TSTP Solution File: NUM009-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:07:25 EDT 2022
% Result : Unsatisfiable 14.96s 15.11s
% Output : Refutation 14.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 1 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 4 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,B)
| little_set(A) ),
file('NUM009-1.p',unknown),
[] ).
cnf(153,axiom,
( member(A,natural_numbers)
| ~ little_set(A)
| member(empty_set,f44(A)) ),
file('NUM009-1.p',unknown),
[] ).
cnf(155,axiom,
( member(A,natural_numbers)
| ~ member(A,f44(A)) ),
file('NUM009-1.p',unknown),
[] ).
cnf(204,axiom,
~ member(empty_set,natural_numbers),
file('NUM009-1.p',unknown),
[] ).
cnf(298,axiom,
member(empty_set,infinity),
file('NUM009-1.p',unknown),
[] ).
cnf(439,plain,
little_set(empty_set),
inference(hyper,[status(thm)],[298,1]),
[iquote('hyper,298,1')] ).
cnf(441,plain,
member(empty_set,f44(empty_set)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[439,153]),204]),
[iquote('hyper,439,153,unit_del,204')] ).
cnf(486,plain,
member(empty_set,natural_numbers),
inference(hyper,[status(thm)],[441,155]),
[iquote('hyper,441,155')] ).
cnf(487,plain,
$false,
inference(binary,[status(thm)],[486,204]),
[iquote('binary,486.1,204.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 09:56:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 14.82/15.02 ----- Otter 3.3f, August 2004 -----
% 14.82/15.02 The process was started by sandbox2 on n022.cluster.edu,
% 14.82/15.02 Wed Jul 27 09:56:20 2022
% 14.82/15.02 The command was "./otter". The process ID is 24477.
% 14.82/15.02
% 14.82/15.02 set(prolog_style_variables).
% 14.82/15.02 set(auto).
% 14.82/15.02 dependent: set(auto1).
% 14.82/15.02 dependent: set(process_input).
% 14.82/15.02 dependent: clear(print_kept).
% 14.82/15.02 dependent: clear(print_new_demod).
% 14.82/15.02 dependent: clear(print_back_demod).
% 14.82/15.02 dependent: clear(print_back_sub).
% 14.82/15.02 dependent: set(control_memory).
% 14.82/15.02 dependent: assign(max_mem, 12000).
% 14.82/15.02 dependent: assign(pick_given_ratio, 4).
% 14.82/15.02 dependent: assign(stats_level, 1).
% 14.82/15.02 dependent: assign(max_seconds, 10800).
% 14.82/15.02 clear(print_given).
% 14.82/15.02
% 14.82/15.02 list(usable).
% 14.82/15.02 0 [] A=A.
% 14.82/15.02 0 [] -member(X,Y)|little_set(X).
% 14.82/15.02 0 [] little_set(f1(X,Y))|X=Y.
% 14.82/15.02 0 [] member(f1(X,Y),X)|member(f1(X,Y),Y)|X=Y.
% 14.82/15.02 0 [] -member(f1(X,Y),X)| -member(f1(X,Y),Y)|X=Y.
% 14.82/15.02 0 [] -member(U,non_ordered_pair(X,Y))|U=X|U=Y.
% 14.82/15.02 0 [] member(U,non_ordered_pair(X,Y))| -little_set(U)|U!=X.
% 14.82/15.02 0 [] member(U,non_ordered_pair(X,Y))| -little_set(U)|U!=Y.
% 14.82/15.02 0 [] little_set(non_ordered_pair(X,Y)).
% 14.82/15.02 0 [] singleton_set(X)=non_ordered_pair(X,X).
% 14.82/15.02 0 [] ordered_pair(X,Y)=non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)).
% 14.82/15.02 0 [] -ordered_pair_predicate(X)|little_set(f2(X)).
% 14.82/15.02 0 [] -ordered_pair_predicate(X)|little_set(f3(X)).
% 14.82/15.02 0 [] -ordered_pair_predicate(X)|X=ordered_pair(f2(X),f3(X)).
% 14.82/15.02 0 [] ordered_pair_predicate(X)| -little_set(Y)| -little_set(Z)|X!=ordered_pair(Y,Z).
% 14.82/15.02 0 [] -member(Z,first(X))|little_set(f4(Z,X)).
% 14.82/15.02 0 [] -member(Z,first(X))|little_set(f5(Z,X)).
% 14.82/15.02 0 [] -member(Z,first(X))|X=ordered_pair(f4(Z,X),f5(Z,X)).
% 14.82/15.02 0 [] -member(Z,first(X))|member(Z,f4(Z,X)).
% 14.82/15.02 0 [] member(Z,first(X))| -little_set(U)| -little_set(V)|X!=ordered_pair(U,V)| -member(Z,U).
% 14.82/15.02 0 [] -member(Z,second(X))|little_set(f6(Z,X)).
% 14.82/15.02 0 [] -member(Z,second(X))|little_set(f7(Z,X)).
% 14.82/15.02 0 [] -member(Z,second(X))|X=ordered_pair(f6(Z,X),f7(Z,X)).
% 14.82/15.02 0 [] -member(Z,second(X))|member(Z,f7(Z,X)).
% 14.82/15.02 0 [] member(Z,second(X))| -little_set(U)| -little_set(V)|X!=ordered_pair(U,V)| -member(Z,V).
% 14.82/15.02 0 [] -member(Z,estin)|ordered_pair_predicate(Z).
% 14.82/15.02 0 [] -member(Z,estin)|member(first(Z),second(Z)).
% 14.82/15.02 0 [] member(Z,estin)| -little_set(Z)| -ordered_pair_predicate(Z)| -member(first(Z),second(Z)).
% 14.82/15.02 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 14.82/15.02 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 14.82/15.02 0 [] member(Z,intersection(X,Y))| -member(Z,X)| -member(Z,Y).
% 14.82/15.02 0 [] -member(Z,complement(X))| -member(Z,X).
% 14.82/15.02 0 [] member(Z,complement(X))| -little_set(Z)|member(Z,X).
% 14.82/15.02 0 [] union(X,Y)=complement(intersection(complement(X),complement(Y))).
% 14.82/15.02 0 [] -member(Z,domain_of(X))|ordered_pair_predicate(f8(Z,X)).
% 14.82/15.02 0 [] -member(Z,domain_of(X))|member(f8(Z,X),X).
% 14.82/15.02 0 [] -member(Z,domain_of(X))|Z=first(f8(Z,X)).
% 14.82/15.02 0 [] member(Z,domain_of(X))| -little_set(Z)| -ordered_pair_predicate(Xp)| -member(Xp,X)|Z!=first(Xp).
% 14.82/15.02 0 [] -member(Z,cross_product(X,Y))|ordered_pair_predicate(Z).
% 14.82/15.02 0 [] -member(Z,cross_product(X,Y))|member(first(Z),X).
% 14.82/15.02 0 [] -member(Z,cross_product(X,Y))|member(second(Z),Y).
% 14.82/15.02 0 [] member(Z,cross_product(X,Y))| -little_set(Z)| -ordered_pair_predicate(Z)| -member(first(Z),X)| -member(second(Z),Y).
% 14.82/15.02 0 [] -member(Z,converse(X))|ordered_pair_predicate(Z).
% 14.82/15.02 0 [] -member(Z,converse(X))|member(ordered_pair(second(Z),first(Z)),X).
% 14.82/15.02 0 [] member(Z,converse(X))| -little_set(Z)| -ordered_pair_predicate(Z)| -member(ordered_pair(second(Z),first(Z)),X).
% 14.82/15.02 0 [] -member(Z,rotate_right(X))|little_set(f9(Z,X)).
% 14.82/15.02 0 [] -member(Z,rotate_right(X))|little_set(f10(Z,X)).
% 14.82/15.02 0 [] -member(Z,rotate_right(X))|little_set(f11(Z,X)).
% 14.82/15.02 0 [] -member(Z,rotate_right(X))|Z=ordered_pair(f9(Z,X),ordered_pair(f10(Z,X),f11(Z,X))).
% 14.82/15.02 0 [] -member(Z,rotate_right(X))|member(ordered_pair(f10(Z,X),ordered_pair(f11(Z,X),f9(Z,X))),X).
% 14.82/15.02 0 [] member(Z,rotate_right(X))| -little_set(Z)| -little_set(U)| -little_set(V)| -little_set(W)|Z!=ordered_pair(U,ordered_pair(V,W))| -member(ordered_pair(V,ordered_pair(W,U)),X).
% 14.82/15.02 0 [] -member(Z,flip_range_of(X))|little_set(f12(Z,X)).
% 14.82/15.02 0 [] -member(Z,flip_range_of(X))|little_set(f13(Z,X)).
% 14.82/15.02 0 [] -member(Z,flip_range_of(X))|little_set(f14(Z,X)).
% 14.82/15.02 0 [] -member(Z,flip_range_of(X))|Z=ordered_pair(f12(Z,X),ordered_pair(f13(Z,X),f14(Z,X))).
% 14.82/15.02 0 [] -member(Z,flip_range_of(X))|member(ordered_pair(f12(Z,X),ordered_pair(f14(Z,X),f13(Z,X))),X).
% 14.82/15.02 0 [] member(Z,flip_range_of(X))| -little_set(Z)| -little_set(U)| -little_set(V)| -little_set(W)|Z!=ordered_pair(U,ordered_pair(V,W))| -member(ordered_pair(U,ordered_pair(W,V)),X).
% 14.82/15.02 0 [] successor(X)=union(X,singleton_set(X)).
% 14.82/15.02 0 [] -member(Z,empty_set).
% 14.82/15.02 0 [] member(Z,universal_set)| -little_set(Z).
% 14.82/15.02 0 [] little_set(infinity).
% 14.82/15.02 0 [] member(empty_set,infinity).
