TSTP Solution File: SET813+4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:18 EDT 2022
% Result : Theorem 1.90s 2.08s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 12 ( 2 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
( member(A,union(B,C))
| ~ member(A,C) ),
file('SET813+4.p',unknown),
[] ).
cnf(19,axiom,
( member(A,singleton(B))
| A != B ),
file('SET813+4.p',unknown),
[] ).
cnf(57,axiom,
( member(A,suc(B))
| ~ member(A,union(B,singleton(B))) ),
file('SET813+4.p',unknown),
[] ).
cnf(58,axiom,
~ member(dollar_c1,suc(dollar_c1)),
file('SET813+4.p',unknown),
[] ).
cnf(66,axiom,
A = A,
file('SET813+4.p',unknown),
[] ).
cnf(92,plain,
member(A,singleton(A)),
inference(hyper,[status(thm)],[66,19]),
[iquote('hyper,66,19')] ).
cnf(154,plain,
member(A,union(B,singleton(A))),
inference(hyper,[status(thm)],[92,13]),
[iquote('hyper,92,13')] ).
cnf(814,plain,
member(A,suc(A)),
inference(hyper,[status(thm)],[154,57]),
[iquote('hyper,154,57')] ).
cnf(815,plain,
$false,
inference(binary,[status(thm)],[814,58]),
[iquote('binary,814.1,58.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 10:42:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.78/2.01 ----- Otter 3.3f, August 2004 -----
% 1.78/2.01 The process was started by sandbox on n003.cluster.edu,
% 1.78/2.01 Wed Jul 27 10:42:56 2022
% 1.78/2.01 The command was "./otter". The process ID is 28310.
% 1.78/2.01
% 1.78/2.01 set(prolog_style_variables).
% 1.78/2.01 set(auto).
% 1.78/2.01 dependent: set(auto1).
% 1.78/2.01 dependent: set(process_input).
% 1.78/2.01 dependent: clear(print_kept).
% 1.78/2.01 dependent: clear(print_new_demod).
% 1.78/2.01 dependent: clear(print_back_demod).
% 1.78/2.01 dependent: clear(print_back_sub).
% 1.78/2.01 dependent: set(control_memory).
% 1.78/2.01 dependent: assign(max_mem, 12000).
% 1.78/2.01 dependent: assign(pick_given_ratio, 4).
% 1.78/2.01 dependent: assign(stats_level, 1).
% 1.78/2.01 dependent: assign(max_seconds, 10800).
% 1.78/2.01 clear(print_given).
% 1.78/2.01
% 1.78/2.01 formula_list(usable).
% 1.78/2.01 all A (A=A).
% 1.78/2.01 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 1.78/2.01 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 1.78/2.01 all X A (member(X,power_set(A))<->subset(X,A)).
% 1.78/2.01 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 1.78/2.01 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 1.78/2.01 all X (-member(X,empty_set)).
% 1.78/2.01 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 1.78/2.01 all X A (member(X,singleton(A))<->X=A).
% 1.78/2.01 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 1.78/2.01 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 1.78/2.01 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 1.78/2.01 all A (member(A,on)<->set(A)&strict_well_order(member_predicate,A)& (all X (member(X,A)->subset(X,A)))).
% 1.78/2.01 all R E (strict_well_order(R,E)<->strict_order(R,E)& (all A (subset(A,E)& (exists X member(X,A))-> (exists Y least(Y,R,A))))).
% 1.78/2.01 all R E M (least(M,R,E)<->member(M,E)& (all X (member(X,E)->M=X|apply(R,M,X)))).
% 1.78/2.01 all X Y (apply(member_predicate,X,Y)<->member(X,Y)).
% 1.78/2.01 all R E (strict_order(R,E)<-> (all X Y (member(X,E)&member(Y,E)-> -(apply(R,X,Y)&apply(R,Y,X))))& (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))))).
% 1.78/2.01 all X (set(X)-> (all Y (member(Y,X)->set(Y)))).
% 1.78/2.01 all X R A Y (member(Y,initial_segment(X,R,A))<->member(Y,A)&apply(R,Y,X)).
