# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X3))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2)))))),file('i/f/real/REAL__LE__MIN', ch4s_reals_REALu_u_LEu_u_MIN)).
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/real/REAL__LE__MIN', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(29, axiom,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))))),file('i/f/real/REAL__LE__MIN', ah4s_reals_REALu_u_LEu_u_TRANS)).
fof(31, axiom,![X2]:![X3]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3)))))<=>s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,X2)),file('i/f/real/REAL__LE__MIN', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(32, axiom,![X2]:![X3]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))))),file('i/f/real/REAL__LE__MIN', ah4s_reals_REALu_u_LEu_u_TOTAL)).
fof(33, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__MIN', ah4s_reals_minu_u_def)).
fof(34, axiom,![X3]:s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X3)))=s(t_h4s_realaxs_real,X3),file('i/f/real/REAL__LE__MIN', ah4s_reals_REALu_u_MINu_u_REFL)).
fof(36, axiom,![X13]:![X4]:![X5]:s(X13,h4s_bools_cond(s(t_bool,t),s(X13,X5),s(X13,X4)))=s(X13,X5),file('i/f/real/REAL__LE__MIN', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(37, axiom,![X13]:![X4]:![X5]:s(X13,h4s_bools_cond(s(t_bool,f),s(X13,X5),s(X13,X4)))=s(X13,X4),file('i/f/real/REAL__LE__MIN', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(38, axiom,p(s(t_bool,t)),file('i/f/real/REAL__LE__MIN', aHLu_TRUTH)).
fof(39, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/real/REAL__LE__MIN', aHLu_BOOLu_CASES)).
fof(42, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/real/REAL__LE__MIN', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(53, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__LE__MIN', aHLu_FALSITY)).
fof(65, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/real/REAL__LE__MIN', ah4s_bools_EQu_u_CLAUSESu_c3)).
# SZS output end CNFRefutation
