TSTP Solution File: SET810+4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:18 EDT 2022
% Result : Theorem 2.07s 2.29s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 0 equ; 12 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET810+4.p',unknown),
[] ).
cnf(29,axiom,
( ~ member(A,on)
| strict_well_order(member_predicate,A) ),
file('SET810+4.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(A,on)
| ~ member(B,A)
| subset(B,A) ),
file('SET810+4.p',unknown),
[] ).
cnf(33,axiom,
( ~ strict_well_order(A,B)
| strict_order(A,B) ),
file('SET810+4.p',unknown),
[] ).
cnf(45,axiom,
( apply(member_predicate,A,B)
| ~ member(A,B) ),
file('SET810+4.p',unknown),
[] ).
cnf(46,axiom,
( ~ strict_order(A,B)
| ~ member(C,B)
| ~ member(D,B)
| ~ apply(A,C,D)
| ~ apply(A,D,C) ),
file('SET810+4.p',unknown),
[] ).
cnf(89,axiom,
member(dollar_c1,on),
file('SET810+4.p',unknown),
[] ).
cnf(90,axiom,
member(dollar_c2,dollar_c1),
file('SET810+4.p',unknown),
[] ).
cnf(91,axiom,
member(dollar_c1,dollar_c2),
file('SET810+4.p',unknown),
[] ).
cnf(121,plain,
strict_well_order(member_predicate,dollar_c1),
inference(hyper,[status(thm)],[89,29]),
[iquote('hyper,89,29')] ).
cnf(152,plain,
apply(member_predicate,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[90,45]),
[iquote('hyper,90,45')] ).
cnf(154,plain,
subset(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[90,30,89]),
[iquote('hyper,90,30,89')] ).
cnf(173,plain,
apply(member_predicate,dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[91,45]),
[iquote('hyper,91,45')] ).
cnf(212,plain,
strict_order(member_predicate,dollar_c1),
inference(hyper,[status(thm)],[121,33]),
[iquote('hyper,121,33')] ).
cnf(317,plain,
member(dollar_c1,dollar_c1),
inference(hyper,[status(thm)],[154,1,91]),
[iquote('hyper,154,1,91')] ).
cnf(724,plain,
$false,
inference(hyper,[status(thm)],[173,46,212,90,317,152]),
[iquote('hyper,173,46,212,90,317,152')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:37:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.07/2.25 ----- Otter 3.3f, August 2004 -----
% 2.07/2.25 The process was started by sandbox2 on n020.cluster.edu,
% 2.07/2.25 Wed Jul 27 10:37:23 2022
% 2.07/2.25 The command was "./otter". The process ID is 8986.
% 2.07/2.25
% 2.07/2.25 set(prolog_style_variables).
% 2.07/2.25 set(auto).
% 2.07/2.25 dependent: set(auto1).
% 2.07/2.25 dependent: set(process_input).
% 2.07/2.25 dependent: clear(print_kept).
% 2.07/2.25 dependent: clear(print_new_demod).
% 2.07/2.25 dependent: clear(print_back_demod).
% 2.07/2.25 dependent: clear(print_back_sub).
% 2.07/2.25 dependent: set(control_memory).
% 2.07/2.25 dependent: assign(max_mem, 12000).
% 2.07/2.25 dependent: assign(pick_given_ratio, 4).
% 2.07/2.25 dependent: assign(stats_level, 1).
% 2.07/2.25 dependent: assign(max_seconds, 10800).
% 2.07/2.25 clear(print_given).
% 2.07/2.25
% 2.07/2.25 formula_list(usable).
% 2.07/2.25 all A (A=A).
% 2.07/2.25 all A B (subset(A,B)<-> (all X (member(X,A)->member(X,B)))).
% 2.07/2.25 all A B (e_qual_set(A,B)<->subset(A,B)&subset(B,A)).
% 2.07/2.25 all X A (member(X,power_set(A))<->subset(X,A)).
% 2.07/2.25 all X A B (member(X,intersection(A,B))<->member(X,A)&member(X,B)).
% 2.07/2.25 all X A B (member(X,union(A,B))<->member(X,A)|member(X,B)).
