# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/gcd/BINARY__GCD_c1', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/gcd/BINARY__GCD_c1', 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/gcd/BINARY__GCD_c1', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/gcd/BINARY__GCD_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/gcd/BINARY__GCD_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X14]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),file('i/f/gcd/BINARY__GCD_c1', ah4s_arithmetics_MULTu_u_COMM)).
fof(16, axiom,![X14]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X14))))<=>~(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X14)))))),file('i/f/gcd/BINARY__GCD_c1', ah4s_arithmetics_ODDu_u_EVEN)).
fof(17, axiom,![X14]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X14))))<=>?[X15]:s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X15)))),file('i/f/gcd/BINARY__GCD_c1', ah4s_arithmetics_EVENu_u_EXISTS)).
fof(18, axiom,![X16]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X16)),file('i/f/gcd/BINARY__GCD_c1', ah4s_arithmetics_MULTu_u_DIV)).
fof(19, axiom,![X17]:![X18]:(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17))))<=>?[X16]:s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X18)))),file('i/f/gcd/BINARY__GCD_c1', ah4s_dividess_dividesu_u_def)).
fof(20, axiom,p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/gcd/BINARY__GCD_c1', ah4s_dividess_PRIMEu_u_2)).
fof(21, axiom,![X19]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,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))))),file('i/f/gcd/BINARY__GCD_c1', ah4s_dividess_PRIMEu_u_POS)).
fof(22, axiom,![X17]:![X18]:s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X18))),file('i/f/gcd/BINARY__GCD_c1', ah4s_gcds_GCDu_u_SYM)).
fof(23, axiom,![X19]:![X17]:(p(s(t_bool,h4s_dividess_prime(s(t_h4s_nums_num,X19))))=>(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X17))))|s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X17)))=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/BINARY__GCD_c1', ah4s_gcds_PRIMEu_u_GCD)).
fof(25, axiom,![X14]:![X15]:![X20]:(s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X20)))=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_gcds_gcd(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X14)))))=s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))),file('i/f/gcd/BINARY__GCD_c1', ah4s_gcds_GCDu_u_CANCELu_u_MULT)).
fof(26, conjecture,![X14]:![X15]:((p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X15))))&p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X14)))))=>s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,X14)))),file('i/f/gcd/BINARY__GCD_c1', ch4s_gcds_BINARYu_u_GCDu_c1)).
# SZS output end CNFRefutation
