TSTP Solution File: SET755+4 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n008.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 : 600s
% DateTime : Tue Jul 19 02:15:56 EDT 2022
% Result : Theorem 86.12s 86.42s
% Output : CNFRefutation 86.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(isomorphism,axiom,
! [F,A,R,B,S] :
( isomorphism(F,A,R,B,S)
<=> ( maps(F,A,B)
& one_to_one(F,A,B)
& ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> ( apply(R,X1,X2)
<=> apply(S,Y1,Y2) ) ) ) ),
input ).
fof(isomorphism_0,plain,
! [A,B,F,R,S] :
( isomorphism(F,A,R,B,S)
| ~ ( maps(F,A,B)
& one_to_one(F,A,B)
& ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> ( apply(R,X1,X2)
<=> apply(S,Y1,Y2) ) ) ) ),
inference(orientation,[status(thm)],[isomorphism]) ).
fof(isomorphism_1,plain,
! [A,B,F,R,S] :
( ~ isomorphism(F,A,R,B,S)
| ( maps(F,A,B)
& one_to_one(F,A,B)
& ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> ( apply(R,X1,X2)
<=> apply(S,Y1,Y2) ) ) ) ),
inference(orientation,[status(thm)],[isomorphism]) ).
fof(decreasing_function,axiom,
! [F,A,R,B,S] :
( decreasing(F,A,R,B,S)
<=> ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y2,Y1) ) ),
input ).
fof(decreasing_function_0,plain,
! [A,B,F,R,S] :
( decreasing(F,A,R,B,S)
| ~ ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y2,Y1) ) ),
inference(orientation,[status(thm)],[decreasing_function]) ).
fof(decreasing_function_1,plain,
! [A,B,F,R,S] :
( ~ decreasing(F,A,R,B,S)
| ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y2,Y1) ) ),
inference(orientation,[status(thm)],[decreasing_function]) ).
fof(increasing_function,axiom,
! [F,A,R,B,S] :
( increasing(F,A,R,B,S)
<=> ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y1,Y2) ) ),
input ).
fof(increasing_function_0,plain,
! [A,B,F,R,S] :
( increasing(F,A,R,B,S)
| ~ ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y1,Y2) ) ),
inference(orientation,[status(thm)],[increasing_function]) ).
fof(increasing_function_1,plain,
! [A,B,F,R,S] :
( ~ increasing(F,A,R,B,S)
| ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y1,Y2) ) ),
inference(orientation,[status(thm)],[increasing_function]) ).
fof(inverse_image3,axiom,
! [F,B,A,X] :
( member(X,inverse_image3(F,B,A))
<=> ( member(X,A)
& ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
input ).
fof(inverse_image3_0,plain,
! [A,B,F,X] :
( member(X,inverse_image3(F,B,A))
| ~ ( member(X,A)
& ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
inference(orientation,[status(thm)],[inverse_image3]) ).
fof(inverse_image3_1,plain,
! [A,B,F,X] :
( ~ member(X,inverse_image3(F,B,A))
| ( member(X,A)
& ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
inference(orientation,[status(thm)],[inverse_image3]) ).
fof(inverse_image2,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
input ).
fof(inverse_image2_0,plain,
! [B,F,X] :
( member(X,inverse_image2(F,B))
| ~ ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
inference(orientation,[status(thm)],[inverse_image2]) ).
fof(inverse_image2_1,plain,
! [B,F,X] :
( ~ member(X,inverse_image2(F,B))
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
inference(orientation,[status(thm)],[inverse_image2]) ).
fof(image3,axiom,
! [F,A,B,Y] :
( member(Y,image3(F,A,B))
<=> ( member(Y,B)
& ? [X] :
( member(X,A)
& apply(F,X,Y) ) ) ),
input ).
fof(image3_0,plain,
! [A,B,F,Y] :
( member(Y,image3(F,A,B))
| ~ ( member(Y,B)
& ? [X] :
( member(X,A)
& apply(F,X,Y) ) ) ),
inference(orientation,[status(thm)],[image3]) ).
fof(image3_1,plain,
! [A,B,F,Y] :
( ~ member(Y,image3(F,A,B))
| ( member(Y,B)
& ? [X] :
( member(X,A)
& apply(F,X,Y) ) ) ),
inference(orientation,[status(thm)],[image3]) ).
fof(image2,axiom,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
input ).
fof(image2_0,plain,
! [A,F,Y] :
( member(Y,image2(F,A))
| ~ ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
inference(orientation,[status(thm)],[image2]) ).
fof(image2_1,plain,
! [A,F,Y] :
( ~ member(Y,image2(F,A))
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
inference(orientation,[status(thm)],[image2]) ).
fof(inverse_predicate,axiom,
! [G,F,A,B] :
( inverse_predicate(G,F,A,B)
<=> ! [X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(G,Y,X) ) ) ),
input ).
fof(inverse_predicate_0,plain,
! [A,B,F,G] :
( inverse_predicate(G,F,A,B)
| ~ ! [X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(G,Y,X) ) ) ),
inference(orientation,[status(thm)],[inverse_predicate]) ).
fof(inverse_predicate_1,plain,
! [A,B,F,G] :
( ~ inverse_predicate(G,F,A,B)
| ! [X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(G,Y,X) ) ) ),
inference(orientation,[status(thm)],[inverse_predicate]) ).
fof(one_to_one,axiom,
! [F,A,B] :
( one_to_one(F,A,B)
<=> ( injective(F,A,B)
& surjective(F,A,B) ) ),
input ).
fof(one_to_one_0,plain,
! [A,B,F] :
( one_to_one(F,A,B)
| ~ ( injective(F,A,B)
& surjective(F,A,B) ) ),
inference(orientation,[status(thm)],[one_to_one]) ).
fof(one_to_one_1,plain,
! [A,B,F] :
( ~ one_to_one(F,A,B)
| ( injective(F,A,B)
& surjective(F,A,B) ) ),
inference(orientation,[status(thm)],[one_to_one]) ).
fof(surjective,axiom,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
input ).
fof(surjective_0,plain,
! [A,B,F] :
( surjective(F,A,B)
| ~ ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(orientation,[status(thm)],[surjective]) ).
fof(surjective_1,plain,
! [A,B,F] :
( ~ surjective(F,A,B)
| ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(orientation,[status(thm)],[surjective]) ).
fof(injective,axiom,
! [F,A,B] :
( injective(F,A,B)
<=> ! [X1,X2,Y] :
( ( member(X1,A)
& member(X2,A)
& member(Y,B) )
=> ( ( apply(F,X1,Y)
& apply(F,X2,Y) )
=> X1 = X2 ) ) ),
input ).
fof(injective_0,plain,
! [A,B,F] :
( injective(F,A,B)
| ~ ! [X1,X2,Y] :
( ( member(X1,A)
& member(X2,A)
& member(Y,B) )
=> ( ( apply(F,X1,Y)
& apply(F,X2,Y) )
=> X1 = X2 ) ) ),
inference(orientation,[status(thm)],[injective]) ).
fof(injective_1,plain,
! [A,B,F] :
( ~ injective(F,A,B)
| ! [X1,X2,Y] :
( ( member(X1,A)
& member(X2,A)
& member(Y,B) )
=> ( ( apply(F,X1,Y)
& apply(F,X2,Y) )
=> X1 = X2 ) ) ),
inference(orientation,[status(thm)],[injective]) ).
fof(identity,axiom,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
input ).
fof(identity_0,plain,
! [A,F] :
( identity(F,A)
| ~ ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
inference(orientation,[status(thm)],[identity]) ).
fof(identity_1,plain,
! [A,F] :
( ~ identity(F,A)
| ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
inference(orientation,[status(thm)],[identity]) ).
fof(equal_maps,axiom,
! [F,G,A,B] :
( equal_maps(F,G,A,B)
<=> ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
input ).
fof(equal_maps_0,plain,
! [A,B,F,G] :
( equal_maps(F,G,A,B)
| ~ ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
inference(orientation,[status(thm)],[equal_maps]) ).
fof(equal_maps_1,plain,
! [A,B,F,G] :
( ~ equal_maps(F,G,A,B)
| ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
inference(orientation,[status(thm)],[equal_maps]) ).
fof(compose_predicate,axiom,
! [H,G,F,A,B,C] :
( compose_predicate(H,G,F,A,B,C)
<=> ! [X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(H,X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ) ),
input ).
fof(compose_predicate_0,plain,
! [A,B,C,F,G,H] :
( compose_predicate(H,G,F,A,B,C)
| ~ ! [X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(H,X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ) ),
inference(orientation,[status(thm)],[compose_predicate]) ).
fof(compose_predicate_1,plain,
! [A,B,C,F,G,H] :
( ~ compose_predicate(H,G,F,A,B,C)
| ! [X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(H,X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ) ),
inference(orientation,[status(thm)],[compose_predicate]) ).
fof(maps,axiom,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
input ).
fof(maps_0,plain,
! [A,B,F] :
( maps(F,A,B)
| ~ ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
inference(orientation,[status(thm)],[maps]) ).
fof(maps_1,plain,
! [A,B,F] :
( ~ maps(F,A,B)
| ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
inference(orientation,[status(thm)],[maps]) ).
fof(product,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
input ).
fof(product_0,plain,
! [A,X] :
( member(X,product(A))
| ~ ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(orientation,[status(thm)],[product]) ).
fof(product_1,plain,
! [A,X] :
( ~ member(X,product(A))
| ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(orientation,[status(thm)],[product]) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
input ).
fof(sum_0,plain,
! [A,X] :
( member(X,sum(A))
| ~ ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(orientation,[status(thm)],[sum]) ).
fof(sum_1,plain,
! [A,X] :
( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(orientation,[status(thm)],[sum]) ).
fof(unordered_pair,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = A
| X = B ) ),
input ).
fof(unordered_pair_0,plain,
! [A,B,X] :
( member(X,unordered_pair(A,B))
| ~ ( X = A
| X = B ) ),
inference(orientation,[status(thm)],[unordered_pair]) ).
fof(unordered_pair_1,plain,
! [A,B,X] :
( ~ member(X,unordered_pair(A,B))
| X = A
| X = B ),
inference(orientation,[status(thm)],[unordered_pair]) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
input ).
fof(singleton_0,plain,
! [A,X] :
( member(X,singleton(A))
| X != A ),
inference(orientation,[status(thm)],[singleton]) ).
fof(singleton_1,plain,
! [A,X] :
( ~ member(X,singleton(A))
| X = A ),
inference(orientation,[status(thm)],[singleton]) ).
fof(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
input ).
fof(difference_0,plain,
! [A,B,E] :
( member(B,difference(E,A))
| ~ ( member(B,E)
& ~ member(B,A) ) ),
inference(orientation,[status(thm)],[difference]) ).
fof(difference_1,plain,
! [A,B,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) ),
inference(orientation,[status(thm)],[difference]) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
input ).
fof(empty_set_0,plain,
! [X] :
( ~ member(X,empty_set)
| $false ),
inference(orientation,[status(thm)],[empty_set]) ).
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
input ).
fof(union_0,plain,
! [A,B,X] :
( member(X,union(A,B))
| ~ ( member(X,A)
| member(X,B) ) ),
inference(orientation,[status(thm)],[union]) ).
fof(union_1,plain,
! [A,B,X] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) ),
inference(orientation,[status(thm)],[union]) ).
fof(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,A)
& member(X,B) ) ),
input ).
fof(intersection_0,plain,
! [A,B,X] :
( member(X,intersection(A,B))
| ~ ( member(X,A)
& member(X,B) ) ),
inference(orientation,[status(thm)],[intersection]) ).
fof(intersection_1,plain,
! [A,B,X] :
( ~ member(X,intersection(A,B))
| ( member(X,A)
& member(X,B) ) ),
inference(orientation,[status(thm)],[intersection]) ).
fof(power_set,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
input ).
fof(power_set_0,plain,
! [A,X] :
( member(X,power_set(A))
| ~ subset(X,A) ),
inference(orientation,[status(thm)],[power_set]) ).
fof(power_set_1,plain,
! [A,X] :
( ~ member(X,power_set(A))
| subset(X,A) ),
inference(orientation,[status(thm)],[power_set]) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
input ).
fof(equal_set_0,plain,
! [A,B] :
( equal_set(A,B)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[equal_set]) ).
fof(equal_set_1,plain,
! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) ),
inference(orientation,[status(thm)],[equal_set]) ).
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
input ).
fof(subset_0,plain,
! [A,B] :
( subset(A,B)
| ~ ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(orientation,[status(thm)],[subset]) ).
fof(subset_1,plain,
! [A,B] :
( ~ subset(A,B)
| ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(orientation,[status(thm)],[subset]) ).
fof(def_lhs_atom1,axiom,
! [B,A] :
( lhs_atom1(B,A)
<=> ~ subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [A,B] :
( lhs_atom1(B,A)
| ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(fold_definition,[status(thm)],[subset_1,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [B,A] :
( lhs_atom2(B,A)
<=> subset(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [A,B] :
( lhs_atom2(B,A)
| ~ ! [X] :
( member(X,A)
=> member(X,B) ) ),
inference(fold_definition,[status(thm)],[subset_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [B,A] :
( lhs_atom3(B,A)
<=> ~ equal_set(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A,B] :
( lhs_atom3(B,A)
| ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[equal_set_1,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [B,A] :
( lhs_atom4(B,A)
<=> equal_set(A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B] :
( lhs_atom4(B,A)
| ~ ( subset(A,B)
& subset(B,A) ) ),
inference(fold_definition,[status(thm)],[equal_set_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [X,A] :
( lhs_atom5(X,A)
<=> ~ member(X,power_set(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [A,X] :
( lhs_atom5(X,A)
| subset(X,A) ),
inference(fold_definition,[status(thm)],[power_set_1,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [X,A] :
( lhs_atom6(X,A)
<=> member(X,power_set(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [A,X] :
( lhs_atom6(X,A)
| ~ subset(X,A) ),
inference(fold_definition,[status(thm)],[power_set_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [X,B,A] :
( lhs_atom7(X,B,A)
<=> ~ member(X,intersection(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,B,X] :
( lhs_atom7(X,B,A)
| ( member(X,A)
& member(X,B) ) ),
inference(fold_definition,[status(thm)],[intersection_1,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [X,B,A] :
( lhs_atom8(X,B,A)
<=> member(X,intersection(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [A,B,X] :
( lhs_atom8(X,B,A)
| ~ ( member(X,A)
& member(X,B) ) ),
inference(fold_definition,[status(thm)],[intersection_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [X,B,A] :
( lhs_atom9(X,B,A)
<=> ~ member(X,union(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [A,B,X] :
( lhs_atom9(X,B,A)
| member(X,A)
| member(X,B) ),
inference(fold_definition,[status(thm)],[union_1,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [X,B,A] :
( lhs_atom10(X,B,A)
<=> member(X,union(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [A,B,X] :
( lhs_atom10(X,B,A)
| ~ ( member(X,A)
| member(X,B) ) ),
inference(fold_definition,[status(thm)],[union_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [X] :
( lhs_atom11(X)
<=> ~ member(X,empty_set) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [X] :
( lhs_atom11(X)
| $false ),
inference(fold_definition,[status(thm)],[empty_set_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [E,B,A] :
( lhs_atom12(E,B,A)
<=> ~ member(B,difference(E,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [A,B,E] :
( lhs_atom12(E,B,A)
| ( member(B,E)
& ~ member(B,A) ) ),
inference(fold_definition,[status(thm)],[difference_1,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [E,B,A] :
( lhs_atom13(E,B,A)
<=> member(B,difference(E,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [A,B,E] :
( lhs_atom13(E,B,A)
| ~ ( member(B,E)
& ~ member(B,A) ) ),
inference(fold_definition,[status(thm)],[difference_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [X,A] :
( lhs_atom14(X,A)
<=> ~ member(X,singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [A,X] :
( lhs_atom14(X,A)
| X = A ),
inference(fold_definition,[status(thm)],[singleton_1,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [X,A] :
( lhs_atom15(X,A)
<=> member(X,singleton(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [A,X] :
( lhs_atom15(X,A)
| X != A ),
inference(fold_definition,[status(thm)],[singleton_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [X,B,A] :
( lhs_atom16(X,B,A)
<=> ~ member(X,unordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [A,B,X] :
( lhs_atom16(X,B,A)
| X = A
| X = B ),
inference(fold_definition,[status(thm)],[unordered_pair_1,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [X,B,A] :
( lhs_atom17(X,B,A)
<=> member(X,unordered_pair(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [A,B,X] :
( lhs_atom17(X,B,A)
| ~ ( X = A
| X = B ) ),
inference(fold_definition,[status(thm)],[unordered_pair_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [X,A] :
( lhs_atom18(X,A)
<=> ~ member(X,sum(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [A,X] :
( lhs_atom18(X,A)
| ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(fold_definition,[status(thm)],[sum_1,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [X,A] :
( lhs_atom19(X,A)
<=> member(X,sum(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [A,X] :
( lhs_atom19(X,A)
| ~ ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
inference(fold_definition,[status(thm)],[sum_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [X,A] :
( lhs_atom20(X,A)
<=> ~ member(X,product(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [A,X] :
( lhs_atom20(X,A)
| ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(fold_definition,[status(thm)],[product_1,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [X,A] :
( lhs_atom21(X,A)
<=> member(X,product(A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [A,X] :
( lhs_atom21(X,A)
| ~ ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
inference(fold_definition,[status(thm)],[product_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [F,B,A] :
( lhs_atom22(F,B,A)
<=> ~ maps(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [A,B,F] :
( lhs_atom22(F,B,A)
| ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
inference(fold_definition,[status(thm)],[maps_1,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [F,B,A] :
( lhs_atom23(F,B,A)
<=> maps(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [A,B,F] :
( lhs_atom23(F,B,A)
| ~ ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
inference(fold_definition,[status(thm)],[maps_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [H,G,F,C,B,A] :
( lhs_atom24(H,G,F,C,B,A)
<=> ~ compose_predicate(H,G,F,A,B,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [A,B,C,F,G,H] :
( lhs_atom24(H,G,F,C,B,A)
| ! [X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(H,X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ) ),
inference(fold_definition,[status(thm)],[compose_predicate_1,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [H,G,F,C,B,A] :
( lhs_atom25(H,G,F,C,B,A)
<=> compose_predicate(H,G,F,A,B,C) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [A,B,C,F,G,H] :
( lhs_atom25(H,G,F,C,B,A)
| ~ ! [X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(H,X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ) ),
inference(fold_definition,[status(thm)],[compose_predicate_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [G,F,B,A] :
( lhs_atom26(G,F,B,A)
<=> ~ equal_maps(F,G,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [A,B,F,G] :
( lhs_atom26(G,F,B,A)
| ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
inference(fold_definition,[status(thm)],[equal_maps_1,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [G,F,B,A] :
( lhs_atom27(G,F,B,A)
<=> equal_maps(F,G,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [A,B,F,G] :
( lhs_atom27(G,F,B,A)
| ~ ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
inference(fold_definition,[status(thm)],[equal_maps_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [F,A] :