% 2.07/2.25 all X (-member(X,empty_set)).
% 2.07/2.25 all B A E (member(B,difference(E,A))<->member(B,E)& -member(B,A)).
% 2.07/2.25 all X A (member(X,singleton(A))<->X=A).
% 2.07/2.25 all X A B (member(X,unordered_pair(A,B))<->X=A|X=B).
% 2.07/2.25 all X A (member(X,sum(A))<-> (exists Y (member(Y,A)&member(X,Y)))).
% 2.07/2.25 all X A (member(X,product(A))<-> (all Y (member(Y,A)->member(X,Y)))).
% 2.07/2.25 all A (member(A,on)<->set(A)&strict_well_order(member_predicate,A)& (all X (member(X,A)->subset(X,A)))).
% 2.07/2.25 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))))).
% 2.07/2.25 all R E M (least(M,R,E)<->member(M,E)& (all X (member(X,E)->M=X|apply(R,M,X)))).
% 2.07/2.25 all X Y (apply(member_predicate,X,Y)<->member(X,Y)).
% 2.07/2.25 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))))).
% 2.07/2.25 all X (set(X)-> (all Y (member(Y,X)->set(Y)))).
% 2.07/2.25 all X R A Y (member(Y,initial_segment(X,R,A))<->member(Y,A)&apply(R,Y,X)).
% 2.07/2.25 all A X (member(X,suc(A))<->member(X,union(A,singleton(A)))).
% 2.07/2.25 -(all A B (member(A,on)&member(B,on)-> -(member(A,B)&member(B,A)))).
% 2.07/2.25 end_of_list.
% 2.07/2.25
% 2.07/2.25 -------> usable clausifies to:
% 2.07/2.25
% 2.07/2.25 list(usable).
% 2.07/2.25 0 [] A=A.
% 2.07/2.25 0 [] -subset(A,B)| -member(X,A)|member(X,B).
% 2.07/2.25 0 [] subset(A,B)|member($f1(A,B),A).
% 2.07/2.25 0 [] subset(A,B)| -member($f1(A,B),B).
% 2.07/2.25 0 [] -e_qual_set(A,B)|subset(A,B).
% 2.07/2.25 0 [] -e_qual_set(A,B)|subset(B,A).
% 2.07/2.25 0 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.07/2.25 0 [] -member(X,power_set(A))|subset(X,A).
% 2.07/2.25 0 [] member(X,power_set(A))| -subset(X,A).
% 2.07/2.25 0 [] -member(X,intersection(A,B))|member(X,A).
% 2.07/2.25 0 [] -member(X,intersection(A,B))|member(X,B).
% 2.07/2.25 0 [] member(X,intersection(A,B))| -member(X,A)| -member(X,B).
% 2.07/2.25 0 [] -member(X,union(A,B))|member(X,A)|member(X,B).
% 2.07/2.25 0 [] member(X,union(A,B))| -member(X,A).
% 2.07/2.25 0 [] member(X,union(A,B))| -member(X,B).
% 2.07/2.25 0 [] -member(X,empty_set).
% 2.07/2.25 0 [] -member(B,difference(E,A))|member(B,E).
% 2.07/2.25 0 [] -member(B,difference(E,A))| -member(B,A).
% 2.07/2.25 0 [] member(B,difference(E,A))| -member(B,E)|member(B,A).
% 2.07/2.25 0 [] -member(X,singleton(A))|X=A.
% 2.07/2.25 0 [] member(X,singleton(A))|X!=A.
% 2.07/2.25 0 [] -member(X,unordered_pair(A,B))|X=A|X=B.
% 2.07/2.25 0 [] member(X,unordered_pair(A,B))|X!=A.
% 2.07/2.25 0 [] member(X,unordered_pair(A,B))|X!=B.
% 2.07/2.25 0 [] -member(X,sum(A))|member($f2(X,A),A).
% 2.07/2.25 0 [] -member(X,sum(A))|member(X,$f2(X,A)).
% 2.07/2.25 0 [] member(X,sum(A))| -member(Y,A)| -member(X,Y).
% 2.07/2.25 0 [] -member(X,product(A))| -member(Y,A)|member(X,Y).