% 1.78/2.01 all A X (member(X,suc(A))<->member(X,union(A,singleton(A)))).
% 1.78/2.01 -(all A (member(A,on)->member(A,suc(A)))).
% 1.78/2.01 end_of_list.
% 1.78/2.01
% 1.78/2.01 -------> usable clausifies to:
% 1.78/2.01
% 1.78/2.01 list(usable).
% 1.78/2.01 0 [] A=A.
% 1.78/2.01 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 1.78/2.01 0 [] subset(A,B)|member($f1(A,B),A).
% 1.78/2.01 0 [] subset(A,B)| -member($f1(A,B),B).
% 1.78/2.01 0 [] -e_qual_set(A,B)|subset(A,B).
% 1.78/2.01 0 [] -e_qual_set(A,B)|subset(B,A).
% 1.78/2.01 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.78/2.01 0 [] -member(X,power_set(A))|subset(X,A).
% 1.78/2.01 0 [] member(X,power_set(A))| -subset(X,A).
% 1.78/2.01 0 [] -member(X,intersection(A,B))|member(X,A).
% 1.78/2.01 0 [] -member(X,intersection(A,B))|member(X,B).
% 1.78/2.01 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 1.78/2.01 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 1.78/2.01 0 [] member(X,union(A,B))| -member(X,A).
% 1.78/2.01 0 [] member(X,union(A,B))| -member(X,B).
% 1.78/2.01 0 [] -member(X,empty_set).
% 1.78/2.01 0 [] -member(B,difference(E,A))|member(B,E).
% 1.78/2.01 0 [] -member(B,difference(E,A))| -member(B,A).
% 1.78/2.01 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 1.78/2.01 0 [] -member(X,singleton(A))|X=A.
% 1.78/2.01 0 [] member(X,singleton(A))|X!=A.
% 1.78/2.01 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 1.78/2.01 0 [] member(X,unordered_pair(A,B))|X!=A.
% 1.78/2.01 0 [] member(X,unordered_pair(A,B))|X!=B.
% 1.78/2.01 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 1.78/2.01 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 1.78/2.01 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 1.78/2.01 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 1.78/2.01 0 [] member(X,product(A))|member($f3(X,A),A).
% 1.78/2.01 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 1.78/2.01 0 [] -member(A,on)|set(A).
% 1.78/2.01 0 [] -member(A,on)|strict_well_order(member_predicate,A).
% 1.78/2.01 0 [] -member(A,on)| -member(X,A)|subset(X,A).
% 1.78/2.01 0 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)|member($f4(A),A).
% 1.78/2.01 0 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)| -subset($f4(A),A).
% 1.78/2.01 0 [] -strict_well_order(R,E)|strict_order(R,E).
% 1.78/2.01 0 [] -strict_well_order(R,E)| -subset(A,E)| -member(X,A)|least($f5(R,E,A),R,A).
% 1.78/2.01 0 [] strict_well_order(R,E)| -strict_order(R,E)|subset($f7(R,E),E).
% 1.78/2.01 0 [] strict_well_order(R,E)| -strict_order(R,E)|member($f6(R,E),$f7(R,E)).
% 1.78/2.01 0 [] strict_well_order(R,E)| -strict_order(R,E)| -least(Y,R,$f7(R,E)).
% 1.78/2.01 0 [] -least(M,R,E)|member(M,E).
% 1.78/2.01 0 [] -least(M,R,E)| -member(X,E)|M=X|apply(R,M,X).
% 1.78/2.01 0 [] least(M,R,E)| -member(M,E)|member($f8(R,E,M),E).
% 1.78/2.01 0 [] least(M,R,E)| -member(M,E)|M!=$f8(R,E,M).
% 1.78/2.01 0 [] least(M,R,E)| -member(M,E)| -apply(R,M,$f8(R,E,M)).
% 1.78/2.01 0 [] -apply(member_predicate,X,Y)|member(X,Y).
% 1.78/2.01 0 [] apply(member_predicate,X,Y)| -member(X,Y).
