%   ORIGINAL: h4/int__bitwise/int__bit__xor
% 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
% Assm: h4/int__bitwise/int__xor__def: h4/int__bitwise/int__xor = h4/int__bitwise/int__bitwise (\x y. ~(x <=> y))
% Assm: h4/int__bitwise/int__bit__bitwise: !n j i f. h4/int__bitwise/int__bit n (h4/int__bitwise/int__bitwise f i j) <=> f (h4/int__bitwise/int__bit n i) (h4/int__bitwise/int__bit n j)
% Goal: !n j i. h4/int__bitwise/int__bit n (h4/int__bitwise/int__xor i j) <=> ~(h4/int__bitwise/int__bit n i <=> h4/int__bitwise/int__bit n j)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_intu_u_bitwises_intu_u_xoru_u_def]: !_1. (!x y. happ (happ _1 x) y <=> ~(x <=> y)) ==> (!_0. (!x. happ _0 x = happ _1 x) ==> h4/int__bitwise/int__xor = h4/int__bitwise/int__bitwise _0)
% Assm [h4s_intu_u_bitwises_intu_u_bitu_u_bitwise]: !n j i f. h4/int__bitwise/int__bit n (happ (happ (h4/int__bitwise/int__bitwise f) i) j) <=> happ (happ f (h4/int__bitwise/int__bit n i)) (h4/int__bitwise/int__bit n j)
% Goal: !n j i. h4/int__bitwise/int__bit n (happ (happ h4/int__bitwise/int__xor i) j) <=> ~(h4/int__bitwise/int__bit n i <=> h4/int__bitwise/int__bit n j)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q79349,TV_Q79345]: ![V_f, V_g]: (![V_x]: s(TV_Q79345,happ(s(t_fun(TV_Q79349,TV_Q79345),V_f),s(TV_Q79349,V_x))) = s(TV_Q79345,happ(s(t_fun(TV_Q79349,TV_Q79345),V_g),s(TV_Q79349,V_x))) => s(t_fun(TV_Q79349,TV_Q79345),V_f) = s(t_fun(TV_Q79349,TV_Q79345),V_g))).
fof(ah4s_intu_u_bitwises_intu_u_xoru_u_def, axiom, ![V_uu_1]: (![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_1),s(t_bool,V_x))),s(t_bool,V_y)))) <=> ~ (s(t_bool,V_x) = s(t_bool,V_y))) => ![V_uu_0]: (![V_x]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_0),s(t_bool,V_x))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_1),s(t_bool,V_x))) => s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_intu_u_bitwises_intu_u_xor) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_intu_u_bitwises_intu_u_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_0)))))).
fof(ah4s_intu_u_bitwises_intu_u_bitu_u_bitwise, axiom, ![V_n, V_j, V_i, V_f]: s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_intu_u_bitwises_intu_u_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_j))))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,V_i))))),s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,V_j)))))).
fof(ch4s_intu_u_bitwises_intu_u_bitu_u_xor, conjecture, ![V_n, V_j, V_i]: (p(s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_intu_u_bitwises_intu_u_xor),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,V_j)))))) <=> ~ (s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,V_i))) = s(t_bool,h4s_intu_u_bitwises_intu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_integers_int,V_j)))))).