( lhs_atom28(F,A)
<=> ~ identity(F,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [A,F] :
( lhs_atom28(F,A)
| ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
inference(fold_definition,[status(thm)],[identity_1,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [F,A] :
( lhs_atom29(F,A)
<=> identity(F,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [A,F] :
( lhs_atom29(F,A)
| ~ ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
inference(fold_definition,[status(thm)],[identity_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [F,B,A] :
( lhs_atom30(F,B,A)
<=> ~ injective(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [A,B,F] :
( lhs_atom30(F,B,A)
| ! [X1,X2,Y] :
( ( member(X1,A)
& member(X2,A)
& member(Y,B) )
=> ( ( apply(F,X1,Y)
& apply(F,X2,Y) )
=> X1 = X2 ) ) ),
inference(fold_definition,[status(thm)],[injective_1,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [F,B,A] :
( lhs_atom31(F,B,A)
<=> injective(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [A,B,F] :
( lhs_atom31(F,B,A)
| ~ ! [X1,X2,Y] :
( ( member(X1,A)
& member(X2,A)
& member(Y,B) )
=> ( ( apply(F,X1,Y)
& apply(F,X2,Y) )
=> X1 = X2 ) ) ),
inference(fold_definition,[status(thm)],[injective_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [F,B,A] :
( lhs_atom32(F,B,A)
<=> ~ surjective(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [A,B,F] :
( lhs_atom32(F,B,A)
| ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(fold_definition,[status(thm)],[surjective_1,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [F,B,A] :
( lhs_atom33(F,B,A)
<=> surjective(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [A,B,F] :
( lhs_atom33(F,B,A)
| ~ ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(fold_definition,[status(thm)],[surjective_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [F,B,A] :
( lhs_atom34(F,B,A)
<=> ~ one_to_one(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [A,B,F] :
( lhs_atom34(F,B,A)
| ( injective(F,A,B)
& surjective(F,A,B) ) ),
inference(fold_definition,[status(thm)],[one_to_one_1,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [F,B,A] :
( lhs_atom35(F,B,A)
<=> one_to_one(F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [A,B,F] :
( lhs_atom35(F,B,A)
| ~ ( injective(F,A,B)
& surjective(F,A,B) ) ),
inference(fold_definition,[status(thm)],[one_to_one_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [G,F,B,A] :
( lhs_atom36(G,F,B,A)
<=> ~ inverse_predicate(G,F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [A,B,F,G] :
( lhs_atom36(G,F,B,A)
| ! [X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(G,Y,X) ) ) ),
inference(fold_definition,[status(thm)],[inverse_predicate_1,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [G,F,B,A] :
( lhs_atom37(G,F,B,A)
<=> inverse_predicate(G,F,A,B) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [A,B,F,G] :
( lhs_atom37(G,F,B,A)
| ~ ! [X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(G,Y,X) ) ) ),
inference(fold_definition,[status(thm)],[inverse_predicate_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [Y,F,A] :
( lhs_atom38(Y,F,A)
<=> ~ member(Y,image2(F,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [A,F,Y] :
( lhs_atom38(Y,F,A)
| ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
inference(fold_definition,[status(thm)],[image2_1,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [Y,F,A] :
( lhs_atom39(Y,F,A)
<=> member(Y,image2(F,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [A,F,Y] :
( lhs_atom39(Y,F,A)
| ~ ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
inference(fold_definition,[status(thm)],[image2_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [Y,F,B,A] :
( lhs_atom40(Y,F,B,A)
<=> ~ member(Y,image3(F,A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [A,B,F,Y] :
( lhs_atom40(Y,F,B,A)
| ( member(Y,B)
& ? [X] :
( member(X,A)
& apply(F,X,Y) ) ) ),
inference(fold_definition,[status(thm)],[image3_1,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [Y,F,B,A] :
( lhs_atom41(Y,F,B,A)
<=> member(Y,image3(F,A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [A,B,F,Y] :
( lhs_atom41(Y,F,B,A)
| ~ ( member(Y,B)
& ? [X] :
( member(X,A)
& apply(F,X,Y) ) ) ),
inference(fold_definition,[status(thm)],[image3_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [X,F,B] :
( lhs_atom42(X,F,B)
<=> ~ member(X,inverse_image2(F,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [B,F,X] :
( lhs_atom42(X,F,B)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
inference(fold_definition,[status(thm)],[inverse_image2_1,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [X,F,B] :
( lhs_atom43(X,F,B)
<=> member(X,inverse_image2(F,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [B,F,X] :
( lhs_atom43(X,F,B)
| ~ ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ),
inference(fold_definition,[status(thm)],[inverse_image2_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [X,F,B,A] :
( lhs_atom44(X,F,B,A)
<=> ~ member(X,inverse_image3(F,B,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [A,B,F,X] :
( lhs_atom44(X,F,B,A)
| ( member(X,A)
& ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
inference(fold_definition,[status(thm)],[inverse_image3_1,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [X,F,B,A] :
( lhs_atom45(X,F,B,A)
<=> member(X,inverse_image3(F,B,A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [A,B,F,X] :
( lhs_atom45(X,F,B,A)
| ~ ( member(X,A)
& ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) ) ),
inference(fold_definition,[status(thm)],[inverse_image3_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [S,R,F,B,A] :
( lhs_atom46(S,R,F,B,A)
<=> ~ increasing(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [A,B,F,R,S] :
( lhs_atom46(S,R,F,B,A)
| ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y1,Y2) ) ),
inference(fold_definition,[status(thm)],[increasing_function_1,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [S,R,F,B,A] :
( lhs_atom47(S,R,F,B,A)
<=> increasing(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
! [A,B,F,R,S] :
( lhs_atom47(S,R,F,B,A)
| ~ ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y1,Y2) ) ),
inference(fold_definition,[status(thm)],[increasing_function_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [S,R,F,B,A] :
( lhs_atom48(S,R,F,B,A)
<=> ~ decreasing(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [A,B,F,R,S] :
( lhs_atom48(S,R,F,B,A)
| ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y2,Y1) ) ),
inference(fold_definition,[status(thm)],[decreasing_function_1,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [S,R,F,B,A] :
( lhs_atom49(S,R,F,B,A)
<=> decreasing(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [A,B,F,R,S] :
( lhs_atom49(S,R,F,B,A)
| ~ ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(R,X1,X2)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> apply(S,Y2,Y1) ) ),
inference(fold_definition,[status(thm)],[decreasing_function_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [S,R,F,B,A] :
( lhs_atom50(S,R,F,B,A)
<=> ~ isomorphism(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
! [A,B,F,R,S] :
( lhs_atom50(S,R,F,B,A)
| ( maps(F,A,B)
& one_to_one(F,A,B)
& ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> ( apply(R,X1,X2)
<=> apply(S,Y1,Y2) ) ) ) ),
inference(fold_definition,[status(thm)],[isomorphism_1,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [S,R,F,B,A] :
( lhs_atom51(S,R,F,B,A)
<=> isomorphism(F,A,R,B,S) ),
inference(definition,[],]) ).
fof(to_be_clausified_50,plain,
! [A,B,F,R,S] :
( lhs_atom51(S,R,F,B,A)
| ~ ( maps(F,A,B)
& one_to_one(F,A,B)
& ! [X1,Y1,X2,Y2] :
( ( member(X1,A)
& member(Y1,B)
& member(X2,A)
& member(Y2,B)
& apply(F,X1,Y1)
& apply(F,X2,Y2) )
=> ( apply(R,X1,X2)
<=> apply(S,Y1,Y2) ) ) ) ),
inference(fold_definition,[status(thm)],[isomorphism_0,def_lhs_atom51]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X9,X10,X6,X11,X1,X2] :
( lhs_atom24(X9,X10,X6,X11,X1,X2)
| ! [X3,X12] :
( ( member(X3,X2)
& member(X12,X11) )
=> ( apply(X9,X3,X12)
<=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5)
& apply(X10,X5,X12) ) ) ) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_1,axiom,
! [X9,X10,X6,X11,X1,X2] :
( lhs_atom25(X9,X10,X6,X11,X1,X2)
| ~ ! [X3,X12] :
( ( member(X3,X2)
& member(X12,X11) )
=> ( apply(X9,X3,X12)
<=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5)
& apply(X10,X5,X12) ) ) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_2,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom51(X15,X16,X6,X1,X2)
| ~ ( maps(X6,X2,X1)
& one_to_one(X6,X2,X1)
& ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> ( apply(X16,X13,X14)
<=> apply(X15,X7,X8) ) ) ) ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_3,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom49(X15,X16,X6,X1,X2)
| ~ ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X8,X7) ) ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_4,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom47(X15,X16,X6,X1,X2)
| ~ ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X7,X8) ) ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_5,axiom,
! [X10,X6,X1,X2] :
( lhs_atom37(X10,X6,X1,X2)
| ~ ! [X3,X5] :
( ( member(X3,X2)
& member(X5,X1) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_6,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom50(X15,X16,X6,X1,X2)
| ( maps(X6,X2,X1)
& one_to_one(X6,X2,X1)
& ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> ( apply(X16,X13,X14)
<=> apply(X15,X7,X8) ) ) ) ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_7,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom48(X15,X16,X6,X1,X2)
| ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X8,X7) ) ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_8,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom46(X15,X16,X6,X1,X2)
| ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X7,X8) ) ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_9,axiom,
! [X10,X6,X1,X2] :
( lhs_atom27(X10,X6,X1,X2)
| ~ ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_10,axiom,
! [X3,X6,X1,X2] :
( lhs_atom44(X3,X6,X1,X2)
| ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_11,axiom,
! [X5,X6,X1,X2] :
( lhs_atom40(X5,X6,X1,X2)
| ( member(X5,X1)
& ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_12,axiom,
! [X6,X1,X2] :
( lhs_atom32(X6,X1,X2)
| ! [X5] :
( member(X5,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X6,X4,X5) ) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_13,axiom,
! [X6,X1,X2] :
( lhs_atom22(X6,X1,X2)
| ( ! [X3] :
( member(X3,X2)
=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_14,axiom,
! [X6,X1,X2] :
( lhs_atom23(X6,X1,X2)
| ~ ( ! [X3] :
( member(X3,X2)
=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_15,axiom,
! [X10,X6,X1,X2] :
( lhs_atom26(X10,X6,X1,X2)
| ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_16,axiom,
! [X10,X6,X1,X2] :
( lhs_atom36(X10,X6,X1,X2)
| ! [X3,X5] :
( ( member(X3,X2)
& member(X5,X1) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_17,axiom,
! [X3,X6,X1,X2] :
( lhs_atom45(X3,X6,X1,X2)
| ~ ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ) ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_18,axiom,
! [X5,X6,X1,X2] :
( lhs_atom41(X5,X6,X1,X2)
| ~ ( member(X5,X1)
& ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_19,axiom,
! [X6,X1,X2] :
( lhs_atom33(X6,X1,X2)
| ~ ! [X5] :
( member(X5,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X6,X4,X5) ) ) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_20,axiom,
! [X6,X1,X2] :
( lhs_atom31(X6,X1,X2)
| ~ ! [X13,X14,X5] :
( ( member(X13,X2)
& member(X14,X2)
& member(X5,X1) )
=> ( ( apply(X6,X13,X5)
& apply(X6,X14,X5) )
=> X13 = X14 ) ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_21,axiom,
! [X6,X1,X2] :
( lhs_atom30(X6,X1,X2)
| ! [X13,X14,X5] :
( ( member(X13,X2)
& member(X14,X2)
& member(X5,X1) )
=> ( ( apply(X6,X13,X5)
& apply(X6,X14,X5) )
=> X13 = X14 ) ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_22,axiom,
! [X6,X1,X2] :
( lhs_atom35(X6,X1,X2)
| ~ ( injective(X6,X2,X1)
& surjective(X6,X2,X1) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_23,axiom,
! [X3,X6,X1] :
( lhs_atom42(X3,X6,X1)
| ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_24,axiom,
! [X5,X6,X2] :
( lhs_atom38(X5,X6,X2)
| ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_25,axiom,
! [X6,X2] :
( lhs_atom29(X6,X2)
| ~ ! [X3] :
( member(X3,X2)
=> apply(X6,X3,X3) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_26,axiom,
! [X3,X6,X1] :
( lhs_atom43(X3,X6,X1)
| ~ ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_27,axiom,
! [X5,X6,X2] :
( lhs_atom39(X5,X6,X2)
| ~ ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_28,axiom,
! [X6,X1,X2] :
( lhs_atom34(X6,X1,X2)
| ( injective(X6,X2,X1)
& surjective(X6,X2,X1) ) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_29,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_30,axiom,
! [X6,X2] :
( lhs_atom28(X6,X2)
| ! [X3] :
( member(X3,X2)
=> apply(X6,X3,X3) ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_31,axiom,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_32,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_33,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_34,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_35,axiom,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_36,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_37,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_38,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_39,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_40,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_41,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_42,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_43,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_44,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_45,axiom,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_46,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_47,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_48,axiom,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_49,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_50,axiom,
! [X3] :
( lhs_atom11(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_51,axiom,
! [X9,X10,X6,X11,X1,X2] :
( lhs_atom24(X9,X10,X6,X11,X1,X2)
| ! [X3,X12] :
( ( member(X3,X2)
& member(X12,X11) )
=> ( apply(X9,X3,X12)
<=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5)
& apply(X10,X5,X12) ) ) ) ),
c_0_0 ).
fof(c_0_52,axiom,
! [X9,X10,X6,X11,X1,X2] :
( lhs_atom25(X9,X10,X6,X11,X1,X2)
| ~ ! [X3,X12] :
( ( member(X3,X2)
& member(X12,X11) )
=> ( apply(X9,X3,X12)
<=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5)
& apply(X10,X5,X12) ) ) ) ),
c_0_1 ).
fof(c_0_53,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom51(X15,X16,X6,X1,X2)
| ~ ( maps(X6,X2,X1)
& one_to_one(X6,X2,X1)
& ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> ( apply(X16,X13,X14)
<=> apply(X15,X7,X8) ) ) ) ),
c_0_2 ).
fof(c_0_54,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom49(X15,X16,X6,X1,X2)
| ~ ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X8,X7) ) ),
c_0_3 ).
fof(c_0_55,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom47(X15,X16,X6,X1,X2)
| ~ ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X7,X8) ) ),
c_0_4 ).
fof(c_0_56,axiom,
! [X10,X6,X1,X2] :
( lhs_atom37(X10,X6,X1,X2)
| ~ ! [X3,X5] :
( ( member(X3,X2)
& member(X5,X1) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
c_0_5 ).
fof(c_0_57,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom50(X15,X16,X6,X1,X2)
| ( maps(X6,X2,X1)
& one_to_one(X6,X2,X1)
& ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> ( apply(X16,X13,X14)
<=> apply(X15,X7,X8) ) ) ) ),
c_0_6 ).
fof(c_0_58,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom48(X15,X16,X6,X1,X2)
| ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X8,X7) ) ),
c_0_7 ).
fof(c_0_59,axiom,
! [X15,X16,X6,X1,X2] :
( lhs_atom46(X15,X16,X6,X1,X2)
| ! [X13,X7,X14,X8] :
( ( member(X13,X2)
& member(X7,X1)
& member(X14,X2)
& member(X8,X1)
& apply(X16,X13,X14)
& apply(X6,X13,X7)
& apply(X6,X14,X8) )
=> apply(X15,X7,X8) ) ),
c_0_8 ).
fof(c_0_60,axiom,
! [X10,X6,X1,X2] :
( lhs_atom27(X10,X6,X1,X2)
| ~ ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
c_0_9 ).
fof(c_0_61,axiom,
! [X3,X6,X1,X2] :
( lhs_atom44(X3,X6,X1,X2)
| ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ) ),
c_0_10 ).
fof(c_0_62,axiom,
! [X5,X6,X1,X2] :
( lhs_atom40(X5,X6,X1,X2)
| ( member(X5,X1)
& ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ) ),
c_0_11 ).
fof(c_0_63,axiom,
! [X6,X1,X2] :
( lhs_atom32(X6,X1,X2)
| ! [X5] :
( member(X5,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X6,X4,X5) ) ) ),
c_0_12 ).
fof(c_0_64,axiom,
! [X6,X1,X2] :
( lhs_atom22(X6,X1,X2)
| ( ! [X3] :
( member(X3,X2)
=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
c_0_13 ).
fof(c_0_65,axiom,
! [X6,X1,X2] :
( lhs_atom23(X6,X1,X2)
| ~ ( ! [X3] :
( member(X3,X2)
=> ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
c_0_14 ).
fof(c_0_66,axiom,
! [X10,X6,X1,X2] :
( lhs_atom26(X10,X6,X1,X2)
| ! [X3,X7,X8] :
( ( member(X3,X2)
& member(X7,X1)
& member(X8,X1) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
c_0_15 ).
fof(c_0_67,axiom,
! [X10,X6,X1,X2] :
( lhs_atom36(X10,X6,X1,X2)
| ! [X3,X5] :
( ( member(X3,X2)
& member(X5,X1) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
c_0_16 ).
fof(c_0_68,axiom,
! [X3,X6,X1,X2] :
( lhs_atom45(X3,X6,X1,X2)
| ~ ( member(X3,X2)
& ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ) ),
c_0_17 ).
fof(c_0_69,axiom,
! [X5,X6,X1,X2] :
( lhs_atom41(X5,X6,X1,X2)
| ~ ( member(X5,X1)
& ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ) ),
c_0_18 ).
fof(c_0_70,axiom,
! [X6,X1,X2] :
( lhs_atom33(X6,X1,X2)
| ~ ! [X5] :
( member(X5,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X6,X4,X5) ) ) ),
c_0_19 ).
fof(c_0_71,axiom,
! [X6,X1,X2] :
( lhs_atom31(X6,X1,X2)
| ~ ! [X13,X14,X5] :
( ( member(X13,X2)
& member(X14,X2)
& member(X5,X1) )
=> ( ( apply(X6,X13,X5)
& apply(X6,X14,X5) )
=> X13 = X14 ) ) ),
c_0_20 ).
fof(c_0_72,axiom,
! [X6,X1,X2] :
( lhs_atom30(X6,X1,X2)
| ! [X13,X14,X5] :
( ( member(X13,X2)
& member(X14,X2)
& member(X5,X1) )
=> ( ( apply(X6,X13,X5)
& apply(X6,X14,X5) )
=> X13 = X14 ) ) ),
c_0_21 ).
fof(c_0_73,axiom,
! [X6,X1,X2] :
( lhs_atom35(X6,X1,X2)
| ~ ( injective(X6,X2,X1)
& surjective(X6,X2,X1) ) ),
c_0_22 ).
fof(c_0_74,axiom,
! [X3,X6,X1] :
( lhs_atom42(X3,X6,X1)
| ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ),
c_0_23 ).
fof(c_0_75,axiom,
! [X5,X6,X2] :
( lhs_atom38(X5,X6,X2)
| ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ),
c_0_24 ).
fof(c_0_76,axiom,
! [X6,X2] :
( lhs_atom29(X6,X2)
| ~ ! [X3] :
( member(X3,X2)
=> apply(X6,X3,X3) ) ),
c_0_25 ).
fof(c_0_77,axiom,
! [X3,X6,X1] :
( lhs_atom43(X3,X6,X1)
| ~ ? [X5] :
( member(X5,X1)
& apply(X6,X3,X5) ) ),
c_0_26 ).
fof(c_0_78,axiom,
! [X5,X6,X2] :
( lhs_atom39(X5,X6,X2)
| ~ ? [X3] :
( member(X3,X2)
& apply(X6,X3,X5) ) ),
c_0_27 ).
fof(c_0_79,axiom,
! [X6,X1,X2] :
( lhs_atom34(X6,X1,X2)
| ( injective(X6,X2,X1)
& surjective(X6,X2,X1) ) ),
c_0_28 ).
fof(c_0_80,axiom,
! [X3,X1,X2] :
( lhs_atom8(X3,X1,X2)
| ~ ( member(X3,X2)
& member(X3,X1) ) ),
c_0_29 ).
fof(c_0_81,axiom,
! [X6,X2] :
( lhs_atom28(X6,X2)
| ! [X3] :
( member(X3,X2)
=> apply(X6,X3,X3) ) ),
c_0_30 ).
