%   ORIGINAL: h4/binary__ieee/float__tests_c2
% 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/words/WORD__NEG__1: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm: h4/binary__ieee/float__accfupds_c2: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm: h4/binary__ieee/float__accfupds_c7: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = f0 (h4/binary__ieee/float__Exponent f)
% Assm: h4/binary__ieee/float__is__normal__def: !x. h4/binary__ieee/float__is__normal x <=> ~(h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0) /\ ~(h4/binary__ieee/float__Exponent x = h4/words/word__T)
% Goal: !s f e. h4/binary__ieee/float__is__normal (h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB))) <=> ~(e = h4/words/n2w h4/num/0) /\ ~(e = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
%   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_wordss_WORDu_u_NEGu_u_1]: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c2]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c7]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = happ f0 (h4/binary__ieee/float__Exponent f)
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_normalu_u_def]: !x. h4/binary__ieee/float__is__normal x <=> ~(h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0) /\ ~(h4/binary__ieee/float__Exponent x = h4/words/word__T)
% Goal: !s f e. h4/binary__ieee/float__is__normal (h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB))) <=> ~(e = h4/words/n2w h4/num/0) /\ ~(e = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q108585,TV_Q108581]: ![V_f, V_g]: (![V_x]: s(TV_Q108581,happ(s(t_fun(TV_Q108585,TV_Q108581),V_f),s(TV_Q108585,V_x))) = s(TV_Q108581,happ(s(t_fun(TV_Q108585,TV_Q108581),V_g),s(TV_Q108585,V_x))) => s(t_fun(TV_Q108585,TV_Q108581),V_f) = s(t_fun(TV_Q108585,TV_Q108581),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_wordss_WORDu_u_NEGu_u_1, axiom, ![TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(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,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c7, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_normalu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_x]: (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_normal(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) <=> (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t))))).
fof(ch4s_binaryu_u_ieees_floatu_u_testsu_c2, conjecture, ![TV_u_27f,TV_u_27e]: ![V_s, V_f, V_e]: (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_normal(s(t_h4s_binaryu_u_ieees_float(TV_u_27f,TV_u_27e),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),V_s))),s(t_h4s_binaryu_u_ieees_float(TV_u_27f,TV_u_27e),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27e),t_h4s_fcps_cart(t_bool,TV_u_27e)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27e),V_e))),s(t_h4s_binaryu_u_ieees_float(TV_u_27f,TV_u_27e),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27f),t_h4s_fcps_cart(t_bool,TV_u_27f)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27f),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27f,TV_u_27e),h4s_bools_arb)))))))))) <=> (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27e),V_e) = s(t_h4s_fcps_cart(t_bool,TV_u_27e),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_fcps_cart(t_bool,TV_u_27e),V_e) = s(t_h4s_fcps_cart(t_bool,TV_u_27e),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27e),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))).
