# 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(37, 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(39, 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_arithmetics_max(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_arithmetics_MAXu_u_COMM)).
fof(40, 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(42, 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_arithmetics_min(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_arithmetics_MINu_u_COMM)).
fof(45, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(46, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(48, 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)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_arithmetics_NOTu_u_LESS)).
fof(52, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_arithmetics_LESSu_u_EQu_u_CASES)).
fof(57, axiom,![X4]:![X5]:![X23]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X23),s(t_bool,X5),s(t_bool,X4))))<=>((~(p(s(t_bool,X23)))|p(s(t_bool,X5)))&(p(s(t_bool,X23))|p(s(t_bool,X4))))),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_CONDu_u_EXPAND)).
fof(59, axiom,![X14]:![X4]:![X5]:s(X14,h4s_bools_cond(s(t_bool,t),s(X14,X5),s(X14,X4)))=s(X14,X5),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(60, axiom,![X14]:![X4]:![X5]:s(X14,h4s_bools_cond(s(t_bool,f),s(X14,X5),s(X14,X4)))=s(X14,X4),file('i/f/arithmetic/MIN__MAX__PRED', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
