# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X4),s(t_h4s_extreals_extreal,X2))))&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,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X4),s(t_h4s_extreals_extreal,X3))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X2),s(t_h4s_extreals_extreal,X1))))))),file('i/f/extreal/min__le2__imp', ch4s_extreals_minu_u_le2u_u_imp)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/min__le2__imp', aHLu_FALSITY)).
fof(19, axiom,![X15]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X15)))),file('i/f/extreal/min__le2__imp', ah4s_extreals_leu_u_refl)).
fof(23, axiom,![X17]:![X18]:![X15]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X18),s(t_h4s_extreals_extreal,X17)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X17))))),file('i/f/extreal/min__le2__imp', ah4s_extreals_leu_u_trans)).
fof(28, axiom,![X18]:![X15]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X18),s(t_h4s_extreals_extreal,X15)))))<=>s(t_h4s_extreals_extreal,X15)=s(t_h4s_extreals_extreal,X18)),file('i/f/extreal/min__le2__imp', ah4s_extreals_leu_u_antisym)).
fof(29, axiom,![X7]:(s(t_bool,f)=s(t_bool,X7)<=>~(p(s(t_bool,X7)))),file('i/f/extreal/min__le2__imp', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(42, axiom,![X17]:![X18]:![X15]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))),s(t_h4s_extreals_extreal,X17))))<=>(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X17))))|p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X18),s(t_h4s_extreals_extreal,X17)))))),file('i/f/extreal/min__le2__imp', ah4s_extreals_minu_u_le)).
fof(43, axiom,![X17]:![X18]:![X15]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X17),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))))))<=>(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X17),s(t_h4s_extreals_extreal,X15))))&p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X17),s(t_h4s_extreals_extreal,X18)))))),file('i/f/extreal/min__le2__imp', ah4s_extreals_leu_u_min)).
fof(44, axiom,![X18]:![X15]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))),s(t_h4s_extreals_extreal,X18)))),file('i/f/extreal/min__le2__imp', ah4s_extreals_minu_u_le2)).
fof(45, axiom,![X18]:![X15]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))),s(t_h4s_extreals_extreal,X15)))),file('i/f/extreal/min__le2__imp', ah4s_extreals_minu_u_le1)).
fof(52, axiom,![X18]:![X15]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_min(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))),s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X18))),file('i/f/extreal/min__le2__imp', ah4s_extreals_extrealu_u_minu_u_def)).
fof(59, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/extreal/min__le2__imp', aHLu_BOOLu_CASES)).
fof(60, axiom,![X13]:![X5]:![X6]:s(X13,h4s_bools_cond(s(t_bool,f),s(X13,X6),s(X13,X5)))=s(X13,X5),file('i/f/extreal/min__le2__imp', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(75, axiom,![X13]:![X5]:![X6]:s(X13,h4s_bools_cond(s(t_bool,t),s(X13,X6),s(X13,X5)))=s(X13,X6),file('i/f/extreal/min__le2__imp', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(77, axiom,p(s(t_bool,t)),file('i/f/extreal/min__le2__imp', aHLu_TRUTH)).
fof(79, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/extreal/min__le2__imp', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