% 14.82/15.02 0 [] -member(X,infinity)|member(successor(X),infinity).
% 14.82/15.02 0 [] -member(Z,sigma(X))|member(f16(Z,X),X).
% 14.82/15.02 0 [] -member(Z,sigma(X))|member(Z,f16(Z,X)).
% 14.82/15.02 0 [] member(Z,sigma(X))| -member(Y,X)| -member(Z,Y).
% 14.82/15.02 0 [] -little_set(U)|little_set(sigma(U)).
% 14.82/15.02 0 [] -subset(X,Y)| -member(U,X)|member(U,Y).
% 14.82/15.02 0 [] subset(X,Y)|member(f17(X,Y),X).
% 14.82/15.02 0 [] subset(X,Y)| -member(f17(X,Y),Y).
% 14.82/15.02 0 [] -proper_subset(X,Y)|subset(X,Y).
% 14.82/15.02 0 [] -proper_subset(X,Y)|X!=Y.
% 14.82/15.02 0 [] proper_subset(X,Y)| -subset(X,Y)|X=Y.
% 14.82/15.02 0 [] -member(Z,powerset(X))|subset(Z,X).
% 14.82/15.02 0 [] member(Z,powerset(X))| -little_set(Z)| -subset(Z,X).
% 14.82/15.02 0 [] -little_set(U)|little_set(powerset(U)).
% 14.82/15.02 0 [] -relation(Z)| -member(X,Z)|ordered_pair_predicate(X).
% 14.82/15.02 0 [] relation(Z)|member(f18(Z),Z).
% 14.82/15.02 0 [] relation(Z)| -ordered_pair_predicate(f18(Z)).
% 14.82/15.02 0 [] -single_valued_set(X)| -little_set(U)| -little_set(V)| -little_set(W)| -member(ordered_pair(U,V),X)| -member(ordered_pair(U,W),X)|V=W.
% 14.82/15.02 0 [] single_valued_set(X)|little_set(f19(X)).
% 14.82/15.02 0 [] single_valued_set(X)|little_set(f20(X)).
% 14.82/15.02 0 [] single_valued_set(X)|little_set(f21(X)).
% 14.82/15.02 0 [] single_valued_set(X)|member(ordered_pair(f19(X),f20(X)),X).
% 14.82/15.02 0 [] single_valued_set(X)|member(ordered_pair(f19(X),f21(X)),X).
% 14.82/15.02 0 [] single_valued_set(X)|f20(X)!=f21(X).
% 14.82/15.02 0 [] -function(Xf)|relation(Xf).
% 14.82/15.02 0 [] -function(Xf)|single_valued_set(Xf).
% 14.82/15.02 0 [] function(Xf)| -relation(Xf)| -single_valued_set(Xf).
% 14.82/15.02 0 [] -member(Z,image(X,Xf))|ordered_pair_predicate(f22(Z,X,Xf)).
% 14.82/15.02 0 [] -member(Z,image(X,Xf))|member(f22(Z,X,Xf),Xf).
% 14.82/15.02 0 [] -member(Z,image(X,Xf))|member(first(f22(Z,X,Xf)),X).
% 14.82/15.02 0 [] -member(Z,image(X,Xf))|second(f22(Z,X,Xf))=Z.
% 14.82/15.02 0 [] member(Z,image(X,Xf))| -little_set(Z)| -ordered_pair_predicate(Y)| -member(Y,Xf)| -member(first(Y),X)|second(Y)!=Z.
% 14.82/15.02 0 [] -little_set(X)| -function(Xf)|little_set(image(X,Xf)).
% 14.82/15.02 0 [] -disjoint(X,Y)| -member(U,X)| -member(U,Y).
% 14.82/15.02 0 [] disjoint(X,Y)|member(f23(X,Y),X).
% 14.82/15.02 0 [] disjoint(X,Y)|member(f23(X,Y),Y).
% 14.82/15.02 0 [] X=empty_set|member(f24(X),X).
% 14.82/15.02 0 [] X=empty_set|disjoint(f24(X),X).
% 14.82/15.02 0 [] function(f25).
% 14.82/15.02 0 [] -little_set(X)|X=empty_set|member(f26(X),X).
% 14.82/15.02 0 [] -little_set(X)|X=empty_set|member(ordered_pair(X,f26(X)),f25).
% 14.82/15.02 0 [] -member(Z,range_of(X))|ordered_pair_predicate(f27(Z,X)).
% 14.82/15.02 0 [] -member(Z,range_of(X))|member(f27(Z,X),X).
% 14.82/15.02 0 [] -member(Z,range_of(X))|Z=second(f27(Z,X)).
% 14.82/15.02 0 [] member(Z,range_of(X))| -little_set(Z)| -ordered_pair_predicate(Xp)| -member(Xp,X)|Z!=second(Xp).
% 14.82/15.02 0 [] -member(Z,identity_relation)|ordered_pair_predicate(Z).
% 14.82/15.02 0 [] -member(Z,identity_relation)|first(Z)=second(Z).
% 14.82/15.02 0 [] member(Z,identity_relation)| -little_set(Z)| -ordered_pair_predicate(Z)|first(Z)!=second(Z).
% 14.82/15.02 0 [] restrict(X,Y)=intersection(X,cross_product(Y,universal_set)).
% 14.82/15.02 0 [] -one_to_one_function(Xf)|function(Xf).
% 14.82/15.02 0 [] -one_to_one_function(Xf)|function(converse(Xf)).
% 14.82/15.02 0 [] one_to_one_function(Xf)| -function(Xf)| -function(converse(Xf)).
% 14.82/15.02 0 [] -member(Z,apply(Xf,Y))|ordered_pair_predicate(f28(Z,Xf,Y)).
% 14.82/15.02 0 [] -member(Z,apply(Xf,Y))|member(f28(Z,Xf,Y),Xf).
% 14.82/15.02 0 [] -member(Z,apply(Xf,Y))|first(f28(Z,Xf,Y))=Y.
% 14.82/15.02 0 [] -member(Z,apply(Xf,Y))|member(Z,second(f28(Z,Xf,Y))).
% 14.82/15.02 0 [] member(Z,apply(Xf,Y))| -ordered_pair_predicate(W)| -member(W,Xf)|first(W)!=Y| -member(Z,second(W)).
% 14.82/15.02 0 [] apply_to_two_arguments(Xf,X,Y)=apply(Xf,ordered_pair(X,Y)).
% 14.82/15.02 0 [] -maps(Xf,X,Y)|function(Xf).
% 14.82/15.02 0 [] -maps(Xf,X,Y)|domain_of(Xf)=X.
% 14.82/15.02 0 [] -maps(Xf,X,Y)|subset(range_of(Xf),Y).
% 14.82/15.02 0 [] maps(Xf,X,Y)| -function(Xf)|domain_of(Xf)!=X| -subset(range_of(Xf),Y).
% 14.82/15.02 0 [] -closed(Xs,Xf)|little_set(Xs).
% 14.82/15.02 0 [] -closed(Xs,Xf)|little_set(Xf).
% 14.82/15.02 0 [] -closed(Xs,Xf)|maps(Xf,cross_product(Xs,Xs),Xs).
% 14.82/15.02 0 [] closed(Xs,Xf)| -little_set(Xs)| -little_set(Xf)| -maps(Xf,cross_product(Xs,Xs),Xs).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|little_set(f29(Z,Xf,Xg)).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|little_set(f30(Z,Xf,Xg)).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|little_set(f31(Z,Xf,Xg)).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|Z=ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf).
% 14.82/15.02 0 [] -member(Z,compose(Xf,Xg))|member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg).
% 14.82/15.02 0 [] member(Z,compose(Xf,Xg))| -little_set(Z)| -little_set(X)| -little_set(Y)| -little_set(W)|Z!=ordered_pair(X,Y)| -member(ordered_pair(X,W),Xf)| -member(ordered_pair(W,Y),Xg).
% 14.82/15.02 0 [] -homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)|closed(Xs1,Xf1).
% 14.82/15.02 0 [] -homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)|closed(Xs2,Xf2).
% 14.82/15.02 0 [] -homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)|maps(Xh,Xs1,Xs2).
% 14.82/15.02 0 [] -homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)| -member(X,Xs1)| -member(Y,Xs1)|apply(Xh,apply_to_two_arguments(Xf1,X,Y))=apply_to_two_arguments(Xf2,apply(Xh,X),apply(Xh,Y)).
% 14.82/15.02 0 [] homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)| -closed(Xs1,Xf1)| -closed(Xs2,Xf2)| -maps(Xh,Xs1,Xs2)|member(f32(Xh,Xs1,Xf1,Xs2,Xf2),Xs1).
% 14.82/15.02 0 [] homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)| -closed(Xs1,Xf1)| -closed(Xs2,Xf2)| -maps(Xh,Xs1,Xs2)|member(f33(Xh,Xs1,Xf1,Xs2,Xf2),Xs1).
% 14.82/15.02 0 [] homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)| -closed(Xs1,Xf1)| -closed(Xs2,Xf2)| -maps(Xh,Xs1,Xs2)|apply(Xh,apply_to_two_arguments(Xf1,f32(Xh,Xs1,Xf1,Xs2,Xf2),f33(Xh,Xs1,Xf1,Xs2,Xf2)))!=apply_to_two_arguments(Xf2,apply(Xh,f32(Xh,Xs1,Xf1,Xs2,Xf2)),apply(Xh,f33(Xh,Xs1,Xf1,Xs2,Xf2))).
% 14.82/15.02 0 [] -associative(Xs,Xf)| -member(X,Xs)| -member(Y,Xs)| -member(Z,Xs)|apply_to_two_arguments(Xf,apply_to_two_arguments(Xf,X,Y),Z)=apply_to_two_arguments(Xf,X,apply_to_two_arguments(Xf,Y,Z)).