% 2.07/2.25 0 [] member(X,product(A))|member($f3(X,A),A).
% 2.07/2.25 0 [] member(X,product(A))| -member(X,$f3(X,A)).
% 2.07/2.25 0 [] -member(A,on)|set(A).
% 2.07/2.25 0 [] -member(A,on)|strict_well_order(member_predicate,A).
% 2.07/2.25 0 [] -member(A,on)| -member(X,A)|subset(X,A).
% 2.07/2.25 0 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)|member($f4(A),A).
% 2.07/2.25 0 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)| -subset($f4(A),A).
% 2.07/2.25 0 [] -strict_well_order(R,E)|strict_order(R,E).
% 2.07/2.25 0 [] -strict_well_order(R,E)| -subset(A,E)| -member(X,A)|least($f5(R,E,A),R,A).
% 2.07/2.25 0 [] strict_well_order(R,E)| -strict_order(R,E)|subset($f7(R,E),E).
% 2.07/2.25 0 [] strict_well_order(R,E)| -strict_order(R,E)|member($f6(R,E),$f7(R,E)).
% 2.07/2.25 0 [] strict_well_order(R,E)| -strict_order(R,E)| -least(Y,R,$f7(R,E)).
% 2.07/2.25 0 [] -least(M,R,E)|member(M,E).
% 2.07/2.25 0 [] -least(M,R,E)| -member(X,E)|M=X|apply(R,M,X).
% 2.07/2.25 0 [] least(M,R,E)| -member(M,E)|member($f8(R,E,M),E).
% 2.07/2.25 0 [] least(M,R,E)| -member(M,E)|M!=$f8(R,E,M).
% 2.07/2.25 0 [] least(M,R,E)| -member(M,E)| -apply(R,M,$f8(R,E,M)).
% 2.07/2.25 0 [] -apply(member_predicate,X,Y)|member(X,Y).
% 2.07/2.25 0 [] apply(member_predicate,X,Y)| -member(X,Y).
% 2.07/2.25 0 [] -strict_order(R,E)| -member(X,E)| -member(Y,E)| -apply(R,X,Y)| -apply(R,Y,X).
% 2.07/2.25 0 [] -strict_order(R,E)| -member(X1,E)| -member(X2,E)| -member(Z,E)| -apply(R,X1,X2)| -apply(R,X2,Z)|apply(R,X1,Z).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f13(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f12(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)|member($f11(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)|apply(R,$f13(R,E),$f12(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)|apply(R,$f12(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|member($f10(R,E),E)| -apply(R,$f13(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f13(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f12(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)|member($f11(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)|apply(R,$f13(R,E),$f12(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)|apply(R,$f12(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|member($f9(R,E),E)| -apply(R,$f13(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f13(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f12(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|member($f11(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|apply(R,$f13(R,E),$f12(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))|apply(R,$f12(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f10(R,E),$f9(R,E))| -apply(R,$f13(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f13(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f12(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|member($f11(R,E),E).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|apply(R,$f13(R,E),$f12(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))|apply(R,$f12(R,E),$f11(R,E)).
% 2.07/2.25 0 [] strict_order(R,E)|apply(R,$f9(R,E),$f10(R,E))| -apply(R,$f13(R,E),$f11(R,E)).
% 2.07/2.25 0 [] -set(X)| -member(Y,X)|set(Y).
% 2.07/2.25 0 [] -member(Y,initial_segment(X,R,A))|member(Y,A).
% 2.07/2.25 0 [] -member(Y,initial_segment(X,R,A))|apply(R,Y,X).
% 2.07/2.25 0 [] member(Y,initial_segment(X,R,A))| -member(Y,A)| -apply(R,Y,X).
% 2.07/2.25 0 [] -member(X,suc(A))|member(X,union(A,singleton(A))).
% 2.07/2.25 0 [] member(X,suc(A))| -member(X,union(A,singleton(A))).
% 2.07/2.25 0 [] member($c2,on).
% 2.07/2.25 0 [] member($c1,on).
% 2.07/2.25 0 [] member($c2,$c1).
% 2.07/2.25 0 [] member($c1,$c2).
