# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2))))=>s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,X1)),file('i/f/real/REAL__MIN__ALT_c1', ch4s_reals_REALu_u_MINu_u_ALTu_c1)).
fof(3, 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__MIN__ALT_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(29, axiom,![X1]:![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,X1),s(t_h4s_realaxs_real,X2)))))<=>s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X1)),file('i/f/real/REAL__MIN__ALT_c1', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(30, axiom,![X1]:![X2]:s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),file('i/f/real/REAL__MIN__ALT_c1', ah4s_reals_minu_u_def)).
fof(32, axiom,![X1]:![X2]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))=>s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,X2)),file('i/f/real/REAL__MIN__ALT_c1', ah4s_reals_REALu_u_MINu_u_ALTu_c0)).
fof(34, axiom,![X1]:![X2]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X1)))),file('i/f/real/REAL__MIN__ALT_c1', ah4s_reals_REALu_u_MINu_u_LE2)).
fof(35, axiom,![X1]:![X2]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X2)))),file('i/f/real/REAL__MIN__ALT_c1', ah4s_reals_REALu_u_MINu_u_LE1)).
fof(39, axiom,![X3]:![X4]:![X5]:s(X3,h4s_bools_cond(s(t_bool,t),s(X3,X5),s(X3,X4)))=s(X3,X5),file('i/f/real/REAL__MIN__ALT_c1', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(41, axiom,![X3]:![X4]:![X5]:s(X3,h4s_bools_cond(s(t_bool,f),s(X3,X5),s(X3,X4)))=s(X3,X4),file('i/f/real/REAL__MIN__ALT_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