fof(c_0_82,plain,
! [X4,X1,X2] :
( lhs_atom13(X4,X1,X2)
| ~ ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_83,axiom,
! [X3,X1,X2] :
( lhs_atom9(X3,X1,X2)
| member(X3,X2)
| member(X3,X1) ),
c_0_32 ).
fof(c_0_84,axiom,
! [X3,X2] :
( lhs_atom21(X3,X2)
| ~ ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_33 ).
fof(c_0_85,axiom,
! [X1,X2] :
( lhs_atom2(X1,X2)
| ~ ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_34 ).
fof(c_0_86,plain,
! [X4,X1,X2] :
( lhs_atom12(X4,X1,X2)
| ( member(X1,X4)
& ~ member(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_87,axiom,
! [X3,X1,X2] :
( lhs_atom10(X3,X1,X2)
| ~ ( member(X3,X2)
| member(X3,X1) ) ),
c_0_36 ).
fof(c_0_88,axiom,
! [X3,X1,X2] :
( lhs_atom7(X3,X1,X2)
| ( member(X3,X2)
& member(X3,X1) ) ),
c_0_37 ).
fof(c_0_89,axiom,
! [X3,X2] :
( lhs_atom19(X3,X2)
| ~ ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_38 ).
fof(c_0_90,axiom,
! [X1,X2] :
( lhs_atom4(X1,X2)
| ~ ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_39 ).
fof(c_0_91,axiom,
! [X3,X1,X2] :
( lhs_atom16(X3,X1,X2)
| X3 = X2
| X3 = X1 ),
c_0_40 ).
fof(c_0_92,axiom,
! [X3,X1,X2] :
( lhs_atom17(X3,X1,X2)
| ~ ( X3 = X2
| X3 = X1 ) ),
c_0_41 ).
fof(c_0_93,axiom,
! [X3,X2] :
( lhs_atom18(X3,X2)
| ? [X5] :
( member(X5,X2)
& member(X3,X5) ) ),
c_0_42 ).
fof(c_0_94,axiom,
! [X3,X2] :
( lhs_atom20(X3,X2)
| ! [X5] :
( member(X5,X2)
=> member(X3,X5) ) ),
c_0_43 ).
fof(c_0_95,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ! [X3] :
( member(X3,X2)
=> member(X3,X1) ) ),
c_0_44 ).
fof(c_0_96,plain,
! [X3,X2] :
( lhs_atom6(X3,X2)
| ~ subset(X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_97,axiom,
! [X3,X2] :
( lhs_atom5(X3,X2)
| subset(X3,X2) ),
c_0_46 ).
fof(c_0_98,axiom,
! [X1,X2] :
( lhs_atom3(X1,X2)
| ( subset(X2,X1)
& subset(X1,X2) ) ),
c_0_47 ).
fof(c_0_99,plain,
! [X3,X2] :
( lhs_atom15(X3,X2)
| X3 != X2 ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_100,axiom,
! [X3,X2] :
( lhs_atom14(X3,X2)
| X3 = X2 ),
c_0_49 ).
fof(c_0_101,plain,
! [X3] : lhs_atom11(X3),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_102,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X22] :
( ( member(esk9_8(X13,X14,X15,X16,X17,X18,X19,X20),X17)
| ~ apply(X13,X19,X20)
| ~ member(X19,X18)
| ~ member(X20,X16)
| lhs_atom24(X13,X14,X15,X16,X17,X18) )
& ( apply(X15,X19,esk9_8(X13,X14,X15,X16,X17,X18,X19,X20))
| ~ apply(X13,X19,X20)
| ~ member(X19,X18)
| ~ member(X20,X16)
| lhs_atom24(X13,X14,X15,X16,X17,X18) )
& ( apply(X14,esk9_8(X13,X14,X15,X16,X17,X18,X19,X20),X20)
| ~ apply(X13,X19,X20)
| ~ member(X19,X18)
| ~ member(X20,X16)
| lhs_atom24(X13,X14,X15,X16,X17,X18) )
& ( ~ member(X22,X17)
| ~ apply(X15,X19,X22)
| ~ apply(X14,X22,X20)
| apply(X13,X19,X20)
| ~ member(X19,X18)
| ~ member(X20,X16)
| lhs_atom24(X13,X14,X15,X16,X17,X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])])]) ).
fof(c_0_103,plain,
! [X13,X14,X15,X16,X17,X18,X21] :
( ( member(esk10_6(X13,X14,X15,X16,X17,X18),X18)
| lhs_atom25(X13,X14,X15,X16,X17,X18) )
& ( member(esk11_6(X13,X14,X15,X16,X17,X18),X16)
| lhs_atom25(X13,X14,X15,X16,X17,X18) )
& ( ~ apply(X13,esk10_6(X13,X14,X15,X16,X17,X18),esk11_6(X13,X14,X15,X16,X17,X18))
| ~ member(X21,X17)
| ~ apply(X15,esk10_6(X13,X14,X15,X16,X17,X18),X21)
| ~ apply(X14,X21,esk11_6(X13,X14,X15,X16,X17,X18))
| lhs_atom25(X13,X14,X15,X16,X17,X18) )
& ( member(esk12_6(X13,X14,X15,X16,X17,X18),X17)
| apply(X13,esk10_6(X13,X14,X15,X16,X17,X18),esk11_6(X13,X14,X15,X16,X17,X18))
| lhs_atom25(X13,X14,X15,X16,X17,X18) )
& ( apply(X15,esk10_6(X13,X14,X15,X16,X17,X18),esk12_6(X13,X14,X15,X16,X17,X18))
| apply(X13,esk10_6(X13,X14,X15,X16,X17,X18),esk11_6(X13,X14,X15,X16,X17,X18))
| lhs_atom25(X13,X14,X15,X16,X17,X18) )
& ( apply(X14,esk12_6(X13,X14,X15,X16,X17,X18),esk11_6(X13,X14,X15,X16,X17,X18))
| apply(X13,esk10_6(X13,X14,X15,X16,X17,X18),esk11_6(X13,X14,X15,X16,X17,X18))
| lhs_atom25(X13,X14,X15,X16,X17,X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])]) ).
fof(c_0_104,plain,
! [X17,X18,X19,X20,X21] :
( ( member(esk36_5(X17,X18,X19,X20,X21),X21)
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( member(esk37_5(X17,X18,X19,X20,X21),X20)
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( member(esk38_5(X17,X18,X19,X20,X21),X21)
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( member(esk39_5(X17,X18,X19,X20,X21),X20)
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( apply(X19,esk36_5(X17,X18,X19,X20,X21),esk37_5(X17,X18,X19,X20,X21))
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( apply(X19,esk38_5(X17,X18,X19,X20,X21),esk39_5(X17,X18,X19,X20,X21))
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( ~ apply(X18,esk36_5(X17,X18,X19,X20,X21),esk38_5(X17,X18,X19,X20,X21))
| ~ apply(X17,esk37_5(X17,X18,X19,X20,X21),esk39_5(X17,X18,X19,X20,X21))
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) )
& ( apply(X18,esk36_5(X17,X18,X19,X20,X21),esk38_5(X17,X18,X19,X20,X21))
| apply(X17,esk37_5(X17,X18,X19,X20,X21),esk39_5(X17,X18,X19,X20,X21))
| ~ one_to_one(X19,X21,X20)
| ~ maps(X19,X21,X20)
| lhs_atom51(X17,X18,X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
fof(c_0_105,plain,
! [X17,X18,X19,X20,X21] :
( ( member(esk32_5(X17,X18,X19,X20,X21),X21)
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( member(esk33_5(X17,X18,X19,X20,X21),X20)
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( member(esk34_5(X17,X18,X19,X20,X21),X21)
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( member(esk35_5(X17,X18,X19,X20,X21),X20)
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( apply(X18,esk32_5(X17,X18,X19,X20,X21),esk34_5(X17,X18,X19,X20,X21))
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( apply(X19,esk32_5(X17,X18,X19,X20,X21),esk33_5(X17,X18,X19,X20,X21))
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( apply(X19,esk34_5(X17,X18,X19,X20,X21),esk35_5(X17,X18,X19,X20,X21))
| lhs_atom49(X17,X18,X19,X20,X21) )
& ( ~ apply(X17,esk35_5(X17,X18,X19,X20,X21),esk33_5(X17,X18,X19,X20,X21))
| lhs_atom49(X17,X18,X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
fof(c_0_106,plain,
! [X17,X18,X19,X20,X21] :
( ( member(esk28_5(X17,X18,X19,X20,X21),X21)
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( member(esk29_5(X17,X18,X19,X20,X21),X20)
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( member(esk30_5(X17,X18,X19,X20,X21),X21)
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( member(esk31_5(X17,X18,X19,X20,X21),X20)
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( apply(X18,esk28_5(X17,X18,X19,X20,X21),esk30_5(X17,X18,X19,X20,X21))
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( apply(X19,esk28_5(X17,X18,X19,X20,X21),esk29_5(X17,X18,X19,X20,X21))
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( apply(X19,esk30_5(X17,X18,X19,X20,X21),esk31_5(X17,X18,X19,X20,X21))
| lhs_atom47(X17,X18,X19,X20,X21) )
& ( ~ apply(X17,esk29_5(X17,X18,X19,X20,X21),esk31_5(X17,X18,X19,X20,X21))
| lhs_atom47(X17,X18,X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
fof(c_0_107,plain,
! [X11,X12,X13,X14] :
( ( member(esk22_4(X11,X12,X13,X14),X14)
| lhs_atom37(X11,X12,X13,X14) )
& ( member(esk23_4(X11,X12,X13,X14),X13)
| lhs_atom37(X11,X12,X13,X14) )
& ( ~ apply(X12,esk22_4(X11,X12,X13,X14),esk23_4(X11,X12,X13,X14))
| ~ apply(X11,esk23_4(X11,X12,X13,X14),esk22_4(X11,X12,X13,X14))
| lhs_atom37(X11,X12,X13,X14) )
& ( apply(X12,esk22_4(X11,X12,X13,X14),esk23_4(X11,X12,X13,X14))
| apply(X11,esk23_4(X11,X12,X13,X14),esk22_4(X11,X12,X13,X14))
| lhs_atom37(X11,X12,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
fof(c_0_108,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24,X25] :
( ( maps(X19,X21,X20)
| lhs_atom50(X17,X18,X19,X20,X21) )
& ( one_to_one(X19,X21,X20)
| lhs_atom50(X17,X18,X19,X20,X21) )
& ( ~ apply(X18,X22,X24)
| apply(X17,X23,X25)
| ~ member(X22,X21)
| ~ member(X23,X20)
| ~ member(X24,X21)
| ~ member(X25,X20)
| ~ apply(X19,X22,X23)
| ~ apply(X19,X24,X25)
| lhs_atom50(X17,X18,X19,X20,X21) )
& ( ~ apply(X17,X23,X25)
| apply(X18,X22,X24)
| ~ member(X22,X21)
| ~ member(X23,X20)
| ~ member(X24,X21)
| ~ member(X25,X20)
| ~ apply(X19,X22,X23)
| ~ apply(X19,X24,X25)
| lhs_atom50(X17,X18,X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_109,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24,X25] :
( lhs_atom48(X17,X18,X19,X20,X21)
| ~ member(X22,X21)
| ~ member(X23,X20)
| ~ member(X24,X21)
| ~ member(X25,X20)
| ~ apply(X18,X22,X24)
| ~ apply(X19,X22,X23)
| ~ apply(X19,X24,X25)
| apply(X17,X25,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
fof(c_0_110,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24,X25] :
( lhs_atom46(X17,X18,X19,X20,X21)
| ~ member(X22,X21)
| ~ member(X23,X20)
| ~ member(X24,X21)
| ~ member(X25,X20)
| ~ apply(X18,X22,X24)
| ~ apply(X19,X22,X23)
| ~ apply(X19,X24,X25)
| apply(X17,X23,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
fof(c_0_111,plain,
! [X11,X12,X13,X14] :
( ( member(esk13_4(X11,X12,X13,X14),X14)
| lhs_atom27(X11,X12,X13,X14) )
& ( member(esk14_4(X11,X12,X13,X14),X13)
| lhs_atom27(X11,X12,X13,X14) )
& ( member(esk15_4(X11,X12,X13,X14),X13)
| lhs_atom27(X11,X12,X13,X14) )
& ( apply(X12,esk13_4(X11,X12,X13,X14),esk14_4(X11,X12,X13,X14))
| lhs_atom27(X11,X12,X13,X14) )
& ( apply(X11,esk13_4(X11,X12,X13,X14),esk15_4(X11,X12,X13,X14))
| lhs_atom27(X11,X12,X13,X14) )
& ( esk14_4(X11,X12,X13,X14) != esk15_4(X11,X12,X13,X14)
| lhs_atom27(X11,X12,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])]) ).
fof(c_0_112,plain,
! [X7,X8,X9,X10] :
( ( member(X7,X10)
| lhs_atom44(X7,X8,X9,X10) )
& ( member(esk27_4(X7,X8,X9,X10),X9)
| lhs_atom44(X7,X8,X9,X10) )
& ( apply(X8,X7,esk27_4(X7,X8,X9,X10))
| lhs_atom44(X7,X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_61])])]) ).
fof(c_0_113,plain,
! [X7,X8,X9,X10] :
( ( member(X7,X9)
| lhs_atom40(X7,X8,X9,X10) )
& ( member(esk25_4(X7,X8,X9,X10),X10)
| lhs_atom40(X7,X8,X9,X10) )
& ( apply(X8,esk25_4(X7,X8,X9,X10),X7)
| lhs_atom40(X7,X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_62])])]) ).
fof(c_0_114,plain,
! [X7,X8,X9,X10] :
( ( member(esk20_4(X7,X8,X9,X10),X9)
| ~ member(X10,X8)
| lhs_atom32(X7,X8,X9) )
& ( apply(X7,esk20_4(X7,X8,X9,X10),X10)
| ~ member(X10,X8)
| lhs_atom32(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])])]) ).
fof(c_0_115,plain,
! [X9,X10,X11,X12,X14,X15,X16] :
( ( member(esk4_4(X9,X10,X11,X12),X10)
| ~ member(X12,X11)
| lhs_atom22(X9,X10,X11) )
& ( apply(X9,X12,esk4_4(X9,X10,X11,X12))
| ~ member(X12,X11)
| lhs_atom22(X9,X10,X11) )
& ( ~ member(X14,X11)
| ~ member(X15,X10)
| ~ member(X16,X10)
| ~ apply(X9,X14,X15)
| ~ apply(X9,X14,X16)
| X15 = X16
| lhs_atom22(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])]) ).
fof(c_0_116,plain,
! [X9,X10,X11,X13] :
( ( member(esk6_3(X9,X10,X11),X11)
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X10)
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( member(esk8_3(X9,X10,X11),X10)
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( esk7_3(X9,X10,X11) != esk8_3(X9,X10,X11)
| member(esk5_3(X9,X10,X11),X11)
| lhs_atom23(X9,X10,X11) )
& ( member(esk6_3(X9,X10,X11),X11)
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) )
& ( member(esk7_3(X9,X10,X11),X10)
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) )
& ( member(esk8_3(X9,X10,X11),X10)
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk7_3(X9,X10,X11))
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) )
& ( apply(X9,esk6_3(X9,X10,X11),esk8_3(X9,X10,X11))
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) )
& ( esk7_3(X9,X10,X11) != esk8_3(X9,X10,X11)
| ~ member(X13,X10)
| ~ apply(X9,esk5_3(X9,X10,X11),X13)
| lhs_atom23(X9,X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])]) ).
fof(c_0_117,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( lhs_atom26(X11,X12,X13,X14)
| ~ member(X15,X14)
| ~ member(X16,X13)
| ~ member(X17,X13)
| ~ apply(X12,X15,X16)
| ~ apply(X11,X15,X17)
| X16 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
fof(c_0_118,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ apply(X12,X15,X16)
| apply(X11,X16,X15)
| ~ member(X15,X14)
| ~ member(X16,X13)
| lhs_atom36(X11,X12,X13,X14) )
& ( ~ apply(X11,X16,X15)
| apply(X12,X15,X16)
| ~ member(X15,X14)
| ~ member(X16,X13)
| lhs_atom36(X11,X12,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])]) ).
fof(c_0_119,plain,
! [X7,X8,X9,X10,X11] :
( lhs_atom45(X7,X8,X9,X10)
| ~ member(X7,X10)
| ~ member(X11,X9)
| ~ apply(X8,X7,X11) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])]) ).
fof(c_0_120,plain,
! [X7,X8,X9,X10,X11] :
( lhs_atom41(X7,X8,X9,X10)
| ~ member(X7,X9)
| ~ member(X11,X10)
| ~ apply(X8,X11,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
fof(c_0_121,plain,
! [X7,X8,X9,X11] :
( ( member(esk21_3(X7,X8,X9),X8)
| lhs_atom33(X7,X8,X9) )
& ( ~ member(X11,X9)
| ~ apply(X7,X11,esk21_3(X7,X8,X9))
| lhs_atom33(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])])]) ).
fof(c_0_122,plain,
! [X15,X16,X17] :
( ( member(esk17_3(X15,X16,X17),X17)
| lhs_atom31(X15,X16,X17) )
& ( member(esk18_3(X15,X16,X17),X17)
| lhs_atom31(X15,X16,X17) )
& ( member(esk19_3(X15,X16,X17),X16)
| lhs_atom31(X15,X16,X17) )
& ( apply(X15,esk17_3(X15,X16,X17),esk19_3(X15,X16,X17))
| lhs_atom31(X15,X16,X17) )
& ( apply(X15,esk18_3(X15,X16,X17),esk19_3(X15,X16,X17))
| lhs_atom31(X15,X16,X17) )
& ( esk17_3(X15,X16,X17) != esk18_3(X15,X16,X17)
| lhs_atom31(X15,X16,X17) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])]) ).
fof(c_0_123,plain,
! [X15,X16,X17,X18,X19,X20] :
( lhs_atom30(X15,X16,X17)
| ~ member(X18,X17)
| ~ member(X19,X17)
| ~ member(X20,X16)
| ~ apply(X15,X18,X20)
| ~ apply(X15,X19,X20)
| X18 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])]) ).
fof(c_0_124,plain,
! [X7,X8,X9] :
( lhs_atom35(X7,X8,X9)
| ~ injective(X7,X9,X8)
| ~ surjective(X7,X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])]) ).
fof(c_0_125,plain,
! [X7,X8,X9] :
( ( member(esk26_3(X7,X8,X9),X9)
| lhs_atom42(X7,X8,X9) )
& ( apply(X8,X7,esk26_3(X7,X8,X9))
| lhs_atom42(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_74])])]) ).
fof(c_0_126,plain,
! [X7,X8,X9] :
( ( member(esk24_3(X7,X8,X9),X9)
| lhs_atom38(X7,X8,X9) )
& ( apply(X8,esk24_3(X7,X8,X9),X7)
| lhs_atom38(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_75])])]) ).
fof(c_0_127,plain,
! [X7,X8] :
( ( member(esk16_2(X7,X8),X8)
| lhs_atom29(X7,X8) )
& ( ~ apply(X7,esk16_2(X7,X8),esk16_2(X7,X8))
| lhs_atom29(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])]) ).
fof(c_0_128,plain,
! [X7,X8,X9,X10] :
( lhs_atom43(X7,X8,X9)
| ~ member(X10,X9)
| ~ apply(X8,X7,X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).
