# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)),file('i/f/arithmetic/MIN__MAX__EQ', ch4s_arithmetics_MINu_u_MAXu_u_EQ)).
fof(3, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MIN__MAX__EQ', ah4s_arithmetics_MAXu_u_DEF)).
fof(6, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/arithmetic/MIN__MAX__EQ', ah4s_arithmetics_MINu_u_DEF)).
fof(9, axiom,![X3]:![X7]:![X8]:s(X3,h4s_bools_cond(s(t_bool,t),s(X3,X8),s(X3,X7)))=s(X3,X8),file('i/f/arithmetic/MIN__MAX__EQ', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(10, axiom,![X3]:![X7]:![X8]:s(X3,h4s_bools_cond(s(t_bool,f),s(X3,X8),s(X3,X7)))=s(X3,X7),file('i/f/arithmetic/MIN__MAX__EQ', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(17, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))=>~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/MIN__MAX__EQ', ah4s_primu_u_recs_LESSu_u_NOTu_u_EQ)).
fof(42, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MIN__MAX__EQ', aHLu_TRUTH)).
fof(43, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)|s(t_bool,X17)=s(t_bool,f)),file('i/f/arithmetic/MIN__MAX__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