% 14.82/15.02 0 [] associative(Xs,Xf)|member(f34(Xs,Xf),Xs).
% 14.82/15.02 0 [] associative(Xs,Xf)|member(f35(Xs,Xf),Xs).
% 14.82/15.02 0 [] associative(Xs,Xf)|member(f36(Xs,Xf),Xs).
% 14.82/15.02 0 [] associative(Xs,Xf)|apply_to_two_arguments(Xf,apply_to_two_arguments(Xf,f34(Xs,Xf),f35(Xs,Xf)),f36(Xs,Xf))!=apply_to_two_arguments(Xf,f34(Xs,Xf),apply_to_two_arguments(Xf,f35(Xs,Xf),f36(Xs,Xf))).
% 14.82/15.02 0 [] -identity(Xs,Xf,Xe)|member(Xe,Xs).
% 14.82/15.02 0 [] -identity(Xs,Xf,Xe)| -member(X,Xs)|apply_to_two_arguments(Xf,Xe,X)=X.
% 14.82/15.02 0 [] -identity(Xs,Xf,Xe)| -member(X,Xs)|apply_to_two_arguments(Xf,X,Xe)=X.
% 14.82/15.02 0 [] identity(Xs,Xf,Xe)| -member(Xe,Xs)|member(f37(Xs,Xf,Xe),Xs).
% 14.82/15.02 0 [] identity(Xs,Xf,Xe)| -member(Xe,Xs)|apply_to_two_arguments(Xf,Xe,f37(Xs,Xf,Xe))!=f37(Xs,Xf,Xe)|apply_to_two_arguments(Xf,f37(Xs,Xf,Xe),Xe)!=f37(Xs,Xf,Xe).
% 14.82/15.02 0 [] -inverse(Xs,Xf,Xe,Xg)|maps(Xg,Xs,Xs).
% 14.82/15.02 0 [] -inverse(Xs,Xf,Xe,Xg)| -member(X,Xs)|apply_to_two_arguments(Xf,apply(Xg,X),X)=Xe.
% 14.82/15.02 0 [] -inverse(Xs,Xf,Xe,Xg)| -member(X,Xs)|apply_to_two_arguments(Xf,X,apply(Xg,X))=Xe.
% 14.82/15.02 0 [] inverse(Xs,Xf,Xe,Xg)| -maps(Xg,Xs,Xs)|member(f38(Xs,Xf,Xe,Xg),Xs).
% 14.82/15.02 0 [] inverse(Xs,Xf,Xe,Xg)| -maps(Xg,Xs,Xs)|apply_to_two_arguments(Xf,apply(Xg,f38(Xs,Xf,Xe,Xg)),f38(Xs,Xf,Xe,Xg))!=Xe|apply_to_two_arguments(Xf,f38(Xs,Xf,Xe,Xg),apply(Xg,f38(Xs,Xf,Xe,Xg)))!=Xe.
% 14.82/15.02 0 [] -group(Xs,Xf)|closed(Xs,Xf).
% 14.82/15.02 0 [] -group(Xs,Xf)|associative(Xs,Xf).
% 14.82/15.02 0 [] -group(Xs,Xf)|identity(Xs,Xf,f39(Xs,Xf)).
% 14.82/15.02 0 [] -group(Xs,Xf)|inverse(Xs,Xf,f39(Xs,Xf),f40(Xs,Xf)).
% 14.82/15.02 0 [] group(Xs,Xf)| -closed(Xs,Xf)| -associative(Xs,Xf)| -identity(Xs,Xf,Xe)| -inverse(Xs,Xf,Xe,Xg).
% 14.82/15.02 0 [] -commutes(Xs,Xf)| -member(X,Xs)| -member(Y,Xs)|apply_to_two_arguments(Xf,X,Y)=apply_to_two_arguments(Xf,Y,X).
% 14.82/15.02 0 [] commutes(Xs,Xf)|member(f41(Xs,Xf),Xs).
% 14.82/15.02 0 [] commutes(Xs,Xf)|member(f42(Xs,Xf),Xs).
% 14.82/15.02 0 [] commutes(Xs,Xf)|apply_to_two_arguments(Xf,f41(Xs,Xf),f42(Xs,Xf))!=apply_to_two_arguments(Xf,f42(Xs,Xf),f41(Xs,Xf)).
% 14.82/15.02 0 [] -member(Z,natural_numbers)| -little_set(Xs)| -member(empty_set,Xs)|member(f43(Z,Xs),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,natural_numbers)| -little_set(Xs)| -member(empty_set,Xs)| -member(successor(f43(Z,Xs)),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] member(Z,natural_numbers)| -little_set(Z)|little_set(f44(Z)).
% 14.82/15.02 0 [] member(Z,natural_numbers)| -little_set(Z)|member(empty_set,f44(Z)).
% 14.82/15.02 0 [] member(Z,natural_numbers)| -little_set(Z)| -member(Xk,f44(Z))|member(successor(Xk),f44(Z)).
% 14.82/15.02 0 [] member(Z,natural_numbers)| -member(Z,f44(Z)).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)|member(f45(Z,Xs),natural_numbers)|member(f46(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)|member(f45(Z,Xs),natural_numbers)|member(f47(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)|member(f45(Z,Xs),natural_numbers)|member(f48(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)|member(f45(Z,Xs),natural_numbers)|member(ordered_pair(ordered_pair(f46(Z,Xs),f47(Z,Xs)),f48(Z,Xs)),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)|member(f45(Z,Xs),natural_numbers)| -member(ordered_pair(ordered_pair(successor(f46(Z,Xs)),f47(Z,Xs)),successor(f48(Z,Xs))),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f45(Z,Xs)),f45(Z,Xs)),Xs)|member(f46(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f45(Z,Xs)),f45(Z,Xs)),Xs)|member(f47(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f45(Z,Xs)),f45(Z,Xs)),Xs)|member(f48(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f45(Z,Xs)),f45(Z,Xs)),Xs)|member(ordered_pair(ordered_pair(f46(Z,Xs),f47(Z,Xs)),f48(Z,Xs)),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,plus)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f45(Z,Xs)),f45(Z,Xs)),Xs)| -member(ordered_pair(ordered_pair(successor(f46(Z,Xs)),f47(Z,Xs)),successor(f48(Z,Xs))),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] member(Z,plus)| -little_set(Z)|little_set(f49(Z)).
% 14.82/15.02 0 [] member(Z,plus)| -little_set(Z)| -member(Xi,natural_numbers)|member(ordered_pair(ordered_pair(empty_set,Xi),Xi),f49(Z)).
% 14.82/15.02 0 [] member(Z,plus)| -little_set(Z)| -member(Uu1,natural_numbers)| -member(Xj,natural_numbers)| -member(Xk,natural_numbers)| -member(ordered_pair(ordered_pair(Uu1,Xj),Xk),f49(Z))|member(ordered_pair(ordered_pair(successor(Uu1),Xj),successor(Xk)),f49(Z)).
% 14.82/15.02 0 [] member(Z,plus)| -member(Z,f49(Z)).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)|member(f50(Z,Xs),natural_numbers)|member(f51(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)|member(f50(Z,Xs),natural_numbers)|member(f52(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)|member(f50(Z,Xs),natural_numbers)|member(f53(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)|member(f50(Z,Xs),natural_numbers)|member(ordered_pair(ordered_pair(f51(Z,Xs),f52(Z,Xs)),f53(Z,Xs)),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)|member(f50(Z,Xs),natural_numbers)| -member(ordered_pair(ordered_pair(successor(f51(Z,Xs)),f52(Z,Xs)),apply_to_two_arguments(plus,f53(Z,Xs),f52(Z,Xs))),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f50(Z,Xs)),empty_set),Xs)|member(f51(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f50(Z,Xs)),empty_set),Xs)|member(f52(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f50(Z,Xs)),empty_set),Xs)|member(f53(Z,Xs),natural_numbers)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f50(Z,Xs)),empty_set),Xs)|member(ordered_pair(ordered_pair(f51(Z,Xs),f52(Z,Xs)),f53(Z,Xs)),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] -member(Z,times)| -little_set(Xs)| -member(ordered_pair(ordered_pair(empty_set,f50(Z,Xs)),empty_set),Xs)| -member(ordered_pair(ordered_pair(successor(f51(Z,Xs)),f52(Z,Xs)),apply_to_two_arguments(plus,f53(Z,Xs),f52(Z,Xs))),Xs)|member(Z,Xs).
% 14.82/15.02 0 [] member(Z,times)| -little_set(Z)|little_set(f54(Z)).
% 14.82/15.02 0 [] member(Z,times)| -little_set(Z)| -member(Xi,natural_numbers)|member(ordered_pair(ordered_pair(empty_set,Xi),empty_set),f54(Z)).
% 14.82/15.02 0 [] member(Z,times)| -little_set(Z)| -member(Uu2,natural_numbers)| -member(Xj,natural_numbers)| -member(Xk,natural_numbers)| -member(ordered_pair(ordered_pair(Uu2,Xj),Xk),f54(Z))|member(ordered_pair(ordered_pair(successor(Uu2),Xj),apply_to_two_arguments(plus,Xk,Xj)),f54(Z)).
% 14.82/15.02 0 [] member(Z,times)| -member(Z,f54(Z)).
% 14.82/15.02 0 [] -member(Z,prime_numbers)|member(Z,natural_numbers).
% 14.82/15.03 0 [] -member(Z,prime_numbers)|Z!=empty_set.
% 14.82/15.03 0 [] -member(Z,prime_numbers)|Z!=successor(empty_set).
% 14.82/15.03 0 [] -member(Z,prime_numbers)| -member(U,natural_numbers)| -member(V,natural_numbers)|apply_to_two_arguments(times,U,V)!=Z|member(U,non_ordered_pair(successor(empty_set),Z)).
