# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_realaxs_real,h4s_reals_min(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X1))),file('i/f/real/REAL__MIN__ADD', ch4s_reals_REALu_u_MINu_u_ADD)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__MIN__ADD', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/real/REAL__MIN__ADD', aHLu_BOOLu_CASES)).
fof(6, 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__MIN__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/real/REAL__MIN__ADD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X7]:![X5]:![X6]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X6),s(X7,X5)))=s(X7,X6),file('i/f/real/REAL__MIN__ADD', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(13, axiom,![X7]:![X5]:![X6]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X6),s(X7,X5)))=s(X7,X5),file('i/f/real/REAL__MIN__ADD', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(18, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__MIN__ADD', ah4s_reals_REALu_u_LEu_u_RADD)).
fof(19, 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__MIN__ADD', ah4s_reals_minu_u_def)).
# SZS output end CNFRefutation
