# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X1)))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))))),file('i/f/arithmetic/MIN__MAX__PRED', ch4s_arithmetics_MINu_u_MAXu_u_PRED)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(22, 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__PRED', ah4s_arithmetics_MAXu_u_DEF)).
fof(23, 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__PRED', ah4s_arithmetics_MINu_u_DEF)).
fof(24, axiom,![X20]:![X18]:![X21]:![X17]:![X15]:![X22]:s(X20,happ(s(t_fun(X18,X20),X15),s(X18,h4s_bools_cond(s(t_bool,X22),s(X18,X17),s(X18,X21)))))=s(X20,h4s_bools_cond(s(t_bool,X22),s(X20,happ(s(t_fun(X18,X20),X15),s(X18,X17))),s(X20,happ(s(t_fun(X18,X20),X15),s(X18,X21))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_CONDu_u_RAND)).
fof(25, axiom,![X4]:![X5]:![X22]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X22),s(t_bool,X5),s(t_bool,X4))))<=>((~(p(s(t_bool,X22)))|p(s(t_bool,X5)))&(p(s(t_bool,X22))|p(s(t_bool,X4))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_CONDu_u_EXPAND)).
# SZS output end CNFRefutation
