%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET705+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:14:07 EDT 2022
% Result : Theorem 2.63s 2.37s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 5 unt; 3 nHn; 7 RR)
% Number of literals : 22 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET705+4.p',unknown),
[] ).
cnf(4,axiom,
( ~ e_qual_set(A,B)
| subset(B,A) ),
file('SET705+4.p',unknown),
[] ).
cnf(5,axiom,
( e_qual_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET705+4.p',unknown),
[] ).
cnf(7,axiom,
( member(A,power_set(B))
| ~ subset(A,B) ),
file('SET705+4.p',unknown),
[] ).
cnf(28,axiom,
~ member(dollar_c1,power_set(dollar_c1)),
file('SET705+4.p',unknown),
[] ).
cnf(29,plain,
( e_qual_set(A,A)
| ~ subset(A,A) ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.2.3')] ).
cnf(35,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET705+4.p',unknown),
[] ).
cnf(112,plain,
( member(dollar_f1(A,A),A)
| e_qual_set(A,A) ),
inference(hyper,[status(thm)],[35,29]),
[iquote('hyper,35,29')] ).
cnf(827,plain,
( e_qual_set(A,A)
| subset(A,A) ),
inference(hyper,[status(thm)],[112,2]),
[iquote('hyper,112,2')] ).
cnf(847,plain,
e_qual_set(A,A),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[827,29])]),
[iquote('hyper,827,29,factor_simp')] ).
cnf(848,plain,
subset(A,A),
inference(hyper,[status(thm)],[847,4]),
[iquote('hyper,847,4')] ).
cnf(849,plain,
member(A,power_set(A)),
inference(hyper,[status(thm)],[848,7]),
[iquote('hyper,848,7')] ).
cnf(850,plain,
$false,
inference(binary,[status(thm)],[849,28]),
[iquote('binary,849.1,28.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET705+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n015.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 10:40:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.41/2.17 ----- Otter 3.3f, August 2004 -----
% 2.41/2.17 The process was started by sandbox2 on n015.cluster.edu,
% 2.41/2.17 Wed Jul 27 10:40:42 2022
% 2.41/2.17 The command was "./otter". The process ID is 31669.
% 2.41/2.17
% 2.41/2.17 set(prolog_style_variables).
% 2.41/2.17 set(auto).
% 2.41/2.17 dependent: set(auto1).
% 2.41/2.17 dependent: set(process_input).
% 2.41/2.17 dependent: clear(print_kept).
% 2.41/2.17 dependent: clear(print_new_demod).
% 2.41/2.17 dependent: clear(print_back_demod).
% 2.41/2.17 dependent: clear(print_back_sub).
% 2.41/2.17 dependent: set(control_memory).
% 2.41/2.17 dependent: assign(max_mem, 12000).
% 2.41/2.17 dependent: assign(pick_given_ratio, 4).
% 2.41/2.17 dependent: assign(stats_level, 1).
% 2.41/2.17 dependent: assign(max_seconds, 10800).
% 2.41/2.17 clear(print_given).
% 2.41/2.17
% 2.41/2.17 formula_list(usable).
% 2.41/2.17 all A (A=A).
% 2.41/2.17 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 2.41/2.17 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 2.41/2.17 all X A (member(X,power_set(A))<->subset(X,A)).
% 2.41/2.17 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 2.41/2.17 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 2.41/2.17 all X (-member(X,empty_set)).
% 2.41/2.17 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 2.41/2.17 all X A (member(X,singleton(A))<->X=A).
% 2.41/2.17 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 2.41/2.17 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 2.41/2.17 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 2.41/2.17 -(all A member(A,power_set(A))).
% 2.41/2.17 end_of_list.
% 2.41/2.17
% 2.41/2.17 -------> usable clausifies to:
% 2.41/2.17
% 2.41/2.17 list(usable).
% 2.41/2.17 0 [] A=A.
% 2.41/2.17 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 2.41/2.17 0 [] subset(A,B)|member($f1(A,B),A).
% 2.41/2.17 0 [] subset(A,B)| -member($f1(A,B),B).
% 2.41/2.17 0 [] -e_qual_set(A,B)|subset(A,B).
% 2.41/2.17 0 [] -e_qual_set(A,B)|subset(B,A).
% 2.41/2.17 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.41/2.17 0 [] -member(X,power_set(A))|subset(X,A).
% 2.41/2.17 0 [] member(X,power_set(A))| -subset(X,A).
% 2.41/2.17 0 [] -member(X,intersection(A,B))|member(X,A).
% 2.41/2.17 0 [] -member(X,intersection(A,B))|member(X,B).
% 2.41/2.17 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 2.41/2.17 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 2.41/2.17 0 [] member(X,union(A,B))| -member(X,A).
% 2.41/2.17 0 [] member(X,union(A,B))| -member(X,B).
% 2.41/2.17 0 [] -member(X,empty_set).
% 2.41/2.17 0 [] -member(B,difference(E,A))|member(B,E).
% 2.41/2.17 0 [] -member(B,difference(E,A))| -member(B,A).
% 2.41/2.17 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 2.41/2.17 0 [] -member(X,singleton(A))|X=A.
