# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/divides/ONE__LT__PRIMES', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/divides/ONE__LT__PRIMES', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/divides/ONE__LT__PRIMES', aHLu_BOOLu_CASES)).
fof(7, axiom,![X10]:p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,h4s_dividess_primes(s(t_h4s_nums_num,X10)))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_dividess_primePRIMES)).
fof(10, axiom,![X12]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X12))))=>?[X13]:s(t_h4s_nums_num,h4s_dividess_primes(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X12)),file('i/f/divides/ONE__LT__PRIMES', ah4s_dividess_PRIMESu_u_ONTO)).
fof(16, axiom,![X12]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X12))))<=>?[X13]:s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_dividess_primes(s(t_h4s_nums_num,X13)))),file('i/f/divides/ONE__LT__PRIMES', ah4s_dividess_PRIMEu_u_INDEX)).
fof(17, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/divides/ONE__LT__PRIMES', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(41, axiom,![X10]:![X14]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X10)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X14))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_NOTu_u_LESS)).
fof(53, axiom,![X10]:![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X10)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X10))),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_LESSu_u_EQ)).
fof(58, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X14),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(59, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/divides/ONE__LT__PRIMES', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(75, axiom,![X10]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(76, axiom,![X10]:![X14]:(~(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X10))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X10))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X14)))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(92, axiom,~(p(s(t_bool,h4s_dividess_prime(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__PRIMES', ah4s_dividess_NOTu_u_PRIMEu_u_1)).
fof(93, axiom,~(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_dividess_NOTu_u_PRIMEu_u_0)).
fof(105, 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__PRIMES', ah4s_arithmetics_ONE)).
fof(125, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_0)))=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__PRIMES', ah4s_arithmetics_EXP0u_c0)).
fof(130, axiom,![X34]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X34),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_MODu_u_ONE)).
fof(131, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_ALTu_u_ZERO)).
fof(132, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/divides/ONE__LT__PRIMES', ah4s_arithmetics_BIT10)).
fof(133, conjecture,![X10]: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,X10)))))),file('i/f/divides/ONE__LT__PRIMES', ch4s_dividess_ONEu_u_LTu_u_PRIMES)).
# SZS output end CNFRefutation