% 2.07/2.25 end_of_list.
% 2.07/2.25
% 2.07/2.25 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.07/2.25
% 2.07/2.25 This ia a non-Horn set with equality. The strategy will be
% 2.07/2.25 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.07/2.25 deletion, with positive clauses in sos and nonpositive
% 2.07/2.25 clauses in usable.
% 2.07/2.25
% 2.07/2.25 dependent: set(knuth_bendix).
% 2.07/2.25 dependent: set(anl_eq).
% 2.07/2.25 dependent: set(para_from).
% 2.07/2.25 dependent: set(para_into).
% 2.07/2.25 dependent: clear(para_from_right).
% 2.07/2.26 dependent: clear(para_into_right).
% 2.07/2.26 dependent: set(para_from_vars).
% 2.07/2.26 dependent: set(eq_units_both_ways).
% 2.07/2.26 dependent: set(dynamic_demod_all).
% 2.07/2.26 dependent: set(dynamic_demod).
% 2.07/2.26 dependent: set(order_eq).
% 2.07/2.26 dependent: set(back_demod).
% 2.07/2.26 dependent: set(lrpo).
% 2.07/2.26 dependent: set(hyper_res).
% 2.07/2.26 dependent: set(unit_deletion).
% 2.07/2.26 dependent: set(factor).
% 2.07/2.26
% 2.07/2.26 ------------> process usable:
% 2.07/2.26 ** KEPT (pick-wt=9): 1 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.07/2.26 ** KEPT (pick-wt=8): 2 [] subset(A,B)| -member($f1(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=6): 3 [] -e_qual_set(A,B)|subset(A,B).
% 2.07/2.26 ** KEPT (pick-wt=6): 4 [] -e_qual_set(A,B)|subset(B,A).
% 2.07/2.26 ** KEPT (pick-wt=9): 5 [] e_qual_set(A,B)| -subset(A,B)| -subset(B,A).
% 2.07/2.26 ** KEPT (pick-wt=7): 6 [] -member(A,power_set(B))|subset(A,B).
% 2.07/2.26 ** KEPT (pick-wt=7): 7 [] member(A,power_set(B))| -subset(A,B).
% 2.07/2.26 ** KEPT (pick-wt=8): 8 [] -member(A,intersection(B,C))|member(A,B).
% 2.07/2.26 ** KEPT (pick-wt=8): 9 [] -member(A,intersection(B,C))|member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=11): 10 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=11): 11 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=8): 12 [] member(A,union(B,C))| -member(A,B).
% 2.07/2.26 ** KEPT (pick-wt=8): 13 [] member(A,union(B,C))| -member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=3): 14 [] -member(A,empty_set).
% 2.07/2.26 ** KEPT (pick-wt=8): 15 [] -member(A,difference(B,C))|member(A,B).
% 2.07/2.26 ** KEPT (pick-wt=8): 16 [] -member(A,difference(B,C))| -member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=11): 17 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=7): 18 [] -member(A,singleton(B))|A=B.
% 2.07/2.26 ** KEPT (pick-wt=7): 19 [] member(A,singleton(B))|A!=B.
% 2.07/2.26 ** KEPT (pick-wt=11): 20 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 2.07/2.26 ** KEPT (pick-wt=8): 21 [] member(A,unordered_pair(B,C))|A!=B.
% 2.07/2.26 ** KEPT (pick-wt=8): 22 [] member(A,unordered_pair(B,C))|A!=C.
% 2.07/2.26 ** KEPT (pick-wt=9): 23 [] -member(A,sum(B))|member($f2(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=9): 24 [] -member(A,sum(B))|member(A,$f2(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=10): 25 [] member(A,sum(B))| -member(C,B)| -member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=10): 26 [] -member(A,product(B))| -member(C,B)|member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=9): 27 [] member(A,product(B))| -member(A,$f3(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=5): 28 [] -member(A,on)|set(A).
% 2.07/2.26 ** KEPT (pick-wt=6): 29 [] -member(A,on)|strict_well_order(member_predicate,A).
% 2.07/2.26 ** KEPT (pick-wt=9): 30 [] -member(A,on)| -member(B,A)|subset(B,A).
