# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_hreals_hreal,X2)=s(t_h4s_hreals_hreal,X1)|(?[X3]:s(t_h4s_hreals_hreal,X1)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X3)))|?[X3]:s(t_h4s_hreals_hreal,X2)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X1),s(t_h4s_hreals_hreal,X3))))),file('i/f/hreal/HREAL__ADD__TOTAL', ch4s_hreals_HREALu_u_ADDu_u_TOTAL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hreal/HREAL__ADD__TOTAL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hreal/HREAL__ADD__TOTAL', 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/hreal/HREAL__ADD__TOTAL', aHLu_BOOLu_CASES)).
fof(5, axiom,![X1]:![X2]:(s(t_h4s_hreals_hreal,X2)=s(t_h4s_hreals_hreal,X1)|(p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X1))))|p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X1),s(t_h4s_hreals_hreal,X2)))))),file('i/f/hreal/HREAL__ADD__TOTAL', ah4s_hreals_HREALu_u_LTu_u_TOTAL)).
fof(6, axiom,![X1]:![X2]:(p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X1))))<=>?[X3]:s(t_h4s_hreals_hreal,X1)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X3)))),file('i/f/hreal/HREAL__ADD__TOTAL', ah4s_hreals_HREALu_u_LT)).
# SZS output end CNFRefutation
