# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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/realax/HREAL__LT__GT', ch4s_realaxs_HREALu_u_LTu_u_GT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/realax/HREAL__LT__GT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/realax/HREAL__LT__GT', aHLu_FALSITY)).
fof(9, axiom,![X7]:![X8]:(p(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,X7))))<=>?[X9]:s(t_h4s_hreals_hreal,X7)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,X9)))),file('i/f/realax/HREAL__LT__GT', ah4s_hreals_HREALu_u_LT)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/realax/HREAL__LT__GT', aHLu_BOOLu_CASES)).
fof(12, axiom,![X10]:![X7]:![X8]:s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X7),s(t_h4s_hreals_hreal,X10)))))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,X7))),s(t_h4s_hreals_hreal,X10))),file('i/f/realax/HREAL__LT__GT', ah4s_hreals_HREALu_u_ADDu_u_ASSOC)).
fof(13, axiom,![X1]:![X2]:~(s(t_h4s_hreals_hreal,X2)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X1)))),file('i/f/realax/HREAL__LT__GT', ah4s_realaxs_HREALu_u_EQu_u_ADDL)).
# SZS output end CNFRefutation
