TSTP Solution File: SET799+4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET799+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:14:16 EDT 2022
% Result : Theorem 1.93s 2.12s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 19 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 15 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET799+4.p',unknown),
[] ).
cnf(77,axiom,
( ~ upper_bound(A,B,C)
| ~ member(D,C)
| apply(B,D,A) ),
file('SET799+4.p',unknown),
[] ).
cnf(101,axiom,
( ~ least_upper_bound(A,B,C,D)
| member(A,B) ),
file('SET799+4.p',unknown),
[] ).
cnf(102,axiom,
( ~ least_upper_bound(A,B,C,D)
| upper_bound(A,C,B) ),
file('SET799+4.p',unknown),
[] ).
cnf(113,axiom,
~ apply(dollar_c6,dollar_c2,dollar_c1),
file('SET799+4.p',unknown),
[] ).
cnf(149,axiom,
subset(dollar_c4,dollar_c3),
file('SET799+4.p',unknown),
[] ).
cnf(150,axiom,
least_upper_bound(dollar_c2,dollar_c4,dollar_c6,dollar_c5),
file('SET799+4.p',unknown),
[] ).
cnf(151,axiom,
least_upper_bound(dollar_c1,dollar_c3,dollar_c6,dollar_c5),
file('SET799+4.p',unknown),
[] ).
cnf(508,plain,
member(dollar_c2,dollar_c4),
inference(hyper,[status(thm)],[150,101]),
[iquote('hyper,150,101')] ).
cnf(560,plain,
member(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[508,1,149]),
[iquote('hyper,508,1,149')] ).
cnf(849,plain,
upper_bound(dollar_c1,dollar_c6,dollar_c3),
inference(hyper,[status(thm)],[151,102]),
[iquote('hyper,151,102')] ).
cnf(930,plain,
apply(dollar_c6,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[849,77,560]),
[iquote('hyper,849,77,560')] ).
cnf(931,plain,
$false,
inference(binary,[status(thm)],[930,113]),
[iquote('binary,930.1,113.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET799+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:52:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.02 ----- Otter 3.3f, August 2004 -----
% 1.80/2.02 The process was started by sandbox on n012.cluster.edu,
% 1.80/2.02 Wed Jul 27 10:52:35 2022
% 1.80/2.02 The command was "./otter". The process ID is 10587.
% 1.80/2.02
% 1.80/2.02 set(prolog_style_variables).
% 1.80/2.02 set(auto).
% 1.80/2.02 dependent: set(auto1).
% 1.80/2.02 dependent: set(process_input).
% 1.80/2.02 dependent: clear(print_kept).
% 1.80/2.02 dependent: clear(print_new_demod).
% 1.80/2.02 dependent: clear(print_back_demod).
% 1.80/2.02 dependent: clear(print_back_sub).
% 1.80/2.02 dependent: set(control_memory).
% 1.80/2.02 dependent: assign(max_mem, 12000).
% 1.80/2.02 dependent: assign(pick_given_ratio, 4).
% 1.80/2.02 dependent: assign(stats_level, 1).
% 1.80/2.02 dependent: assign(max_seconds, 10800).
% 1.80/2.02 clear(print_given).
% 1.80/2.02
% 1.80/2.02 formula_list(usable).
% 1.80/2.02 all A (A=A).
% 1.80/2.02 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 1.80/2.02 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 1.80/2.02 all X A (member(X,power_set(A))<->subset(X,A)).
% 1.80/2.02 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 1.80/2.02 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 1.80/2.02 all X (-member(X,empty_set)).
% 1.80/2.02 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 1.80/2.02 all X A (member(X,singleton(A))<->X=A).
% 1.80/2.02 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 1.80/2.02 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 1.80/2.02 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 1.80/2.02 all R E (order(R,E)<-> (all X (member(X,E)->apply(R,X,X)))& (all X Y (member(X,E)&member(Y,E)-> (apply(R,X,Y)&apply(R,Y,X)->X=Y)))& (all X Y Z (member(X,E)&member(Y,E)&member(Z,E)-> (apply(R,X,Y)&apply(R,Y,Z)->apply(R,X,Z))))).
