# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(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)))=s(t_bool,h4s_realaxs_trealu_u_eq(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/TREAL__EQ__SYM', ch4s_realaxs_TREALu_u_EQu_u_SYM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/realax/TREAL__EQ__SYM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/realax/TREAL__EQ__SYM', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/realax/TREAL__EQ__SYM', aHLu_BOOLu_CASES)).
fof(6, axiom,![X5]:![X6]:![X7]:![X8]:(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,X8),s(t_h4s_hreals_hreal,X6))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,X7),s(t_h4s_hreals_hreal,X5))))))<=>s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X8),s(t_h4s_hreals_hreal,X5)))=s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,X7),s(t_h4s_hreals_hreal,X6)))),file('i/f/realax/TREAL__EQ__SYM', ah4s_realaxs_trealu_u_eq0)).
fof(7, axiom,![X4]:![X9]:![X2]:s(t_h4s_pairs_prod(X4,X9),h4s_pairs_u_2c(s(X4,h4s_pairs_fst(s(t_h4s_pairs_prod(X4,X9),X2))),s(X9,h4s_pairs_snd(s(t_h4s_pairs_prod(X4,X9),X2)))))=s(t_h4s_pairs_prod(X4,X9),X2),file('i/f/realax/TREAL__EQ__SYM', ah4s_pairs_PAIR)).
# SZS output end CNFRefutation
