# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(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_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bags_emptyu_u_bag),file('i/f/primeFactor/PRIME__FACTORS__1', ch4s_primeFactors_PRIMEu_u_FACTORSu_u_1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/primeFactor/PRIME__FACTORS__1', aHLu_FALSITY)).
fof(10, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(26, axiom,![X4]:![X5]:~(p(s(t_bool,h4s_bags_bagu_u_in(s(X4,X5),s(t_fun(X4,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_bags_NOTu_u_INu_u_EMPTYu_u_BAG)).
fof(27, axiom,![X4]:p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X4,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_bags_FINITEu_u_BAGu_u_THMu_c0)).
fof(28, axiom,![X13]:s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_prod(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X13),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_bags_BAGu_u_GENu_u_PRODu_u_EMPTY)).
fof(32, axiom,![X13]:![X20]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X13)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X20))))),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_arithmetics_NOTu_u_LESS)).
fof(33, axiom,![X13]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_numerals_numeralu_u_distribu_c27)).
fof(34, axiom,![X13]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_numerals_numeralu_u_lteu_c1)).
fof(35, axiom,![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13))))=>![X21]:((p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21))))&(![X5]:(p(s(t_bool,h4s_bags_bagu_u_in(s(t_h4s_nums_num,X5),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21))))=>p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X5)))))&s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_prod(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21),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,X13)))=>s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(s(t_h4s_nums_num,X13))))),file('i/f/primeFactor/PRIME__FACTORS__1', ah4s_primeFactors_PRIMEu_u_FACTORIZATION)).
# SZS output end CNFRefutation