% 1.80/2.02 all R E (total_order(R,E)<->order(R,E)& (all X Y (member(X,E)&member(Y,E)->apply(R,X,Y)|apply(R,Y,X)))).
% 1.80/2.02 all R E M (upper_bound(M,R,E)<-> (all X (member(X,E)->apply(R,X,M)))).
% 1.80/2.02 all R E M (lower_bound(M,R,E)<-> (all X (member(X,E)->apply(R,M,X)))).
% 1.80/2.02 all R E M (greatest(M,R,E)<->member(M,E)& (all X (member(X,E)->apply(R,X,M)))).
% 1.80/2.02 all R E M (least(M,R,E)<->member(M,E)& (all X (member(X,E)->apply(R,M,X)))).
% 1.80/2.02 all R E M (max(M,R,E)<->member(M,E)& (all X (member(X,E)&apply(R,M,X)->M=X))).
% 1.80/2.02 all R E M (min(M,R,E)<->member(M,E)& (all X (member(X,E)&apply(R,X,M)->M=X))).
% 1.80/2.02 all A X R E (least_upper_bound(A,X,R,E)<->member(A,X)&upper_bound(A,R,X)& (all M (member(M,E)&upper_bound(M,R,X)->apply(R,A,M)))).
% 1.80/2.02 all A X R E (greatest_lower_bound(A,X,R,E)<->member(A,X)&lower_bound(A,R,X)& (all M (member(M,E)&lower_bound(M,R,X)->apply(R,M,A)))).
% 1.80/2.02 -(all R E (order(R,E)-> (all X1 X2 (subset(X1,E)&subset(X2,E)&subset(X1,X2)-> (all M1 M2 (least_upper_bound(M1,X1,R,E)&least_upper_bound(M2,X2,R,E)->apply(R,M1,M2))))))).
% 1.80/2.02 end_of_list.
% 1.80/2.02
% 1.80/2.02 -------> usable clausifies to:
% 1.80/2.02
% 1.80/2.02 list(usable).
% 1.80/2.02 0 [] A=A.
% 1.80/2.02 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 1.80/2.02 0 [] subset(A,B)|member($f1(A,B),A).
% 1.80/2.02 0 [] subset(A,B)| -member($f1(A,B),B).
% 1.80/2.02 0 [] -e_qual_set(A,B)|subset(A,B).
% 1.80/2.02 0 [] -e_qual_set(A,B)|subset(B,A).
% 1.80/2.02 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.80/2.02 0 [] -member(X,power_set(A))|subset(X,A).
% 1.80/2.02 0 [] member(X,power_set(A))| -subset(X,A).
% 1.80/2.02 0 [] -member(X,intersection(A,B))|member(X,A).
% 1.80/2.02 0 [] -member(X,intersection(A,B))|member(X,B).
% 1.80/2.02 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 1.80/2.02 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 1.80/2.02 0 [] member(X,union(A,B))| -member(X,A).
% 1.80/2.02 0 [] member(X,union(A,B))| -member(X,B).
% 1.80/2.02 0 [] -member(X,empty_set).
% 1.80/2.02 0 [] -member(B,difference(E,A))|member(B,E).
% 1.80/2.02 0 [] -member(B,difference(E,A))| -member(B,A).
% 1.80/2.02 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 1.80/2.02 0 [] -member(X,singleton(A))|X=A.
% 1.80/2.02 0 [] member(X,singleton(A))|X!=A.
% 1.80/2.02 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 1.80/2.02 0 [] member(X,unordered_pair(A,B))|X!=A.
% 1.80/2.02 0 [] member(X,unordered_pair(A,B))|X!=B.
