# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:![X9]:![X10]:![X11]:(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X11))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X9))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),h4s_combins_k(s(t_fun(X1,t_fun(X1,X1)),X4))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),h4s_combins_k(s(t_fun(X1,t_fun(X1,X1)),X7))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),h4s_combins_k(s(t_fun(X1,X1),X5))),s(t_h4s_rings_ring(X1),h4s_bools_arb)))))))))))=s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X10))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X8))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),h4s_combins_k(s(t_fun(X1,t_fun(X1,X1)),X3))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),h4s_combins_k(s(t_fun(X1,t_fun(X1,X1)),X6))),s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),h4s_combins_k(s(t_fun(X1,X1),X2))),s(t_h4s_rings_ring(X1),h4s_bools_arb)))))))))))<=>(s(X1,X11)=s(X1,X10)&(s(X1,X9)=s(X1,X8)&(s(t_fun(X1,t_fun(X1,X1)),X4)=s(t_fun(X1,t_fun(X1,X1)),X3)&(s(t_fun(X1,t_fun(X1,X1)),X7)=s(t_fun(X1,t_fun(X1,X1)),X6)&s(t_fun(X1,X1),X5)=s(t_fun(X1,X1),X2)))))),file('i/f/ring/ring__literal__11', ch4s_rings_ringu_u_literalu_u_11)).
fof(3, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c12)).
fof(4, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c13)).
fof(5, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c16)).
fof(6, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c17)).
fof(7, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c8)).
fof(8, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c9)).
fof(9, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c14)).
fof(10, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c18)).
fof(11, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X17))))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c22)).
fof(12, axiom,![X1]:![X17]:![X14]:s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c4)).
fof(13, axiom,![X1]:![X17]:![X14]:s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(X1,happ(s(t_fun(X1,X1),X14),s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X17))))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c20)).
fof(14, axiom,![X1]:![X17]:![X14]:s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),X14),s(t_h4s_rings_ring(X1),X17)))))=s(X1,happ(s(t_fun(X1,X1),X14),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X17))))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c21)).
fof(15, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X17))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c19)).
fof(16, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,t_fun(X1,X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X14),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X17))))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c23)).
fof(17, axiom,![X1]:![X17]:![X14]:s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X14),s(t_h4s_rings_ring(X1),X17)))))=s(t_fun(X1,X1),happ(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X14),s(t_fun(X1,X1),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X17))))),file('i/f/ring/ring__literal__11', ah4s_rings_ringu_u_accfupdsu_c24)).
fof(18, axiom,![X18]:![X1]:![X19]:![X16]:s(X1,happ(s(t_fun(X18,X1),h4s_combins_k(s(X1,X16))),s(X18,X19)))=s(X1,X16),file('i/f/ring/ring__literal__11', ah4s_combins_Ku_u_THM)).
# SZS output end CNFRefutation