% 14.82/15.03 0 [] member(Z,prime_numbers)| -member(Z,natural_numbers)|Z=empty_set|Z=successor(empty_set)|member(f55(Z),natural_numbers).
% 14.82/15.03 0 [] member(Z,prime_numbers)| -member(Z,natural_numbers)|Z=empty_set|Z=successor(empty_set)|member(f56(Z),natural_numbers).
% 14.82/15.03 0 [] member(Z,prime_numbers)| -member(Z,natural_numbers)|Z=empty_set|Z=successor(empty_set)|apply_to_two_arguments(times,f55(Z),f56(Z))=Z.
% 14.82/15.03 0 [] member(Z,prime_numbers)| -member(Z,natural_numbers)|Z=empty_set|Z=successor(empty_set)| -member(f55(Z),non_ordered_pair(successor(empty_set),Z)).
% 14.82/15.03 0 [] -finite(X)|member(f57(X),natural_numbers).
% 14.82/15.03 0 [] -finite(X)|maps(f58(X),f57(X),X).
% 14.82/15.03 0 [] -finite(X)|range_of(f58(X))=X.
% 14.82/15.03 0 [] -finite(X)|one_to_one_function(f58(X)).
% 14.82/15.03 0 [] finite(X)| -member(Xn,natural_numbers)| -maps(Xf,Xn,X)|range_of(Xf)!=X| -one_to_one_function(Xf).
% 14.82/15.03 0 [] -member(Z,twin_prime_numbers)|member(Z,prime_numbers).
% 14.82/15.03 0 [] -member(Z,twin_prime_numbers)|member(successor(successor(Z)),prime_numbers).
% 14.82/15.03 0 [] member(Z,twin_prime_numbers)| -member(Z,prime_numbers)| -member(successor(successor(Z)),prime_numbers).
% 14.82/15.03 0 [] -member(Z,even_numbers)|member(Z,natural_numbers).
% 14.82/15.03 0 [] -member(Z,even_numbers)|member(f59(Z),natural_numbers).
% 14.82/15.03 0 [] -member(Z,even_numbers)|apply_to_two_arguments(plus,f59(Z),f59(Z))=Z.
% 14.82/15.03 0 [] member(Z,even_numbers)| -member(Z,natural_numbers)| -member(X,natural_numbers)|apply_to_two_arguments(plus,X,X)!=Z.
% 14.82/15.03 0 [] -member(empty_set,natural_numbers).
% 14.82/15.03 end_of_list.
% 14.82/15.03
% 14.82/15.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 14.82/15.03
% 14.82/15.03 This ia a non-Horn set with equality. The strategy will be
% 14.82/15.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 14.82/15.03 deletion, with positive clauses in sos and nonpositive
% 14.82/15.03 clauses in usable.
% 14.82/15.03
% 14.82/15.03 dependent: set(knuth_bendix).
% 14.82/15.03 dependent: set(anl_eq).
% 14.82/15.03 dependent: set(para_from).
% 14.82/15.03 dependent: set(para_into).
% 14.82/15.03 dependent: clear(para_from_right).
% 14.82/15.03 dependent: clear(para_into_right).
% 14.82/15.03 dependent: set(para_from_vars).
% 14.82/15.03 dependent: set(eq_units_both_ways).
% 14.82/15.03 dependent: set(dynamic_demod_all).
% 14.82/15.03 dependent: set(dynamic_demod).
% 14.82/15.03 dependent: set(order_eq).
% 14.82/15.03 dependent: set(back_demod).
% 14.82/15.03 dependent: set(lrpo).
% 14.82/15.03 dependent: set(hyper_res).
% 14.82/15.03 dependent: set(unit_deletion).
% 14.82/15.03 dependent: set(factor).
% 14.82/15.03
% 14.82/15.03 ------------> process usable:
% 14.82/15.03 ** KEPT (pick-wt=5): 1 [] -member(A,B)|little_set(A).
% 14.82/15.03 ** KEPT (pick-wt=13): 2 [] -member(f1(A,B),A)| -member(f1(A,B),B)|A=B.
% 14.82/15.03 ** KEPT (pick-wt=11): 3 [] -member(A,non_ordered_pair(B,C))|A=B|A=C.
% 14.82/15.03 ** KEPT (pick-wt=10): 4 [] member(A,non_ordered_pair(B,C))| -little_set(A)|A!=B.
% 14.82/15.03 ** KEPT (pick-wt=10): 5 [] member(A,non_ordered_pair(B,C))| -little_set(A)|A!=C.
% 14.82/15.03 ** KEPT (pick-wt=5): 6 [] -ordered_pair_predicate(A)|little_set(f2(A)).
% 14.82/15.03 ** KEPT (pick-wt=5): 7 [] -ordered_pair_predicate(A)|little_set(f3(A)).
% 14.82/15.03 ** KEPT (pick-wt=9): 9 [copy,8,flip.2] -ordered_pair_predicate(A)|ordered_pair(f2(A),f3(A))=A.
% 14.82/15.03 ** KEPT (pick-wt=11): 10 [] ordered_pair_predicate(A)| -little_set(B)| -little_set(C)|A!=ordered_pair(B,C).
% 14.82/15.03 ** KEPT (pick-wt=8): 11 [] -member(A,first(B))|little_set(f4(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 12 [] -member(A,first(B))|little_set(f5(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=13): 14 [copy,13,flip.2] -member(A,first(B))|ordered_pair(f4(A,B),f5(A,B))=B.
% 14.82/15.03 ** KEPT (pick-wt=9): 15 [] -member(A,first(B))|member(A,f4(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=16): 16 [] member(A,first(B))| -little_set(C)| -little_set(D)|B!=ordered_pair(C,D)| -member(A,C).
% 14.82/15.03 ** KEPT (pick-wt=8): 17 [] -member(A,second(B))|little_set(f6(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 18 [] -member(A,second(B))|little_set(f7(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=13): 20 [copy,19,flip.2] -member(A,second(B))|ordered_pair(f6(A,B),f7(A,B))=B.
% 14.82/15.03 ** KEPT (pick-wt=9): 21 [] -member(A,second(B))|member(A,f7(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=16): 22 [] member(A,second(B))| -little_set(C)| -little_set(D)|B!=ordered_pair(C,D)| -member(A,D).
% 14.82/15.03 ** KEPT (pick-wt=5): 23 [] -member(A,estin)|ordered_pair_predicate(A).
% 14.82/15.03 ** KEPT (pick-wt=8): 24 [] -member(A,estin)|member(first(A),second(A)).
% 14.82/15.03 ** KEPT (pick-wt=12): 25 [] member(A,estin)| -little_set(A)| -ordered_pair_predicate(A)| -member(first(A),second(A)).
% 14.82/15.03 ** KEPT (pick-wt=8): 26 [] -member(A,intersection(B,C))|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=8): 27 [] -member(A,intersection(B,C))|member(A,C).
% 14.82/15.03 ** KEPT (pick-wt=11): 28 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 14.82/15.03 ** KEPT (pick-wt=7): 29 [] -member(A,complement(B))| -member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=9): 30 [] member(A,complement(B))| -little_set(A)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=8): 31 [] -member(A,domain_of(B))|ordered_pair_predicate(f8(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=9): 32 [] -member(A,domain_of(B))|member(f8(A,B),B).
% 14.82/15.03 ** KEPT (pick-wt=10): 34 [copy,33,flip.2] -member(A,domain_of(B))|first(f8(A,B))=A.
% 14.82/15.03 ** KEPT (pick-wt=15): 35 [] member(A,domain_of(B))| -little_set(A)| -ordered_pair_predicate(C)| -member(C,B)|A!=first(C).
% 14.82/15.03 ** KEPT (pick-wt=7): 36 [] -member(A,cross_product(B,C))|ordered_pair_predicate(A).
% 14.82/15.03 ** KEPT (pick-wt=9): 37 [] -member(A,cross_product(B,C))|member(first(A),B).
% 14.82/15.03 ** KEPT (pick-wt=9): 38 [] -member(A,cross_product(B,C))|member(second(A),C).
% 14.82/15.03 ** KEPT (pick-wt=17): 39 [] member(A,cross_product(B,C))| -little_set(A)| -ordered_pair_predicate(A)| -member(first(A),B)| -member(second(A),C).
% 14.82/15.03 ** KEPT (pick-wt=6): 40 [] -member(A,converse(B))|ordered_pair_predicate(A).
% 14.82/15.03 ** KEPT (pick-wt=11): 41 [] -member(A,converse(B))|member(ordered_pair(second(A),first(A)),B).
% 14.82/15.03 ** KEPT (pick-wt=15): 42 [] member(A,converse(B))| -little_set(A)| -ordered_pair_predicate(A)| -member(ordered_pair(second(A),first(A)),B).
% 14.82/15.03 ** KEPT (pick-wt=8): 43 [] -member(A,rotate_right(B))|little_set(f9(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 44 [] -member(A,rotate_right(B))|little_set(f10(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 45 [] -member(A,rotate_right(B))|little_set(f11(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=17): 47 [copy,46,flip.2] -member(A,rotate_right(B))|ordered_pair(f9(A,B),ordered_pair(f10(A,B),f11(A,B)))=A.
% 14.82/15.03 ** KEPT (pick-wt=17): 48 [] -member(A,rotate_right(B))|member(ordered_pair(f10(A,B),ordered_pair(f11(A,B),f9(A,B))),B).
% 14.82/15.03 ** KEPT (pick-wt=26): 49 [] member(A,rotate_right(B))| -little_set(A)| -little_set(C)| -little_set(D)| -little_set(E)|A!=ordered_pair(C,ordered_pair(D,E))| -member(ordered_pair(D,ordered_pair(E,C)),B).