fof(c_0_129,plain,
! [X7,X8,X9,X10] :
( lhs_atom39(X7,X8,X9)
| ~ member(X10,X9)
| ~ apply(X8,X10,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])]) ).
fof(c_0_130,plain,
! [X7,X8,X9] :
( ( injective(X7,X9,X8)
| lhs_atom34(X7,X8,X9) )
& ( surjective(X7,X9,X8)
| lhs_atom34(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_79])]) ).
fof(c_0_131,plain,
! [X4,X5,X6] :
( lhs_atom8(X4,X5,X6)
| ~ member(X4,X6)
| ~ member(X4,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])]) ).
fof(c_0_132,plain,
! [X7,X8,X9] :
( lhs_atom28(X7,X8)
| ~ member(X9,X8)
| apply(X7,X9,X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])])]) ).
fof(c_0_133,plain,
! [X5,X6,X7] :
( lhs_atom13(X5,X6,X7)
| ~ member(X6,X5)
| member(X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])]) ).
fof(c_0_134,plain,
! [X4,X5,X6] :
( lhs_atom9(X4,X5,X6)
| member(X4,X6)
| member(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_83]) ).
fof(c_0_135,plain,
! [X6,X7] :
( ( member(esk3_2(X6,X7),X7)
| lhs_atom21(X6,X7) )
& ( ~ member(X6,esk3_2(X6,X7))
| lhs_atom21(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])]) ).
fof(c_0_136,plain,
! [X4,X5] :
( ( member(esk1_2(X4,X5),X5)
| lhs_atom2(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X4)
| lhs_atom2(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
fof(c_0_137,plain,
! [X5,X6,X7] :
( ( member(X6,X5)
| lhs_atom12(X5,X6,X7) )
& ( ~ member(X6,X7)
| lhs_atom12(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_86])]) ).
fof(c_0_138,plain,
! [X4,X5,X6] :
( ( ~ member(X4,X6)
| lhs_atom10(X4,X5,X6) )
& ( ~ member(X4,X5)
| lhs_atom10(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])]) ).
fof(c_0_139,plain,
! [X4,X5,X6] :
( ( member(X4,X6)
| lhs_atom7(X4,X5,X6) )
& ( member(X4,X5)
| lhs_atom7(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_88])]) ).
fof(c_0_140,plain,
! [X6,X7,X8] :
( lhs_atom19(X6,X7)
| ~ member(X8,X7)
| ~ member(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])]) ).
fof(c_0_141,plain,
! [X3,X4] :
( lhs_atom4(X3,X4)
| ~ subset(X4,X3)
| ~ subset(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])]) ).
fof(c_0_142,plain,
! [X4,X5,X6] :
( lhs_atom16(X4,X5,X6)
| X4 = X6
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_91]) ).
fof(c_0_143,plain,
! [X4,X5,X6] :
( ( X4 != X6
| lhs_atom17(X4,X5,X6) )
& ( X4 != X5
| lhs_atom17(X4,X5,X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])]) ).
fof(c_0_144,plain,
! [X6,X7] :
( ( member(esk2_2(X6,X7),X7)
| lhs_atom18(X6,X7) )
& ( member(X6,esk2_2(X6,X7))
| lhs_atom18(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_93])])]) ).
fof(c_0_145,plain,
! [X6,X7,X8] :
( lhs_atom20(X6,X7)
| ~ member(X8,X7)
| member(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])]) ).
fof(c_0_146,plain,
! [X4,X5,X6] :
( lhs_atom1(X4,X5)
| ~ member(X6,X5)
| member(X6,X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])]) ).
fof(c_0_147,plain,
! [X4,X5] :
( lhs_atom6(X4,X5)
| ~ subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_96]) ).
fof(c_0_148,plain,
! [X4,X5] :
( lhs_atom5(X4,X5)
| subset(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_97]) ).
fof(c_0_149,plain,
! [X3,X4] :
( ( subset(X4,X3)
| lhs_atom3(X3,X4) )
& ( subset(X3,X4)
| lhs_atom3(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_98])]) ).
fof(c_0_150,plain,
! [X4,X5] :
( lhs_atom15(X4,X5)
| X4 != X5 ),
inference(variable_rename,[status(thm)],[c_0_99]) ).
fof(c_0_151,plain,
! [X4,X5] :
( lhs_atom14(X4,X5)
| X4 = X5 ),
inference(variable_rename,[status(thm)],[c_0_100]) ).
fof(c_0_152,plain,
! [X4] : lhs_atom11(X4),
inference(variable_rename,[status(thm)],[c_0_101]) ).
cnf(c_0_153,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X3,X8,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7))
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_154,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X2,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_155,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| member(esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X5)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_156,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| ~ apply(X2,X7,esk11_6(X1,X2,X3,X4,X5,X6))
| ~ apply(X3,esk10_6(X1,X2,X3,X4,X5,X6),X7)
| ~ member(X7,X5)
| ~ apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_157,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X3,esk10_6(X1,X2,X3,X4,X5,X6),esk12_6(X1,X2,X3,X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_158,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X2,esk12_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_159,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| member(esk12_6(X1,X2,X3,X4,X5,X6),X5) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_160,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| member(esk10_6(X1,X2,X3,X4,X5,X6),X6) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_161,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| member(esk11_6(X1,X2,X3,X4,X5,X6),X4) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_162,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4)
| ~ apply(X1,esk37_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| ~ apply(X2,esk36_5(X1,X2,X3,X4,X5),esk38_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_163,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X1,esk37_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| apply(X2,esk36_5(X1,X2,X3,X4,X5),esk38_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_164,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| ~ apply(X1,esk35_5(X1,X2,X3,X4,X5),esk33_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_165,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| ~ apply(X1,esk29_5(X1,X2,X3,X4,X5),esk31_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_166,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X1,X8,X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X2,X9,X7)
| ~ apply(X3,X8,X9)
| ~ member(X9,X5) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_167,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X3,esk36_5(X1,X2,X3,X4,X5),esk37_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_168,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X3,esk38_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_169,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X2,esk32_5(X1,X2,X3,X4,X5),esk34_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_170,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X3,esk32_5(X1,X2,X3,X4,X5),esk33_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_171,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X3,esk34_5(X1,X2,X3,X4,X5),esk35_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_172,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X2,esk28_5(X1,X2,X3,X4,X5),esk30_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_173,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X3,esk28_5(X1,X2,X3,X4,X5),esk29_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_174,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X3,esk30_5(X1,X2,X3,X4,X5),esk31_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_175,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk36_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_176,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk37_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_177,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk38_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_178,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk39_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_179,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk32_5(X1,X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_180,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk33_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_181,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk34_5(X1,X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_182,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk35_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_183,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk28_5(X1,X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_184,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk29_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_185,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk30_5(X1,X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_186,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk31_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_187,plain,
( lhs_atom37(X1,X2,X3,X4)
| ~ apply(X1,esk23_4(X1,X2,X3,X4),esk22_4(X1,X2,X3,X4))
| ~ apply(X2,esk22_4(X1,X2,X3,X4),esk23_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_188,plain,
( lhs_atom37(X1,X2,X3,X4)
| apply(X1,esk23_4(X1,X2,X3,X4),esk22_4(X1,X2,X3,X4))
| apply(X2,esk22_4(X1,X2,X3,X4),esk23_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_189,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| apply(X1,X9,X7)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X2,X8,X6) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_190,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| apply(X2,X8,X6)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X1,X9,X7) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_191,plain,
( apply(X1,X2,X3)
| lhs_atom48(X1,X7,X4,X8,X9)
| ~ apply(X4,X5,X2)
| ~ apply(X4,X6,X3)
| ~ apply(X7,X6,X5)
| ~ member(X2,X8)
| ~ member(X5,X9)
| ~ member(X3,X8)
| ~ member(X6,X9) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_192,plain,
( apply(X1,X2,X3)
| lhs_atom46(X1,X7,X4,X8,X9)
| ~ apply(X4,X5,X3)
| ~ apply(X4,X6,X2)
| ~ apply(X7,X6,X5)
| ~ member(X3,X8)
| ~ member(X5,X9)
| ~ member(X2,X8)
| ~ member(X6,X9) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_193,plain,
( lhs_atom27(X1,X2,X3,X4)
| apply(X2,esk13_4(X1,X2,X3,X4),esk14_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_194,plain,
( lhs_atom27(X1,X2,X3,X4)
| apply(X1,esk13_4(X1,X2,X3,X4),esk15_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_195,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| maps(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_196,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| one_to_one(X3,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_197,plain,
( lhs_atom27(X1,X2,X3,X4)
| esk14_4(X1,X2,X3,X4) != esk15_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_198,plain,
( lhs_atom44(X1,X2,X3,X4)
| apply(X2,X1,esk27_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_199,plain,
( lhs_atom40(X1,X2,X3,X4)
| apply(X2,esk25_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_200,plain,
( lhs_atom44(X1,X2,X3,X4)
| member(esk27_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_201,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(esk25_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_202,plain,
( lhs_atom37(X1,X2,X3,X4)
| member(esk22_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_203,plain,
( lhs_atom37(X1,X2,X3,X4)
| member(esk23_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_204,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk13_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_205,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk14_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_206,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk15_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_207,plain,
( lhs_atom32(X1,X2,X3)
| apply(X1,esk20_4(X1,X2,X3,X4),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_208,plain,
( lhs_atom22(X1,X2,X3)
| apply(X1,X4,esk4_4(X1,X2,X3,X4))
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_209,plain,
( lhs_atom23(X1,X2,X3)
| apply(X1,esk6_3(X1,X2,X3),esk7_3(X1,X2,X3))
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_210,plain,
( lhs_atom23(X1,X2,X3)
| apply(X1,esk6_3(X1,X2,X3),esk8_3(X1,X2,X3))
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_211,plain,
( lhs_atom32(X1,X2,X3)
| member(esk20_4(X1,X2,X3,X4),X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_212,plain,
( lhs_atom22(X1,X2,X3)
| member(esk4_4(X1,X2,X3,X4),X2)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_213,plain,
( lhs_atom23(X1,X2,X3)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2)
| esk7_3(X1,X2,X3) != esk8_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_214,plain,
( X1 = X2
| lhs_atom26(X3,X5,X6,X7)
| ~ apply(X3,X4,X2)
| ~ apply(X5,X4,X1)
| ~ member(X2,X6)
| ~ member(X1,X6)
| ~ member(X4,X7) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_215,plain,
( lhs_atom23(X1,X2,X3)
| member(esk6_3(X1,X2,X3),X3)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_216,plain,
( lhs_atom23(X1,X2,X3)
| member(esk7_3(X1,X2,X3),X2)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_217,plain,
( lhs_atom23(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X2)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_218,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| apply(X1,esk6_3(X1,X2,X3),esk7_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_219,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| apply(X1,esk6_3(X1,X2,X3),esk8_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_220,plain,
( lhs_atom36(X1,X2,X3,X4)
| apply(X1,X5,X6)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X2,X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_221,plain,
( lhs_atom36(X1,X2,X3,X4)
| apply(X2,X6,X5)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_222,plain,
( lhs_atom45(X2,X1,X4,X5)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4)
| ~ member(X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_223,plain,
( lhs_atom41(X3,X1,X5,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4)
| ~ member(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_224,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| esk7_3(X1,X2,X3) != esk8_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_225,plain,
( lhs_atom33(X1,X2,X3)
| ~ apply(X1,X4,esk21_3(X1,X2,X3))
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_226,plain,
( lhs_atom31(X1,X2,X3)
| apply(X1,esk17_3(X1,X2,X3),esk19_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_227,plain,
( lhs_atom31(X1,X2,X3)
| apply(X1,esk18_3(X1,X2,X3),esk19_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_228,plain,
( X1 = X2
| lhs_atom30(X3,X5,X6)
| ~ apply(X3,X2,X4)
| ~ apply(X3,X1,X4)
| ~ member(X4,X5)
| ~ member(X2,X6)
| ~ member(X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_229,plain,
( lhs_atom22(X1,X2,X3)
| X4 = X5
| ~ apply(X1,X6,X5)
| ~ apply(X1,X6,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_230,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_231,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_232,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk8_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_233,plain,
( lhs_atom44(X1,X2,X3,X4)
| member(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_234,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_235,plain,
( lhs_atom35(X1,X3,X2)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_236,plain,
( lhs_atom31(X1,X2,X3)
| esk17_3(X1,X2,X3) != esk18_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_237,plain,
( lhs_atom42(X1,X2,X3)
| apply(X2,X1,esk26_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_238,plain,
( lhs_atom38(X1,X2,X3)
| apply(X2,esk24_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_239,plain,
( lhs_atom29(X1,X2)
| ~ apply(X1,esk16_2(X1,X2),esk16_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_240,plain,
( lhs_atom42(X1,X2,X3)
| member(esk26_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_241,plain,
( lhs_atom38(X1,X2,X3)
| member(esk24_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_242,plain,
( lhs_atom33(X1,X2,X3)
| member(esk21_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_243,plain,
( lhs_atom31(X1,X2,X3)
| member(esk17_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_244,plain,
( lhs_atom31(X1,X2,X3)
| member(esk18_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_245,plain,
( lhs_atom31(X1,X2,X3)
| member(esk19_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_246,plain,
( lhs_atom43(X2,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_247,plain,
( lhs_atom39(X3,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_248,plain,
( lhs_atom34(X1,X2,X3)
| injective(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_249,plain,
( lhs_atom34(X1,X2,X3)
| surjective(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_250,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_251,plain,
( apply(X1,X2,X2)
| lhs_atom28(X1,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_252,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_253,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_254,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_255,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_256,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_257,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_258,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_259,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_260,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_261,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_262,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_263,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_264,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_265,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_266,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_267,plain,
( lhs_atom29(X1,X2)
| member(esk16_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_268,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_269,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_270,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_271,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_272,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_273,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_274,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_275,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_276,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_277,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_278,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_279,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_280,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_281,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X3,X8,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7))
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
c_0_153,
[final] ).
cnf(c_0_282,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X2,esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
c_0_154,
[final] ).
cnf(c_0_283,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| member(esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X5)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
c_0_155,
[final] ).
cnf(c_0_284,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| ~ apply(X2,X7,esk11_6(X1,X2,X3,X4,X5,X6))
| ~ apply(X3,esk10_6(X1,X2,X3,X4,X5,X6),X7)
| ~ member(X7,X5)
| ~ apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6)) ),
c_0_156,
[final] ).
cnf(c_0_285,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X3,esk10_6(X1,X2,X3,X4,X5,X6),esk12_6(X1,X2,X3,X4,X5,X6)) ),
c_0_157,
[final] ).
cnf(c_0_286,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X2,esk12_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6)) ),
c_0_158,
[final] ).
cnf(c_0_287,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| apply(X1,esk10_6(X1,X2,X3,X4,X5,X6),esk11_6(X1,X2,X3,X4,X5,X6))
| member(esk12_6(X1,X2,X3,X4,X5,X6),X5) ),
c_0_159,
[final] ).
cnf(c_0_288,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| member(esk10_6(X1,X2,X3,X4,X5,X6),X6) ),
c_0_160,
[final] ).
cnf(c_0_289,plain,
( lhs_atom25(X1,X2,X3,X4,X5,X6)
| member(esk11_6(X1,X2,X3,X4,X5,X6),X4) ),
c_0_161,
[final] ).
cnf(c_0_290,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4)
| ~ apply(X1,esk37_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| ~ apply(X2,esk36_5(X1,X2,X3,X4,X5),esk38_5(X1,X2,X3,X4,X5)) ),
c_0_162,
[final] ).
cnf(c_0_291,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X1,esk37_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| apply(X2,esk36_5(X1,X2,X3,X4,X5),esk38_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_163,
[final] ).
cnf(c_0_292,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| ~ apply(X1,esk35_5(X1,X2,X3,X4,X5),esk33_5(X1,X2,X3,X4,X5)) ),
c_0_164,
[final] ).
cnf(c_0_293,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| ~ apply(X1,esk29_5(X1,X2,X3,X4,X5),esk31_5(X1,X2,X3,X4,X5)) ),
c_0_165,
[final] ).
cnf(c_0_294,plain,
( lhs_atom24(X1,X2,X3,X4,X5,X6)
| apply(X1,X8,X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X2,X9,X7)
| ~ apply(X3,X8,X9)
| ~ member(X9,X5) ),
c_0_166,
[final] ).
cnf(c_0_295,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X3,esk36_5(X1,X2,X3,X4,X5),esk37_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_167,
[final] ).
cnf(c_0_296,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| apply(X3,esk38_5(X1,X2,X3,X4,X5),esk39_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_168,
[final] ).
cnf(c_0_297,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X2,esk32_5(X1,X2,X3,X4,X5),esk34_5(X1,X2,X3,X4,X5)) ),
c_0_169,
[final] ).
cnf(c_0_298,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X3,esk32_5(X1,X2,X3,X4,X5),esk33_5(X1,X2,X3,X4,X5)) ),
c_0_170,
[final] ).
cnf(c_0_299,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| apply(X3,esk34_5(X1,X2,X3,X4,X5),esk35_5(X1,X2,X3,X4,X5)) ),
c_0_171,
[final] ).
cnf(c_0_300,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X2,esk28_5(X1,X2,X3,X4,X5),esk30_5(X1,X2,X3,X4,X5)) ),
c_0_172,
[final] ).
cnf(c_0_301,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X3,esk28_5(X1,X2,X3,X4,X5),esk29_5(X1,X2,X3,X4,X5)) ),
c_0_173,
[final] ).
cnf(c_0_302,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| apply(X3,esk30_5(X1,X2,X3,X4,X5),esk31_5(X1,X2,X3,X4,X5)) ),
c_0_174,
[final] ).
cnf(c_0_303,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk36_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_175,
[final] ).
cnf(c_0_304,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk37_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_176,
[final] ).
cnf(c_0_305,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk38_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_177,
[final] ).
cnf(c_0_306,plain,
( lhs_atom51(X1,X2,X3,X4,X5)
| member(esk39_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
c_0_178,
[final] ).
cnf(c_0_307,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk32_5(X1,X2,X3,X4,X5),X5) ),
c_0_179,
[final] ).
cnf(c_0_308,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk33_5(X1,X2,X3,X4,X5),X4) ),
c_0_180,
[final] ).
cnf(c_0_309,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk34_5(X1,X2,X3,X4,X5),X5) ),
c_0_181,
[final] ).
cnf(c_0_310,plain,
( lhs_atom49(X1,X2,X3,X4,X5)
| member(esk35_5(X1,X2,X3,X4,X5),X4) ),
c_0_182,
[final] ).
cnf(c_0_311,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk28_5(X1,X2,X3,X4,X5),X5) ),
c_0_183,
[final] ).
cnf(c_0_312,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk29_5(X1,X2,X3,X4,X5),X4) ),
c_0_184,
[final] ).
cnf(c_0_313,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk30_5(X1,X2,X3,X4,X5),X5) ),
c_0_185,
[final] ).
cnf(c_0_314,plain,
( lhs_atom47(X1,X2,X3,X4,X5)
| member(esk31_5(X1,X2,X3,X4,X5),X4) ),
c_0_186,
[final] ).
cnf(c_0_315,plain,
( lhs_atom37(X1,X2,X3,X4)
| ~ apply(X1,esk23_4(X1,X2,X3,X4),esk22_4(X1,X2,X3,X4))
| ~ apply(X2,esk22_4(X1,X2,X3,X4),esk23_4(X1,X2,X3,X4)) ),
c_0_187,
[final] ).
cnf(c_0_316,plain,
( lhs_atom37(X1,X2,X3,X4)
| apply(X1,esk23_4(X1,X2,X3,X4),esk22_4(X1,X2,X3,X4))
| apply(X2,esk22_4(X1,X2,X3,X4),esk23_4(X1,X2,X3,X4)) ),
c_0_188,
[final] ).
