%   ORIGINAL: h4/binary__ieee/float__components_c26
% 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/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/binary__ieee/float__accfupds_c6: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Sign__fupd f0 f) = f0 (h4/binary__ieee/float__Sign f)
% Assm: h4/binary__ieee/float__negate__def: !x. h4/binary__ieee/float__negate x = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/word__1comp (h4/binary__ieee/float__Sign x))) x
% Goal: !x. h4/binary__ieee/float__Sign (h4/binary__ieee/float__negate x) = h4/words/word__1comp (h4/binary__ieee/float__Sign x)
%   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_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c6]: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Sign__fupd f0 f) = happ f0 (h4/binary__ieee/float__Sign f)
% Assm [h4s_binaryu_u_ieees_floatu_u_negateu_u_def]: !x. h4/binary__ieee/float__negate x = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/word__1comp (h4/binary__ieee/float__Sign x))) x
% Goal: !x. h4/binary__ieee/float__Sign (h4/binary__ieee/float__negate x) = h4/words/word__1comp (h4/binary__ieee/float__Sign x)
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_Q104245,TV_Q104241]: ![V_f, V_g]: (![V_x]: s(TV_Q104241,happ(s(t_fun(TV_Q104245,TV_Q104241),V_f),s(TV_Q104245,V_x))) = s(TV_Q104241,happ(s(t_fun(TV_Q104245,TV_Q104241),V_g),s(TV_Q104245,V_x))) => s(t_fun(TV_Q104245,TV_Q104241),V_f) = s(t_fun(TV_Q104245,TV_Q104241),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c6, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_negateu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_x]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))).
fof(ch4s_binaryu_u_ieees_floatu_u_componentsu_c26, conjecture, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x)))))).
