# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),X3),s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X5))))))=>![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),X3),s(t_h4s_pairs_prod(X1,X2),X6))))),file('i/f/pair/pair__induction', ch4s_pairs_pairu_u_induction)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pair/pair__induction', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pair/pair__induction', aHLu_FALSITY)).
fof(7, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/pair/pair__induction', aHLu_BOOLu_CASES)).
fof(9, axiom,![X1]:![X2]:![X14]:?[X15]:?[X16]:s(t_h4s_pairs_prod(X1,X2),X14)=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X15),s(X2,X16))),file('i/f/pair/pair__induction', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
# SZS output end CNFRefutation
