%   ORIGINAL: h4/binary__ieee/min__properties_c12
% 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/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/combin/K__o__THM_c0: !v f. h4/combin/o (h4/combin/K v) f = h4/combin/K v
% Assm: h4/arithmetic/LESS__MOD: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% Assm: h4/arithmetic/ZERO__MOD: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/words/ZERO__LT__dimword: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/ONE__LT__dimword: h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% 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/words/WORD__NOT__0: h4/words/word__1comp (h4/words/n2w h4/num/0) = 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_c4: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm: h4/binary__ieee/float__accfupds_c5: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% 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__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__accfupds_c8: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = f0 (h4/binary__ieee/float__Significand f)
% Assm: h4/binary__ieee/float__fupdfupds_c0: !g f0 f. h4/binary__ieee/float__Sign__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g) f
% Assm: h4/binary__ieee/float__is__subnormal__def: !x. h4/binary__ieee/float__is__subnormal x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ ~(h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0)
% 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
% Assm: h4/binary__ieee/float__plus__min__def: h4/binary__ieee/float__plus__min h4/bool/the__value = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/bool/ARB))
% Assm: h4/binary__ieee/float__minus__min__def: h4/binary__ieee/float__minus__min h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__min h4/bool/the__value)
% Goal: h4/binary__ieee/float__is__subnormal (h4/binary__ieee/float__minus__min h4/bool/the__value)
%   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_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_combins_Ku_u_ou_u_THMu_c0]: !v f. h4/combin/o (h4/combin/K v) f = h4/combin/K v
% Assm [h4s_arithmetics_LESSu_u_MOD]: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% Assm [h4s_arithmetics_ZEROu_u_MOD]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_wordss_ZEROu_u_LTu_u_dimword]: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_ONEu_u_LTu_u_dimword]: h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% 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_wordss_WORDu_u_NOTu_u_0]: h4/words/word__1comp (h4/words/n2w h4/num/0) = 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_c4]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c5]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% 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_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_accfupdsu_c8]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = happ f0 (h4/binary__ieee/float__Significand f)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0]: !g f0 f. h4/binary__ieee/float__Sign__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g) f
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_subnormalu_u_def]: !x. h4/binary__ieee/float__is__subnormal x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ ~(h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0)
% 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
% Assm [h4s_binaryu_u_ieees_floatu_u_plusu_u_minu_u_def]: h4/binary__ieee/float__plus__min h4/bool/the__value = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/bool/ARB))
% Assm [h4s_binaryu_u_ieees_floatu_u_minusu_u_minu_u_def]: h4/binary__ieee/float__minus__min h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__min h4/bool/the__value)
% Goal: h4/binary__ieee/float__is__subnormal (h4/binary__ieee/float__minus__min h4/bool/the__value)
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_Q106709,TV_Q106705]: ![V_f, V_g]: (![V_x]: s(TV_Q106705,happ(s(t_fun(TV_Q106709,TV_Q106705),V_f),s(TV_Q106709,V_x))) = s(TV_Q106705,happ(s(t_fun(TV_Q106709,TV_Q106705),V_g),s(TV_Q106709,V_x))) => s(t_fun(TV_Q106709,TV_Q106705),V_f) = s(t_fun(TV_Q106709,TV_Q106705),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> 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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_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_combins_Ku_u_ou_u_THMu_c0, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_v, V_f]: s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),h4s_combins_k(s(TV_u_27c,V_v))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_k(s(TV_u_27c,V_v)))).
fof(ah4s_arithmetics_LESSu_u_MOD, axiom, ![V_n, V_k]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_k))).
fof(ah4s_arithmetics_ZEROu_u_MOD, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_wordss_ZEROu_u_LTu_u_dimword, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_wordss_ONEu_u_LTu_u_dimword, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(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_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_wordss_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
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_wordss_WORDu_u_NOTu_u_0, axiom, ![TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = 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_c4, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(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_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c5, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(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_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
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_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_accfupdsu_c8, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),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_27t),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: 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),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_g),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = 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_o(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_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_subnormalu_u_def, axiom, ![TV_u_27w,TV_u_27t]: ![V_x]: (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_subnormal(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_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))))).
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(ah4s_binaryu_u_ieees_floatu_u_plusu_u_minu_u_def, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = 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_n2w(s(t_h4s_nums_num,h4s_nums_0))))),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)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),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_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_minusu_u_minu_u_def, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = 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),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))).
fof(ch4s_binaryu_u_ieees_minu_u_propertiesu_c12, conjecture, ![TV_u_27t,TV_u_27w]: p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_subnormal(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))))).