% 1.80/2.02 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 1.80/2.02 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 1.80/2.02 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 1.80/2.02 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 1.80/2.02 0 [] member(X,product(A))|member($f3(X,A),A).
% 1.80/2.02 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 1.80/2.02 0 [] -order(R,E)| -member(X,E)|apply(R,X,X).
% 1.80/2.02 0 [] -order(R,E)| -member(X3,E)| -member(Y,E)| -apply(R,X3,Y)| -apply(R,Y,X3)|X3=Y.
% 1.80/2.02 0 [] -order(R,E)| -member(X4,E)| -member(X5,E)| -member(Z,E)| -apply(R,X4,X5)| -apply(R,X5,Z)|apply(R,X4,Z).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f6(R,E),E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|member($f5(R,E),E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f6(R,E),$f5(R,E))| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|apply(R,$f5(R,E),$f6(R,E))| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)|member($f4(R,E),E)|$f6(R,E)!=$f5(R,E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f6(R,E),E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|member($f5(R,E),E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))|member($f9(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))|member($f8(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))|member($f7(R,E),E).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f6(R,E),$f5(R,E))| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.02 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))|member($f9(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))|member($f8(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))|member($f7(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|apply(R,$f5(R,E),$f6(R,E))| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)|member($f9(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)|member($f8(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)|member($f7(R,E),E).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)|apply(R,$f9(R,E),$f8(R,E)).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)|apply(R,$f8(R,E),$f7(R,E)).
% 1.80/2.03 0 [] order(R,E)| -apply(R,$f4(R,E),$f4(R,E))|$f6(R,E)!=$f5(R,E)| -apply(R,$f9(R,E),$f7(R,E)).
% 1.80/2.03 0 [] -total_order(R,E)|order(R,E).
% 1.80/2.03 0 [] -total_order(R,E)| -member(X,E)| -member(Y,E)|apply(R,X,Y)|apply(R,Y,X).
% 1.80/2.03 0 [] total_order(R,E)| -order(R,E)|member($f11(R,E),E).
% 1.80/2.03 0 [] total_order(R,E)| -order(R,E)|member($f10(R,E),E).
% 1.80/2.03 0 [] total_order(R,E)| -order(R,E)| -apply(R,$f11(R,E),$f10(R,E)).
% 1.80/2.03 0 [] total_order(R,E)| -order(R,E)| -apply(R,$f10(R,E),$f11(R,E)).
% 1.80/2.03 0 [] -upper_bound(M,R,E)| -member(X,E)|apply(R,X,M).
% 1.80/2.03 0 [] upper_bound(M,R,E)|member($f12(R,E,M),E).
% 1.80/2.03 0 [] upper_bound(M,R,E)| -apply(R,$f12(R,E,M),M).
% 1.80/2.03 0 [] -lower_bound(M,R,E)| -member(X,E)|apply(R,M,X).
% 1.80/2.03 0 [] lower_bound(M,R,E)|member($f13(R,E,M),E).
% 1.80/2.03 0 [] lower_bound(M,R,E)| -apply(R,M,$f13(R,E,M)).
% 1.80/2.03 0 [] -greatest(M,R,E)|member(M,E).
% 1.80/2.03 0 [] -greatest(M,R,E)| -member(X,E)|apply(R,X,M).
% 1.80/2.03 0 [] greatest(M,R,E)| -member(M,E)|member($f14(R,E,M),E).
% 1.80/2.03 0 [] greatest(M,R,E)| -member(M,E)| -apply(R,$f14(R,E,M),M).
% 1.80/2.03 0 [] -least(M,R,E)|member(M,E).
% 1.80/2.03 0 [] -least(M,R,E)| -member(X,E)|apply(R,M,X).
% 1.80/2.03 0 [] least(M,R,E)| -member(M,E)|member($f15(R,E,M),E).
% 1.80/2.03 0 [] least(M,R,E)| -member(M,E)| -apply(R,M,$f15(R,E,M)).
% 1.80/2.03 0 [] -max(M,R,E)|member(M,E).
