# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X1))))=>(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2),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/gcd/PRIME__IS__GCD', ch4s_gcds_PRIMEu_u_ISu_u_GCD)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/gcd/PRIME__IS__GCD', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/gcd/PRIME__IS__GCD', aHLu_FALSITY)).
fof(19, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/gcd/PRIME__IS__GCD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(20, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/gcd/PRIME__IS__GCD', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(40, axiom,![X15]:![X2]:![X16]:(p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X15))))<=>(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))))&(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2))))&![X17]:((p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X2)))))=>p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X15)))))))),file('i/f/gcd/PRIME__IS__GCD', ah4s_gcds_isu_u_gcdu_u_def)).
fof(41, axiom,![X16]:p(s(t_bool,h4s_dividess_divides(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/gcd/PRIME__IS__GCD', ah4s_dividess_ONEu_u_DIVIDESu_u_ALL)).
fof(42, axiom,![X16]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X16))))<=>(~(s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))&![X2]:(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X16))))=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X16)|s(t_h4s_nums_num,X2)=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/gcd/PRIME__IS__GCD', ah4s_dividess_primeu_u_def)).
fof(43, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/gcd/PRIME__IS__GCD', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
