# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X1),X2))))=>![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X2)))))=s(X1,X3)),file('i/f/ring/mult__one__right', ch4s_rings_multu_u_oneu_u_right)).
fof(10, axiom,![X1]:![X2]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X1),X2))))<=>(![X3]:![X11]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X11)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X11))),s(X1,X3)))&(![X3]:![X11]:![X12]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X11))),s(X1,X12)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X11))))),s(X1,X12)))&(![X3]:![X11]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X11)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X11))),s(X1,X3)))&(![X3]:![X11]:![X12]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X11))),s(X1,X12)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X11))))),s(X1,X12)))&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X2))))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X2))))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X2),s(X1,X3)))))=s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X2)))&![X3]:![X11]:![X12]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X11))))),s(X1,X12)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X3))),s(X1,X12))))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2))),s(X1,X11))),s(X1,X12))))))))))))),file('i/f/ring/mult__one__right', ah4s_rings_isu_u_ringu_u_def)).
# SZS output end CNFRefutation
