%   ORIGINAL: h4/prim__rec/LESS__NOT__EQ
% 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/FALSITY: !t. F ==> t
% Assm: h4/prim__rec/LESS__REFL: !n. ~h4/prim__rec/_3C n n
% Goal: !n m. h4/prim__rec/_3C m 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_FALSITY]: !t. F ==> t
% Assm [h4s_primu_u_recs_LESSu_u_REFL]: !n. ~h4/prim__rec/_3C n n
% Goal: !n m. h4/prim__rec/_3C m 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_Q187718,TV_Q187714]: ![V_f, V_g]: (![V_x]: s(TV_Q187714,happ(s(t_fun(TV_Q187718,TV_Q187714),V_f),s(TV_Q187718,V_x))) = s(TV_Q187714,happ(s(t_fun(TV_Q187718,TV_Q187714),V_g),s(TV_Q187718,V_x))) => s(t_fun(TV_Q187718,TV_Q187714),V_f) = s(t_fun(TV_Q187718,TV_Q187714),V_g))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_primu_u_recs_LESSu_u_REFL, axiom, ![V_n]: ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))))).
fof(ch4s_primu_u_recs_LESSu_u_NOTu_u_EQ, conjecture, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) => ~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)))).
