# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![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,X1)))))=>p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1))))),file('i/f/extreal/lte__trans', ch4s_extreals_lteu_u_trans)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/lte__trans', aHLu_FALSITY)).
fof(21, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/extreal/lte__trans', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(43, 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/lte__trans', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(45, 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,X3),s(t_h4s_extreals_extreal,X2))))),file('i/f/extreal/lte__trans', ah4s_extreals_ltu_u_impu_u_le)).
fof(48, axiom,![X2]:![X3]:(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/lte__trans', ah4s_extreals_ltu_u_impu_u_ne)).
fof(59, 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/lte__trans', ah4s_extreals_leu_u_antisym)).
fof(60, axiom,![X1]:![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,X1)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1))))),file('i/f/extreal/lte__trans', ah4s_extreals_leu_u_trans)).
fof(75, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/extreal/lte__trans', aHLu_BOOLu_CASES)).
fof(76, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/extreal/lte__trans', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
