# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))))<=>(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X2)))))),file('i/f/extreal/le__min', ch4s_extreals_leu_u_min)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/le__min', aHLu_FALSITY)).
fof(19, axiom,![X3]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X3)))),file('i/f/extreal/le__min', ah4s_extreals_leu_u_refl)).
fof(23, axiom,![X2]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))|p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3))))),file('i/f/extreal/le__min', ah4s_extreals_leu_u_total)).
fof(32, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/extreal/le__min', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(41, axiom,![X2]:![X3]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3)))))<=>s(t_h4s_extreals_extreal,X3)=s(t_h4s_extreals_extreal,X2)),file('i/f/extreal/le__min', ah4s_extreals_leu_u_antisym)).
fof(51, axiom,![X2]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))<=>~(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X3)))))),file('i/f/extreal/le__min', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(52, axiom,![X2]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))<=>(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))))|s(t_h4s_extreals_extreal,X3)=s(t_h4s_extreals_extreal,X2))),file('i/f/extreal/le__min', ah4s_extreals_leu_u_lt)).
fof(62, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))),s(t_h4s_extreals_extreal,X1))))<=>(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1))))|p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1)))))),file('i/f/extreal/le__min', ah4s_extreals_minu_u_le)).
fof(63, axiom,![X2]:![X3]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))),s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))),file('i/f/extreal/le__min', ah4s_extreals_extrealu_u_minu_u_def)).
fof(64, axiom,![X2]:![X3]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))),s(t_h4s_extreals_extreal,X2)))),file('i/f/extreal/le__min', ah4s_extreals_minu_u_le2)).
fof(65, axiom,![X2]:![X3]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X2))),s(t_h4s_extreals_extreal,X3)))),file('i/f/extreal/le__min', ah4s_extreals_minu_u_le1)).
fof(66, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/extreal/le__min', aHLu_BOOLu_CASES)).
fof(67, axiom,![X12]:![X4]:![X5]:s(X12,h4s_bools_cond(s(t_bool,f),s(X12,X5),s(X12,X4)))=s(X12,X4),file('i/f/extreal/le__min', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(68, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/extreal/le__min', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(80, axiom,![X12]:![X4]:![X5]:s(X12,h4s_bools_cond(s(t_bool,t),s(X12,X5),s(X12,X4)))=s(X12,X5),file('i/f/extreal/le__min', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
