# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X2))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X2),s(t_h4s_hrats_hrat,X1)))))=>p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X1))))),file('i/f/hreal/HRAT__LT__TRANS', ch4s_hreals_HRATu_u_LTu_u_TRANS)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/hreal/HRAT__LT__TRANS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X2]:![X3]:(p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X2))))<=>?[X12]:s(t_h4s_hrats_hrat,X2)=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X12)))),file('i/f/hreal/HRAT__LT__TRANS', ah4s_hreals_hratu_u_lt0)).
fof(13, axiom,![X13]:![X14]:~(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X14),s(t_h4s_hrats_hrat,X13)))=s(t_h4s_hrats_hrat,X14)),file('i/f/hreal/HRAT__LT__TRANS', ah4s_hrats_HRATu_u_NOZERO)).
fof(14, axiom,![X15]:![X13]:![X14]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X14),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X13),s(t_h4s_hrats_hrat,X15)))))=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X14),s(t_h4s_hrats_hrat,X13))),s(t_h4s_hrats_hrat,X15))),file('i/f/hreal/HRAT__LT__TRANS', ah4s_hrats_HRATu_u_ADDu_u_ASSOC)).
fof(15, axiom,![X13]:![X14]:(s(t_h4s_hrats_hrat,X14)=s(t_h4s_hrats_hrat,X13)|(?[X12]:s(t_h4s_hrats_hrat,X14)=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X13),s(t_h4s_hrats_hrat,X12)))|?[X12]:s(t_h4s_hrats_hrat,X13)=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X14),s(t_h4s_hrats_hrat,X12))))),file('i/f/hreal/HRAT__LT__TRANS', ah4s_hrats_HRATu_u_ADDu_u_TOTAL)).
fof(16, axiom,![X13]:![X14]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X14),s(t_h4s_hrats_hrat,X13)))=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X13),s(t_h4s_hrats_hrat,X14))),file('i/f/hreal/HRAT__LT__TRANS', ah4s_hrats_HRATu_u_ADDu_u_SYM)).
# SZS output end CNFRefutation