cnf(c_0_317,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| apply(X1,X9,X7)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X2,X8,X6) ),
c_0_189,
[final] ).
cnf(c_0_318,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| apply(X2,X8,X6)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X1,X9,X7) ),
c_0_190,
[final] ).
cnf(c_0_319,plain,
( apply(X1,X2,X3)
| lhs_atom48(X1,X7,X4,X8,X9)
| ~ apply(X4,X5,X2)
| ~ apply(X4,X6,X3)
| ~ apply(X7,X6,X5)
| ~ member(X2,X8)
| ~ member(X5,X9)
| ~ member(X3,X8)
| ~ member(X6,X9) ),
c_0_191,
[final] ).
cnf(c_0_320,plain,
( apply(X1,X2,X3)
| lhs_atom46(X1,X7,X4,X8,X9)
| ~ apply(X4,X5,X3)
| ~ apply(X4,X6,X2)
| ~ apply(X7,X6,X5)
| ~ member(X3,X8)
| ~ member(X5,X9)
| ~ member(X2,X8)
| ~ member(X6,X9) ),
c_0_192,
[final] ).
cnf(c_0_321,plain,
( lhs_atom27(X1,X2,X3,X4)
| apply(X2,esk13_4(X1,X2,X3,X4),esk14_4(X1,X2,X3,X4)) ),
c_0_193,
[final] ).
cnf(c_0_322,plain,
( lhs_atom27(X1,X2,X3,X4)
| apply(X1,esk13_4(X1,X2,X3,X4),esk15_4(X1,X2,X3,X4)) ),
c_0_194,
[final] ).
cnf(c_0_323,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| maps(X3,X5,X4) ),
c_0_195,
[final] ).
cnf(c_0_324,plain,
( lhs_atom50(X1,X2,X3,X4,X5)
| one_to_one(X3,X5,X4) ),
c_0_196,
[final] ).
cnf(c_0_325,plain,
( lhs_atom27(X1,X2,X3,X4)
| esk15_4(X1,X2,X3,X4) != esk14_4(X1,X2,X3,X4) ),
c_0_197,
[final] ).
cnf(c_0_326,plain,
( lhs_atom44(X1,X2,X3,X4)
| apply(X2,X1,esk27_4(X1,X2,X3,X4)) ),
c_0_198,
[final] ).
cnf(c_0_327,plain,
( lhs_atom40(X1,X2,X3,X4)
| apply(X2,esk25_4(X1,X2,X3,X4),X1) ),
c_0_199,
[final] ).
cnf(c_0_328,plain,
( lhs_atom44(X1,X2,X3,X4)
| member(esk27_4(X1,X2,X3,X4),X3) ),
c_0_200,
[final] ).
cnf(c_0_329,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(esk25_4(X1,X2,X3,X4),X4) ),
c_0_201,
[final] ).
cnf(c_0_330,plain,
( lhs_atom37(X1,X2,X3,X4)
| member(esk22_4(X1,X2,X3,X4),X4) ),
c_0_202,
[final] ).
cnf(c_0_331,plain,
( lhs_atom37(X1,X2,X3,X4)
| member(esk23_4(X1,X2,X3,X4),X3) ),
c_0_203,
[final] ).
cnf(c_0_332,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk13_4(X1,X2,X3,X4),X4) ),
c_0_204,
[final] ).
cnf(c_0_333,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk14_4(X1,X2,X3,X4),X3) ),
c_0_205,
[final] ).
cnf(c_0_334,plain,
( lhs_atom27(X1,X2,X3,X4)
| member(esk15_4(X1,X2,X3,X4),X3) ),
c_0_206,
[final] ).
cnf(c_0_335,plain,
( lhs_atom32(X1,X2,X3)
| apply(X1,esk20_4(X1,X2,X3,X4),X4)
| ~ member(X4,X2) ),
c_0_207,
[final] ).
cnf(c_0_336,plain,
( lhs_atom22(X1,X2,X3)
| apply(X1,X4,esk4_4(X1,X2,X3,X4))
| ~ member(X4,X3) ),
c_0_208,
[final] ).
cnf(c_0_337,plain,
( lhs_atom23(X1,X2,X3)
| apply(X1,esk6_3(X1,X2,X3),esk7_3(X1,X2,X3))
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
c_0_209,
[final] ).
cnf(c_0_338,plain,
( lhs_atom23(X1,X2,X3)
| apply(X1,esk6_3(X1,X2,X3),esk8_3(X1,X2,X3))
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
c_0_210,
[final] ).
cnf(c_0_339,plain,
( lhs_atom32(X1,X2,X3)
| member(esk20_4(X1,X2,X3,X4),X3)
| ~ member(X4,X2) ),
c_0_211,
[final] ).
cnf(c_0_340,plain,
( lhs_atom22(X1,X2,X3)
| member(esk4_4(X1,X2,X3,X4),X2)
| ~ member(X4,X3) ),
c_0_212,
[final] ).
cnf(c_0_341,plain,
( lhs_atom23(X1,X2,X3)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2)
| esk8_3(X1,X2,X3) != esk7_3(X1,X2,X3) ),
c_0_213,
[final] ).
cnf(c_0_342,plain,
( X1 = X2
| lhs_atom26(X3,X5,X6,X7)
| ~ apply(X3,X4,X2)
| ~ apply(X5,X4,X1)
| ~ member(X2,X6)
| ~ member(X1,X6)
| ~ member(X4,X7) ),
c_0_214,
[final] ).
cnf(c_0_343,plain,
( lhs_atom23(X1,X2,X3)
| member(esk6_3(X1,X2,X3),X3)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
c_0_215,
[final] ).
cnf(c_0_344,plain,
( lhs_atom23(X1,X2,X3)
| member(esk7_3(X1,X2,X3),X2)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
c_0_216,
[final] ).
cnf(c_0_345,plain,
( lhs_atom23(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X2)
| ~ apply(X1,esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
c_0_217,
[final] ).
cnf(c_0_346,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| apply(X1,esk6_3(X1,X2,X3),esk7_3(X1,X2,X3)) ),
c_0_218,
[final] ).
cnf(c_0_347,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| apply(X1,esk6_3(X1,X2,X3),esk8_3(X1,X2,X3)) ),
c_0_219,
[final] ).
cnf(c_0_348,plain,
( lhs_atom36(X1,X2,X3,X4)
| apply(X1,X5,X6)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X2,X6,X5) ),
c_0_220,
[final] ).
cnf(c_0_349,plain,
( lhs_atom36(X1,X2,X3,X4)
| apply(X2,X6,X5)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X1,X5,X6) ),
c_0_221,
[final] ).
cnf(c_0_350,plain,
( lhs_atom45(X2,X1,X4,X5)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4)
| ~ member(X2,X5) ),
c_0_222,
[final] ).
cnf(c_0_351,plain,
( lhs_atom41(X3,X1,X5,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4)
| ~ member(X3,X5) ),
c_0_223,
[final] ).
cnf(c_0_352,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| esk8_3(X1,X2,X3) != esk7_3(X1,X2,X3) ),
c_0_224,
[final] ).
cnf(c_0_353,plain,
( lhs_atom33(X1,X2,X3)
| ~ apply(X1,X4,esk21_3(X1,X2,X3))
| ~ member(X4,X3) ),
c_0_225,
[final] ).
cnf(c_0_354,plain,
( lhs_atom31(X1,X2,X3)
| apply(X1,esk17_3(X1,X2,X3),esk19_3(X1,X2,X3)) ),
c_0_226,
[final] ).
cnf(c_0_355,plain,
( lhs_atom31(X1,X2,X3)
| apply(X1,esk18_3(X1,X2,X3),esk19_3(X1,X2,X3)) ),
c_0_227,
[final] ).
cnf(c_0_356,plain,
( X1 = X2
| lhs_atom30(X3,X5,X6)
| ~ apply(X3,X2,X4)
| ~ apply(X3,X1,X4)
| ~ member(X4,X5)
| ~ member(X2,X6)
| ~ member(X1,X6) ),
c_0_228,
[final] ).
cnf(c_0_357,plain,
( lhs_atom22(X1,X2,X3)
| X4 = X5
| ~ apply(X1,X6,X5)
| ~ apply(X1,X6,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X6,X3) ),
c_0_229,
[final] ).
cnf(c_0_358,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk6_3(X1,X2,X3),X3) ),
c_0_230,
[final] ).
cnf(c_0_359,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk7_3(X1,X2,X3),X2) ),
c_0_231,
[final] ).
cnf(c_0_360,plain,
( lhs_atom23(X1,X2,X3)
| member(esk5_3(X1,X2,X3),X3)
| member(esk8_3(X1,X2,X3),X2) ),
c_0_232,
[final] ).
cnf(c_0_361,plain,
( lhs_atom44(X1,X2,X3,X4)
| member(X1,X4) ),
c_0_233,
[final] ).
cnf(c_0_362,plain,
( lhs_atom40(X1,X2,X3,X4)
| member(X1,X3) ),
c_0_234,
[final] ).
cnf(c_0_363,plain,
( lhs_atom35(X1,X3,X2)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
c_0_235,
[final] ).
cnf(c_0_364,plain,
( lhs_atom31(X1,X2,X3)
| esk18_3(X1,X2,X3) != esk17_3(X1,X2,X3) ),
c_0_236,
[final] ).
cnf(c_0_365,plain,
( lhs_atom42(X1,X2,X3)
| apply(X2,X1,esk26_3(X1,X2,X3)) ),
c_0_237,
[final] ).
cnf(c_0_366,plain,
( lhs_atom38(X1,X2,X3)
| apply(X2,esk24_3(X1,X2,X3),X1) ),
c_0_238,
[final] ).
cnf(c_0_367,plain,
( lhs_atom29(X1,X2)
| ~ apply(X1,esk16_2(X1,X2),esk16_2(X1,X2)) ),
c_0_239,
[final] ).
cnf(c_0_368,plain,
( lhs_atom42(X1,X2,X3)
| member(esk26_3(X1,X2,X3),X3) ),
c_0_240,
[final] ).
cnf(c_0_369,plain,
( lhs_atom38(X1,X2,X3)
| member(esk24_3(X1,X2,X3),X3) ),
c_0_241,
[final] ).
cnf(c_0_370,plain,
( lhs_atom33(X1,X2,X3)
| member(esk21_3(X1,X2,X3),X2) ),
c_0_242,
[final] ).
cnf(c_0_371,plain,
( lhs_atom31(X1,X2,X3)
| member(esk17_3(X1,X2,X3),X3) ),
c_0_243,
[final] ).
cnf(c_0_372,plain,
( lhs_atom31(X1,X2,X3)
| member(esk18_3(X1,X2,X3),X3) ),
c_0_244,
[final] ).
cnf(c_0_373,plain,
( lhs_atom31(X1,X2,X3)
| member(esk19_3(X1,X2,X3),X2) ),
c_0_245,
[final] ).
cnf(c_0_374,plain,
( lhs_atom43(X2,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4) ),
c_0_246,
[final] ).
cnf(c_0_375,plain,
( lhs_atom39(X3,X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
c_0_247,
[final] ).
cnf(c_0_376,plain,
( lhs_atom34(X1,X2,X3)
| injective(X1,X3,X2) ),
c_0_248,
[final] ).
cnf(c_0_377,plain,
( lhs_atom34(X1,X2,X3)
| surjective(X1,X3,X2) ),
c_0_249,
[final] ).
cnf(c_0_378,plain,
( lhs_atom8(X1,X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_250,
[final] ).
cnf(c_0_379,plain,
( apply(X1,X2,X2)
| lhs_atom28(X1,X3)
| ~ member(X2,X3) ),
c_0_251,
[final] ).
cnf(c_0_380,plain,
( member(X1,X2)
| lhs_atom13(X3,X1,X2)
| ~ member(X1,X3) ),
c_0_252,
[final] ).
cnf(c_0_381,plain,
( member(X1,X2)
| member(X1,X3)
| lhs_atom9(X1,X2,X3) ),
c_0_253,
[final] ).
cnf(c_0_382,plain,
( lhs_atom21(X1,X2)
| ~ member(X1,esk3_2(X1,X2)) ),
c_0_254,
[final] ).
cnf(c_0_383,plain,
( lhs_atom2(X1,X2)
| ~ member(esk1_2(X1,X2),X1) ),
c_0_255,
[final] ).
cnf(c_0_384,plain,
( lhs_atom12(X1,X2,X3)
| ~ member(X2,X3) ),
c_0_256,
[final] ).
cnf(c_0_385,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X3) ),
c_0_257,
[final] ).
cnf(c_0_386,plain,
( lhs_atom10(X1,X2,X3)
| ~ member(X1,X2) ),
c_0_258,
[final] ).
cnf(c_0_387,plain,
( lhs_atom12(X1,X2,X3)
| member(X2,X1) ),
c_0_259,
[final] ).
cnf(c_0_388,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X3) ),
c_0_260,
[final] ).
cnf(c_0_389,plain,
( lhs_atom7(X1,X2,X3)
| member(X1,X2) ),
c_0_261,
[final] ).
cnf(c_0_390,plain,
( lhs_atom19(X1,X3)
| ~ member(X1,X2)
| ~ member(X2,X3) ),
c_0_262,
[final] ).
cnf(c_0_391,plain,
( lhs_atom4(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
c_0_263,
[final] ).
cnf(c_0_392,plain,
( X1 = X2
| X1 = X3
| lhs_atom16(X1,X2,X3) ),
c_0_264,
[final] ).
cnf(c_0_393,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X3 ),
c_0_265,
[final] ).
cnf(c_0_394,plain,
( lhs_atom17(X1,X2,X3)
| X1 != X2 ),
c_0_266,
[final] ).
cnf(c_0_395,plain,
( lhs_atom29(X1,X2)
| member(esk16_2(X1,X2),X2) ),
c_0_267,
[final] ).
cnf(c_0_396,plain,
( lhs_atom21(X1,X2)
| member(esk3_2(X1,X2),X2) ),
c_0_268,
[final] ).
cnf(c_0_397,plain,
( lhs_atom18(X1,X2)
| member(esk2_2(X1,X2),X2) ),
c_0_269,
[final] ).
cnf(c_0_398,plain,
( lhs_atom18(X1,X2)
| member(X1,esk2_2(X1,X2)) ),
c_0_270,
[final] ).
cnf(c_0_399,plain,
( lhs_atom2(X1,X2)
| member(esk1_2(X1,X2),X2) ),
c_0_271,
[final] ).
cnf(c_0_400,plain,
( member(X1,X2)
| lhs_atom20(X1,X3)
| ~ member(X2,X3) ),
c_0_272,
[final] ).
cnf(c_0_401,plain,
( member(X1,X2)
| lhs_atom1(X2,X3)
| ~ member(X1,X3) ),
c_0_273,
[final] ).
cnf(c_0_402,plain,
( lhs_atom6(X1,X2)
| ~ subset(X1,X2) ),
c_0_274,
[final] ).
cnf(c_0_403,plain,
( subset(X1,X2)
| lhs_atom5(X1,X2) ),
c_0_275,
[final] ).
cnf(c_0_404,plain,
( lhs_atom3(X1,X2)
| subset(X2,X1) ),
c_0_276,
[final] ).
cnf(c_0_405,plain,
( lhs_atom3(X1,X2)
| subset(X1,X2) ),
c_0_277,
[final] ).
cnf(c_0_406,plain,
( lhs_atom15(X1,X2)
| X1 != X2 ),
c_0_278,
[final] ).
cnf(c_0_407,plain,
( X1 = X2
| lhs_atom14(X1,X2) ),
c_0_279,
[final] ).
cnf(c_0_408,plain,
lhs_atom11(X1),
c_0_280,
[final] ).
% End CNF derivation
cnf(c_0_281_0,axiom,
( ~ compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X3,X8,sk1_esk9_8(X1,X2,X3,X4,X5,X6,X8,X7))
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(unfold_definition,[status(thm)],[c_0_281,def_lhs_atom24]) ).
cnf(c_0_282_0,axiom,
( ~ compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X2,sk1_esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(unfold_definition,[status(thm)],[c_0_282,def_lhs_atom24]) ).
cnf(c_0_283_0,axiom,
( ~ compose_predicate(X1,X2,X3,X6,X5,X4)
| member(sk1_esk9_8(X1,X2,X3,X4,X5,X6,X8,X7),X5)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X1,X8,X7) ),
inference(unfold_definition,[status(thm)],[c_0_283,def_lhs_atom24]) ).
cnf(c_0_284_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| ~ apply(X2,X7,sk1_esk11_6(X1,X2,X3,X4,X5,X6))
| ~ apply(X3,sk1_esk10_6(X1,X2,X3,X4,X5,X6),X7)
| ~ member(X7,X5)
| ~ apply(X1,sk1_esk10_6(X1,X2,X3,X4,X5,X6),sk1_esk11_6(X1,X2,X3,X4,X5,X6)) ),
inference(unfold_definition,[status(thm)],[c_0_284,def_lhs_atom25]) ).
cnf(c_0_285_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X1,sk1_esk10_6(X1,X2,X3,X4,X5,X6),sk1_esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X3,sk1_esk10_6(X1,X2,X3,X4,X5,X6),sk1_esk12_6(X1,X2,X3,X4,X5,X6)) ),
inference(unfold_definition,[status(thm)],[c_0_285,def_lhs_atom25]) ).
cnf(c_0_286_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X1,sk1_esk10_6(X1,X2,X3,X4,X5,X6),sk1_esk11_6(X1,X2,X3,X4,X5,X6))
| apply(X2,sk1_esk12_6(X1,X2,X3,X4,X5,X6),sk1_esk11_6(X1,X2,X3,X4,X5,X6)) ),
inference(unfold_definition,[status(thm)],[c_0_286,def_lhs_atom25]) ).
cnf(c_0_287_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X1,sk1_esk10_6(X1,X2,X3,X4,X5,X6),sk1_esk11_6(X1,X2,X3,X4,X5,X6))
| member(sk1_esk12_6(X1,X2,X3,X4,X5,X6),X5) ),
inference(unfold_definition,[status(thm)],[c_0_287,def_lhs_atom25]) ).
cnf(c_0_288_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| member(sk1_esk10_6(X1,X2,X3,X4,X5,X6),X6) ),
inference(unfold_definition,[status(thm)],[c_0_288,def_lhs_atom25]) ).
cnf(c_0_289_0,axiom,
( compose_predicate(X1,X2,X3,X6,X5,X4)
| member(sk1_esk11_6(X1,X2,X3,X4,X5,X6),X4) ),
inference(unfold_definition,[status(thm)],[c_0_289,def_lhs_atom25]) ).
cnf(c_0_290_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4)
| ~ apply(X1,sk1_esk37_5(X1,X2,X3,X4,X5),sk1_esk39_5(X1,X2,X3,X4,X5))
| ~ apply(X2,sk1_esk36_5(X1,X2,X3,X4,X5),sk1_esk38_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_290,def_lhs_atom51]) ).
cnf(c_0_291_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| apply(X1,sk1_esk37_5(X1,X2,X3,X4,X5),sk1_esk39_5(X1,X2,X3,X4,X5))
| apply(X2,sk1_esk36_5(X1,X2,X3,X4,X5),sk1_esk38_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_291,def_lhs_atom51]) ).
cnf(c_0_292_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| ~ apply(X1,sk1_esk35_5(X1,X2,X3,X4,X5),sk1_esk33_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_292,def_lhs_atom49]) ).
