# 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(2, axiom,~(p(s(t_bool,f))),file('i/f/bit/MOD__LEQ', aHLu_FALSITY)).
fof(9, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/bit/MOD__LEQ', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(22, axiom,![X15]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(24, axiom,![X14]:![X15]:![X16]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(25, axiom,![X15]:![X16]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X16))))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_NOTu_u_LEQ)).
fof(29, axiom,![X15]:![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(32, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/bit/MOD__LEQ', ah4s_numerals_numeralu_u_distribu_c1)).
fof(33, axiom,![X15]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15))))=>![X18]:(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X15)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X15)))))),file('i/f/bit/MOD__LEQ', ah4s_arithmetics_DIVISION)).
fof(39, axiom,p(s(t_bool,t)),file('i/f/bit/MOD__LEQ', aHLu_TRUTH)).
fof(41, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/bit/MOD__LEQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