% 1.80/2.03 0 [] -max(M,R,E)| -member(X,E)| -apply(R,M,X)|M=X.
% 1.80/2.03 0 [] max(M,R,E)| -member(M,E)|member($f16(R,E,M),E).
% 1.80/2.03 0 [] max(M,R,E)| -member(M,E)|apply(R,M,$f16(R,E,M)).
% 1.80/2.03 0 [] max(M,R,E)| -member(M,E)|M!=$f16(R,E,M).
% 1.80/2.03 0 [] -min(M,R,E)|member(M,E).
% 1.80/2.03 0 [] -min(M,R,E)| -member(X,E)| -apply(R,X,M)|M=X.
% 1.80/2.03 0 [] min(M,R,E)| -member(M,E)|member($f17(R,E,M),E).
% 1.80/2.03 0 [] min(M,R,E)| -member(M,E)|apply(R,$f17(R,E,M),M).
% 1.80/2.03 0 [] min(M,R,E)| -member(M,E)|M!=$f17(R,E,M).
% 1.80/2.03 0 [] -least_upper_bound(A,X,R,E)|member(A,X).
% 1.80/2.03 0 [] -least_upper_bound(A,X,R,E)|upper_bound(A,R,X).
% 1.80/2.03 0 [] -least_upper_bound(A,X,R,E)| -member(M,E)| -upper_bound(M,R,X)|apply(R,A,M).
% 1.80/2.03 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)|member($f18(A,X,R,E),E).
% 1.80/2.03 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)|upper_bound($f18(A,X,R,E),R,X).
% 1.80/2.03 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)| -apply(R,A,$f18(A,X,R,E)).
% 1.80/2.03 0 [] -greatest_lower_bound(A,X,R,E)|member(A,X).
% 1.80/2.03 0 [] -greatest_lower_bound(A,X,R,E)|lower_bound(A,R,X).
% 1.80/2.03 0 [] -greatest_lower_bound(A,X,R,E)| -member(M,E)| -lower_bound(M,R,X)|apply(R,M,A).
% 1.80/2.03 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)|member($f19(A,X,R,E),E).
% 1.80/2.03 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)|lower_bound($f19(A,X,R,E),R,X).
% 1.80/2.03 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)| -apply(R,$f19(A,X,R,E),A).
% 1.80/2.03 0 [] order($c6,$c5).
% 1.80/2.03 0 [] subset($c4,$c5).
% 1.80/2.03 0 [] subset($c3,$c5).
% 1.80/2.03 0 [] subset($c4,$c3).
% 1.80/2.03 0 [] least_upper_bound($c2,$c4,$c6,$c5).
% 1.80/2.03 0 [] least_upper_bound($c1,$c3,$c6,$c5).
% 1.80/2.03 0 [] -apply($c6,$c2,$c1).
% 1.80/2.03 end_of_list.
% 1.80/2.03
% 1.80/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.80/2.03
% 1.80/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.80/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/2.03 deletion, with positive clauses in sos and nonpositive
% 1.80/2.03 clauses in usable.
% 1.80/2.03
% 1.80/2.03 dependent: set(knuth_bendix).
% 1.80/2.03 dependent: set(anl_eq).
% 1.80/2.03 dependent: set(para_from).
% 1.80/2.03 dependent: set(para_into).
% 1.80/2.03 dependent: clear(para_from_right).
% 1.80/2.03 dependent: clear(para_into_right).
% 1.80/2.03 dependent: set(para_from_vars).
% 1.80/2.03 dependent: set(eq_units_both_ways).
% 1.80/2.03 dependent: set(dynamic_demod_all).
% 1.80/2.03 dependent: set(dynamic_demod).
% 1.80/2.03 dependent: set(order_eq).
% 1.80/2.03 dependent: set(back_demod).
% 1.80/2.03 dependent: set(lrpo).
% 1.80/2.03 dependent: set(hyper_res).
