%   ORIGINAL: h4/frac/FRAC__DNMPOS
% 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/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/frac/frac__bij_c0: !a. h4/frac/abs__frac (h4/frac/rep__frac a) = a
% Assm: h4/frac/frac__bij_c1: !r. (\f. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/pair/SND f)) r <=> h4/frac/rep__frac (h4/frac/abs__frac r) = r
% Assm: h4/frac/frac__dnm__def: !f. h4/frac/frac__dnm f = h4/pair/SND (h4/frac/rep__frac f)
% Goal: !f. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/frac/frac__dnm f)
%   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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_fracs_fracu_u_biju_c0]: !a. h4/frac/abs__frac (h4/frac/rep__frac a) = a
% Assm [h4s_fracs_fracu_u_biju_c1]: !r. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/pair/SND r) <=> h4/frac/rep__frac (h4/frac/abs__frac r) = r
% Assm [h4s_fracs_fracu_u_dnmu_u_def]: !f. h4/frac/frac__dnm f = h4/pair/SND (h4/frac/rep__frac f)
% Goal: !f. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/frac/frac__dnm f)
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_Q199372,TV_Q199368]: ![V_f, V_g]: (![V_x]: s(TV_Q199368,happ(s(t_fun(TV_Q199372,TV_Q199368),V_f),s(TV_Q199372,V_x))) = s(TV_Q199368,happ(s(t_fun(TV_Q199372,TV_Q199368),V_g),s(TV_Q199372,V_x))) => s(t_fun(TV_Q199372,TV_Q199368),V_f) = s(t_fun(TV_Q199372,TV_Q199368),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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_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_fracs_fracu_u_biju_c0, axiom, ![V_a]: s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,V_a))))) = s(t_h4s_fracs_frac,V_a)).
fof(ah4s_fracs_fracu_u_biju_c1, axiom, ![V_r]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),V_r)))))) <=> s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),V_r))))) = s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),V_r))).
fof(ah4s_fracs_fracu_u_dnmu_u_def, axiom, ![V_f]: s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,V_f))) = s(t_h4s_integers_int,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,V_f)))))).
fof(ch4s_fracs_FRACu_u_DNMPOS, conjecture, ![V_f]: p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,V_f))))))).
