# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:![X5]:![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_bool),X2),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_ring(X1))))),h4s_semiu_u_rings_semiu_u_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))))))=>![X7]:p(s(t_bool,happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_bool),X2),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X7))))),file('i/f/semi_ring/semi__ring__induction', ch4s_semiu_u_rings_semiu_u_ringu_u_induction)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/semi_ring/semi__ring__induction', aHLu_TRUTH)).
fof(32, axiom,![X1]:![X24]:?[X3]:?[X4]:?[X5]:?[X6]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X24)=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_ring(X1))))),h4s_semiu_u_rings_semiu_u_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))),file('i/f/semi_ring/semi__ring__induction', ah4s_semiu_u_rings_semiu_u_ringu_u_nchotomy)).
fof(75, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f1)),file('i/f/semi_ring/semi__ring__induction', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