% 2.07/2.26 ** KEPT (pick-wt=12): 31 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)|member($f4(A),A).
% 2.07/2.26 ** KEPT (pick-wt=12): 32 [] member(A,on)| -set(A)| -strict_well_order(member_predicate,A)| -subset($f4(A),A).
% 2.07/2.26 ** KEPT (pick-wt=6): 33 [] -strict_well_order(A,B)|strict_order(A,B).
% 2.07/2.26 ** KEPT (pick-wt=16): 34 [] -strict_well_order(A,B)| -subset(C,B)| -member(D,C)|least($f5(A,B,C),A,C).
% 2.07/2.26 ** KEPT (pick-wt=11): 35 [] strict_well_order(A,B)| -strict_order(A,B)|subset($f7(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=13): 36 [] strict_well_order(A,B)| -strict_order(A,B)|member($f6(A,B),$f7(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=12): 37 [] strict_well_order(A,B)| -strict_order(A,B)| -least(C,A,$f7(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=7): 38 [] -least(A,B,C)|member(A,C).
% 2.07/2.26 ** KEPT (pick-wt=14): 39 [] -least(A,B,C)| -member(D,C)|A=D|apply(B,A,D).
% 2.07/2.26 ** KEPT (pick-wt=13): 40 [] least(A,B,C)| -member(A,C)|member($f8(B,C,A),C).
% 2.07/2.26 ** KEPT (pick-wt=13): 42 [copy,41,flip.3] least(A,B,C)| -member(A,C)|$f8(B,C,A)!=A.
% 2.07/2.26 ** KEPT (pick-wt=14): 43 [] least(A,B,C)| -member(A,C)| -apply(B,A,$f8(B,C,A)).
% 2.07/2.26 ** KEPT (pick-wt=7): 44 [] -apply(member_predicate,A,B)|member(A,B).
% 2.07/2.26 ** KEPT (pick-wt=7): 45 [] apply(member_predicate,A,B)| -member(A,B).
% 2.07/2.26 ** KEPT (pick-wt=17): 46 [] -strict_order(A,B)| -member(C,B)| -member(D,B)| -apply(A,C,D)| -apply(A,D,C).
% 2.07/2.26 ** KEPT (pick-wt=24): 47 [] -strict_order(A,B)| -member(C,B)| -member(D,B)| -member(E,B)| -apply(A,C,D)| -apply(A,D,E)|apply(A,C,E).
% 2.07/2.26 ** KEPT (pick-wt=16): 48 [] strict_order(A,B)|member($f10(A,B),B)| -apply(A,$f13(A,B),$f11(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=16): 49 [] strict_order(A,B)|member($f9(A,B),B)| -apply(A,$f13(A,B),$f11(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=19): 50 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))| -apply(A,$f13(A,B),$f11(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=19): 51 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))| -apply(A,$f13(A,B),$f11(A,B)).
% 2.07/2.26 ** KEPT (pick-wt=7): 52 [] -set(A)| -member(B,A)|set(B).
% 2.07/2.26 ** KEPT (pick-wt=9): 53 [] -member(A,initial_segment(B,C,D))|member(A,D).
% 2.07/2.26 ** KEPT (pick-wt=10): 54 [] -member(A,initial_segment(B,C,D))|apply(C,A,B).
% 2.07/2.26 ** KEPT (pick-wt=13): 55 [] member(A,initial_segment(B,C,D))| -member(A,D)| -apply(C,A,B).
% 2.07/2.26 ** KEPT (pick-wt=10): 56 [] -member(A,suc(B))|member(A,union(B,singleton(B))).
% 2.07/2.26 ** KEPT (pick-wt=10): 57 [] member(A,suc(B))| -member(A,union(B,singleton(B))).
% 2.07/2.26
% 2.07/2.26 ------------> process sos:
% 2.07/2.26 ** KEPT (pick-wt=3): 65 [] A=A.
% 2.07/2.26 ** KEPT (pick-wt=8): 66 [] subset(A,B)|member($f1(A,B),A).