% 1.78/2.01 0 [] -strict_order(R,E)| -member(X,E)| -member(Y,E)| -apply(R,X,Y)| -apply(R,Y,X).
% 1.78/2.01 0 [] -strict_order(R,E)| -member(X1,E)| -member(X2,E)| -member(Z,E)| -apply(R,X1,X2)| -apply(R,X2,Z)|apply(R,X1,Z).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f13(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f12(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f11(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)|apply(R,$f13(R,E),$f12(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)|apply(R,$f12(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|member($f10(R,E),E)| -apply(R,$f13(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f13(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f12(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f11(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)|apply(R,$f13(R,E),$f12(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)|apply(R,$f12(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|member($f9(R,E),E)| -apply(R,$f13(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f13(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f12(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f11(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|apply(R,$f13(R,E),$f12(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|apply(R,$f12(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))| -apply(R,$f13(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f13(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f12(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f11(R,E),E).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|apply(R,$f13(R,E),$f12(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|apply(R,$f12(R,E),$f11(R,E)).
% 1.78/2.01 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))| -apply(R,$f13(R,E),$f11(R,E)).
% 1.78/2.01 0 [] -set(X)| -member(Y,X)|set(Y).
% 1.78/2.01 0 [] -member(Y,initial_segment(X,R,A))|member(Y,A).
% 1.78/2.01 0 [] -member(Y,initial_segment(X,R,A))|apply(R,Y,X).
% 1.78/2.01 0 [] member(Y,initial_segment(X,R,A))| -member(Y,A)| -apply(R,Y,X).
% 1.78/2.01 0 [] -member(X,suc(A))|member(X,union(A,singleton(A))).
% 1.78/2.01 0 [] member(X,suc(A))| -member(X,union(A,singleton(A))).
% 1.78/2.01 0 [] member($c1,on).
% 1.78/2.01 0 [] -member($c1,suc($c1)).
% 1.78/2.01 end_of_list.
% 1.78/2.01
% 1.78/2.01 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.78/2.01
% 1.78/2.01 This ia a non-Horn set with equality. The strategy will be
% 1.78/2.01 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/2.01 deletion, with positive clauses in sos and nonpositive
% 1.78/2.01 clauses in usable.
% 1.78/2.01
% 1.78/2.01 dependent: set(knuth_bendix).
% 1.78/2.01 dependent: set(anl_eq).
% 1.78/2.01 dependent: set(para_from).
% 1.78/2.01 dependent: set(para_into).
% 1.78/2.01 dependent: clear(para_from_right).
% 1.78/2.01 dependent: clear(para_into_right).
% 1.78/2.01 dependent: set(para_from_vars).
% 1.78/2.01 dependent: set(eq_units_both_ways).
% 1.78/2.01 dependent: set(dynamic_demod_all).
% 1.78/2.01 dependent: set(dynamic_demod).
% 1.78/2.01 dependent: set(order_eq).
% 1.78/2.01 dependent: set(back_demod).
% 1.78/2.01 dependent: set(lrpo).
% 1.78/2.01 dependent: set(hyper_res).
% 1.78/2.01 dependent: set(unit_deletion).
% 1.78/2.01 dependent: set(factor).
% 1.78/2.01
% 1.78/2.01 ------------> process usable:
% 1.78/2.01 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.78/2.01 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 1.78/2.01 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 1.78/2.01 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 1.78/2.01 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 1.78/2.01 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 1.78/2.01 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 1.78/2.01 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 1.78/2.01 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 1.78/2.01 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 1.78/2.01 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 1.78/2.01 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 1.78/2.01 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 1.78/2.01 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 1.78/2.01 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 1.78/2.01 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=5): 28 [] -member(A,on)|set(A).
% 1.78/2.01 ** KEPT (pick-wt=6): 29 [] -member(A,on)|strict_well_order(member_predicate,A).
% 1.78/2.01 ** KEPT (pick-wt=9): 30 [] -member(A,on)| -member(B,A)|subset(B,A).
