# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(X1,h4s_pairs_uncurry(s(t_fun(X2,t_fun(X3,X1)),X5),s(t_h4s_pairs_prod(X2,X3),X4)))=s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(X2,t_fun(X3,X1)),X5),s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X3),X4))))),s(X3,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X3),X4))))),file('i/f/util_prob/PAIRED__BETA__THM', ch4s_utilu_u_probs_PAIREDu_u_BETAu_u_THM)).
fof(6, axiom,![X2]:![X3]:![X9]:?[X10]:?[X11]:s(t_h4s_pairs_prod(X2,X3),X9)=s(t_h4s_pairs_prod(X2,X3),h4s_pairs_u_2c(s(X2,X10),s(X3,X11))),file('i/f/util_prob/PAIRED__BETA__THM', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(7, axiom,![X1]:![X2]:![X3]:![X12]:![X9]:![X5]:s(X1,h4s_pairs_uncurry(s(t_fun(X2,t_fun(X3,X1)),X5),s(t_h4s_pairs_prod(X2,X3),h4s_pairs_u_2c(s(X2,X9),s(X3,X12)))))=s(X1,happ(s(t_fun(X3,X1),happ(s(t_fun(X2,t_fun(X3,X1)),X5),s(X2,X9))),s(X3,X12))),file('i/f/util_prob/PAIRED__BETA__THM', ah4s_pairs_UNCURRYu_u_DEF)).
fof(8, axiom,![X2]:![X3]:![X12]:![X9]:s(X3,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X3),h4s_pairs_u_2c(s(X2,X9),s(X3,X12)))))=s(X3,X12),file('i/f/util_prob/PAIRED__BETA__THM', ah4s_pairs_SND0)).
fof(9, axiom,![X3]:![X2]:![X12]:![X9]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X3),h4s_pairs_u_2c(s(X2,X9),s(X3,X12)))))=s(X2,X9),file('i/f/util_prob/PAIRED__BETA__THM', ah4s_pairs_FST0)).
# SZS output end CNFRefutation
