# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X2))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3))),s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))))),file('i/f/real/REAL__IMP__MIN__LE2', ch4s_reals_REALu_u_IMPu_u_MINu_u_LE2)).
fof(2, 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/real/REAL__IMP__MIN__LE2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(17, axiom,![X13]:![X15]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X15))))),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_reals_REALu_u_LEu_u_TOTAL)).
fof(18, axiom,![X20]:![X13]:![X15]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X20)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X20))))),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_reals_REALu_u_LEu_u_TRANS)).
fof(19, axiom,![X13]:![X15]:s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13)))=s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13))),s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13))),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_reals_minu_u_def)).
fof(20, axiom,![X20]:![X13]:![X15]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X13))),s(t_h4s_realaxs_real,X20))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X15),s(t_h4s_realaxs_real,X20))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X20)))))),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_reals_REALu_u_MINu_u_LE)).
fof(21, axiom,![X19]:![X5]:![X6]:s(X19,h4s_bools_cond(s(t_bool,t),s(X19,X6),s(X19,X5)))=s(X19,X6),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(22, axiom,![X19]:![X5]:![X6]:s(X19,h4s_bools_cond(s(t_bool,f),s(X19,X6),s(X19,X5)))=s(X19,X5),file('i/f/real/REAL__IMP__MIN__LE2', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