% 14.82/15.03 ** KEPT (pick-wt=8): 50 [] -member(A,flip_range_of(B))|little_set(f12(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 51 [] -member(A,flip_range_of(B))|little_set(f13(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=8): 52 [] -member(A,flip_range_of(B))|little_set(f14(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=17): 54 [copy,53,flip.2] -member(A,flip_range_of(B))|ordered_pair(f12(A,B),ordered_pair(f13(A,B),f14(A,B)))=A.
% 14.82/15.03 ** KEPT (pick-wt=17): 55 [] -member(A,flip_range_of(B))|member(ordered_pair(f12(A,B),ordered_pair(f14(A,B),f13(A,B))),B).
% 14.82/15.03 ** KEPT (pick-wt=26): 56 [] member(A,flip_range_of(B))| -little_set(A)| -little_set(C)| -little_set(D)| -little_set(E)|A!=ordered_pair(C,ordered_pair(D,E))| -member(ordered_pair(C,ordered_pair(E,D)),B).
% 14.82/15.03 ** KEPT (pick-wt=3): 57 [] -member(A,empty_set).
% 14.82/15.03 ** KEPT (pick-wt=5): 58 [] member(A,universal_set)| -little_set(A).
% 14.82/15.03 ** KEPT (pick-wt=7): 59 [] -member(A,infinity)|member(successor(A),infinity).
% 14.82/15.03 ** KEPT (pick-wt=9): 60 [] -member(A,sigma(B))|member(f16(A,B),B).
% 14.82/15.03 ** KEPT (pick-wt=9): 61 [] -member(A,sigma(B))|member(A,f16(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=10): 62 [] member(A,sigma(B))| -member(C,B)| -member(A,C).
% 14.82/15.03 ** KEPT (pick-wt=5): 63 [] -little_set(A)|little_set(sigma(A)).
% 14.82/15.03 ** KEPT (pick-wt=9): 64 [] -subset(A,B)| -member(C,A)|member(C,B).
% 14.82/15.03 ** KEPT (pick-wt=8): 65 [] subset(A,B)| -member(f17(A,B),B).
% 14.82/15.03 ** KEPT (pick-wt=6): 66 [] -proper_subset(A,B)|subset(A,B).
% 14.82/15.03 ** KEPT (pick-wt=6): 67 [] -proper_subset(A,B)|A!=B.
% 14.82/15.03 ** KEPT (pick-wt=9): 68 [] proper_subset(A,B)| -subset(A,B)|A=B.
% 14.82/15.03 ** KEPT (pick-wt=7): 69 [] -member(A,powerset(B))|subset(A,B).
% 14.82/15.03 ** KEPT (pick-wt=9): 70 [] member(A,powerset(B))| -little_set(A)| -subset(A,B).
% 14.82/15.03 ** KEPT (pick-wt=5): 71 [] -little_set(A)|little_set(powerset(A)).
% 14.82/15.03 ** KEPT (pick-wt=7): 72 [] -relation(A)| -member(B,A)|ordered_pair_predicate(B).
% 14.82/15.03 ** KEPT (pick-wt=5): 73 [] relation(A)| -ordered_pair_predicate(f18(A)).
% 14.82/15.03 ** KEPT (pick-wt=21): 74 [] -single_valued_set(A)| -little_set(B)| -little_set(C)| -little_set(D)| -member(ordered_pair(B,C),A)| -member(ordered_pair(B,D),A)|C=D.
% 14.82/15.03 ** KEPT (pick-wt=7): 76 [copy,75,flip.2] single_valued_set(A)|f21(A)!=f20(A).
% 14.82/15.03 ** KEPT (pick-wt=4): 77 [] -function(A)|relation(A).
% 14.82/15.03 ** KEPT (pick-wt=4): 78 [] -function(A)|single_valued_set(A).
% 14.82/15.03 ** KEPT (pick-wt=6): 79 [] function(A)| -relation(A)| -single_valued_set(A).
% 14.82/15.03 ** KEPT (pick-wt=10): 80 [] -member(A,image(B,C))|ordered_pair_predicate(f22(A,B,C)).
% 14.82/15.03 ** KEPT (pick-wt=11): 81 [] -member(A,image(B,C))|member(f22(A,B,C),C).
% 14.82/15.03 ** KEPT (pick-wt=12): 82 [] -member(A,image(B,C))|member(first(f22(A,B,C)),B).
% 14.82/15.03 ** KEPT (pick-wt=12): 83 [] -member(A,image(B,C))|second(f22(A,B,C))=A.
% 14.82/15.03 ** KEPT (pick-wt=20): 84 [] member(A,image(B,C))| -little_set(A)| -ordered_pair_predicate(D)| -member(D,C)| -member(first(D),B)|second(D)!=A.
% 14.82/15.03 ** KEPT (pick-wt=8): 85 [] -little_set(A)| -function(B)|little_set(image(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=9): 86 [] -disjoint(A,B)| -member(C,A)| -member(C,B).
% 14.82/15.03 ** KEPT (pick-wt=9): 87 [] -little_set(A)|A=empty_set|member(f26(A),A).
% 14.82/15.03 ** KEPT (pick-wt=11): 88 [] -little_set(A)|A=empty_set|member(ordered_pair(A,f26(A)),f25).
% 14.82/15.03 ** KEPT (pick-wt=8): 89 [] -member(A,range_of(B))|ordered_pair_predicate(f27(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=9): 90 [] -member(A,range_of(B))|member(f27(A,B),B).
% 14.82/15.03 ** KEPT (pick-wt=10): 92 [copy,91,flip.2] -member(A,range_of(B))|second(f27(A,B))=A.
% 14.82/15.03 ** KEPT (pick-wt=15): 93 [] member(A,range_of(B))| -little_set(A)| -ordered_pair_predicate(C)| -member(C,B)|A!=second(C).
% 14.82/15.03 ** KEPT (pick-wt=5): 94 [] -member(A,identity_relation)|ordered_pair_predicate(A).
% 14.82/15.03 ** KEPT (pick-wt=8): 96 [copy,95,flip.2] -member(A,identity_relation)|second(A)=first(A).
% 14.82/15.03 ** KEPT (pick-wt=12): 98 [copy,97,flip.4] member(A,identity_relation)| -little_set(A)| -ordered_pair_predicate(A)|second(A)!=first(A).
% 14.82/15.03 ** KEPT (pick-wt=4): 99 [] -one_to_one_function(A)|function(A).
% 14.82/15.03 ** KEPT (pick-wt=5): 100 [] -one_to_one_function(A)|function(converse(A)).
% 14.82/15.03 ** KEPT (pick-wt=7): 101 [] one_to_one_function(A)| -function(A)| -function(converse(A)).
% 14.82/15.03 ** KEPT (pick-wt=10): 102 [] -member(A,apply(B,C))|ordered_pair_predicate(f28(A,B,C)).
% 14.82/15.03 ** KEPT (pick-wt=11): 103 [] -member(A,apply(B,C))|member(f28(A,B,C),B).
% 14.82/15.03 ** KEPT (pick-wt=12): 104 [] -member(A,apply(B,C))|first(f28(A,B,C))=C.
% 14.82/15.03 ** KEPT (pick-wt=12): 105 [] -member(A,apply(B,C))|member(A,second(f28(A,B,C))).
% 14.82/15.03 ** KEPT (pick-wt=18): 106 [] member(A,apply(B,C))| -ordered_pair_predicate(D)| -member(D,B)|first(D)!=C| -member(A,second(D)).
% 14.82/15.03 ** KEPT (pick-wt=6): 107 [] -maps(A,B,C)|function(A).
% 14.82/15.03 ** KEPT (pick-wt=8): 108 [] -maps(A,B,C)|domain_of(A)=B.
% 14.82/15.03 ** KEPT (pick-wt=8): 109 [] -maps(A,B,C)|subset(range_of(A),C).
% 14.82/15.03 ** KEPT (pick-wt=14): 110 [] maps(A,B,C)| -function(A)|domain_of(A)!=B| -subset(range_of(A),C).
% 14.82/15.03 ** KEPT (pick-wt=5): 111 [] -closed(A,B)|little_set(A).
% 14.82/15.03 ** KEPT (pick-wt=5): 112 [] -closed(A,B)|little_set(B).
% 14.82/15.03 ** KEPT (pick-wt=9): 113 [] -closed(A,B)|maps(B,cross_product(A,A),A).
% 14.82/15.03 ** KEPT (pick-wt=13): 114 [] closed(A,B)| -little_set(A)| -little_set(B)| -maps(B,cross_product(A,A),A).
% 14.82/15.03 ** KEPT (pick-wt=10): 115 [] -member(A,compose(B,C))|little_set(f29(A,B,C)).
% 14.82/15.03 ** KEPT (pick-wt=10): 116 [] -member(A,compose(B,C))|little_set(f30(A,B,C)).
% 14.82/15.03 ** KEPT (pick-wt=10): 117 [] -member(A,compose(B,C))|little_set(f31(A,B,C)).
% 14.82/15.03 ** KEPT (pick-wt=16): 119 [copy,118,flip.2] -member(A,compose(B,C))|ordered_pair(f29(A,B,C),f30(A,B,C))=A.
% 14.82/15.03 ** KEPT (pick-wt=16): 120 [] -member(A,compose(B,C))|member(ordered_pair(f29(A,B,C),f31(A,B,C)),B).
% 14.82/15.03 ** KEPT (pick-wt=16): 121 [] -member(A,compose(B,C))|member(ordered_pair(f31(A,B,C),f30(A,B,C)),C).
% 14.82/15.03 ** KEPT (pick-wt=28): 122 [] member(A,compose(B,C))| -little_set(A)| -little_set(D)| -little_set(E)| -little_set(F)|A!=ordered_pair(D,E)| -member(ordered_pair(D,F),B)| -member(ordered_pair(F,E),C).
% 14.82/15.03 ** KEPT (pick-wt=9): 123 [] -homomorphism(A,B,C,D,E)|closed(B,C).
