# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2))))),file('i/f/bit/MOD__LEQ', ch4s_bits_MODu_u_LEQ)).
fof(4, axiom,![X4]:![X6]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X4))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X6)),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_LESSu_u_MOD)).
fof(6, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/bit/MOD__LEQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(36, axiom,![X4]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/bit/MOD__LEQ', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(54, axiom,![X19]:![X7]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X7))))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_MODu_u_LESSu_u_EQ)).
fof(55, axiom,![X4]:![X5]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),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,X5))))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
