# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(![X6]:![X7]:![X8]:![X9]:s(X1,happ(s(t_fun(X4,X1),happ(s(t_fun(X2,t_fun(X4,X1)),happ(s(t_fun(X3,t_fun(X2,t_fun(X4,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X2,t_fun(X4,X1)))),X5),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X3,X7))),s(X2,X8))),s(X4,X9)))=s(X1,happ(s(t_fun(X2,X1),happ(s(t_fun(X4,t_fun(X2,X1)),happ(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6),s(X3,X7))),s(X4,X9))),s(X2,X8)))=>![X10]:(![X6]:![X8]:![X7]:s(t_fun(X4,X1),happ(s(t_fun(X3,t_fun(X4,X1)),happ(s(t_fun(X2,t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X2,t_fun(X3,t_fun(X4,X1)))),X10),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X2,X8))),s(X3,X7)))=s(t_fun(X4,X1),happ(s(t_fun(X2,t_fun(X4,X1)),happ(s(t_fun(X3,t_fun(X2,t_fun(X4,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X2,t_fun(X4,X1)))),X5),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X3,X7))),s(X2,X8)))=>![X11]:(![X6]:![X7]:![X9]:s(t_fun(X2,X1),happ(s(t_fun(X4,t_fun(X2,X1)),happ(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X4,t_fun(X2,X1)))),X11),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X3,X7))),s(X4,X9)))=s(t_fun(X2,X1),happ(s(t_fun(X4,t_fun(X2,X1)),happ(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6),s(X3,X7))),s(X4,X9)))=>![X12]:(![X6]:![X7]:s(t_fun(X4,t_fun(X2,X1)),happ(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X4,t_fun(X2,X1)))),X12),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X3,X7)))=s(t_fun(X4,t_fun(X2,X1)),happ(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X4,t_fun(X2,X1)))),X11),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X3,X7)))=>![X8]:![X6]:![X13]:s(X1,happ(s(t_fun(X2,X1),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(X3,X4),t_fun(X2,X1)),h4s_pairs_uncurry(s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X3,t_fun(X4,t_fun(X2,X1)))),X12),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))))),s(t_h4s_pairs_prod(X3,X4),X13))),s(X2,X8)))=s(X1,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(X3,X4),X1),h4s_pairs_uncurry(s(t_fun(X3,t_fun(X4,X1)),happ(s(t_fun(X2,t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X3,t_fun(X4,t_fun(X2,X1))),t_fun(X2,t_fun(X3,t_fun(X4,X1)))),X10),s(t_fun(X3,t_fun(X4,t_fun(X2,X1))),X6))),s(X2,X8))))),s(t_h4s_pairs_prod(X3,X4),X13))))))),file('i/f/pair/LET2__RATOR', ch4s_pairs_LET2u_u_RATOR)).
fof(23, axiom,![X2]:![X18]:![X7]:![X30]:s(X2,h4s_bools_let(s(t_fun(X18,X2),X7),s(X18,X30)))=s(X2,happ(s(t_fun(X18,X2),X7),s(X18,X30))),file('i/f/pair/LET2__RATOR', ah4s_bools_LETu_u_DEF)).
fof(32, axiom,![X18]:![X2]:![X7]:?[X32]:?[X33]:s(t_h4s_pairs_prod(X18,X2),X7)=s(t_h4s_pairs_prod(X18,X2),h4s_pairs_u_2c(s(X18,X32),s(X2,X33))),file('i/f/pair/LET2__RATOR', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(33, axiom,![X18]:![X2]:![X9]:![X7]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X18,X2),h4s_pairs_u_2c(s(X18,X7),s(X2,X9)))))=s(X2,X9),file('i/f/pair/LET2__RATOR', ah4s_pairs_SND0)).
fof(34, axiom,![X2]:![X18]:![X9]:![X7]:s(X18,h4s_pairs_fst(s(t_h4s_pairs_prod(X18,X2),h4s_pairs_u_2c(s(X18,X7),s(X2,X9)))))=s(X18,X7),file('i/f/pair/LET2__RATOR', ah4s_pairs_FST0)).
fof(35, axiom,![X1]:![X18]:![X2]:![X25]:![X16]:s(X1,happ(s(t_fun(t_h4s_pairs_prod(X18,X2),X1),h4s_pairs_uncurry(s(t_fun(X18,t_fun(X2,X1)),X16))),s(t_h4s_pairs_prod(X18,X2),X25)))=s(X1,happ(s(t_fun(X2,X1),happ(s(t_fun(X18,t_fun(X2,X1)),X16),s(X18,h4s_pairs_fst(s(t_h4s_pairs_prod(X18,X2),X25))))),s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X18,X2),X25))))),file('i/f/pair/LET2__RATOR', ah4s_pairs_UNCURRY0)).
# SZS output end CNFRefutation