% 1.78/2.01 ** KEPT (pick-wt=12): 31 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)|member($f4(A),A).
% 1.78/2.01 ** KEPT (pick-wt=12): 32 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)| -subset($f4(A),A).
% 1.78/2.01 ** KEPT (pick-wt=6): 33 [] -strict_well_order(A,B)|strict_order(A,B).
% 1.78/2.01 ** KEPT (pick-wt=16): 34 [] -strict_well_order(A,B)| -subset(C,B)| -member(D,C)|least($f5(A,B,C),A,C).
% 1.78/2.01 ** KEPT (pick-wt=11): 35 [] strict_well_order(A,B)| -strict_order(A,B)|subset($f7(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=13): 36 [] strict_well_order(A,B)| -strict_order(A,B)|member($f6(A,B),$f7(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=12): 37 [] strict_well_order(A,B)| -strict_order(A,B)| -least(C,A,$f7(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=7): 38 [] -least(A,B,C)|member(A,C).
% 1.78/2.01 ** KEPT (pick-wt=14): 39 [] -least(A,B,C)| -member(D,C)|A=D|apply(B,A,D).
% 1.78/2.01 ** KEPT (pick-wt=13): 40 [] least(A,B,C)| -member(A,C)|member($f8(B,C,A),C).
% 1.78/2.01 ** KEPT (pick-wt=13): 42 [copy,41,flip.3] least(A,B,C)| -member(A,C)|$f8(B,C,A)!=A.
% 1.78/2.01 ** KEPT (pick-wt=14): 43 [] least(A,B,C)| -member(A,C)| -apply(B,A,$f8(B,C,A)).
% 1.78/2.01 ** KEPT (pick-wt=7): 44 [] -apply(member_predicate,A,B)|member(A,B).
% 1.78/2.01 ** KEPT (pick-wt=7): 45 [] apply(member_predicate,A,B)| -member(A,B).
% 1.78/2.01 ** KEPT (pick-wt=17): 46 [] -strict_order(A,B)| -member(C,B)| -member(D,B)| -apply(A,C,D)| -apply(A,D,C).
% 1.78/2.01 ** KEPT (pick-wt=24): 47 [] -strict_order(A,B)| -member(C,B)| -member(D,B)| -member(E,B)| -apply(A,C,D)| -apply(A,D,E)|apply(A,C,E).
% 1.78/2.01 ** KEPT (pick-wt=16): 48 [] strict_order(A,B)|member($f10(A,B),B)| -apply(A,$f13(A,B),$f11(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=16): 49 [] strict_order(A,B)|member($f9(A,B),B)| -apply(A,$f13(A,B),$f11(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=19): 50 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))| -apply(A,$f13(A,B),$f11(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=19): 51 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))| -apply(A,$f13(A,B),$f11(A,B)).
% 1.78/2.01 ** KEPT (pick-wt=7): 52 [] -set(A)| -member(B,A)|set(B).
% 1.78/2.01 ** KEPT (pick-wt=9): 53 [] -member(A,initial_segment(B,C,D))|member(A,D).
% 1.78/2.01 ** KEPT (pick-wt=10): 54 [] -member(A,initial_segment(B,C,D))|apply(C,A,B).
% 1.78/2.01 ** KEPT (pick-wt=13): 55 [] member(A,initial_segment(B,C,D))| -member(A,D)| -apply(C,A,B).
% 1.78/2.01 ** KEPT (pick-wt=10): 56 [] -member(A,suc(B))|member(A,union(B,singleton(B))).
% 1.78/2.01 ** KEPT (pick-wt=10): 57 [] member(A,suc(B))| -member(A,union(B,singleton(B))).
% 1.78/2.01 ** KEPT (pick-wt=4): 58 [] -member($c1,suc($c1)).
% 1.78/2.01
% 1.78/2.01 ------------> process sos:
% 1.78/2.01 ** KEPT (pick-wt=3): 66 [] A=A.
% 1.78/2.01 ** KEPT (pick-wt=8): 67 [] subset(A,B)|member($f1(A,B),A).