% 14.82/15.03 ** KEPT (pick-wt=9): 124 [] -homomorphism(A,B,C,D,E)|closed(D,E).
% 14.82/15.03 ** KEPT (pick-wt=10): 125 [] -homomorphism(A,B,C,D,E)|maps(A,B,D).
% 14.82/15.03 ** KEPT (pick-wt=27): 126 [] -homomorphism(A,B,C,D,E)| -member(F,B)| -member(G,B)|apply(A,apply_to_two_arguments(C,F,G))=apply_to_two_arguments(E,apply(A,F),apply(A,G)).
% 14.82/15.03 ** KEPT (pick-wt=24): 127 [] homomorphism(A,B,C,D,E)| -closed(B,C)| -closed(D,E)| -maps(A,B,D)|member(f32(A,B,C,D,E),B).
% 14.82/15.03 ** KEPT (pick-wt=24): 128 [] homomorphism(A,B,C,D,E)| -closed(B,C)| -closed(D,E)| -maps(A,B,D)|member(f33(A,B,C,D,E),B).
% 14.82/15.03 ** KEPT (pick-wt=51): 129 [] homomorphism(A,B,C,D,E)| -closed(B,C)| -closed(D,E)| -maps(A,B,D)|apply(A,apply_to_two_arguments(C,f32(A,B,C,D,E),f33(A,B,C,D,E)))!=apply_to_two_arguments(E,apply(A,f32(A,B,C,D,E)),apply(A,f33(A,B,C,D,E))).
% 14.82/15.03 ** KEPT (pick-wt=27): 130 [] -associative(A,B)| -member(C,A)| -member(D,A)| -member(E,A)|apply_to_two_arguments(B,apply_to_two_arguments(B,C,D),E)=apply_to_two_arguments(B,C,apply_to_two_arguments(B,D,E)).
% 14.82/15.03 ** KEPT (pick-wt=30): 131 [] associative(A,B)|apply_to_two_arguments(B,apply_to_two_arguments(B,f34(A,B),f35(A,B)),f36(A,B))!=apply_to_two_arguments(B,f34(A,B),apply_to_two_arguments(B,f35(A,B),f36(A,B))).
% 14.82/15.03 ** KEPT (pick-wt=7): 132 [] -identity(A,B,C)|member(C,A).
% 14.82/15.03 ** KEPT (pick-wt=13): 133 [] -identity(A,B,C)| -member(D,A)|apply_to_two_arguments(B,C,D)=D.
% 14.82/15.03 ** KEPT (pick-wt=13): 134 [] -identity(A,B,C)| -member(D,A)|apply_to_two_arguments(B,D,C)=D.
% 14.82/15.03 ** KEPT (pick-wt=13): 135 [] identity(A,B,C)| -member(C,A)|member(f37(A,B,C),A).
% 14.82/15.03 ** KEPT (pick-wt=31): 136 [] identity(A,B,C)| -member(C,A)|apply_to_two_arguments(B,C,f37(A,B,C))!=f37(A,B,C)|apply_to_two_arguments(B,f37(A,B,C),C)!=f37(A,B,C).
% 14.82/15.03 ** KEPT (pick-wt=9): 137 [] -inverse(A,B,C,D)|maps(D,A,A).
% 14.82/15.03 ** KEPT (pick-wt=16): 138 [] -inverse(A,B,C,D)| -member(E,A)|apply_to_two_arguments(B,apply(D,E),E)=C.
% 14.82/15.03 ** KEPT (pick-wt=16): 139 [] -inverse(A,B,C,D)| -member(E,A)|apply_to_two_arguments(B,E,apply(D,E))=C.
% 14.82/15.03 ** KEPT (pick-wt=16): 140 [] inverse(A,B,C,D)| -maps(D,A,A)|member(f38(A,B,C,D),A).
% 14.82/15.03 ** KEPT (pick-wt=41): 141 [] inverse(A,B,C,D)| -maps(D,A,A)|apply_to_two_arguments(B,apply(D,f38(A,B,C,D)),f38(A,B,C,D))!=C|apply_to_two_arguments(B,f38(A,B,C,D),apply(D,f38(A,B,C,D)))!=C.
% 14.82/15.03 ** KEPT (pick-wt=6): 142 [] -group(A,B)|closed(A,B).
% 14.82/15.03 ** KEPT (pick-wt=6): 143 [] -group(A,B)|associative(A,B).
% 14.82/15.03 ** KEPT (pick-wt=9): 144 [] -group(A,B)|identity(A,B,f39(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=12): 145 [] -group(A,B)|inverse(A,B,f39(A,B),f40(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=18): 146 [] group(A,B)| -closed(A,B)| -associative(A,B)| -identity(A,B,C)| -inverse(A,B,C,D).
% 14.82/15.03 ** KEPT (pick-wt=18): 147 [] -commutes(A,B)| -member(C,A)| -member(D,A)|apply_to_two_arguments(B,C,D)=apply_to_two_arguments(B,D,C).
% 14.82/15.03 ** KEPT (pick-wt=20): 149 [copy,148,flip.2] commutes(A,B)|apply_to_two_arguments(B,f42(A,B),f41(A,B))!=apply_to_two_arguments(B,f41(A,B),f42(A,B)).
% 14.82/15.03 ** KEPT (pick-wt=16): 150 [] -member(A,natural_numbers)| -little_set(B)| -member(empty_set,B)|member(f43(A,B),B)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=17): 151 [] -member(A,natural_numbers)| -little_set(B)| -member(empty_set,B)| -member(successor(f43(A,B)),B)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=8): 152 [] member(A,natural_numbers)| -little_set(A)|little_set(f44(A)).
% 14.82/15.03 ** KEPT (pick-wt=9): 153 [] member(A,natural_numbers)| -little_set(A)|member(empty_set,f44(A)).
% 14.82/15.03 ** KEPT (pick-wt=14): 154 [] member(A,natural_numbers)| -little_set(A)| -member(B,f44(A))|member(successor(B),f44(A)).
% 14.82/15.03 ** KEPT (pick-wt=7): 155 [] member(A,natural_numbers)| -member(A,f44(A)).
% 14.82/15.03 ** KEPT (pick-wt=18): 156 [] -member(A,plus)| -little_set(B)|member(f45(A,B),natural_numbers)|member(f46(A,B),natural_numbers)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=18): 157 [] -member(A,plus)| -little_set(B)|member(f45(A,B),natural_numbers)|member(f47(A,B),natural_numbers)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=18): 158 [] -member(A,plus)| -little_set(B)|member(f45(A,B),natural_numbers)|member(f48(A,B),natural_numbers)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=26): 159 [] -member(A,plus)| -little_set(B)|member(f45(A,B),natural_numbers)|member(ordered_pair(ordered_pair(f46(A,B),f47(A,B)),f48(A,B)),B)|member(A,B).
% 14.82/15.03 ** KEPT (pick-wt=28): 160 [] -member(A,plus)| -little_set(B)|member(f45(A,B),natural_numbers)| -member(ordered_pair(ordered_pair(successor(f46(A,B)),f47(A,B)),successor(f48(A,B))),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=24): 161 [] -member(A,plus)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f45(A,B)),f45(A,B)),B)|member(f46(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=24): 162 [] -member(A,plus)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f45(A,B)),f45(A,B)),B)|member(f47(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=24): 163 [] -member(A,plus)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f45(A,B)),f45(A,B)),B)|member(f48(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=32): 164 [] -member(A,plus)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f45(A,B)),f45(A,B)),B)|member(ordered_pair(ordered_pair(f46(A,B),f47(A,B)),f48(A,B)),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=34): 165 [] -member(A,plus)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f45(A,B)),f45(A,B)),B)| -member(ordered_pair(ordered_pair(successor(f46(A,B)),f47(A,B)),successor(f48(A,B))),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=8): 166 [] member(A,plus)| -little_set(A)|little_set(f49(A)).
% 14.82/15.04 ** KEPT (pick-wt=16): 167 [] member(A,plus)| -little_set(A)| -member(B,natural_numbers)|member(ordered_pair(ordered_pair(empty_set,B),B),f49(A)).
% 14.82/15.04 ** KEPT (pick-wt=32): 168 [] member(A,plus)| -little_set(A)| -member(B,natural_numbers)| -member(C,natural_numbers)| -member(D,natural_numbers)| -member(ordered_pair(ordered_pair(B,C),D),f49(A))|member(ordered_pair(ordered_pair(successor(B),C),successor(D)),f49(A)).
% 14.82/15.04 ** KEPT (pick-wt=7): 169 [] member(A,plus)| -member(A,f49(A)).
% 14.82/15.04 ** KEPT (pick-wt=18): 170 [] -member(A,times)| -little_set(B)|member(f50(A,B),natural_numbers)|member(f51(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=18): 171 [] -member(A,times)| -little_set(B)|member(f50(A,B),natural_numbers)|member(f52(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=18): 172 [] -member(A,times)| -little_set(B)|member(f50(A,B),natural_numbers)|member(f53(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=26): 173 [] -member(A,times)| -little_set(B)|member(f50(A,B),natural_numbers)|member(ordered_pair(ordered_pair(f51(A,B),f52(A,B)),f53(A,B)),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=32): 174 [] -member(A,times)| -little_set(B)|member(f50(A,B),natural_numbers)| -member(ordered_pair(ordered_pair(successor(f51(A,B)),f52(A,B)),apply_to_two_arguments(plus,f53(A,B),f52(A,B))),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=22): 175 [] -member(A,times)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f50(A,B)),empty_set),B)|member(f51(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=22): 176 [] -member(A,times)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f50(A,B)),empty_set),B)|member(f52(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=22): 177 [] -member(A,times)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f50(A,B)),empty_set),B)|member(f53(A,B),natural_numbers)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=30): 178 [] -member(A,times)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f50(A,B)),empty_set),B)|member(ordered_pair(ordered_pair(f51(A,B),f52(A,B)),f53(A,B)),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=36): 179 [] -member(A,times)| -little_set(B)| -member(ordered_pair(ordered_pair(empty_set,f50(A,B)),empty_set),B)| -member(ordered_pair(ordered_pair(successor(f51(A,B)),f52(A,B)),apply_to_two_arguments(plus,f53(A,B),f52(A,B))),B)|member(A,B).
