# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X3),s(t_h4s_rats_rat,X2))))&p(s(t_bool,h4s_rats_ratu_u_leq(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1)))))=>p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X3),s(t_h4s_rats_rat,X1))))),file('i/f/rat/RAT__LES__LEQ__TRANS', ch4s_rats_RATu_u_LESu_u_LEQu_u_TRANS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__LES__LEQ__TRANS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__LES__LEQ__TRANS', aHLu_FALSITY)).
fof(7, axiom,![X6]:![X7]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))=>~(s(t_h4s_rats_rat,X7)=s(t_h4s_rats_rat,X6))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_RATu_u_LESu_u_IMPu_u_NEQ)).
fof(8, axiom,![X6]:![X7]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))|(s(t_h4s_rats_rat,X7)=s(t_h4s_rats_rat,X6)|p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X6),s(t_h4s_rats_rat,X7)))))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_RATu_u_LESu_u_TOTAL)).
fof(13, axiom,![X15]:![X6]:![X7]:((p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))&p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X6),s(t_h4s_rats_rat,X15)))))=>p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X15))))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_RATu_u_LESu_u_TRANS)).
fof(27, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)<=>p(s(t_bool,X14))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(39, axiom,![X14]:(s(t_bool,X14)=s(t_bool,f)<=>~(p(s(t_bool,X14)))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(51, axiom,![X6]:![X7]:(p(s(t_bool,h4s_rats_ratu_u_leq(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))<=>(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))|s(t_h4s_rats_rat,X7)=s(t_h4s_rats_rat,X6))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_ratu_u_lequ_u_def)).
fof(53, axiom,![X6]:![X7]:(~(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X6),s(t_h4s_rats_rat,X7)))))<=>p(s(t_bool,h4s_rats_ratu_u_leq(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_RATu_u_LEQu_u_LES)).
fof(59, axiom,![X6]:![X7]:((p(s(t_bool,h4s_rats_ratu_u_leq(s(t_h4s_rats_rat,X7),s(t_h4s_rats_rat,X6))))&p(s(t_bool,h4s_rats_ratu_u_leq(s(t_h4s_rats_rat,X6),s(t_h4s_rats_rat,X7)))))=>s(t_h4s_rats_rat,X7)=s(t_h4s_rats_rat,X6)),file('i/f/rat/RAT__LES__LEQ__TRANS', ah4s_rats_RATu_u_LEQu_u_ANTISYM)).
fof(64, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)|s(t_bool,X14)=s(t_bool,f)),file('i/f/rat/RAT__LES__LEQ__TRANS', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