cnf(c_0_293_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| ~ apply(X1,sk1_esk29_5(X1,X2,X3,X4,X5),sk1_esk31_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_293,def_lhs_atom47]) ).
cnf(c_0_294_0,axiom,
( ~ compose_predicate(X1,X2,X3,X6,X5,X4)
| apply(X1,X8,X7)
| ~ member(X7,X4)
| ~ member(X8,X6)
| ~ apply(X2,X9,X7)
| ~ apply(X3,X8,X9)
| ~ member(X9,X5) ),
inference(unfold_definition,[status(thm)],[c_0_294,def_lhs_atom24]) ).
cnf(c_0_295_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk36_5(X1,X2,X3,X4,X5),sk1_esk37_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_295,def_lhs_atom51]) ).
cnf(c_0_296_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk38_5(X1,X2,X3,X4,X5),sk1_esk39_5(X1,X2,X3,X4,X5))
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_296,def_lhs_atom51]) ).
cnf(c_0_297_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| apply(X2,sk1_esk32_5(X1,X2,X3,X4,X5),sk1_esk34_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_297,def_lhs_atom49]) ).
cnf(c_0_298_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk32_5(X1,X2,X3,X4,X5),sk1_esk33_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_298,def_lhs_atom49]) ).
cnf(c_0_299_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk34_5(X1,X2,X3,X4,X5),sk1_esk35_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_299,def_lhs_atom49]) ).
cnf(c_0_300_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| apply(X2,sk1_esk28_5(X1,X2,X3,X4,X5),sk1_esk30_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_300,def_lhs_atom47]) ).
cnf(c_0_301_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk28_5(X1,X2,X3,X4,X5),sk1_esk29_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_301,def_lhs_atom47]) ).
cnf(c_0_302_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| apply(X3,sk1_esk30_5(X1,X2,X3,X4,X5),sk1_esk31_5(X1,X2,X3,X4,X5)) ),
inference(unfold_definition,[status(thm)],[c_0_302,def_lhs_atom47]) ).
cnf(c_0_303_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| member(sk1_esk36_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_303,def_lhs_atom51]) ).
cnf(c_0_304_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| member(sk1_esk37_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_304,def_lhs_atom51]) ).
cnf(c_0_305_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| member(sk1_esk38_5(X1,X2,X3,X4,X5),X5)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_305,def_lhs_atom51]) ).
cnf(c_0_306_0,axiom,
( isomorphism(X3,X5,X2,X4,X1)
| member(sk1_esk39_5(X1,X2,X3,X4,X5),X4)
| ~ maps(X3,X5,X4)
| ~ one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_306,def_lhs_atom51]) ).
cnf(c_0_307_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| member(sk1_esk32_5(X1,X2,X3,X4,X5),X5) ),
inference(unfold_definition,[status(thm)],[c_0_307,def_lhs_atom49]) ).
cnf(c_0_308_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| member(sk1_esk33_5(X1,X2,X3,X4,X5),X4) ),
inference(unfold_definition,[status(thm)],[c_0_308,def_lhs_atom49]) ).
cnf(c_0_309_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| member(sk1_esk34_5(X1,X2,X3,X4,X5),X5) ),
inference(unfold_definition,[status(thm)],[c_0_309,def_lhs_atom49]) ).
cnf(c_0_310_0,axiom,
( decreasing(X3,X5,X2,X4,X1)
| member(sk1_esk35_5(X1,X2,X3,X4,X5),X4) ),
inference(unfold_definition,[status(thm)],[c_0_310,def_lhs_atom49]) ).
cnf(c_0_311_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| member(sk1_esk28_5(X1,X2,X3,X4,X5),X5) ),
inference(unfold_definition,[status(thm)],[c_0_311,def_lhs_atom47]) ).
cnf(c_0_312_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| member(sk1_esk29_5(X1,X2,X3,X4,X5),X4) ),
inference(unfold_definition,[status(thm)],[c_0_312,def_lhs_atom47]) ).
cnf(c_0_313_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| member(sk1_esk30_5(X1,X2,X3,X4,X5),X5) ),
inference(unfold_definition,[status(thm)],[c_0_313,def_lhs_atom47]) ).
cnf(c_0_314_0,axiom,
( increasing(X3,X5,X2,X4,X1)
| member(sk1_esk31_5(X1,X2,X3,X4,X5),X4) ),
inference(unfold_definition,[status(thm)],[c_0_314,def_lhs_atom47]) ).
cnf(c_0_315_0,axiom,
( inverse_predicate(X1,X2,X4,X3)
| ~ apply(X1,sk1_esk23_4(X1,X2,X3,X4),sk1_esk22_4(X1,X2,X3,X4))
| ~ apply(X2,sk1_esk22_4(X1,X2,X3,X4),sk1_esk23_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_315,def_lhs_atom37]) ).
cnf(c_0_316_0,axiom,
( inverse_predicate(X1,X2,X4,X3)
| apply(X1,sk1_esk23_4(X1,X2,X3,X4),sk1_esk22_4(X1,X2,X3,X4))
| apply(X2,sk1_esk22_4(X1,X2,X3,X4),sk1_esk23_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_316,def_lhs_atom37]) ).
cnf(c_0_317_0,axiom,
( ~ isomorphism(X3,X5,X2,X4,X1)
| apply(X1,X9,X7)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X2,X8,X6) ),
inference(unfold_definition,[status(thm)],[c_0_317,def_lhs_atom50]) ).
cnf(c_0_318_0,axiom,
( ~ isomorphism(X3,X5,X2,X4,X1)
| apply(X2,X8,X6)
| ~ apply(X3,X6,X7)
| ~ apply(X3,X8,X9)
| ~ member(X7,X4)
| ~ member(X6,X5)
| ~ member(X9,X4)
| ~ member(X8,X5)
| ~ apply(X1,X9,X7) ),
inference(unfold_definition,[status(thm)],[c_0_318,def_lhs_atom50]) ).
cnf(c_0_319_0,axiom,
( ~ decreasing(X4,X9,X7,X8,X1)
| apply(X1,X2,X3)
| ~ apply(X4,X5,X2)
| ~ apply(X4,X6,X3)
| ~ apply(X7,X6,X5)
| ~ member(X2,X8)
| ~ member(X5,X9)
| ~ member(X3,X8)
| ~ member(X6,X9) ),
inference(unfold_definition,[status(thm)],[c_0_319,def_lhs_atom48]) ).
cnf(c_0_320_0,axiom,
( ~ increasing(X4,X9,X7,X8,X1)
| apply(X1,X2,X3)
| ~ apply(X4,X5,X3)
| ~ apply(X4,X6,X2)
| ~ apply(X7,X6,X5)
| ~ member(X3,X8)
| ~ member(X5,X9)
| ~ member(X2,X8)
| ~ member(X6,X9) ),
inference(unfold_definition,[status(thm)],[c_0_320,def_lhs_atom46]) ).
cnf(c_0_321_0,axiom,
( equal_maps(X2,X1,X4,X3)
| apply(X2,sk1_esk13_4(X1,X2,X3,X4),sk1_esk14_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_321,def_lhs_atom27]) ).
cnf(c_0_322_0,axiom,
( equal_maps(X2,X1,X4,X3)
| apply(X1,sk1_esk13_4(X1,X2,X3,X4),sk1_esk15_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_322,def_lhs_atom27]) ).
cnf(c_0_323_0,axiom,
( ~ isomorphism(X3,X5,X2,X4,X1)
| maps(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_323,def_lhs_atom50]) ).
cnf(c_0_324_0,axiom,
( ~ isomorphism(X3,X5,X2,X4,X1)
| one_to_one(X3,X5,X4) ),
inference(unfold_definition,[status(thm)],[c_0_324,def_lhs_atom50]) ).
cnf(c_0_325_0,axiom,
( equal_maps(X2,X1,X4,X3)
| sk1_esk15_4(X1,X2,X3,X4) != sk1_esk14_4(X1,X2,X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_325,def_lhs_atom27]) ).
cnf(c_0_326_0,axiom,
( ~ member(X1,inverse_image3(X2,X3,X4))
| apply(X2,X1,sk1_esk27_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_326,def_lhs_atom44]) ).
cnf(c_0_327_0,axiom,
( ~ member(X1,image3(X2,X4,X3))
| apply(X2,sk1_esk25_4(X1,X2,X3,X4),X1) ),
inference(unfold_definition,[status(thm)],[c_0_327,def_lhs_atom40]) ).
cnf(c_0_328_0,axiom,
( ~ member(X1,inverse_image3(X2,X3,X4))
| member(sk1_esk27_4(X1,X2,X3,X4),X3) ),
inference(unfold_definition,[status(thm)],[c_0_328,def_lhs_atom44]) ).
cnf(c_0_329_0,axiom,
( ~ member(X1,image3(X2,X4,X3))
| member(sk1_esk25_4(X1,X2,X3,X4),X4) ),
inference(unfold_definition,[status(thm)],[c_0_329,def_lhs_atom40]) ).
cnf(c_0_330_0,axiom,
( inverse_predicate(X1,X2,X4,X3)
| member(sk1_esk22_4(X1,X2,X3,X4),X4) ),
inference(unfold_definition,[status(thm)],[c_0_330,def_lhs_atom37]) ).
cnf(c_0_331_0,axiom,
( inverse_predicate(X1,X2,X4,X3)
| member(sk1_esk23_4(X1,X2,X3,X4),X3) ),
inference(unfold_definition,[status(thm)],[c_0_331,def_lhs_atom37]) ).
cnf(c_0_332_0,axiom,
( equal_maps(X2,X1,X4,X3)
| member(sk1_esk13_4(X1,X2,X3,X4),X4) ),
inference(unfold_definition,[status(thm)],[c_0_332,def_lhs_atom27]) ).
cnf(c_0_333_0,axiom,
( equal_maps(X2,X1,X4,X3)
| member(sk1_esk14_4(X1,X2,X3,X4),X3) ),
inference(unfold_definition,[status(thm)],[c_0_333,def_lhs_atom27]) ).
cnf(c_0_334_0,axiom,
( equal_maps(X2,X1,X4,X3)
| member(sk1_esk15_4(X1,X2,X3,X4),X3) ),
inference(unfold_definition,[status(thm)],[c_0_334,def_lhs_atom27]) ).
cnf(c_0_335_0,axiom,
( ~ surjective(X1,X3,X2)
| apply(X1,sk1_esk20_4(X1,X2,X3,X4),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_335,def_lhs_atom32]) ).
cnf(c_0_336_0,axiom,
( ~ maps(X1,X3,X2)
| apply(X1,X4,sk1_esk4_4(X1,X2,X3,X4))
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_336,def_lhs_atom22]) ).
cnf(c_0_337_0,axiom,
( maps(X1,X3,X2)
| apply(X1,sk1_esk6_3(X1,X2,X3),sk1_esk7_3(X1,X2,X3))
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_337,def_lhs_atom23]) ).
cnf(c_0_338_0,axiom,
( maps(X1,X3,X2)
| apply(X1,sk1_esk6_3(X1,X2,X3),sk1_esk8_3(X1,X2,X3))
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_338,def_lhs_atom23]) ).
cnf(c_0_339_0,axiom,
( ~ surjective(X1,X3,X2)
| member(sk1_esk20_4(X1,X2,X3,X4),X3)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_339,def_lhs_atom32]) ).
cnf(c_0_340_0,axiom,
( ~ maps(X1,X3,X2)
| member(sk1_esk4_4(X1,X2,X3,X4),X2)
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_340,def_lhs_atom22]) ).
cnf(c_0_341_0,axiom,
( maps(X1,X3,X2)
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2)
| sk1_esk8_3(X1,X2,X3) != sk1_esk7_3(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_341,def_lhs_atom23]) ).
cnf(c_0_342_0,axiom,
( ~ equal_maps(X5,X3,X7,X6)
| X1 = X2
| ~ apply(X3,X4,X2)
| ~ apply(X5,X4,X1)
| ~ member(X2,X6)
| ~ member(X1,X6)
| ~ member(X4,X7) ),
inference(unfold_definition,[status(thm)],[c_0_342,def_lhs_atom26]) ).
cnf(c_0_343_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk6_3(X1,X2,X3),X3)
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_343,def_lhs_atom23]) ).
cnf(c_0_344_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk7_3(X1,X2,X3),X2)
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_344,def_lhs_atom23]) ).
cnf(c_0_345_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk8_3(X1,X2,X3),X2)
| ~ apply(X1,sk1_esk5_3(X1,X2,X3),X4)
| ~ member(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_345,def_lhs_atom23]) ).
cnf(c_0_346_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| apply(X1,sk1_esk6_3(X1,X2,X3),sk1_esk7_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_346,def_lhs_atom23]) ).
cnf(c_0_347_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| apply(X1,sk1_esk6_3(X1,X2,X3),sk1_esk8_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_347,def_lhs_atom23]) ).
cnf(c_0_348_0,axiom,
( ~ inverse_predicate(X1,X2,X4,X3)
| apply(X1,X5,X6)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X2,X6,X5) ),
inference(unfold_definition,[status(thm)],[c_0_348,def_lhs_atom36]) ).
cnf(c_0_349_0,axiom,
( ~ inverse_predicate(X1,X2,X4,X3)
| apply(X2,X6,X5)
| ~ member(X5,X3)
| ~ member(X6,X4)
| ~ apply(X1,X5,X6) ),
inference(unfold_definition,[status(thm)],[c_0_349,def_lhs_atom36]) ).
cnf(c_0_350_0,axiom,
( member(X2,inverse_image3(X1,X4,X5))
| ~ apply(X1,X2,X3)
| ~ member(X3,X4)
| ~ member(X2,X5) ),
inference(unfold_definition,[status(thm)],[c_0_350,def_lhs_atom45]) ).
cnf(c_0_351_0,axiom,
( member(X3,image3(X1,X4,X5))
| ~ apply(X1,X2,X3)
| ~ member(X2,X4)
| ~ member(X3,X5) ),
inference(unfold_definition,[status(thm)],[c_0_351,def_lhs_atom41]) ).
cnf(c_0_352_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| sk1_esk8_3(X1,X2,X3) != sk1_esk7_3(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_352,def_lhs_atom23]) ).
cnf(c_0_353_0,axiom,
( surjective(X1,X3,X2)
| ~ apply(X1,X4,sk1_esk21_3(X1,X2,X3))
| ~ member(X4,X3) ),
inference(unfold_definition,[status(thm)],[c_0_353,def_lhs_atom33]) ).
cnf(c_0_354_0,axiom,
( injective(X1,X3,X2)
| apply(X1,sk1_esk17_3(X1,X2,X3),sk1_esk19_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_354,def_lhs_atom31]) ).
cnf(c_0_355_0,axiom,
( injective(X1,X3,X2)
| apply(X1,sk1_esk18_3(X1,X2,X3),sk1_esk19_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_355,def_lhs_atom31]) ).
cnf(c_0_356_0,axiom,
( ~ injective(X3,X6,X5)
| X1 = X2
| ~ apply(X3,X2,X4)
| ~ apply(X3,X1,X4)
| ~ member(X4,X5)
| ~ member(X2,X6)
| ~ member(X1,X6) ),
inference(unfold_definition,[status(thm)],[c_0_356,def_lhs_atom30]) ).
cnf(c_0_357_0,axiom,
( ~ maps(X1,X3,X2)
| X4 = X5
| ~ apply(X1,X6,X5)
| ~ apply(X1,X6,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X6,X3) ),
inference(unfold_definition,[status(thm)],[c_0_357,def_lhs_atom22]) ).
cnf(c_0_358_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| member(sk1_esk6_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_358,def_lhs_atom23]) ).
cnf(c_0_359_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| member(sk1_esk7_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_359,def_lhs_atom23]) ).
cnf(c_0_360_0,axiom,
( maps(X1,X3,X2)
| member(sk1_esk5_3(X1,X2,X3),X3)
| member(sk1_esk8_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_360,def_lhs_atom23]) ).
cnf(c_0_361_0,axiom,
( ~ member(X1,inverse_image3(X2,X3,X4))
| member(X1,X4) ),
inference(unfold_definition,[status(thm)],[c_0_361,def_lhs_atom44]) ).
cnf(c_0_362_0,axiom,
( ~ member(X1,image3(X2,X4,X3))
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_362,def_lhs_atom40]) ).
cnf(c_0_363_0,axiom,
( one_to_one(X1,X2,X3)
| ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_363,def_lhs_atom35]) ).
cnf(c_0_364_0,axiom,
( injective(X1,X3,X2)
| sk1_esk18_3(X1,X2,X3) != sk1_esk17_3(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_364,def_lhs_atom31]) ).
cnf(c_0_365_0,axiom,
( ~ member(X1,inverse_image2(X2,X3))
| apply(X2,X1,sk1_esk26_3(X1,X2,X3)) ),
inference(unfold_definition,[status(thm)],[c_0_365,def_lhs_atom42]) ).
cnf(c_0_366_0,axiom,
( ~ member(X1,image2(X2,X3))
| apply(X2,sk1_esk24_3(X1,X2,X3),X1) ),
inference(unfold_definition,[status(thm)],[c_0_366,def_lhs_atom38]) ).
cnf(c_0_367_0,axiom,
( identity(X1,X2)
| ~ apply(X1,sk1_esk16_2(X1,X2),sk1_esk16_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_367,def_lhs_atom29]) ).
cnf(c_0_368_0,axiom,
( ~ member(X1,inverse_image2(X2,X3))
| member(sk1_esk26_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_368,def_lhs_atom42]) ).
cnf(c_0_369_0,axiom,
( ~ member(X1,image2(X2,X3))
| member(sk1_esk24_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_369,def_lhs_atom38]) ).
cnf(c_0_370_0,axiom,
( surjective(X1,X3,X2)
| member(sk1_esk21_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_370,def_lhs_atom33]) ).
cnf(c_0_371_0,axiom,
( injective(X1,X3,X2)
| member(sk1_esk17_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_371,def_lhs_atom31]) ).
cnf(c_0_372_0,axiom,
( injective(X1,X3,X2)
| member(sk1_esk18_3(X1,X2,X3),X3) ),
inference(unfold_definition,[status(thm)],[c_0_372,def_lhs_atom31]) ).
cnf(c_0_373_0,axiom,
( injective(X1,X3,X2)
| member(sk1_esk19_3(X1,X2,X3),X2) ),
inference(unfold_definition,[status(thm)],[c_0_373,def_lhs_atom31]) ).
cnf(c_0_374_0,axiom,
( member(X2,inverse_image2(X1,X4))
| ~ apply(X1,X2,X3)
| ~ member(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_374,def_lhs_atom43]) ).
cnf(c_0_375_0,axiom,
( member(X3,image2(X1,X4))
| ~ apply(X1,X2,X3)
| ~ member(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_375,def_lhs_atom39]) ).
cnf(c_0_376_0,axiom,
( ~ one_to_one(X1,X3,X2)
| injective(X1,X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_376,def_lhs_atom34]) ).
cnf(c_0_377_0,axiom,
( ~ one_to_one(X1,X3,X2)
| surjective(X1,X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_377,def_lhs_atom34]) ).
cnf(c_0_378_0,axiom,
( member(X1,intersection(X3,X2))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_378,def_lhs_atom8]) ).
cnf(c_0_379_0,axiom,
( ~ identity(X1,X3)
| apply(X1,X2,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_379,def_lhs_atom28]) ).
cnf(c_0_380_0,axiom,
( member(X1,difference(X3,X2))
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_380,def_lhs_atom13]) ).
cnf(c_0_381_0,axiom,
( ~ member(X1,union(X3,X2))
| member(X1,X2)
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_381,def_lhs_atom9]) ).
