# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/primeFactor/PRIME__FACTORIZATION', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/primeFactor/PRIME__FACTORIZATION', 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/primeFactor/PRIME__FACTORIZATION', aHLu_BOOLu_CASES)).
fof(8, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/primeFactor/PRIME__FACTORIZATION', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/primeFactor/PRIME__FACTORIZATION', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(35, axiom,![X19]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19))))=>(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(s(t_h4s_nums_num,X19))))))&(![X20]:(p(s(t_bool,h4s_bags_bagu_u_in(s(t_h4s_nums_num,X20),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(s(t_h4s_nums_num,X19))))))=>p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X20)))))&s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_prod(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(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/primeFactor/PRIME__FACTORIZATION', ah4s_primeFactors_PRIMEu_u_FACTORSu_u_def)).
fof(36, axiom,![X19]:![X21]:![X22]:(((p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X22))))&(![X20]:(p(s(t_bool,h4s_bags_bagu_u_in(s(t_h4s_nums_num,X20),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X22))))=>p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X20)))))&s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_prod(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X22),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))&(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21))))&(![X20]:(p(s(t_bool,h4s_bags_bagu_u_in(s(t_h4s_nums_num,X20),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21))))=>p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X20)))))&s(t_h4s_nums_num,X19)=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_fun(t_h4s_nums_num,t_h4s_nums_num),X22)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X21)),file('i/f/primeFactor/PRIME__FACTORIZATION', ah4s_primeFactors_UNIQUEu_u_PRIMEu_u_FACTORS)).
fof(37, conjecture,![X19]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19))))=>![X23]:((p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X23))))&(![X6]:(p(s(t_bool,h4s_bags_bagu_u_in(s(t_h4s_nums_num,X6),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X23))))=>p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X6)))))&s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_prod(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X23),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,X19)))=>s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X23)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_primefactors_primeu_u_factors(s(t_h4s_nums_num,X19))))),file('i/f/primeFactor/PRIME__FACTORIZATION', ch4s_primeFactors_PRIMEu_u_FACTORIZATION)).
# SZS output end CNFRefutation
