# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0),s(t_h4s_realaxs_real,X1)))))=>![X2]:p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,X2))))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ch4s_realaxs_SUPu_u_ALLPOSu_u_LEMMA4)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/realax/SUP__ALLPOS__LEMMA4', aHLu_TRUTH)).
fof(6, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X7]:![X8]:![X9]:![X10]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X7,t_fun(X7,t_bool)),X11),s(t_fun(X7,X8),X10),s(t_fun(X8,X7),X9))))=>![X2]:![X1]:(s(X8,X2)=s(X8,X1)<=>p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X11),s(X7,happ(s(t_fun(X8,X7),X9),s(X8,X2))))),s(X7,happ(s(t_fun(X8,X7),X9),s(X8,X1)))))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_quotients_EQUALSu_u_PRS)).
fof(13, axiom,![X21]:![X22]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X22),s(t_h4s_realaxs_real,X21)))=s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X22))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X21))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_realaxs_realu_u_lt0)).
fof(14, axiom,![X23]:p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,X23)))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_realaxs_REALu_u_POS)).
fof(16, axiom,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))))|(p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))))|p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2)))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_realaxs_TREALu_u_LTu_u_TOTAL)).
fof(17, axiom,![X26]:![X1]:![X2]:((p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))))&p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X26)))))=>p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X26))))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_realaxs_TREALu_u_LTu_u_TRANS)).
fof(19, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_h4s_realaxs_real),h4s_realaxs_realu_u_abs),s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep)))),file('i/f/realax/SUP__ALLPOS__LEMMA4', ah4s_realaxs_realu_u_QUOTIENT)).
fof(20, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/realax/SUP__ALLPOS__LEMMA4', aHLu_BOOLu_CASES)).
fof(31, axiom,~(p(s(t_bool,f))),file('i/f/realax/SUP__ALLPOS__LEMMA4', aHLu_FALSITY)).
# SZS output end CNFRefutation