% 2.07/2.26 ** KEPT (pick-wt=9): 67 [] member(A,product(B))|member($f3(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=13): 68 [] strict_order(A,B)|member($f10(A,B),B)|member($f13(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=13): 69 [] strict_order(A,B)|member($f10(A,B),B)|member($f12(A,B),B).
% 2.07/2.26 ** KEPT (pick-wt=13): 70 [] strict_order(A,B)|member($f10(A,B),B)|member($f11(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 71 [] strict_order(A,B)|member($f10(A,B),B)|apply(A,$f13(A,B),$f12(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=16): 72 [] strict_order(A,B)|member($f10(A,B),B)|apply(A,$f12(A,B),$f11(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=13): 73 [] strict_order(A,B)|member($f9(A,B),B)|member($f13(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=13): 74 [] strict_order(A,B)|member($f9(A,B),B)|member($f12(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=13): 75 [] strict_order(A,B)|member($f9(A,B),B)|member($f11(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 76 [] strict_order(A,B)|member($f9(A,B),B)|apply(A,$f13(A,B),$f12(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=16): 77 [] strict_order(A,B)|member($f9(A,B),B)|apply(A,$f12(A,B),$f11(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=16): 78 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f13(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 79 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f12(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 80 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|member($f11(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=19): 81 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|apply(A,$f13(A,B),$f12(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=19): 82 [] strict_order(A,B)|apply(A,$f10(A,B),$f9(A,B))|apply(A,$f12(A,B),$f11(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=16): 83 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f13(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 84 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f12(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=16): 85 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|member($f11(A,B),B).
% 2.07/2.29 ** KEPT (pick-wt=19): 86 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|apply(A,$f13(A,B),$f12(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=19): 87 [] strict_order(A,B)|apply(A,$f9(A,B),$f10(A,B))|apply(A,$f12(A,B),$f11(A,B)).
% 2.07/2.29 ** KEPT (pick-wt=3): 88 [] member($c2,on).
% 2.07/2.29 ** KEPT (pick-wt=3): 89 [] member($c1,on).
% 2.07/2.29 ** KEPT (pick-wt=3): 90 [] member($c2,$c1).
% 2.07/2.29 ** KEPT (pick-wt=3): 91 [] member($c1,$c2).
% 2.07/2.29 Following clause subsumed by 65 during input processing: 0 [copy,65,flip.1] A=A.
% 2.07/2.29
% 2.07/2.29 ======= end of input processing =======
% 2.07/2.29
% 2.07/2.29 =========== start of search ===========
% 2.07/2.29
% 2.07/2.29 -------- PROOF --------
% 2.07/2.29
% 2.07/2.29 -----> EMPTY CLAUSE at 0.04 sec ----> 724 [hyper,173,46,212,90,317,152] $F.
% 2.07/2.29
% 2.07/2.29 Length of proof is 6. Level of proof is 2.
% 2.07/2.29
% 2.07/2.29 ---------------- PROOF ----------------
% 2.07/2.29 % SZS status Theorem
% 2.07/2.29 % SZS output start Refutation
% See solution above
% 2.07/2.29 ------------ end of proof -------------
% 2.07/2.29
% 2.07/2.29
% 2.07/2.29 Search stopped by max_proofs option.
% 2.07/2.29
% 2.07/2.29
% 2.07/2.29 Search stopped by max_proofs option.
% 2.07/2.29
% 2.07/2.29 ============ end of search ============
% 2.07/2.29
% 2.07/2.29 -------------- statistics -------------
% 2.07/2.29 clauses given 33
% 2.07/2.29 clauses generated 793
% 2.07/2.29 clauses kept 722
% 2.07/2.29 clauses forward subsumed 151
% 2.07/2.29 clauses back subsumed 6
% 2.07/2.29 Kbytes malloced 2929
% 2.07/2.29
% 2.07/2.29 ----------- times (seconds) -----------
% 2.07/2.29 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 2.07/2.29 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.07/2.29 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.07/2.29
% 2.07/2.29 That finishes the proof of the theorem.
% 2.07/2.29
% 2.07/2.29 Process 8986 finished Wed Jul 27 10:37:25 2022
% 2.07/2.29 Otter interrupted
% 2.07/2.29 PROOF FOUND
%------------------------------------------------------------------------------