% 1.80/2.03 dependent: set(unit_deletion).
% 1.80/2.03 dependent: set(factor).
% 1.80/2.03
% 1.80/2.03 ------------> process usable:
% 1.80/2.03 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 1.80/2.03 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.80/2.03 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 1.80/2.03 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 1.80/2.03 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 1.80/2.03 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 1.80/2.03 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.80/2.03 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 1.80/2.03 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 1.80/2.03 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=10): 28 [] -order(A,B)| -member(C,B)|apply(A,C,C).
% 1.80/2.03 ** KEPT (pick-wt=20): 29 [] -order(A,B)| -member(C,B)| -member(D,B)| -apply(A,C,D)| -apply(A,D,C)|C=D.
% 1.80/2.03 ** KEPT (pick-wt=24): 30 [] -order(A,B)| -member(C,B)| -member(D,B)| -member(E,B)| -apply(A,C,D)| -apply(A,D,E)|apply(A,C,E).
% 1.80/2.03 ** KEPT (pick-wt=21): 31 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 32 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 33 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 34 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=20): 35 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=20): 36 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=20): 37 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=23): 38 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=23): 39 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=23): 40 [] order(A,B)|member($f4(A,B),B)|$f6(A,B)!=$f5(A,B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 41 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 42 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 43 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 44 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 45 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 46 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f6(A,B),B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 47 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 48 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 49 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 50 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 51 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 52 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|member($f5(A,B),B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 53 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 54 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 55 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=27): 56 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=27): 57 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=27): 58 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f6(A,B),$f5(A,B))| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 59 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 60 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 61 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=27): 62 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=27): 63 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=27): 64 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|apply(A,$f5(A,B),$f6(A,B))| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=23): 65 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=23): 66 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=23): 67 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=26): 68 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=26): 69 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=26): 70 [] order(A,B)| -apply(A,$f4(A,B),$f4(A,B))|$f6(A,B)!=$f5(A,B)| -apply(A,$f9(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=6): 71 [] -total_order(A,B)|order(A,B).
% 1.80/2.03 ** KEPT (pick-wt=17): 72 [] -total_order(A,B)| -member(C,B)| -member(D,B)|apply(A,C,D)|apply(A,D,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 73 [] total_order(A,B)| -order(A,B)|member($f11(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=11): 74 [] total_order(A,B)| -order(A,B)|member($f10(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=14): 75 [] total_order(A,B)| -order(A,B)| -apply(A,$f11(A,B),$f10(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=14): 76 [] total_order(A,B)| -order(A,B)| -apply(A,$f10(A,B),$f11(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=11): 77 [] -upper_bound(A,B,C)| -member(D,C)|apply(B,D,A).
% 1.80/2.03 ** KEPT (pick-wt=11): 78 [] upper_bound(A,B,C)| -apply(B,$f12(B,C,A),A).
% 1.80/2.03 ** KEPT (pick-wt=11): 79 [] -lower_bound(A,B,C)| -member(D,C)|apply(B,A,D).
% 1.80/2.03 ** KEPT (pick-wt=11): 80 [] lower_bound(A,B,C)| -apply(B,A,$f13(B,C,A)).
% 1.80/2.03 ** KEPT (pick-wt=7): 81 [] -greatest(A,B,C)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 82 [] -greatest(A,B,C)| -member(D,C)|apply(B,D,A).
% 1.80/2.03 ** KEPT (pick-wt=13): 83 [] greatest(A,B,C)| -member(A,C)|member($f14(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=14): 84 [] greatest(A,B,C)| -member(A,C)| -apply(B,$f14(B,C,A),A).
% 1.80/2.03 ** KEPT (pick-wt=7): 85 [] -least(A,B,C)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=11): 86 [] -least(A,B,C)| -member(D,C)|apply(B,A,D).
% 1.80/2.03 ** KEPT (pick-wt=13): 87 [] least(A,B,C)| -member(A,C)|member($f15(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=14): 88 [] least(A,B,C)| -member(A,C)| -apply(B,A,$f15(B,C,A)).
