%   ORIGINAL: 'h4/thm/res_quan/RES_EXISTS_REORDER_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !P Q R. 'h4/const/bool/RES_EXISTS' P (\i. 'h4/const/bool/RES_EXISTS' Q (\j. R i j)) <=> 'h4/const/bool/RES_EXISTS' Q (\j. 'h4/const/bool/RES_EXISTS' P (\i. R i j))
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !_3. (!R j i. happ (happ (happ _3 R) j) i <=> happ (happ R i) j) ==> (!_2. (!P R j. happ (happ (happ _2 P) R) j <=> 'h4/const/bool/RES_EXISTS' P (happ (happ _3 R) j)) ==> (!_1. (!R i j. happ (happ (happ _1 R) i) j <=> happ (happ R i) j) ==> (!_0. (!Q R i. happ (happ (happ _0 Q) R) i <=> 'h4/const/bool/RES_EXISTS' Q (happ (happ _1 R) i)) ==> (!P Q R. 'h4/const/bool/RES_EXISTS' P (happ (happ _0 Q) R) <=> 'h4/const/bool/RES_EXISTS' Q (happ (happ _2 P) R)))))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f31053,V_3f31049]: ![F, G]: (![X]: s(V_3f31049,happ(s(fun(V_3f31053,V_3f31049),F),s(V_3f31053,X))) = s(V_3f31049,happ(s(fun(V_3f31053,V_3f31049),G),s(V_3f31053,X))) => s(fun(V_3f31053,V_3f31049),F) = s(fun(V_3f31053,V_3f31049),G))).
fof('h4/thm/res_quan/RES_EXISTS_REORDER_', conjecture, ![A,B]: ![V__3]: (![R, J, I]: s(bool,happ(s(fun(A,bool),happ(s(fun(B,fun(A,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),V__3),s(fun(A,fun(B,bool)),R))),s(B,J))),s(A,I))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R),s(A,I))),s(B,J))) => ![V__2]: (![P, R, J]: s(bool,happ(s(fun(B,bool),happ(s(fun(fun(A,fun(B,bool)),fun(B,bool)),happ(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,bool))),V__2),s(fun(A,bool),P))),s(fun(A,fun(B,bool)),R))),s(B,J))) = s(bool,'h4/const/bool/RES_EXISTS'(s(fun(A,bool),P),s(fun(A,bool),happ(s(fun(B,fun(A,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),V__3),s(fun(A,fun(B,bool)),R))),s(B,J))))) => ![V__1]: (![R, I, J]: s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__1),s(fun(A,fun(B,bool)),R))),s(A,I))),s(B,J))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R),s(A,I))),s(B,J))) => ![V__0]: (![Q, R, I]: s(bool,happ(s(fun(A,bool),happ(s(fun(fun(A,fun(B,bool)),fun(A,bool)),happ(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,bool))),V__0),s(fun(B,bool),Q))),s(fun(A,fun(B,bool)),R))),s(A,I))) = s(bool,'h4/const/bool/RES_EXISTS'(s(fun(B,bool),Q),s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__1),s(fun(A,fun(B,bool)),R))),s(A,I))))) => ![P, Q, R]: s(bool,'h4/const/bool/RES_EXISTS'(s(fun(A,bool),P),s(fun(A,bool),happ(s(fun(fun(A,fun(B,bool)),fun(A,bool)),happ(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,bool))),V__0),s(fun(B,bool),Q))),s(fun(A,fun(B,bool)),R))))) = s(bool,'h4/const/bool/RES_EXISTS'(s(fun(B,bool),Q),s(fun(B,bool),happ(s(fun(fun(A,fun(B,bool)),fun(B,bool)),happ(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,bool))),V__2),s(fun(A,bool),P))),s(fun(A,fun(B,bool)),R)))))))))).