cnf(c_0_382_0,axiom,
( member(X1,product(X2))
| ~ member(X1,sk1_esk3_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_382,def_lhs_atom21]) ).
cnf(c_0_383_0,axiom,
( subset(X2,X1)
| ~ member(sk1_esk1_2(X1,X2),X1) ),
inference(unfold_definition,[status(thm)],[c_0_383,def_lhs_atom2]) ).
cnf(c_0_384_0,axiom,
( ~ member(X2,difference(X1,X3))
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_384,def_lhs_atom12]) ).
cnf(c_0_385_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_385,def_lhs_atom10]) ).
cnf(c_0_386_0,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_386,def_lhs_atom10]) ).
cnf(c_0_387_0,axiom,
( ~ member(X2,difference(X1,X3))
| member(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_387,def_lhs_atom12]) ).
cnf(c_0_388_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_388,def_lhs_atom7]) ).
cnf(c_0_389_0,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_389,def_lhs_atom7]) ).
cnf(c_0_390_0,axiom,
( member(X1,sum(X3))
| ~ member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_390,def_lhs_atom19]) ).
cnf(c_0_391_0,axiom,
( equal_set(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_391,def_lhs_atom4]) ).
cnf(c_0_392_0,axiom,
( ~ member(X1,unordered_pair(X3,X2))
| X1 = X2
| X1 = X3 ),
inference(unfold_definition,[status(thm)],[c_0_392,def_lhs_atom16]) ).
cnf(c_0_393_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_393,def_lhs_atom17]) ).
cnf(c_0_394_0,axiom,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_394,def_lhs_atom17]) ).
cnf(c_0_395_0,axiom,
( identity(X1,X2)
| member(sk1_esk16_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_395,def_lhs_atom29]) ).
cnf(c_0_396_0,axiom,
( member(X1,product(X2))
| member(sk1_esk3_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_396,def_lhs_atom21]) ).
cnf(c_0_397_0,axiom,
( ~ member(X1,sum(X2))
| member(sk1_esk2_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_397,def_lhs_atom18]) ).
cnf(c_0_398_0,axiom,
( ~ member(X1,sum(X2))
| member(X1,sk1_esk2_2(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_398,def_lhs_atom18]) ).
cnf(c_0_399_0,axiom,
( subset(X2,X1)
| member(sk1_esk1_2(X1,X2),X2) ),
inference(unfold_definition,[status(thm)],[c_0_399,def_lhs_atom2]) ).
cnf(c_0_400_0,axiom,
( ~ member(X1,product(X3))
| member(X1,X2)
| ~ member(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_400,def_lhs_atom20]) ).
cnf(c_0_401_0,axiom,
( ~ subset(X3,X2)
| member(X1,X2)
| ~ member(X1,X3) ),
inference(unfold_definition,[status(thm)],[c_0_401,def_lhs_atom1]) ).
cnf(c_0_402_0,axiom,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_402,def_lhs_atom6]) ).
cnf(c_0_403_0,axiom,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_403,def_lhs_atom5]) ).
cnf(c_0_404_0,axiom,
( ~ equal_set(X2,X1)
| subset(X2,X1) ),
inference(unfold_definition,[status(thm)],[c_0_404,def_lhs_atom3]) ).
cnf(c_0_405_0,axiom,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_405,def_lhs_atom3]) ).
cnf(c_0_406_0,axiom,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(unfold_definition,[status(thm)],[c_0_406,def_lhs_atom15]) ).
cnf(c_0_407_0,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(unfold_definition,[status(thm)],[c_0_407,def_lhs_atom14]) ).
cnf(c_0_408_0,axiom,
~ member(X1,empty_set),
inference(unfold_definition,[status(thm)],[c_0_408,def_lhs_atom11]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X6,X1,X2,X3,X7,X4,X8] :
( ( member(X4,X2)
& member(X8,X7) )
=> ( apply(compose_function(X6,X1,X2,X3,X7),X4,X8)
<=> ? [X5] :
( member(X5,X3)
& apply(X1,X4,X5)
& apply(X6,X5,X8) ) ) ),
file('<stdin>',compose_function) ).
fof(c_0_1_002,axiom,
! [X1,X2,X3,X4,X5] :
( ( member(X4,X2)
& member(X5,X3) )
=> ( apply(X1,X4,X5)
<=> apply(inverse_function(X1,X2,X3),X5,X4) ) ),
file('<stdin>',inverse_function) ).
fof(c_0_2_003,axiom,
! [X6,X1,X2,X3,X7,X4,X8] :
( ( member(X4,X2)
& member(X8,X7) )
=> ( apply(compose_function(X6,X1,X2,X3,X7),X4,X8)
<=> ? [X5] :
( member(X5,X3)
& apply(X1,X4,X5)
& apply(X6,X5,X8) ) ) ),
c_0_0 ).
fof(c_0_3_004,axiom,
! [X1,X2,X3,X4,X5] :
( ( member(X4,X2)
& member(X5,X3) )
=> ( apply(X1,X4,X5)
<=> apply(inverse_function(X1,X2,X3),X5,X4) ) ),
c_0_1 ).
fof(c_0_4_005,plain,
! [X9,X10,X11,X12,X13,X14,X15,X17] :
( ( member(esk1_7(X9,X10,X11,X12,X13,X14,X15),X12)
| ~ apply(compose_function(X9,X10,X11,X12,X13),X14,X15)
| ~ member(X14,X11)
| ~ member(X15,X13) )
& ( apply(X10,X14,esk1_7(X9,X10,X11,X12,X13,X14,X15))
| ~ apply(compose_function(X9,X10,X11,X12,X13),X14,X15)
| ~ member(X14,X11)
| ~ member(X15,X13) )
& ( apply(X9,esk1_7(X9,X10,X11,X12,X13,X14,X15),X15)
| ~ apply(compose_function(X9,X10,X11,X12,X13),X14,X15)
| ~ member(X14,X11)
| ~ member(X15,X13) )
& ( ~ member(X17,X12)
| ~ apply(X10,X14,X17)
| ~ apply(X9,X17,X15)
| apply(compose_function(X9,X10,X11,X12,X13),X14,X15)
| ~ member(X14,X11)
| ~ member(X15,X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
fof(c_0_5_006,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ apply(X6,X9,X10)
| apply(inverse_function(X6,X7,X8),X10,X9)
| ~ member(X9,X7)
| ~ member(X10,X8) )
& ( ~ apply(inverse_function(X6,X7,X8),X10,X9)
| apply(X6,X9,X10)
| ~ member(X9,X7)
| ~ member(X10,X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6_007,plain,
( apply(X6,X3,esk1_7(X5,X6,X4,X7,X2,X3,X1))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_008,plain,
( apply(X5,esk1_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8_009,plain,
( member(esk1_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9_010,plain,
( apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10_011,plain,
( apply(X5,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11_012,plain,
( apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12_013,plain,
( apply(X6,X3,esk1_7(X5,X6,X4,X7,X2,X3,X1))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
c_0_6,
[final] ).
cnf(c_0_13_014,plain,
( apply(X5,esk1_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
c_0_7,
[final] ).
cnf(c_0_14_015,plain,
( member(esk1_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
c_0_8,
[final] ).
cnf(c_0_15_016,plain,
( apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
c_0_9,
[final] ).
cnf(c_0_16_017,plain,
( apply(X5,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
c_0_10,
[final] ).
cnf(c_0_17_018,plain,
( apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
c_0_11,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_12_0,axiom,
( apply(X6,X3,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_12]) ).
cnf(c_0_12_1,axiom,
( ~ member(X1,X2)
| apply(X6,X3,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1))
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_12]) ).
cnf(c_0_12_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X6,X3,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1))
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_12]) ).
cnf(c_0_12_3,axiom,
( ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X6,X3,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_12]) ).
cnf(c_0_13_0,axiom,
( apply(X5,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_13_1,axiom,
( ~ member(X1,X2)
| apply(X5,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_13_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X5,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X1)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_13_3,axiom,
( ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X5,sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_13]) ).
cnf(c_0_14_0,axiom,
( member(sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_14_1,axiom,
( ~ member(X1,X2)
| member(sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ member(X3,X4)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_14_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X7)
| ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_14_3,axiom,
( ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| member(sk2_esk1_7(X5,X6,X4,X7,X2,X3,X1),X7) ),
inference(literals_permutation,[status(thm)],[c_0_14]) ).
cnf(c_0_15_0,axiom,
( apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_15_1,axiom,
( ~ member(X1,X2)
| apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X3,X4)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_15_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ apply(X5,X8,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_15_3,axiom,
( ~ apply(X5,X8,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ apply(X6,X3,X8)
| ~ member(X8,X7) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_15_4,axiom,
( ~ apply(X6,X3,X8)
| ~ apply(X5,X8,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(compose_function(X5,X6,X4,X7,X2),X3,X1)
| ~ member(X8,X7) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_15_5,axiom,
( ~ member(X8,X7)
| ~ apply(X6,X3,X8)
| ~ apply(X5,X8,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_15]) ).
cnf(c_0_16_0,axiom,
( apply(X5,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_16_1,axiom,
( ~ member(X1,X2)
| apply(X5,X3,X1)
| ~ member(X3,X4)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_16_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X5,X3,X1)
| ~ apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_16_3,axiom,
( ~ apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(X5,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_16]) ).
cnf(c_0_17_0,axiom,
( apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_1,axiom,
( ~ member(X1,X2)
| apply(inverse_function(X5,X4,X2),X1,X3)
| ~ member(X3,X4)
| ~ apply(X5,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_2,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| apply(inverse_function(X5,X4,X2),X1,X3)
| ~ apply(X5,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
cnf(c_0_17_3,axiom,
( ~ apply(X5,X3,X1)
| ~ member(X3,X4)
| ~ member(X1,X2)
| apply(inverse_function(X5,X4,X2),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_17]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_019,conjecture,
! [X1,X2,X3,X4,X5] :
( ( maps(X1,X2,X3)
& subset(X4,X3)
& subset(X5,X3)
& subset(X4,X5) )
=> subset(inverse_image2(X1,X4),inverse_image2(X1,X5)) ),
file('<stdin>',thIIa05) ).
fof(c_0_1_020,negated_conjecture,
~ ! [X1,X2,X3,X4,X5] :
( ( maps(X1,X2,X3)
& subset(X4,X3)
& subset(X5,X3)
& subset(X4,X5) )
=> subset(inverse_image2(X1,X4),inverse_image2(X1,X5)) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).
fof(c_0_2_021,negated_conjecture,
( maps(esk1_0,esk2_0,esk3_0)
& subset(esk4_0,esk3_0)
& subset(esk5_0,esk3_0)
& subset(esk4_0,esk5_0)
& ~ subset(inverse_image2(esk1_0,esk4_0),inverse_image2(esk1_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
cnf(c_0_3_022,negated_conjecture,
~ subset(inverse_image2(esk1_0,esk4_0),inverse_image2(esk1_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_023,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_024,negated_conjecture,
subset(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_025,negated_conjecture,
subset(esk5_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7_026,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8_027,negated_conjecture,
~ subset(inverse_image2(esk1_0,esk4_0),inverse_image2(esk1_0,esk5_0)),
c_0_3,
[final] ).
cnf(c_0_9_028,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
c_0_4,
[final] ).
cnf(c_0_10_029,negated_conjecture,
subset(esk4_0,esk3_0),
c_0_5,
[final] ).
cnf(c_0_11_030,negated_conjecture,
subset(esk5_0,esk3_0),
c_0_6,
[final] ).
cnf(c_0_12_031,negated_conjecture,
subset(esk4_0,esk5_0),
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_60,plain,
( ~ member(X0,X1)
| ~ apply(X2,X3,X0)
| member(X3,inverse_image2(X2,X1)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_374_0) ).
cnf(c_374,plain,
( ~ member(X0,X1)
| ~ apply(X2,X3,X0)
| member(X3,inverse_image2(X2,X1)) ),
inference(copy,[status(esa)],[c_60]) ).
cnf(c_549715,plain,
( ~ apply(X0,X1,sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0))
| ~ member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk5_0)
| member(X1,inverse_image2(X0,sk3_esk5_0)) ),
inference(instantiation,[status(thm)],[c_374]) ).
cnf(c_1035442,plain,
( ~ apply(sk3_esk1_0,sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0))
| member(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),inverse_image2(sk3_esk1_0,sk3_esk5_0))
| ~ member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk5_0) ),
inference(instantiation,[status(thm)],[c_549715]) ).
cnf(c_33,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_401_0) ).
cnf(c_347,plain,
( ~ member(X0,X1)
| member(X0,X2)
| ~ subset(X1,X2) ),
inference(copy,[status(esa)],[c_33]) ).
cnf(c_123001,plain,
( ~ member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk4_0)
| member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),X0)
| ~ subset(sk3_esk4_0,X0) ),
inference(instantiation,[status(thm)],[c_347]) ).
cnf(c_547816,plain,
( ~ member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk4_0)
| member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk5_0)
| ~ subset(sk3_esk4_0,sk3_esk5_0) ),
inference(instantiation,[status(thm)],[c_123001]) ).
cnf(c_69,plain,
( apply(X0,X1,sk1_esk26_3(X1,X0,X2))
| ~ member(X1,inverse_image2(X0,X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_365_0) ).
cnf(c_383,plain,
( apply(X0,X1,sk1_esk26_3(X1,X0,X2))
| ~ member(X1,inverse_image2(X0,X2)) ),
inference(copy,[status(esa)],[c_69]) ).
cnf(c_122716,plain,
( apply(sk3_esk1_0,sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0))
| ~ member(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),inverse_image2(sk3_esk1_0,sk3_esk4_0)) ),
inference(instantiation,[status(thm)],[c_383]) ).
cnf(c_66,plain,
( member(sk1_esk26_3(X0,X1,X2),X2)
| ~ member(X0,inverse_image2(X1,X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_368_0) ).
cnf(c_380,plain,
( member(sk1_esk26_3(X0,X1,X2),X2)
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(copy,[status(esa)],[c_66]) ).
cnf(c_122715,plain,
( ~ member(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),inverse_image2(sk3_esk1_0,sk3_esk4_0))
| member(sk1_esk26_3(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),sk3_esk1_0,sk3_esk4_0),sk3_esk4_0) ),
inference(instantiation,[status(thm)],[c_380]) ).
cnf(c_51,plain,
( ~ member(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_383_0) ).
cnf(c_365,plain,
( ~ member(sk1_esk1_2(X0,X1),X0)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_51]) ).
cnf(c_122453,plain,
( ~ member(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),inverse_image2(sk3_esk1_0,sk3_esk5_0))
| subset(inverse_image2(sk3_esk1_0,sk3_esk4_0),inverse_image2(sk3_esk1_0,sk3_esk5_0)) ),
inference(instantiation,[status(thm)],[c_365]) ).
cnf(c_35,plain,
( member(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_399_0) ).
cnf(c_349,plain,
( member(sk1_esk1_2(X0,X1),X1)
| subset(X1,X0) ),
inference(copy,[status(esa)],[c_35]) ).
cnf(c_122452,plain,
( member(sk1_esk1_2(inverse_image2(sk3_esk1_0,sk3_esk5_0),inverse_image2(sk3_esk1_0,sk3_esk4_0)),inverse_image2(sk3_esk1_0,sk3_esk4_0))
| subset(inverse_image2(sk3_esk1_0,sk3_esk4_0),inverse_image2(sk3_esk1_0,sk3_esk5_0)) ),
inference(instantiation,[status(thm)],[c_349]) ).
cnf(c_154,negated_conjecture,
~ subset(inverse_image2(sk3_esk1_0,sk3_esk4_0),inverse_image2(sk3_esk1_0,sk3_esk5_0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_8) ).
cnf(c_158,negated_conjecture,
subset(sk3_esk4_0,sk3_esk5_0),
file('/export/starexec/sandbox/tmp/iprover_modulo_07a456.p',c_0_12) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_1035442,c_547816,c_122716,c_122715,c_122453,c_122452,c_154,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 00:41:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.43 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.43 % FOF problem with conjecture
% 0.20/0.43 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_7d3a32.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_07a456.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_b97d24 | grep -v "SZS"
% 0.20/0.45
% 0.20/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ iProver source info
% 0.20/0.45
% 0.20/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.45 % git: non_committed_changes: true
% 0.20/0.45 % git: last_make_outside_of_git: true
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ Input Options
% 0.20/0.45
% 0.20/0.45 % --out_options all
% 0.20/0.45 % --tptp_safe_out true
% 0.20/0.45 % --problem_path ""
% 0.20/0.45 % --include_path ""
% 0.20/0.45 % --clausifier .//eprover
% 0.20/0.45 % --clausifier_options --tstp-format
% 0.20/0.45 % --stdin false
% 0.20/0.45 % --dbg_backtrace false
% 0.20/0.45 % --dbg_dump_prop_clauses false
% 0.20/0.45 % --dbg_dump_prop_clauses_file -
% 0.20/0.45 % --dbg_out_stat false
% 0.20/0.45
% 0.20/0.45 % ------ General Options
% 0.20/0.45
% 0.20/0.45 % --fof false
% 0.20/0.45 % --time_out_real 150.
% 0.20/0.45 % --time_out_prep_mult 0.2
% 0.20/0.45 % --time_out_virtual -1.