% 1.80/2.03 ** KEPT (pick-wt=7): 89 [] -max(A,B,C)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=14): 90 [] -max(A,B,C)| -member(D,C)| -apply(B,A,D)|A=D.
% 1.80/2.03 ** KEPT (pick-wt=13): 91 [] max(A,B,C)| -member(A,C)|member($f16(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=14): 92 [] max(A,B,C)| -member(A,C)|apply(B,A,$f16(B,C,A)).
% 1.80/2.03 ** KEPT (pick-wt=13): 94 [copy,93,flip.3] max(A,B,C)| -member(A,C)|$f16(B,C,A)!=A.
% 1.80/2.03 ** KEPT (pick-wt=7): 95 [] -min(A,B,C)|member(A,C).
% 1.80/2.03 ** KEPT (pick-wt=14): 96 [] -min(A,B,C)| -member(D,C)| -apply(B,D,A)|A=D.
% 1.80/2.03 ** KEPT (pick-wt=13): 97 [] min(A,B,C)| -member(A,C)|member($f17(B,C,A),C).
% 1.80/2.03 ** KEPT (pick-wt=14): 98 [] min(A,B,C)| -member(A,C)|apply(B,$f17(B,C,A),A).
% 1.80/2.03 ** KEPT (pick-wt=13): 100 [copy,99,flip.3] min(A,B,C)| -member(A,C)|$f17(B,C,A)!=A.
% 1.80/2.03 ** KEPT (pick-wt=8): 101 [] -least_upper_bound(A,B,C,D)|member(A,B).
% 1.80/2.03 ** KEPT (pick-wt=9): 102 [] -least_upper_bound(A,B,C,D)|upper_bound(A,C,B).
% 1.80/2.03 ** KEPT (pick-wt=16): 103 [] -least_upper_bound(A,B,C,D)| -member(E,D)| -upper_bound(E,C,B)|apply(C,A,E).
% 1.80/2.03 ** KEPT (pick-wt=19): 104 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)|member($f18(A,B,C,D),D).
% 1.80/2.03 ** KEPT (pick-wt=20): 105 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)|upper_bound($f18(A,B,C,D),C,B).
% 1.80/2.03 ** KEPT (pick-wt=20): 106 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)| -apply(C,A,$f18(A,B,C,D)).
% 1.80/2.03 ** KEPT (pick-wt=8): 107 [] -greatest_lower_bound(A,B,C,D)|member(A,B).
% 1.80/2.03 ** KEPT (pick-wt=9): 108 [] -greatest_lower_bound(A,B,C,D)|lower_bound(A,C,B).
% 1.80/2.03 ** KEPT (pick-wt=16): 109 [] -greatest_lower_bound(A,B,C,D)| -member(E,D)| -lower_bound(E,C,B)|apply(C,E,A).
% 1.80/2.03 ** KEPT (pick-wt=19): 110 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)|member($f19(A,B,C,D),D).
% 1.80/2.03 ** KEPT (pick-wt=20): 111 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)|lower_bound($f19(A,B,C,D),C,B).
% 1.80/2.03 ** KEPT (pick-wt=20): 112 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)| -apply(C,$f19(A,B,C,D),A).
% 1.80/2.03 ** KEPT (pick-wt=4): 113 [] -apply($c6,$c2,$c1).
% 1.80/2.03
% 1.80/2.03 ------------> process sos:
% 1.80/2.03 ** KEPT (pick-wt=3): 121 [] A=A.
% 1.80/2.03 ** KEPT (pick-wt=8): 122 [] subset(A,B)|member($f1(A,B),A).
