -------- PROOF --------
% 2.10/2.26
% 2.10/2.26 -----> EMPTY CLAUSE at 0.10 sec ----> 982 [para_from,979.1.1,2.2.1,unit_del,28,37] $F.
% 2.10/2.26
% 2.10/2.26 Length of proof is 2. Level of proof is 2.
% 2.10/2.26
% 2.10/2.26 ---------------- PROOF ----------------
% 2.10/2.26 % SZS status Theorem
% 2.10/2.26 % SZS output start Refutation
% See solution above
% 2.10/2.26 ------------ end of proof -------------
% 2.10/2.26
% 2.10/2.26
% 2.10/2.26 Search stopped by max_proofs option.
% 2.10/2.26
% 2.10/2.26
% 2.10/2.26 Search stopped by max_proofs option.
% 2.10/2.26
% 2.10/2.26 ============ end of search ============
% 2.10/2.26
% 2.10/2.26 -------------- statistics -------------
% 2.10/2.26 clauses given 77
% 2.10/2.26 clauses generated 7025
% 2.10/2.26 clauses kept 980
% 2.10/2.26 clauses forward subsumed 1227
% 2.10/2.26 clauses back subsumed 10
% 2.10/2.26 Kbytes malloced 4882
% 2.10/2.26
% 2.10/2.26 ----------- times (seconds) -----------
% 2.10/2.26 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 2.10/2.26 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.10/2.26 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.10/2.26
% 2.10/2.26 That finishes the proof of the theorem.
% 2.10/2.26
% 2.10/2.26 Process 26924 finished Wed Jul 27 10:50:10 2022
% 2.10/2.26 Otter interrupted
% 2.10/2.26 PROOF FOUND
%------------------------------------------------------------------------------