# 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_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__LT', ch4s_arithmetics_MINu_u_MAXu_u_LT)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, 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__LT', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(22, axiom,![X1]:![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_primu_u_recs_NOTu_u_LESSu_u_EQ)).
fof(28, 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)))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_arithmetics_LESSu_u_CASESu_u_IMP)).
fof(33, 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_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__LT', ah4s_arithmetics_MINu_u_MAXu_u_EQ)).
fof(34, 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__LT', ah4s_arithmetics_MAXu_u_DEF)).
fof(35, axiom,![X13]:![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_arithmetics_max(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,X13))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_arithmetics_MAXu_u_ASSOC)).
fof(36, 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__LT', ah4s_arithmetics_MAXu_u_COMM)).
fof(37, 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__LT', ah4s_arithmetics_MINu_u_DEF)).
fof(38, 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__LT', ah4s_arithmetics_MINu_u_COMM)).
fof(39, axiom,![X13]:![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_arithmetics_min(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,X13))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_arithmetics_MINu_u_ASSOC)).
fof(43, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_primu_u_recs_LESSu_u_0)).
fof(45, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X4),s(X6,X3)))=s(X6,X4),file('i/f/arithmetic/MIN__MAX__LT', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(46, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/arithmetic/MIN__MAX__LT', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(48, axiom,![X3]:![X4]:![X19]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X19),s(t_bool,X4),s(t_bool,X3))))<=>((~(p(s(t_bool,X19)))|p(s(t_bool,X4)))&(p(s(t_bool,X19))|p(s(t_bool,X3))))),file('i/f/arithmetic/MIN__MAX__LT', ah4s_bools_CONDu_u_EXPAND)).
# SZS output end CNFRefutation
