# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_dividess_primes(s(t_h4s_nums_num,X1)))))),file('i/f/divides/ZERO__LT__PRIMES', ch4s_dividess_ZEROu_u_LTu_u_PRIMES)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/divides/ZERO__LT__PRIMES', aHLu_FALSITY)).
fof(9, axiom,![X2]:((p(s(t_bool,X2))=>p(s(t_bool,f)))<=>s(t_bool,X2)=s(t_bool,f)),file('i/f/divides/ZERO__LT__PRIMES', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(22, axiom,![X7]:![X1]:![X8]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X7)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))),file('i/f/divides/ZERO__LT__PRIMES', ah4s_arithmetics_LESSu_u_TRANS)).
fof(23, axiom,![X1]:![X8]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X8))))),file('i/f/divides/ZERO__LT__PRIMES', ah4s_arithmetics_NOTu_u_LESS)).
fof(24, axiom,![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,h4s_dividess_primes(s(t_h4s_nums_num,X1)))))),file('i/f/divides/ZERO__LT__PRIMES', ah4s_dividess_ONEu_u_LTu_u_PRIMES)).
fof(25, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/divides/ZERO__LT__PRIMES', ah4s_numerals_numeralu_u_distribu_c27)).
fof(26, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/divides/ZERO__LT__PRIMES', ah4s_numerals_numeralu_u_lteu_c1)).
# SZS output end CNFRefutation
