# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:![X5]:![X6]:![X7]:p(s(t_bool,happ(s(t_fun(t_h4s_rings_ring(X1),t_bool),X2),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)))),happ(s(t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1))))),happ(s(t_fun(X1,t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)))))),h4s_rings_ring0),s(X1,X3))),s(X1,X4))),s(t_fun(X1,t_fun(X1,X1)),X5))),s(t_fun(X1,t_fun(X1,X1)),X6))),s(t_fun(X1,X1),X7))))))=>![X8]:p(s(t_bool,happ(s(t_fun(t_h4s_rings_ring(X1),t_bool),X2),s(t_h4s_rings_ring(X1),X8))))),file('i/f/ring/ring__induction', ch4s_rings_ringu_u_induction)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/ring/ring__induction', aHLu_TRUTH)).
fof(19, axiom,![X1]:![X21]:?[X3]:?[X4]:?[X5]:?[X6]:?[X7]:s(t_h4s_rings_ring(X1),X21)=s(t_h4s_rings_ring(X1),happ(s(t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)))),happ(s(t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1))))),happ(s(t_fun(X1,t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,X1),t_h4s_rings_ring(X1)))))),h4s_rings_ring0),s(X1,X3))),s(X1,X4))),s(t_fun(X1,t_fun(X1,X1)),X5))),s(t_fun(X1,t_fun(X1,X1)),X6))),s(t_fun(X1,X1),X7))),file('i/f/ring/ring__induction', ah4s_rings_ringu_u_nchotomy)).
fof(53, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f2)),file('i/f/ring/ring__induction', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
