# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_fun(X1,t_h4s_rings_ring(X2)),happ(s(t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2))),happ(s(t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2)))),h4s_combins_o),s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X5))))),s(t_fun(X1,t_h4s_rings_ring(X2)),happ(s(t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2))),happ(s(t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2)))),h4s_combins_o),s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X4))))),s(t_fun(X1,t_h4s_rings_ring(X2)),X3)))))=s(t_fun(X1,t_h4s_rings_ring(X2)),happ(s(t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2))),happ(s(t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_fun(X1,t_h4s_rings_ring(X2)),t_fun(X1,t_h4s_rings_ring(X2)))),h4s_combins_o),s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),happ(s(t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2)))),happ(s(t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))))),h4s_combins_o),s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X5))),s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X4))))))),s(t_fun(X1,t_h4s_rings_ring(X2)),X3))),file('i/f/ring/ring__fupdfupds__comp_c7', ch4s_rings_ringu_u_fupdfupdsu_u_compu_c7)).
fof(5, axiom,![X1]:![X2]:![X11]:![X9]:![X3]:![X4]:![X5]:s(t_fun(X11,X1),happ(s(t_fun(t_fun(X11,X2),t_fun(X11,X1)),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X11,X2),t_fun(X11,X1))),h4s_combins_o),s(t_fun(X2,X1),X5))),s(t_fun(X11,X2),happ(s(t_fun(t_fun(X11,X9),t_fun(X11,X2)),happ(s(t_fun(t_fun(X9,X2),t_fun(t_fun(X11,X9),t_fun(X11,X2))),h4s_combins_o),s(t_fun(X9,X2),X4))),s(t_fun(X11,X9),X3)))))=s(t_fun(X11,X1),happ(s(t_fun(t_fun(X11,X9),t_fun(X11,X1)),happ(s(t_fun(t_fun(X9,X1),t_fun(t_fun(X11,X9),t_fun(X11,X1))),h4s_combins_o),s(t_fun(X9,X1),happ(s(t_fun(t_fun(X9,X2),t_fun(X9,X1)),happ(s(t_fun(t_fun(X2,X1),t_fun(t_fun(X9,X2),t_fun(X9,X1))),h4s_combins_o),s(t_fun(X2,X1),X5))),s(t_fun(X9,X2),X4))))),s(t_fun(X11,X9),X3))),file('i/f/ring/ring__fupdfupds__comp_c7', ah4s_combins_ou_u_ASSOC)).
fof(12, axiom,![X2]:![X4]:![X5]:s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),happ(s(t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2))),happ(s(t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)))),h4s_combins_o),s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X5))))),s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X4)))))=s(t_fun(t_h4s_rings_ring(X2),t_h4s_rings_ring(X2)),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),happ(s(t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2)))),happ(s(t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))))),h4s_combins_o),s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X5))),s(t_fun(t_fun(X2,t_fun(X2,X2)),t_fun(X2,t_fun(X2,X2))),X4))))),file('i/f/ring/ring__fupdfupds__comp_c7', ah4s_rings_ringu_u_fupdfupdsu_u_compu_c6)).
# SZS output end CNFRefutation
