# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,~(p(s(t_bool,happ(s(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),h4s_realaxs_trealu_u_1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0))))),file('i/f/realax/TREAL__10', ch4s_realaxs_TREALu_u_10)).
fof(20, axiom,s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0)=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),file('i/f/realax/TREAL__10', ah4s_realaxs_trealu_u_00)).
fof(21, axiom,![X5]:p(s(t_bool,happ(s(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),X5))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X5)))),file('i/f/realax/TREAL__10', ah4s_realaxs_TREALu_u_EQu_u_REFL)).
fof(22, axiom,![X17]:![X18]:![X19]:![X20]:(p(s(t_bool,happ(s(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),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X20),s(t_h4s_hreals_hreal,X18))))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X19),s(t_h4s_hreals_hreal,X17))))))<=>s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X20),s(t_h4s_hreals_hreal,X17)))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X19),s(t_h4s_hreals_hreal,X18)))),file('i/f/realax/TREAL__10', ah4s_realaxs_trealu_u_eq0)).
fof(24, axiom,![X11]:![X5]:s(t_bool,happ(s(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),X5))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X11)))=s(t_bool,happ(s(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),X11))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X5))),file('i/f/realax/TREAL__10', ah4s_realaxs_TREALu_u_EQu_u_SYM)).
fof(25, axiom,![X6]:![X7]:(p(s(t_bool,happ(s(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),X7))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X6))))<=>s(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),X7)))=s(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),X6)))),file('i/f/realax/TREAL__10', ah4s_realaxs_TREALu_u_EQu_u_EQUIV)).
fof(27, axiom,s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_1)=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),file('i/f/realax/TREAL__10', ah4s_realaxs_trealu_u_10)).
fof(28, axiom,![X22]:![X23]:![X24]:s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X24),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X23),s(t_h4s_hreals_hreal,X22)))))=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,X24),s(t_h4s_hreals_hreal,X23))),s(t_h4s_hreals_hreal,X22))),file('i/f/realax/TREAL__10', ah4s_hreals_HREALu_u_ADDu_u_ASSOC)).
fof(30, axiom,![X23]:![X24]:s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X24),s(t_h4s_hreals_hreal,X23)))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X23),s(t_h4s_hreals_hreal,X24))),file('i/f/realax/TREAL__10', ah4s_hreals_HREALu_u_ADDu_u_SYM)).
fof(31, axiom,![X11]:![X5]:~(s(t_h4s_hreals_hreal,X5)=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,X11)))),file('i/f/realax/TREAL__10', ah4s_realaxs_HREALu_u_EQu_u_ADDL)).
# SZS output end CNFRefutation