% 0.20/0.45 % --schedule none
% 0.20/0.45 % --ground_splitting input
% 0.20/0.45 % --splitting_nvd 16
% 0.20/0.45 % --non_eq_to_eq false
% 0.20/0.45 % --prep_gs_sim true
% 0.20/0.45 % --prep_unflatten false
% 0.20/0.45 % --prep_res_sim true
% 0.20/0.45 % --prep_upred true
% 0.20/0.45 % --res_sim_input true
% 0.20/0.45 % --clause_weak_htbl true
% 0.20/0.45 % --gc_record_bc_elim false
% 0.20/0.45 % --symbol_type_check false
% 0.20/0.45 % --clausify_out false
% 0.20/0.45 % --large_theory_mode false
% 0.20/0.45 % --prep_sem_filter none
% 0.20/0.45 % --prep_sem_filter_out false
% 0.20/0.45 % --preprocessed_out false
% 0.20/0.45 % --sub_typing false
% 0.20/0.45 % --brand_transform false
% 0.20/0.45 % --pure_diseq_elim true
% 0.20/0.45 % --min_unsat_core false
% 0.20/0.45 % --pred_elim true
% 0.20/0.45 % --add_important_lit false
% 0.20/0.45 % --soft_assumptions false
% 0.20/0.45 % --reset_solvers false
% 0.20/0.45 % --bc_imp_inh []
% 0.20/0.45 % --conj_cone_tolerance 1.5
% 0.20/0.45 % --prolific_symb_bound 500
% 0.20/0.45 % --lt_threshold 2000
% 0.20/0.45
% 0.20/0.45 % ------ SAT Options
% 0.20/0.45
% 0.20/0.45 % --sat_mode false
% 0.20/0.45 % --sat_fm_restart_options ""
% 0.20/0.45 % --sat_gr_def false
% 0.20/0.45 % --sat_epr_types true
% 0.20/0.45 % --sat_non_cyclic_types false
% 0.20/0.45 % --sat_finite_models false
% 0.20/0.45 % --sat_fm_lemmas false
% 0.20/0.45 % --sat_fm_prep false
% 0.20/0.45 % --sat_fm_uc_incr true
% 0.20/0.45 % --sat_out_model small
% 0.20/0.45 % --sat_out_clauses false
% 0.20/0.45
% 0.20/0.45 % ------ QBF Options
% 0.20/0.45
% 0.20/0.45 % --qbf_mode false
% 0.20/0.45 % --qbf_elim_univ true
% 0.20/0.45 % --qbf_sk_in true
% 0.20/0.45 % --qbf_pred_elim true
% 0.20/0.45 % --qbf_split 32
% 0.20/0.45
% 0.20/0.45 % ------ BMC1 Options
% 0.20/0.45
% 0.20/0.45 % --bmc1_incremental false
% 0.20/0.45 % --bmc1_axioms reachable_all
% 0.20/0.45 % --bmc1_min_bound 0
% 0.20/0.45 % --bmc1_max_bound -1
% 0.20/0.45 % --bmc1_max_bound_default -1
% 0.20/0.45 % --bmc1_symbol_reachability true
% 0.20/0.45 % --bmc1_property_lemmas false
% 0.20/0.45 % --bmc1_k_induction false
% 0.20/0.45 % --bmc1_non_equiv_states false
% 0.20/0.45 % --bmc1_deadlock false
% 0.20/0.45 % --bmc1_ucm false
% 0.20/0.45 % --bmc1_add_unsat_core none
% 0.20/0.45 % --bmc1_unsat_core_children false
% 0.20/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.45 % --bmc1_out_stat full
% 0.20/0.45 % --bmc1_ground_init false
% 0.20/0.45 % --bmc1_pre_inst_next_state false
% 0.20/0.45 % --bmc1_pre_inst_state false
% 0.20/0.45 % --bmc1_pre_inst_reach_state false
% 0.20/0.45 % --bmc1_out_unsat_core false
% 0.20/0.45 % --bmc1_aig_witness_out false
% 0.20/0.45 % --bmc1_verbose false
% 0.20/0.45 % --bmc1_dump_clauses_tptp false
% 0.20/0.48 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.48 % --bmc1_dump_file -
% 0.20/0.48 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.48 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.48 % --bmc1_ucm_extend_mode 1
% 0.20/0.48 % --bmc1_ucm_init_mode 2
% 0.20/0.48 % --bmc1_ucm_cone_mode none
% 0.20/0.48 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.48 % --bmc1_ucm_relax_model 4
% 0.20/0.48 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.48 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.48 % --bmc1_ucm_layered_model none
% 0.20/0.48 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.48
% 0.20/0.48 % ------ AIG Options
% 0.20/0.48
% 0.20/0.48 % --aig_mode false
% 0.20/0.48
% 0.20/0.48 % ------ Instantiation Options
% 0.20/0.48
% 0.20/0.48 % --instantiation_flag true
% 0.20/0.48 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.48 % --inst_solver_per_active 750
% 0.20/0.48 % --inst_solver_calls_frac 0.5
% 0.20/0.48 % --inst_passive_queue_type priority_queues
% 0.20/0.48 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.48 % --inst_passive_queues_freq [25;2]
% 0.20/0.48 % --inst_dismatching true
% 0.20/0.48 % --inst_eager_unprocessed_to_passive true
% 0.20/0.48 % --inst_prop_sim_given true
% 0.20/0.48 % --inst_prop_sim_new false
% 0.20/0.48 % --inst_orphan_elimination true
% 0.20/0.48 % --inst_learning_loop_flag true
% 0.20/0.48 % --inst_learning_start 3000
% 0.20/0.48 % --inst_learning_factor 2
% 0.20/0.48 % --inst_start_prop_sim_after_learn 3
% 0.20/0.48 % --inst_sel_renew solver
% 0.20/0.48 % --inst_lit_activity_flag true
% 0.20/0.48 % --inst_out_proof true
% 0.20/0.48
% 0.20/0.48 % ------ Resolution Options
% 0.20/0.48
% 0.20/0.48 % --resolution_flag true
% 0.20/0.48 % --res_lit_sel kbo_max
% 0.20/0.48 % --res_to_prop_solver none
% 0.20/0.48 % --res_prop_simpl_new false
% 0.20/0.48 % --res_prop_simpl_given false
% 0.20/0.48 % --res_passive_queue_type priority_queues
% 0.20/0.48 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.48 % --res_passive_queues_freq [15;5]
% 0.20/0.48 % --res_forward_subs full
% 0.20/0.48 % --res_backward_subs full
% 0.20/0.48 % --res_forward_subs_resolution true
% 0.20/0.48 % --res_backward_subs_resolution true
% 0.20/0.48 % --res_orphan_elimination false
% 0.20/0.48 % --res_time_limit 1000.
% 0.20/0.48 % --res_out_proof true
% 0.20/0.48 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_7d3a32.s
% 0.20/0.48 % --modulo true
% 0.20/0.48
% 0.20/0.48 % ------ Combination Options
% 0.20/0.48
% 0.20/0.48 % --comb_res_mult 1000
% 0.20/0.48 % --comb_inst_mult 300
% 0.20/0.48 % ------
% 0.20/0.48
% 0.20/0.48 % ------ Parsing...% successful
% 0.20/0.48
% 0.20/0.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 0.20/0.48
% 0.20/0.48 % ------ Proving...
% 0.20/0.48 % ------ Problem Properties
% 0.20/0.48
% 0.20/0.48 %
% 0.20/0.48 % EPR false
% 0.20/0.48 % Horn false
% 0.20/0.48 % Has equality true
% 0.20/0.48
% 0.20/0.48 % % ------ Input Options Time Limit: Unbounded
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 % % ------ Current options:
% 0.20/0.48
% 0.20/0.48 % ------ Input Options
% 0.20/0.48
% 0.20/0.48 % --out_options all
% 0.20/0.48 % --tptp_safe_out true
% 0.20/0.48 % --problem_path ""
% 0.20/0.48 % --include_path ""
% 0.20/0.48 % --clausifier .//eprover
% 0.20/0.48 % --clausifier_options --tstp-format
% 0.20/0.48 % --stdin false
% 0.20/0.48 % --dbg_backtrace false
% 0.20/0.48 % --dbg_dump_prop_clauses false
% 0.20/0.48 % --dbg_dump_prop_clauses_file -
% 0.20/0.48 % --dbg_out_stat false
% 0.20/0.48
% 0.20/0.48 % ------ General Options
% 0.20/0.48
% 0.20/0.48 % --fof false
% 0.20/0.48 % --time_out_real 150.
% 0.20/0.48 % --time_out_prep_mult 0.2
% 0.20/0.48 % --time_out_virtual -1.
% 0.20/0.48 % --schedule none
% 0.20/0.48 % --ground_splitting input
% 0.20/0.48 % --splitting_nvd 16
% 0.20/0.48 % --non_eq_to_eq false
% 0.20/0.48 % --prep_gs_sim true
% 0.20/0.48 % --prep_unflatten false
% 0.20/0.48 % --prep_res_sim true
% 0.20/0.48 % --prep_upred true
% 0.20/0.48 % --res_sim_input true
% 0.20/0.48 % --clause_weak_htbl true
% 0.20/0.48 % --gc_record_bc_elim false
% 0.20/0.48 % --symbol_type_check false
% 0.20/0.48 % --clausify_out false
% 0.20/0.48 % --large_theory_mode false
% 0.20/0.48 % --prep_sem_filter none
% 0.20/0.48 % --prep_sem_filter_out false
% 0.20/0.48 % --preprocessed_out false
% 0.20/0.48 % --sub_typing false
% 0.20/0.48 % --brand_transform false
% 0.20/0.48 % --pure_diseq_elim true
% 0.20/0.48 % --min_unsat_core false
% 0.20/0.48 % --pred_elim true
% 0.20/0.48 % --add_important_lit false
% 0.20/0.48 % --soft_assumptions false
% 0.20/0.48 % --reset_solvers false
% 0.20/0.48 % --bc_imp_inh []
% 0.20/0.48 % --conj_cone_tolerance 1.5
% 0.20/0.48 % --prolific_symb_bound 500
% 0.20/0.48 % --lt_threshold 2000
% 0.20/0.48
% 0.20/0.48 % ------ SAT Options
% 0.20/0.48
% 0.20/0.48 % --sat_mode false
% 0.20/0.48 % --sat_fm_restart_options ""
% 0.20/0.48 % --sat_gr_def false
% 0.20/0.48 % --sat_epr_types true
% 0.20/0.48 % --sat_non_cyclic_types false
% 0.20/0.48 % --sat_finite_models false
% 0.20/0.48 % --sat_fm_lemmas false
% 0.20/0.48 % --sat_fm_prep false
% 0.20/0.48 % --sat_fm_uc_incr true
% 0.20/0.48 % --sat_out_model small
% 0.20/0.48 % --sat_out_clauses false
% 0.20/0.48
% 0.20/0.48 % ------ QBF Options
% 0.20/0.48
% 0.20/0.48 % --qbf_mode false
% 0.20/0.48 % --qbf_elim_univ true
% 0.20/0.48 % --qbf_sk_in true
% 0.20/0.48 % --qbf_pred_elim true
% 0.20/0.48 % --qbf_split 32
% 0.20/0.48
% 0.20/0.48 % ------ BMC1 Options
% 0.20/0.48
% 0.20/0.48 % --bmc1_incremental false
% 0.20/0.48 % --bmc1_axioms reachable_all
% 0.20/0.48 % --bmc1_min_bound 0
% 0.20/0.48 % --bmc1_max_bound -1
% 0.20/0.48 % --bmc1_max_bound_default -1
% 0.20/0.48 % --bmc1_symbol_reachability true
% 0.20/0.48 % --bmc1_property_lemmas false
% 0.20/0.48 % --bmc1_k_induction false
% 0.20/0.48 % --bmc1_non_equiv_states false
% 0.20/0.48 % --bmc1_deadlock false
% 0.20/0.48 % --bmc1_ucm false
% 0.20/0.48 % --bmc1_add_unsat_core none
% 0.20/0.48 % --bmc1_unsat_core_children false
% 0.20/0.48 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.48 % --bmc1_out_stat full
% 0.20/0.48 % --bmc1_ground_init false
% 0.20/0.48 % --bmc1_pre_inst_next_state false
% 0.20/0.48 % --bmc1_pre_inst_state false
% 0.20/0.48 % --bmc1_pre_inst_reach_state false
% 0.20/0.48 % --bmc1_out_unsat_core false
% 0.20/0.48 % --bmc1_aig_witness_out false
% 0.20/0.48 % --bmc1_verbose false
% 0.20/0.48 % --bmc1_dump_clauses_tptp false
% 0.20/0.48 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.48 % --bmc1_dump_file -
% 0.20/0.48 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.48 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.48 % --bmc1_ucm_extend_mode 1
% 0.20/0.48 % --bmc1_ucm_init_mode 2
% 0.20/0.48 % --bmc1_ucm_cone_mode none
% 0.20/0.48 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.48 % --bmc1_ucm_relax_model 4
% 0.20/0.48 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.48 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.48 % --bmc1_ucm_layered_model none
% 0.20/0.48 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.48
% 0.20/0.48 % ------ AIG Options
% 0.20/0.48
% 0.20/0.48 % --aig_mode false
% 0.20/0.48
% 0.20/0.48 % ------ Instantiation Options
% 0.20/0.48
% 0.20/0.48 % --instantiation_flag true
% 0.20/0.48 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.48 % --inst_solver_per_active 750
% 0.20/0.48 % --inst_solver_calls_frac 0.5
% 0.20/0.48 % --inst_passive_queue_type priority_queues
% 0.20/0.48 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.48 % --inst_passive_queues_freq [25;2]
% 0.20/0.48 % --inst_dismatching true
% 0.20/0.48 % --inst_eager_unprocessed_to_passive true
% 0.20/0.48 % --inst_prop_sim_given true
% 86.12/86.41 % --inst_prop_sim_new false
% 86.12/86.41 % --inst_orphan_elimination true
% 86.12/86.41 % --inst_learning_loop_flag true
% 86.12/86.41 % --inst_learning_start 3000
% 86.12/86.41 % --inst_learning_factor 2
% 86.12/86.41 % --inst_start_prop_sim_after_learn 3
% 86.12/86.41 % --inst_sel_renew solver
% 86.12/86.41 % --inst_lit_activity_flag true
% 86.12/86.41 % --inst_out_proof true
% 86.12/86.41
% 86.12/86.41 % ------ Resolution Options
% 86.12/86.41
% 86.12/86.41 % --resolution_flag true
% 86.12/86.41 % --res_lit_sel kbo_max
% 86.12/86.41 % --res_to_prop_solver none
% 86.12/86.41 % --res_prop_simpl_new false
% 86.12/86.41 % --res_prop_simpl_given false
% 86.12/86.41 % --res_passive_queue_type priority_queues
% 86.12/86.41 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 86.12/86.41 % --res_passive_queues_freq [15;5]
% 86.12/86.41 % --res_forward_subs full
% 86.12/86.41 % --res_backward_subs full
% 86.12/86.41 % --res_forward_subs_resolution true
% 86.12/86.41 % --res_backward_subs_resolution true
% 86.12/86.41 % --res_orphan_elimination false
% 86.12/86.41 % --res_time_limit 1000.
% 86.12/86.41 % --res_out_proof true
% 86.12/86.41 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_7d3a32.s
% 86.12/86.41 % --modulo true
% 86.12/86.41
% 86.12/86.41 % ------ Combination Options
% 86.12/86.41
% 86.12/86.41 % --comb_res_mult 1000
% 86.12/86.41 % --comb_inst_mult 300
% 86.12/86.41 % ------
% 86.12/86.41
% 86.12/86.41
% 86.12/86.41
% 86.12/86.41 % ------ Proving...
% 86.12/86.41 %
% 86.12/86.41
% 86.12/86.41
% 86.12/86.41 % ------ Statistics
% 86.12/86.41
% 86.12/86.41 % ------ General
% 86.12/86.41
% 86.12/86.41 % num_of_input_clauses: 159
% 86.12/86.41 % num_of_input_neg_conjectures: 5
% 86.12/86.41 % num_of_splits: 0
% 86.12/86.41 % num_of_split_atoms: 0
% 86.12/86.41 % num_of_sem_filtered_clauses: 0
% 86.12/86.41 % num_of_subtypes: 0
% 86.12/86.41 % monotx_restored_types: 0
% 86.12/86.41 % sat_num_of_epr_types: 0
% 86.12/86.41 % sat_num_of_non_cyclic_types: 0
% 86.12/86.41 % sat_guarded_non_collapsed_types: 0
% 86.12/86.41 % is_epr: 0
% 86.12/86.41 % is_horn: 0
% 86.12/86.41 % has_eq: 1
% 86.12/86.41 % num_pure_diseq_elim: 0
% 86.12/86.41 % simp_replaced_by: 0
% 86.12/86.41 % res_preprocessed: 10
% 86.12/86.41 % prep_upred: 0
% 86.12/86.41 % prep_unflattend: 0
% 86.12/86.41 % pred_elim_cands: 0
% 86.12/86.41 % pred_elim: 0
% 86.12/86.41 % pred_elim_cl: 0
% 86.12/86.41 % pred_elim_cycles: 0
% 86.12/86.41 % forced_gc_time: 0
% 86.12/86.41 % gc_basic_clause_elim: 0
% 86.12/86.41 % parsing_time: 0.01
% 86.12/86.41 % sem_filter_time: 0.
% 86.12/86.41 % pred_elim_time: 0.
% 86.12/86.41 % out_proof_time: 0.001
% 86.12/86.41 % monotx_time: 0.
% 86.12/86.41 % subtype_inf_time: 0.
% 86.12/86.41 % unif_index_cands_time: 0.157
% 86.12/86.41 % unif_index_add_time: 0.012
% 86.12/86.41 % total_time: 85.982
% 86.12/86.41 % num_of_symbols: 100
% 86.12/86.41 % num_of_terms: 208765
% 86.12/86.41
% 86.12/86.41 % ------ Propositional Solver
% 86.12/86.41
% 86.12/86.41 % prop_solver_calls: 10
% 86.12/86.41 % prop_fast_solver_calls: 15
% 86.12/86.41 % prop_num_of_clauses: 5801
% 86.12/86.41 % prop_preprocess_simplified: 6346
% 86.12/86.41 % prop_fo_subsumed: 0
% 86.12/86.41 % prop_solver_time: 0.002
% 86.12/86.41 % prop_fast_solver_time: 0.
% 86.12/86.41 % prop_unsat_core_time: 0.
% 86.12/86.41
% 86.12/86.41 % ------ QBF
% 86.12/86.41
% 86.12/86.41 % qbf_q_res: 0
% 86.12/86.41 % qbf_num_tautologies: 0
% 86.12/86.41 % qbf_prep_cycles: 0
% 86.12/86.41
% 86.12/86.41 % ------ BMC1
% 86.12/86.41
% 86.12/86.41 % bmc1_current_bound: -1
% 86.12/86.41 % bmc1_last_solved_bound: -1
% 86.12/86.41 % bmc1_unsat_core_size: -1
% 86.12/86.41 % bmc1_unsat_core_parents_size: -1
% 86.12/86.41 % bmc1_merge_next_fun: 0
% 86.12/86.41 % bmc1_unsat_core_clauses_time: 0.
% 86.12/86.41
% 86.12/86.41 % ------ Instantiation
% 86.12/86.41
% 86.12/86.41 % inst_num_of_clauses: 3104
% 86.12/86.41 % inst_num_in_passive: 2365
% 86.12/86.41 % inst_num_in_active: 582
% 86.12/86.41 % inst_num_in_unprocessed: 154
% 86.12/86.41 % inst_num_of_loops: 690
% 86.12/86.42 % inst_num_of_learning_restarts: 0
% 86.12/86.42 % inst_num_moves_active_passive: 105
% 86.12/86.42 % inst_lit_activity: 508
% 86.12/86.42 % inst_lit_activity_moves: 1
% 86.12/86.42 % inst_num_tautologies: 1
% 86.12/86.42 % inst_num_prop_implied: 0
% 86.12/86.42 % inst_num_existing_simplified: 0
% 86.12/86.42 % inst_num_eq_res_simplified: 0
% 86.12/86.42 % inst_num_child_elim: 0
% 86.12/86.42 % inst_num_of_dismatching_blockings: 3187
% 86.12/86.42 % inst_num_of_non_proper_insts: 2438
% 86.12/86.42 % inst_num_of_duplicates: 1214
% 86.12/86.42 % inst_inst_num_from_inst_to_res: 0
% 86.12/86.42 % inst_dismatching_checking_time: 0.013
% 86.12/86.42
% 86.12/86.42 % ------ Resolution
% 86.12/86.42
% 86.12/86.42 % res_num_of_clauses: 455287
% 86.12/86.42 % res_num_in_passive: 452303
% 86.12/86.42 % res_num_in_active: 2900
% 86.12/86.42 % res_num_of_loops: 3000
% 86.12/86.42 % res_forward_subset_subsumed: 27529
% 86.12/86.42 % res_backward_subset_subsumed: 15
% 86.12/86.42 % res_forward_subsumed: 138
% 86.12/86.42 % res_backward_subsumed: 0
% 86.12/86.42 % res_forward_subsumption_resolution: 155
% 86.12/86.42 % res_backward_subsumption_resolution: 0
% 86.12/86.42 % res_clause_to_clause_subsumption: 50387
% 86.12/86.42 % res_orphan_elimination: 0
% 86.12/86.42 % res_tautology_del: 251
% 86.12/86.42 % res_num_eq_res_simplified: 0
% 86.12/86.42 % res_num_sel_changes: 0
% 86.12/86.42 % res_moves_from_active_to_pass: 0
% 86.12/86.42
% 86.12/86.42 % Status Unsatisfiable
% 86.12/86.42 % SZS status Theorem
% 86.12/86.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------