% 14.82/15.04 ** KEPT (pick-wt=8): 180 [] member(A,times)| -little_set(A)|little_set(f54(A)).
% 14.82/15.04 ** KEPT (pick-wt=16): 181 [] member(A,times)| -little_set(A)| -member(B,natural_numbers)|member(ordered_pair(ordered_pair(empty_set,B),empty_set),f54(A)).
% 14.82/15.04 ** KEPT (pick-wt=34): 182 [] member(A,times)| -little_set(A)| -member(B,natural_numbers)| -member(C,natural_numbers)| -member(D,natural_numbers)| -member(ordered_pair(ordered_pair(B,C),D),f54(A))|member(ordered_pair(ordered_pair(successor(B),C),apply_to_two_arguments(plus,D,C)),f54(A)).
% 14.82/15.04 ** KEPT (pick-wt=7): 183 [] member(A,times)| -member(A,f54(A)).
% 14.82/15.04 ** KEPT (pick-wt=6): 184 [] -member(A,prime_numbers)|member(A,natural_numbers).
% 14.82/15.04 ** KEPT (pick-wt=6): 185 [] -member(A,prime_numbers)|A!=empty_set.
% 14.82/15.06 ** KEPT (pick-wt=7): 186 [] -member(A,prime_numbers)|A!=successor(empty_set).
% 14.82/15.06 ** KEPT (pick-wt=21): 187 [] -member(A,prime_numbers)| -member(B,natural_numbers)| -member(C,natural_numbers)|apply_to_two_arguments(times,B,C)!=A|member(B,non_ordered_pair(successor(empty_set),A)).
% 14.82/15.06 ** KEPT (pick-wt=17): 188 [] member(A,prime_numbers)| -member(A,natural_numbers)|A=empty_set|A=successor(empty_set)|member(f55(A),natural_numbers).
% 14.82/15.06 ** KEPT (pick-wt=17): 189 [] member(A,prime_numbers)| -member(A,natural_numbers)|A=empty_set|A=successor(empty_set)|member(f56(A),natural_numbers).
% 14.82/15.06 ** KEPT (pick-wt=21): 190 [] member(A,prime_numbers)| -member(A,natural_numbers)|A=empty_set|A=successor(empty_set)|apply_to_two_arguments(times,f55(A),f56(A))=A.
% 14.82/15.06 ** KEPT (pick-wt=20): 191 [] member(A,prime_numbers)| -member(A,natural_numbers)|A=empty_set|A=successor(empty_set)| -member(f55(A),non_ordered_pair(successor(empty_set),A)).
% 14.82/15.06 ** KEPT (pick-wt=6): 192 [] -finite(A)|member(f57(A),natural_numbers).
% 14.82/15.06 ** KEPT (pick-wt=8): 193 [] -finite(A)|maps(f58(A),f57(A),A).
% 14.82/15.06 ** KEPT (pick-wt=7): 194 [] -finite(A)|range_of(f58(A))=A.
% 14.82/15.06 ** KEPT (pick-wt=5): 195 [] -finite(A)|one_to_one_function(f58(A)).
% 14.82/15.06 ** KEPT (pick-wt=15): 196 [] finite(A)| -member(B,natural_numbers)| -maps(C,B,A)|range_of(C)!=A| -one_to_one_function(C).
% 14.82/15.06 ** KEPT (pick-wt=6): 197 [] -member(A,twin_prime_numbers)|member(A,prime_numbers).
% 14.82/15.06 ** KEPT (pick-wt=8): 198 [] -member(A,twin_prime_numbers)|member(successor(successor(A)),prime_numbers).
% 14.82/15.06 ** KEPT (pick-wt=11): 199 [] member(A,twin_prime_numbers)| -member(A,prime_numbers)| -member(successor(successor(A)),prime_numbers).
% 14.82/15.06 ** KEPT (pick-wt=6): 200 [] -member(A,even_numbers)|member(A,natural_numbers).
% 14.82/15.06 ** KEPT (pick-wt=7): 201 [] -member(A,even_numbers)|member(f59(A),natural_numbers).
% 14.82/15.06 ** KEPT (pick-wt=11): 202 [] -member(A,even_numbers)|apply_to_two_arguments(plus,f59(A),f59(A))=A.
% 14.82/15.06 ** KEPT (pick-wt=15): 203 [] member(A,even_numbers)| -member(A,natural_numbers)| -member(B,natural_numbers)|apply_to_two_arguments(plus,B,B)!=A.
% 14.82/15.06 ** KEPT (pick-wt=3): 204 [] -member(empty_set,natural_numbers).
% 14.82/15.06
% 14.82/15.06 ------------> process sos:
% 14.82/15.06 ** KEPT (pick-wt=3): 282 [] A=A.
% 14.82/15.06 ** KEPT (pick-wt=7): 283 [] little_set(f1(A,B))|A=B.
% 14.82/15.06 ** KEPT (pick-wt=13): 284 [] member(f1(A,B),A)|member(f1(A,B),B)|A=B.
% 14.82/15.06 ** KEPT (pick-wt=4): 285 [] little_set(non_ordered_pair(A,B)).
% 14.82/15.06 ** KEPT (pick-wt=6): 286 [] singleton_set(A)=non_ordered_pair(A,A).
% 14.82/15.06 ---> New Demodulator: 287 [new_demod,286] singleton_set(A)=non_ordered_pair(A,A).
% 14.82/15.06 ** KEPT (pick-wt=11): 289 [copy,288,demod,287] ordered_pair(A,B)=non_ordered_pair(non_ordered_pair(A,A),non_ordered_pair(A,B)).
% 14.82/15.06 ---> New Demodulator: 290 [new_demod,289] ordered_pair(A,B)=non_ordered_pair(non_ordered_pair(A,A),non_ordered_pair(A,B)).
% 14.82/15.06 ** KEPT (pick-wt=10): 292 [copy,291,flip.1] complement(intersection(complement(A),complement(B)))=union(A,B).
% 14.82/15.06 ---> New Demodulator: 293 [new_demod,292] complement(intersection(complement(A),complement(B)))=union(A,B).
% 14.82/15.06 ** KEPT (pick-wt=8): 295 [copy,294,demod,287] successor(A)=union(A,non_ordered_pair(A,A)).
% 14.82/15.06 ---> New Demodulator: 296 [new_demod,295] successor(A)=union(A,non_ordered_pair(A,A)).
% 14.82/15.06 ** KEPT (pick-wt=2): 297 [] little_set(infinity).
% 14.82/15.06 ** KEPT (pick-wt=3): 298 [] member(empty_set,infinity).
% 14.82/15.06 ** KEPT (pick-wt=8): 299 [] subset(A,B)|member(f17(A,B),A).
% 14.82/15.06 ** KEPT (pick-wt=6): 300 [] relation(A)|member(f18(A),A).
% 14.82/15.06 ** KEPT (pick-wt=5): 301 [] single_valued_set(A)|little_set(f19(A)).
% 14.82/15.06 ** KEPT (pick-wt=5): 302 [] single_valued_set(A)|little_set(f20(A)).
% 14.82/15.06 ** KEPT (pick-wt=5): 303 [] single_valued_set(A)|little_set(f21(A)).
% 14.82/15.06 ** KEPT (pick-wt=15): 305 [copy,304,demod,290] single_valued_set(A)|member(non_ordered_pair(non_ordered_pair(f19(A),f19(A)),non_ordered_pair(f19(A),f20(A))),A).
% 14.82/15.06 ** KEPT (pick-wt=15): 307 [copy,306,demod,290] single_valued_set(A)|member(non_ordered_pair(non_ordered_pair(f19(A),f19(A)),non_ordered_pair(f19(A),f21(A))),A).
% 14.82/15.06 ** KEPT (pick-wt=8): 308 [] disjoint(A,B)|member(f23(A,B),A).
% 14.82/15.06 ** KEPT (pick-wt=8): 309 [] disjoint(A,B)|member(f23(A,B),B).
% 14.82/15.06 ** KEPT (pick-wt=7): 310 [] A=empty_set|member(f24(A),A).
% 14.82/15.06 ** KEPT (pick-wt=7): 311 [] A=empty_set|disjoint(f24(A),A).
% 14.93/15.07 ** KEPT (pick-wt=2): 312 [] function(f25).
% 14.93/15.07 ** KEPT (pick-wt=9): 313 [] restrict(A,B)=intersection(A,cross_product(B,universal_set)).
% 14.93/15.07 ---> New Demodulator: 314 [new_demod,313] restrict(A,B)=intersection(A,cross_product(B,universal_set)).
% 14.93/15.07 ** KEPT (pick-wt=14): 316 [copy,315,demod,290,flip.1] apply(A,non_ordered_pair(non_ordered_pair(B,B),non_ordered_pair(B,C)))=apply_to_two_arguments(A,B,C).
% 14.93/15.07 ---> New Demodulator: 317 [new_demod,316] apply(A,non_ordered_pair(non_ordered_pair(B,B),non_ordered_pair(B,C)))=apply_to_two_arguments(A,B,C).
% 14.93/15.07 ** KEPT (pick-wt=8): 318 [] associative(A,B)|member(f34(A,B),A).
% 14.93/15.07 ** KEPT (pick-wt=8): 319 [] associative(A,B)|member(f35(A,B),A).
