%   ORIGINAL: h4/num/INV__SUC
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/ONE__ONE__THM: !f. h4/bool/ONE__ONE f <=> (!x1 x2. f x1 = f x2 ==> x1 = x2)
% Assm: h4/num/SUC__REP__DEF_c0: h4/bool/ONE__ONE h4/num/SUC__REP
% Assm: h4/num/SUC__REP__DEF_c1: ~h4/bool/ONTO h4/num/SUC__REP
% Assm: h4/num/IS__NUM__REP0: !m. h4/num/IS__NUM__REP m <=> (!P. P h4/num/ZERO__REP /\ (!n. P n ==> P (h4/num/SUC__REP n)) ==> P m)
% Assm: h4/num/num__ISO__DEF_c0: !a. h4/num/ABS__num (h4/num/REP__num a) = a
% Assm: h4/num/num__ISO__DEF_c1: !r. h4/num/IS__NUM__REP r <=> h4/num/REP__num (h4/num/ABS__num r) = r
% Assm: h4/num/SUC__DEF: !m. h4/num/SUC m = h4/num/ABS__num (h4/num/SUC__REP (h4/num/REP__num m))
% Goal: !n m. h4/num/SUC m = h4/num/SUC n ==> m = n
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ONEu_u_ONEu_u_THM]: !f. h4/bool/ONE__ONE f <=> (!x1 x2. happ f x1 = happ f x2 ==> x1 = x2)
% Assm [h4s_nums_SUCu_u_REPu_u_DEFu_c0]: h4/bool/ONE__ONE h4/num/SUC__REP
% Assm [h4s_nums_SUCu_u_REPu_u_DEFu_c1]: ~h4/bool/ONTO h4/num/SUC__REP
% Assm [h4s_nums_ISu_u_NUMu_u_REP0]: !m. h4/num/IS__NUM__REP m <=> (!P. happ P h4/num/ZERO__REP /\ (!n. happ P n ==> happ P (happ h4/num/SUC__REP n)) ==> happ P m)
% Assm [h4s_nums_numu_u_ISOu_u_DEFu_c0]: !a. h4/num/ABS__num (h4/num/REP__num a) = a
% Assm [h4s_nums_numu_u_ISOu_u_DEFu_c1]: !r. h4/num/IS__NUM__REP r <=> h4/num/REP__num (h4/num/ABS__num r) = r
% Assm [h4s_nums_SUCu_u_DEF]: !m. h4/num/SUC m = h4/num/ABS__num (happ h4/num/SUC__REP (h4/num/REP__num m))
% Goal: !n m. h4/num/SUC m = h4/num/SUC n ==> m = n
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_Q283773,TV_Q283769]: ![V_f, V_g]: (![V_x]: s(TV_Q283769,happ(s(t_fun(TV_Q283773,TV_Q283769),V_f),s(TV_Q283773,V_x))) = s(TV_Q283769,happ(s(t_fun(TV_Q283773,TV_Q283769),V_g),s(TV_Q283773,V_x))) => s(t_fun(TV_Q283773,TV_Q283769),V_f) = s(t_fun(TV_Q283773,TV_Q283769),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> 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_bools_ONEu_u_ONEu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_f]: (p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(TV_u_27a,TV_u_27b),V_f)))) <=> ![V_x1, V_x2]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x1))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x2))) => s(TV_u_27a,V_x1) = s(TV_u_27a,V_x2)))).
fof(ah4s_nums_SUCu_u_REPu_u_DEFu_c0, axiom, p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(t_h4s_mins_ind,t_h4s_mins_ind),h4s_nums_sucu_u_rep))))).
fof(ah4s_nums_SUCu_u_REPu_u_DEFu_c1, axiom, ~ (p(s(t_bool,h4s_bools_onto(s(t_fun(t_h4s_mins_ind,t_h4s_mins_ind),h4s_nums_sucu_u_rep)))))).
fof(ah4s_nums_ISu_u_NUMu_u_REP0, axiom, ![V_m]: (p(s(t_bool,h4s_nums_isu_u_numu_u_rep(s(t_h4s_mins_ind,V_m)))) <=> ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_mins_ind,t_bool),V_P),s(t_h4s_mins_ind,h4s_nums_zerou_u_rep)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_mins_ind,t_bool),V_P),s(t_h4s_mins_ind,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_mins_ind,t_bool),V_P),s(t_h4s_mins_ind,happ(s(t_fun(t_h4s_mins_ind,t_h4s_mins_ind),h4s_nums_sucu_u_rep),s(t_h4s_mins_ind,V_n)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_mins_ind,t_bool),V_P),s(t_h4s_mins_ind,V_m))))))).
fof(ah4s_nums_numu_u_ISOu_u_DEFu_c0, axiom, ![V_a]: s(t_h4s_nums_num,h4s_nums_absu_u_num(s(t_h4s_mins_ind,h4s_nums_repu_u_num(s(t_h4s_nums_num,V_a))))) = s(t_h4s_nums_num,V_a)).
fof(ah4s_nums_numu_u_ISOu_u_DEFu_c1, axiom, ![V_r]: (p(s(t_bool,h4s_nums_isu_u_numu_u_rep(s(t_h4s_mins_ind,V_r)))) <=> s(t_h4s_mins_ind,h4s_nums_repu_u_num(s(t_h4s_nums_num,h4s_nums_absu_u_num(s(t_h4s_mins_ind,V_r))))) = s(t_h4s_mins_ind,V_r))).
fof(ah4s_nums_SUCu_u_DEF, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_absu_u_num(s(t_h4s_mins_ind,happ(s(t_fun(t_h4s_mins_ind,t_h4s_mins_ind),h4s_nums_sucu_u_rep),s(t_h4s_mins_ind,h4s_nums_repu_u_num(s(t_h4s_nums_num,V_m)))))))).
fof(ch4s_nums_INVu_u_SUC, conjecture, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) => s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