% 1.80/2.03 ** KEPT (pick-wt=9): 123 [] member(A,product(B))|member($f3(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=18): 124 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=18): 125 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=18): 126 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 127 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 128 [] order(A,B)|member($f4(A,B),B)|member($f6(A,B),B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=18): 129 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=18): 130 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=18): 131 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 132 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 133 [] order(A,B)|member($f4(A,B),B)|member($f5(A,B),B)|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 134 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 135 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))|member($f8(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 136 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))|member($f7(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=24): 137 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))|apply(A,$f9(A,B),$f8(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=24): 138 [] order(A,B)|member($f4(A,B),B)|apply(A,$f6(A,B),$f5(A,B))|apply(A,$f8(A,B),$f7(A,B)).
% 1.80/2.03 ** KEPT (pick-wt=21): 139 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))|member($f9(A,B),B).
% 1.80/2.03 ** KEPT (pick-wt=21): 140 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))|member($f8(A,B),B).
% 1.93/2.12 ** KEPT (pick-wt=21): 141 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))|member($f7(A,B),B).
% 1.93/2.12 ** KEPT (pick-wt=24): 142 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))|apply(A,$f9(A,B),$f8(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=24): 143 [] order(A,B)|member($f4(A,B),B)|apply(A,$f5(A,B),$f6(A,B))|apply(A,$f8(A,B),$f7(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=10): 144 [] upper_bound(A,B,C)|member($f12(B,C,A),C).
% 1.93/2.12 ** KEPT (pick-wt=10): 145 [] lower_bound(A,B,C)|member($f13(B,C,A),C).
% 1.93/2.12 ** KEPT (pick-wt=3): 146 [] order($c6,$c5).
% 1.93/2.12 ** KEPT (pick-wt=3): 147 [] subset($c4,$c5).
% 1.93/2.12 ** KEPT (pick-wt=3): 148 [] subset($c3,$c5).
% 1.93/2.12 ** KEPT (pick-wt=3): 149 [] subset($c4,$c3).
% 1.93/2.12 ** KEPT (pick-wt=5): 150 [] least_upper_bound($c2,$c4,$c6,$c5).
% 1.93/2.12 ** KEPT (pick-wt=5): 151 [] least_upper_bound($c1,$c3,$c6,$c5).
% 1.93/2.12 Following clause subsumed by 121 during input processing: 0 [copy,121,flip.1] A=A.
% 1.93/2.12 121 back subsumes 119.
% 1.93/2.12
% 1.93/2.12 ======= end of input processing =======
% 1.93/2.12
% 1.93/2.12 =========== start of search ===========
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Resetting weight limit to 6.
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Resetting weight limit to 6.
% 1.93/2.12
% 1.93/2.12 sos_size=773
% 1.93/2.12
% 1.93/2.12 -------- PROOF --------
% 1.93/2.12
% 1.93/2.12 ----> UNIT CONFLICT at 0.10 sec ----> 931 [binary,930.1,113.1] $F.
% 1.93/2.12
% 1.93/2.12 Length of proof is 4. Level of proof is 3.
% 1.93/2.12
% 1.93/2.12 ---------------- PROOF ----------------
% 1.93/2.12 % SZS status Theorem
% 1.93/2.12 % SZS output start Refutation
% See solution above
% 1.93/2.12 ------------ end of proof -------------
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12 ============ end of search ============
% 1.93/2.12
% 1.93/2.12 -------------- statistics -------------
% 1.93/2.12 clauses given 25
% 1.93/2.12 clauses generated 1082
% 1.93/2.12 clauses kept 928
% 1.93/2.12 clauses forward subsumed 262
% 1.93/2.12 clauses back subsumed 2
% 1.93/2.12 Kbytes malloced 4882
% 1.93/2.12
% 1.93/2.12 ----------- times (seconds) -----------
% 1.93/2.12 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.93/2.12 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.93/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.12
% 1.93/2.12 That finishes the proof of the theorem.
% 1.93/2.12
% 1.93/2.12 Process 10587 finished Wed Jul 27 10:52:37 2022
% 1.93/2.12 Otter interrupted
% 1.93/2.12 PROOF FOUND
%------------------------------------------------------------------------------