% 14.93/15.07 ** KEPT (pick-wt=8): 320 [] associative(A,B)|member(f36(A,B),A).
% 14.93/15.07 ** KEPT (pick-wt=8): 321 [] commutes(A,B)|member(f41(A,B),A).
% 14.93/15.07 ** KEPT (pick-wt=8): 322 [] commutes(A,B)|member(f42(A,B),A).
% 14.93/15.07 Following clause subsumed by 282 during input processing: 0 [copy,282,flip.1] A=A.
% 14.93/15.07 282 back subsumes 267.
% 14.93/15.07 282 back subsumes 244.
% 14.93/15.07 282 back subsumes 226.
% 14.93/15.07 282 back subsumes 205.
% 14.93/15.07 >>>> Starting back demodulation with 287.
% 14.93/15.07 >>>> Starting back demodulation with 290.
% 14.93/15.07 >> back demodulating 281 with 290.
% 14.93/15.07 >> back demodulating 280 with 290.
% 14.93/15.07 >> back demodulating 279 with 290.
% 14.93/15.07 >> back demodulating 278 with 290.
% 14.93/15.07 >> back demodulating 277 with 290.
% 14.93/15.07 >> back demodulating 275 with 290.
% 14.93/15.07 >> back demodulating 274 with 290.
% 14.93/15.07 >> back demodulating 273 with 290.
% 14.93/15.07 >> back demodulating 272 with 290.
% 14.93/15.07 >> back demodulating 271 with 290.
% 14.93/15.07 >> back demodulating 270 with 290.
% 14.93/15.07 >> back demodulating 269 with 290.
% 14.93/15.07 >> back demodulating 268 with 290.
% 14.93/15.07 >> back demodulating 266 with 290.
% 14.93/15.07 >> back demodulating 265 with 290.
% 14.93/15.07 >> back demodulating 264 with 290.
% 14.93/15.07 >> back demodulating 263 with 290.
% 14.93/15.07 >> back demodulating 262 with 290.
% 14.93/15.07 >> back demodulating 261 with 290.
% 14.93/15.07 >> back demodulating 260 with 290.
% 14.93/15.07 >> back demodulating 259 with 290.
% 14.93/15.07 >> back demodulating 258 with 290.
% 14.93/15.07 >> back demodulating 257 with 290.
% 14.93/15.07 >> back demodulating 256 with 290.
% 14.93/15.07 >> back demodulating 255 with 290.
% 14.93/15.07 >> back demodulating 254 with 290.
% 14.93/15.07 >> back demodulating 253 with 290.
% 14.93/15.07 >> back demodulating 250 with 290.
% 14.93/15.07 >> back demodulating 249 with 290.
% 14.93/15.07 >> back demodulating 248 with 290.
% 14.93/15.07 >> back demodulating 247 with 290.
% 14.93/15.07 >> back demodulating 246 with 290.
% 14.93/15.07 >> back demodulating 245 with 290.
% 14.93/15.07 >> back demodulating 236 with 290.
% 14.93/15.07 >> back demodulating 235 with 290.
% 14.93/15.07 >> back demodulating 234 with 290.
% 14.93/15.07 >> back demodulating 233 with 290.
% 14.93/15.07 >> back demodulating 232 with 290.
% 14.93/15.07 >> back demodulating 231 with 290.
% 14.93/15.07 >> back demodulating 230 with 290.
% 14.93/15.07 >> back demodulating 225 with 290.
% 14.93/15.07 >> back demodulating 224 with 290.
% 14.93/15.07 >> back demodulating 222 with 290.
% 14.93/15.07 >> back demodulating 221 with 290.
% 14.93/15.07 >> back demodulating 220 with 290.
% 14.93/15.07 >> back demodulating 219 with 290.
% 14.93/15.07 >> back demodulating 218 with 290.
% 14.93/15.07 >> back demodulating 217 with 290.
% 14.93/15.07 >> back demodulating 216 with 290.
% 14.93/15.07 >> back demodulating 215 with 290.
% 14.93/15.07 >> back demodulating 214 with 290.
% 14.93/15.07 >> back demodulating 213 with 290.
% 14.93/15.07 >> back demodulating 212 with 290.
% 14.93/15.07 >> back demodulating 211 with 290.
% 14.93/15.07 >> back demodulating 209 with 290.
% 14.93/15.07 >> back demodulating 208 with 290.
% 14.93/15.07 >> back demodulating 207 with 290.
% 14.93/15.07 >> back demodulating 182 with 290.
% 14.93/15.07 >> back demodulating 181 with 290.
% 14.93/15.07 >> back demodulating 179 with 290.
% 14.93/15.07 >> back demodulating 178 with 290.
% 14.93/15.07 >> back demodulating 177 with 290.
% 14.93/15.07 >> back demodulating 176 with 290.
% 14.93/15.07 >> back demodulating 175 with 290.
% 14.93/15.07 >> back demodulating 174 with 290.
% 14.93/15.07 >> back demodulating 173 with 290.
% 14.93/15.07 >> back demodulating 168 with 290.
% 14.93/15.07 >> back demodulating 167 with 290.
% 14.93/15.07 >> back demodulating 165 with 290.
% 14.93/15.07 >> back demodulating 164 with 290.
% 14.93/15.07 >> back demodulating 163 with 290.
% 14.93/15.07 >> back demodulating 162 with 290.
% 14.93/15.07 >> back demodulating 161 with 290.
% 14.93/15.07 >> back demodulating 160 with 290.
% 14.93/15.07 >> back demodulating 159 with 290.
% 14.93/15.07 >> back demodulating 122 with 290.
% 14.96/15.11 >> back demodulating 121 with 290.
% 14.96/15.11 >> back demodulating 120 with 290.
% 14.96/15.11 >> back demodulating 119 with 290.
% 14.96/15.11 >> back demodulating 88 with 290.
% 14.96/15.11 >> back demodulating 74 with 290.
% 14.96/15.11 >> back demodulating 56 with 290.
% 14.96/15.11 >> back demodulating 55 with 290.
% 14.96/15.11 >> back demodulating 54 with 290.
% 14.96/15.11 >> back demodulating 49 with 290.
% 14.96/15.11 >> back demodulating 48 with 290.
% 14.96/15.11 >> back demodulating 47 with 290.
% 14.96/15.11 >> back demodulating 42 with 290.
% 14.96/15.11 >> back demodulating 41 with 290.
% 14.96/15.11 >> back demodulating 22 with 290.
% 14.96/15.11 >> back demodulating 20 with 290.
% 14.96/15.11 >> back demodulating 16 with 290.
% 14.96/15.11 >> back demodulating 14 with 290.
% 14.96/15.11 >> back demodulating 10 with 290.
% 14.96/15.11 >> back demodulating 9 with 290.
% 14.96/15.11 >>>> Starting back demodulation with 293.
% 14.96/15.11 >>>> Starting back demodulation with 296.
% 14.96/15.11 >> back demodulating 251 with 296.
% 14.96/15.11 >> back demodulating 199 with 296.
% 14.96/15.11 >> back demodulating 198 with 296.
% 14.96/15.11 >> back demodulating 191 with 296.
% 14.96/15.11 >> back demodulating 190 with 296.
% 14.96/15.11 >> back demodulating 189 with 296.
% 14.96/15.11 >> back demodulating 188 with 296.
% 14.96/15.11 >> back demodulating 187 with 296.
% 14.96/15.11 >> back demodulating 186 with 296.
% 14.96/15.11 >> back demodulating 154 with 296.
% 14.96/15.11 >> back demodulating 151 with 296.
% 14.96/15.11 >> back demodulating 59 with 296.
% 14.96/15.11 >>>> Starting back demodulation with 314.
% 14.96/15.11 >>>> Starting back demodulation with 317.
% 14.96/15.11
% 14.96/15.11 ======= end of input processing =======
% 14.96/15.11
% 14.96/15.11 =========== start of search ===========
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Resetting weight limit to 5.
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Resetting weight limit to 5.
% 14.96/15.11
% 14.96/15.11 sos_size=135
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Resetting weight limit to 4.
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Resetting weight limit to 4.
% 14.96/15.11
% 14.96/15.11 sos_size=171
% 14.96/15.11
% 14.96/15.11 -------- PROOF --------
% 14.96/15.11
% 14.96/15.11 ----> UNIT CONFLICT at 0.09 sec ----> 487 [binary,486.1,204.1] $F.
% 14.96/15.11
% 14.96/15.11 Length of proof is 3. Level of proof is 3.
% 14.96/15.11
% 14.96/15.11 ---------------- PROOF ----------------
% 14.96/15.11 % SZS status Unsatisfiable
% 14.96/15.11 % SZS output start Refutation
% See solution above
% 14.96/15.11 ------------ end of proof -------------
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Search stopped by max_proofs option.
% 14.96/15.11
% 14.96/15.11
% 14.96/15.11 Search stopped by max_proofs option.
% 14.96/15.11
% 14.96/15.11 ============ end of search ============
% 14.96/15.11
% 14.96/15.11 -------------- statistics -------------
% 14.96/15.11 clauses given 22
% 14.96/15.11 clauses generated 1562
% 14.96/15.11 clauses kept 462
% 14.96/15.11 clauses forward subsumed 231
% 14.96/15.11 clauses back subsumed 4
% 14.96/15.11 Kbytes malloced 7812
% 14.96/15.11
% 14.96/15.11 ----------- times (seconds) -----------
% 14.96/15.11 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 14.96/15.11 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 14.96/15.11 wall-clock time 15 (0 hr, 0 min, 15 sec)
% 14.96/15.11
% 14.96/15.11 That finishes the proof of the theorem.
% 14.96/15.11
% 14.96/15.11 Process 24477 finished Wed Jul 27 09:56:35 2022
% 14.96/15.11 Otter interrupted
% 14.96/15.11 PROOF FOUND
%------------------------------------------------------------------------------