# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),happ(s(t_fun(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1))),happ(s(t_fun(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),t_fun(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)))),h4s_combins_o),s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X3))))),s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X2)))))=s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),happ(s(t_fun(t_fun(X1,X1),t_fun(t_fun(X1,X1),t_fun(X1,X1))),h4s_combins_o),s(t_fun(X1,X1),X3))),s(t_fun(X1,X1),X2))))),file('i/f/ring/ring__fupdfupds__comp_c0', ch4s_rings_ringu_u_fupdfupdsu_u_compu_c0)).
fof(4, axiom,![X1]:![X9]:![X2]:![X3]:s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X3))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X2))),s(t_h4s_rings_ring(X1),X9)))))=s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),happ(s(t_fun(t_fun(X1,X1),t_fun(t_fun(X1,X1),t_fun(X1,X1))),h4s_combins_o),s(t_fun(X1,X1),X3))),s(t_fun(X1,X1),X2))))),s(t_h4s_rings_ring(X1),X9))),file('i/f/ring/ring__fupdfupds__comp_c0', ah4s_rings_ringu_u_fupdfupdsu_c0)).
fof(5, axiom,![X10]:![X11]:![X3]:![X2]:(![X12]:s(X11,happ(s(t_fun(X10,X11),X3),s(X10,X12)))=s(X11,happ(s(t_fun(X10,X11),X2),s(X10,X12)))=>s(t_fun(X10,X11),X3)=s(t_fun(X10,X11),X2)),file('i/f/ring/ring__fupdfupds__comp_c0', aHLu_EXT)).
fof(8, axiom,![X13]:![X1]:![X16]:![X12]:![X2]:![X3]:s(X13,happ(s(t_fun(X16,X13),happ(s(t_fun(t_fun(X16,X1),t_fun(X16,X13)),happ(s(t_fun(t_fun(X1,X13),t_fun(t_fun(X16,X1),t_fun(X16,X13))),h4s_combins_o),s(t_fun(X1,X13),X3))),s(t_fun(X16,X1),X2))),s(X16,X12)))=s(X13,happ(s(t_fun(X1,X13),X3),s(X1,happ(s(t_fun(X16,X1),X2),s(X16,X12))))),file('i/f/ring/ring__fupdfupds__comp_c0', ah4s_combins_ou_u_THM)).
# SZS output end CNFRefutation
