%   ORIGINAL: h4/float/RRRC6
% 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/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/arithmetic/ZERO__LT__EXP: !y x. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP x y) <=> h4/prim__rec/_3C h4/num/0 x \/ y = 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__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/real/REAL__OF__NUM__POW: !x n. h4/real/pow (h4/real/real__of__num x) n = h4/real/real__of__num (h4/arithmetic/EXP x n)
% Assm: h4/float/REAL__OF__NUM__LT0: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Goal: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (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_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_arithmetics_ZEROu_u_LTu_u_EXP]: !y x. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP x y) <=> h4/prim__rec/_3C h4/num/0 x \/ y = 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_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_reals_REALu_u_OFu_u_NUMu_u_POW]: !x n. h4/real/pow (h4/real/real__of__num x) n = h4/real/real__of__num (h4/arithmetic/EXP x n)
% Assm [h4s_floats_REALu_u_OFu_u_NUMu_u_LT0]: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Goal: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))
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_Q96565,TV_Q96561]: ![V_f, V_g]: (![V_x]: s(TV_Q96561,happ(s(t_fun(TV_Q96565,TV_Q96561),V_f),s(TV_Q96565,V_x))) = s(TV_Q96561,happ(s(t_fun(TV_Q96565,TV_Q96561),V_g),s(TV_Q96565,V_x))) => s(t_fun(TV_Q96565,TV_Q96561),V_f) = s(t_fun(TV_Q96565,TV_Q96561),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_arithmetics_ZEROu_u_LTu_u_EXP, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y)))))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_x)))) | s(t_h4s_nums_num,V_y) = 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_distribu_c21, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_reals_REALu_u_OFu_u_NUMu_u_POW, axiom, ![V_x, V_n]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_n))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_floats_REALu_u_OFu_u_NUMu_u_LT0, axiom, ![V_n, V_m]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ch4s_floats_RRRC6, conjecture, p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))))).
