# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(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_realaxs_trealu_u_0)))),file('i/f/realax/TREAL__INV__0', ch4s_realaxs_TREALu_u_INVu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/realax/TREAL__INV__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/realax/TREAL__INV__0', aHLu_FALSITY)).
fof(6, axiom,![X3]:![X4]:![X5]:![X6]:(p(s(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,X6),s(t_h4s_hreals_hreal,X4))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,X3))))))<=>s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X6),s(t_h4s_hreals_hreal,X3)))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X5),s(t_h4s_hreals_hreal,X4)))),file('i/f/realax/TREAL__INV__0', ah4s_realaxs_trealu_u_eq0)).
fof(7, 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__INV__0', ah4s_realaxs_trealu_u_00)).
fof(8, axiom,![X7]:![X2]:?[X8]:((p(s(t_bool,X8))<=>s(t_h4s_hreals_hreal,X2)=s(t_h4s_hreals_hreal,X7))&s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X7)))))=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_bools_cond(s(t_bool,X8),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_bools_cond(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,X7),s(t_h4s_hreals_hreal,X2))),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_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,X2),s(t_h4s_hreals_hreal,X7))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_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_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,X7),s(t_h4s_hreals_hreal,X2))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)))))))))),file('i/f/realax/TREAL__INV__0', ah4s_realaxs_trealu_u_inv0)).
fof(9, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/realax/TREAL__INV__0', aHLu_BOOLu_CASES)).
fof(10, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X11),s(X1,X10)))=s(X1,X11),file('i/f/realax/TREAL__INV__0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
