# 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(32, axiom,![X4]:![X3]:![X8]:![X16]:s(X4,h4s_bools_let(s(t_fun(X3,X4),X16),s(X3,X8)))=s(X4,happ(s(t_fun(X3,X4),X16),s(X3,X8))),file('i/f/pair/LET2__RAND', ah4s_bools_LETu_u_THM)).
fof(39, axiom,![X4]:![X3]:![X9]:![X8]:s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X8),s(X4,X9)))))=s(X3,X8),file('i/f/pair/LET2__RAND', ah4s_pairs_FST0)).
fof(40, axiom,![X3]:![X4]:![X9]:![X8]:s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X8),s(X4,X9)))))=s(X4,X9),file('i/f/pair/LET2__RAND', ah4s_pairs_SND0)).
fof(42, axiom,![X2]:![X3]:![X4]:![X27]:![X16]:s(X2,happ(s(t_fun(t_h4s_pairs_prod(X3,X4),X2),h4s_pairs_uncurry(s(t_fun(X3,t_fun(X4,X2)),X16))),s(t_h4s_pairs_prod(X3,X4),X27)))=s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),X16),s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,X4),X27))))),s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X4),X27))))),file('i/f/pair/LET2__RAND', ah4s_pairs_UNCURRY0)).
fof(46, axiom,![X3]:![X4]:![X8]:?[X28]:?[X30]:s(t_h4s_pairs_prod(X3,X4),X8)=s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X28),s(X4,X30))),file('i/f/pair/LET2__RAND', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(71, axiom,![X2]:![X3]:![X4]:![X9]:![X8]:![X16]:s(X2,happ(s(t_fun(X3,X2),h4s_combins_c(s(t_fun(X3,t_fun(X4,X2)),X16),s(X4,X8))),s(X3,X9)))=s(X2,happ(s(t_fun(X4,X2),happ(s(t_fun(X3,t_fun(X4,X2)),X16),s(X3,X9))),s(X4,X8))),file('i/f/pair/LET2__RAND', ah4s_combins_Cu_u_THM)).
# SZS output end CNFRefutation
