# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))))=>![X3]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_gcds_lcm(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))))=>(~(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3)))))|~(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3)))))))),file('i/f/gcd/LCM__LEAST', ch4s_gcds_LCMu_u_LEAST)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/gcd/LCM__LEAST', aHLu_FALSITY)).
fof(5, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/gcd/LCM__LEAST', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X7]:((p(s(t_bool,X7))=>p(s(t_bool,f)))<=>s(t_bool,X7)=s(t_bool,f)),file('i/f/gcd/LCM__LEAST', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(44, axiom,![X3]:![X1]:![X2]:((p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3)))))=>p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,h4s_gcds_lcm(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X3))))),file('i/f/gcd/LCM__LEAST', ah4s_gcds_LCMu_u_ISu_u_LEASTu_u_COMMONu_u_MULTIPLEu_c2)).
fof(47, axiom,![X18]:![X19]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X18))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19)))))=>~(p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))))),file('i/f/gcd/LCM__LEAST', ah4s_dividess_NOTu_u_LTu_u_DIVIDES)).
fof(77, axiom,![X18]:![X19]:s(t_h4s_nums_num,h4s_gcds_lcm(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_gcds_lcm(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))),file('i/f/gcd/LCM__LEAST', ah4s_gcds_LCMu_u_COMM)).
# SZS output end CNFRefutation