% 2.41/2.17 0 [] member(X,singleton(A))|X!=A.
% 2.41/2.17 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 2.41/2.17 0 [] member(X,unordered_pair(A,B))|X!=A.
% 2.41/2.17 0 [] member(X,unordered_pair(A,B))|X!=B.
% 2.41/2.17 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 2.41/2.17 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 2.41/2.17 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 2.41/2.17 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 2.41/2.17 0 [] member(X,product(A))|member($f3(X,A),A).
% 2.41/2.17 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 2.41/2.17 0 [] -member($c1,power_set($c1)).
% 2.41/2.17 end_of_list.
% 2.41/2.17
% 2.41/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.41/2.17
% 2.41/2.17 This ia a non-Horn set with equality. The strategy will be
% 2.41/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.41/2.17 deletion, with positive clauses in sos and nonpositive
% 2.41/2.17 clauses in usable.
% 2.41/2.17
% 2.41/2.17 dependent: set(knuth_bendix).
% 2.41/2.17 dependent: set(anl_eq).
% 2.41/2.17 dependent: set(para_from).
% 2.41/2.17 dependent: set(para_into).
% 2.41/2.17 dependent: clear(para_from_right).
% 2.41/2.17 dependent: clear(para_into_right).
% 2.41/2.17 dependent: set(para_from_vars).
% 2.41/2.17 dependent: set(eq_units_both_ways).
% 2.41/2.17 dependent: set(dynamic_demod_all).
% 2.41/2.17 dependent: set(dynamic_demod).
% 2.41/2.17 dependent: set(order_eq).
% 2.41/2.17 dependent: set(back_demod).
% 2.41/2.17 dependent: set(lrpo).
% 2.41/2.17 dependent: set(hyper_res).
% 2.41/2.17 dependent: set(unit_deletion).
% 2.41/2.17 dependent: set(factor).
% 2.41/2.17
% 2.41/2.17 ------------> process usable:
% 2.41/2.17 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.41/2.17 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 2.41/2.17 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 2.41/2.17 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 2.41/2.17 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.41/2.17 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 2.41/2.17 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 2.41/2.17 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 2.41/2.17 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 2.41/2.17 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.63/2.36 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.63/2.36 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 2.63/2.36 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 2.63/2.36 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 2.63/2.36 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 2.63/2.36 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 2.63/2.36 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 2.63/2.36 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 2.63/2.36 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 2.63/2.36 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.63/2.36 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 2.63/2.36 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 2.63/2.36 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 2.63/2.36 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 2.63/2.36 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 2.63/2.37 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 2.63/2.37 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 2.63/2.37 ** KEPT (pick-wt=4): 28 [] -member($c1,power_set($c1)).
% 2.63/2.37
% 2.63/2.37 ------------> process sos:
% 2.63/2.37 ** KEPT (pick-wt=3): 34 [] A=A.
% 2.63/2.37 ** KEPT (pick-wt=8): 35 [] subset(A,B)|member($f1(A,B),A).
% 2.63/2.37 ** KEPT (pick-wt=9): 36 [] member(A,product(B))|member($f3(A,B),B).
% 2.63/2.37 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 2.63/2.37
% 2.63/2.37 ======= end of input processing =======
% 2.63/2.37
% 2.63/2.37 =========== start of search ===========
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Resetting weight limit to 8.
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Resetting weight limit to 8.
% 2.63/2.37
% 2.63/2.37 sos_size=649
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Resetting weight limit to 7.
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Resetting weight limit to 7.
% 2.63/2.37
% 2.63/2.37 sos_size=699
% 2.63/2.37
% 2.63/2.37 -------- PROOF --------
% 2.63/2.37
% 2.63/2.37 ----> UNIT CONFLICT at 0.19 sec ----> 850 [binary,849.1,28.1] $F.
% 2.63/2.37
% 2.63/2.37 Length of proof is 6. Level of proof is 6.
% 2.63/2.37
% 2.63/2.37 ---------------- PROOF ----------------
% 2.63/2.37 % SZS status Theorem
% 2.63/2.37 % SZS output start Refutation
% See solution above
% 2.63/2.37 ------------ end of proof -------------
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Search stopped by max_proofs option.
% 2.63/2.37
% 2.63/2.37
% 2.63/2.37 Search stopped by max_proofs option.
% 2.63/2.37
% 2.63/2.37 ============ end of search ============
% 2.63/2.37
% 2.63/2.37 -------------- statistics -------------
% 2.63/2.37 clauses given 160
% 2.63/2.37 clauses generated 24689
% 2.63/2.37 clauses kept 849
% 2.63/2.37 clauses forward subsumed 4063
% 2.63/2.37 clauses back subsumed 18
% 2.63/2.37 Kbytes malloced 6835
% 2.63/2.37
% 2.63/2.37 ----------- times (seconds) -----------
% 2.63/2.37 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 2.63/2.37 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.63/2.37 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.63/2.37
% 2.63/2.37 That finishes the proof of the theorem.
% 2.63/2.37
% 2.63/2.37 Process 31669 finished Wed Jul 27 10:40:44 2022
% 2.63/2.37 Otter interrupted
% 2.63/2.37 PROOF FOUND
%------------------------------------------------------------------------------