# 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(X3,t_fun(X4,X1)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1)))),X5),s(t_fun(X2,X1),X6))),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8))),s(X4,X9)))=s(X1,happ(s(t_fun(X2,X1),X6),s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),X7),s(X3,X8))),s(X4,X9)))))=>![X10]:(![X6]:![X7]:![X8]:s(t_fun(X4,X1),happ(s(t_fun(X3,t_fun(X4,X1)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1)))),X10),s(t_fun(X2,X1),X6))),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8)))=s(t_fun(X4,X1),happ(s(t_fun(X3,t_fun(X4,X1)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1)))),X5),s(t_fun(X2,X1),X6))),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8)))=>![X11]:(![X7]:![X8]:![X9]:s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X2))),X11),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8))),s(X4,X9)))=s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),X7),s(X3,X8))),s(X4,X9)))=>![X12]:(![X7]:![X8]:s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X2))),X12),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8)))=s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X2))),X11),s(t_fun(X3,t_fun(X4,X2)),X7))),s(X3,X8)))=>![X6]:![X7]:![X13]:s(X1,happ(s(t_fun(X2,X1),X6),s(X2,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(X3,X4),X2),h4s_pairs_uncurry(s(t_fun(X3,t_fun(X4,X2)),happ(s(t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X2))),X12),s(t_fun(X3,t_fun(X4,X2)),X7))))),s(t_h4s_pairs_prod(X3,X4),X13)))))=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(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1))),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X3,t_fun(X4,X2)),t_fun(X3,t_fun(X4,X1)))),X10),s(t_fun(X2,X1),X6))),s(t_fun(X3,t_fun(X4,X2)),X7))))),s(t_h4s_pairs_prod(X3,X4),X13))))))),file('i/f/pair/LET2__RAND', ch4s_pairs_LET2u_u_RAND)).
fof(5, axiom,![X15]:![X16]:![X17]:![X18]:(![X8]:s(X16,happ(s(t_fun(X15,X16),X17),s(X15,X8)))=s(X16,happ(s(t_fun(X15,X16),X18),s(X15,X8)))=>s(t_fun(X15,X16),X17)=s(t_fun(X15,X16),X18)),file('i/f/pair/LET2__RAND', aHLu_EXT)).
fof(6, axiom,![X4]:![X3]:![X8]:![X19]:s(X4,h4s_bools_let(s(t_fun(X3,X4),X8),s(X3,X19)))=s(X4,happ(s(t_fun(X3,X4),X8),s(X3,X19))),file('i/f/pair/LET2__RAND', ah4s_bools_LETu_u_DEF)).
fof(7, axiom,![X3]:![X4]:![X8]:?[X20]:?[X21]:s(t_h4s_pairs_prod(X3,X4),X8)=s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X20),s(X4,X21))),file('i/f/pair/LET2__RAND', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(8, axiom,![X2]:![X3]:![X4]:![X9]:![X8]:![X17]:s(X2,happ(s(t_fun(t_h4s_pairs_prod(X3,X4),X2),h4s_pairs_uncurry(s(t_fun(X3,t_fun(X4,X2)),X17))),s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X8),s(X4,X9)))))=s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),X17),s(X3,X8))),s(X4,X9))),file('i/f/pair/LET2__RAND', ah4s_pairs_UNCURRYu_u_DEF)).
# SZS output end CNFRefutation