% 1.78/2.01 ** KEPT (pick-wt=9): 68 [] member(A,product(B))|member($f3(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=13): 69 [] strict_order(A,B)|member($f10(A,B),B)|member($f13(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=13): 70 [] strict_order(A,B)|member($f10(A,B),B)|member($f12(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=13): 71 [] strict_order(A,B)|member($f10(A,B),B)|member($f11(A,B),B).
% 1.78/2.01 ** KEPT (pick-wt=16): 72 [] strict_order(A,B)|member($f10(A,B),B)|apply(A,$f13(A,B),$f12(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=16): 73 [] strict_order(A,B)|member($f10(A,B),B)|apply(A,$f12(A,B),$f11(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=13): 74 [] strict_order(A,B)|member($f9(A,B),B)|member($f13(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=13): 75 [] strict_order(A,B)|member($f9(A,B),B)|member($f12(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=13): 76 [] strict_order(A,B)|member($f9(A,B),B)|member($f11(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=16): 77 [] strict_order(A,B)|member($f9(A,B),B)|apply(A,$f13(A,B),$f12(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=16): 78 [] strict_order(A,B)|member($f9(A,B),B)|apply(A,$f12(A,B),$f11(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=16): 79 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f13(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=16): 80 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f12(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=16): 81 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f11(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=19): 82 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|apply(A,$f13(A,B),$f12(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=19): 83 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|apply(A,$f12(A,B),$f11(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=16): 84 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f13(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=16): 85 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f12(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=16): 86 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f11(A,B),B).
% 1.90/2.08 ** KEPT (pick-wt=19): 87 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|apply(A,$f13(A,B),$f12(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=19): 88 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|apply(A,$f12(A,B),$f11(A,B)).
% 1.90/2.08 ** KEPT (pick-wt=3): 89 [] member($c1,on).
% 1.90/2.08 Following clause subsumed by 66 during input processing: 0 [copy,66,flip.1] A=A.
% 1.90/2.08
% 1.90/2.08 ======= end of input processing =======
% 1.90/2.08
% 1.90/2.08 =========== start of search ===========
% 1.90/2.08
% 1.90/2.08
% 1.90/2.08 Resetting weight limit to 7.
% 1.90/2.08
% 1.90/2.08
% 1.90/2.08 Resetting weight limit to 7.
% 1.90/2.08
% 1.90/2.08 sos_size=696
% 1.90/2.08
% 1.90/2.08 -------- PROOF --------
% 1.90/2.08
% 1.90/2.08 ----> UNIT CONFLICT at 0.08 sec ----> 815 [binary,814.1,58.1] $F.
% 1.90/2.08
% 1.90/2.08 Length of proof is 3. Level of proof is 3.
% 1.90/2.08
% 1.90/2.08 ---------------- PROOF ----------------
% 1.90/2.08 % SZS status Theorem
% 1.90/2.08 % SZS output start Refutation
% See solution above
% 1.90/2.08 ------------ end of proof -------------
% 1.90/2.08
% 1.90/2.08
% 1.90/2.08 Search stopped by max_proofs option.
% 1.90/2.08
% 1.90/2.08
% 1.90/2.08 Search stopped by max_proofs option.
% 1.90/2.08
% 1.90/2.08 ============ end of search ============
% 1.90/2.08
% 1.90/2.08 -------------- statistics -------------
% 1.90/2.08 clauses given 33
% 1.90/2.08 clauses generated 1993
% 1.90/2.08 clauses kept 813
% 1.90/2.08 clauses forward subsumed 531
% 1.90/2.08 clauses back subsumed 6
% 1.90/2.08 Kbytes malloced 4882
% 1.90/2.08
% 1.90/2.08 ----------- times (seconds) -----------
% 1.90/2.08 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.90/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.08
% 1.90/2.08 That finishes the proof of the theorem.
% 1.90/2.08
% 1.90/2.08 Process 28310 finished Wed Jul 27 10:42:58 2022
% 1.90/2.08 Otter interrupted
% 1.90/2.08 PROOF FOUND
%------------------------------------------------------------------------------