# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1))))),file('i/f/divides/ONE__LT__PRIME', ch4s_dividess_ONEu_u_LTu_u_PRIME)).
fof(4, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/divides/ONE__LT__PRIME', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X16]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_LESSu_u_EQ)).
fof(29, axiom,![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X16))),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_distribu_c21)).
fof(30, axiom,![X16]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X16))))),file('i/f/divides/ONE__LT__PRIME', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(31, axiom,![X16]:(~(s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16))))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(33, axiom,![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X16)))))=s(t_bool,t),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_ltu_c0)).
fof(34, axiom,![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_ltu_c2)).
fof(40, axiom,![X16]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X16))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(41, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_ONE)).
fof(42, axiom,![X16]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_equ_c1)).
fof(45, axiom,![X18]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X18))))<=>(~(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))&![X19]:(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))=>(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,X18)|s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),file('i/f/divides/ONE__LT__PRIME', ah4s_dividess_primeu_u_def)).
fof(46, axiom,![X1]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))),file('i/f/divides/ONE__LT__PRIME', ah4s_dividess_PRIMEu_u_POS)).
fof(52, axiom,![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0)|?[X16]:s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16)))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_numu_u_CASES)).
fof(54, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_sucu_c0)).
fof(56, axiom,![X16]:![X17]:(~(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X17)))))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(59, axiom,![X16]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X16)))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X16))),file('i/f/divides/ONE__LT__PRIME', ah4s_numerals_numeralu_u_sucu_c1)).
fof(61, axiom,![X1]:![X16]:![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X1))),file('i/f/divides/ONE__LT__PRIME', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
