# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/LESS__EQ__SUC__REFL', ch4s_arithmetics_LESSu_u_EQu_u_SUCu_u_REFL)).
fof(17, axiom,![X4]:![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4))))<=>?[X5]:(![X19]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X5),s(t_h4s_nums_num,X19)))))&(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X5),s(t_h4s_nums_num,X1))))&~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X5),s(t_h4s_nums_num,X4)))))))),file('i/f/arithmetic/LESS__EQ__SUC__REFL', ah4s_primu_u_recs_LESSu_u_DEF)).
fof(48, axiom,![X4]:![X1]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4))))|s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,X4))),file('i/f/arithmetic/LESS__EQ__SUC__REFL', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(51, axiom,![X4]:![X1]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X4))),file('i/f/arithmetic/LESS__EQ__SUC__REFL', ah4s_arithmetics_LESSu_u_EQ)).
fof(54, axiom,![X4]:![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X4))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/LESS__EQ__SUC__REFL', ah4s_arithmetics_LESSu_u_CASES)).
# SZS output end CNFRefutation
