# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(?[X3]:p(s(t_bool,happ(s(t_fun(t_h4s_rings_ring(X1),t_bool),X2),s(t_h4s_rings_ring(X1),X3))))<=>?[X4]:?[X5]:?[X6]:?[X7]:?[X8]:p(s(t_bool,happ(s(t_fun(t_h4s_rings_ring(X1),t_bool),X2),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),h4s_combins_k(s(X1,X4))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X5))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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)),X6))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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),happ(s(t_fun(t_h4s_rings_ring(X1),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),X8))))),s(t_h4s_rings_ring(X1),h4s_bools_arb))))))))))))))),file('i/f/ring/EXISTS__ring', ch4s_rings_EXISTSu_u_ring)).
fof(25, axiom,![X1]:![X3]:?[X4]:?[X5]:?[X6]:?[X7]:?[X8]:s(t_h4s_rings_ring(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),h4s_combins_k(s(X1,X4))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(X1,X1),h4s_combins_k(s(X1,X5))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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)),X6))))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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),happ(s(t_fun(t_h4s_rings_ring(X1),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),X8))))),s(t_h4s_rings_ring(X1),h4s_bools_arb))))))))))),file('i/f/ring/EXISTS__ring', ah4s_rings_ringu_u_literalu_u_nchotomy)).
fof(28, axiom,![X1]:![X3]:![X24]:![X8]:s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X8))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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))),X24))),s(t_h4s_rings_ring(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_rmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X24))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X8))),s(t_h4s_rings_ring(X1),X3))))),file('i/f/ring/EXISTS__ring', ah4s_rings_ringu_u_fupdcanonu_c9)).
fof(29, axiom,![X1]:![X3]:![X24]:![X8]:s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X8))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),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))),X24))),s(t_h4s_rings_ring(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_rpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),X24))),s(t_h4s_rings_ring(X1),happ(s(t_fun(t_h4s_rings_ring(X1),t_h4s_rings_ring(X1)),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(X1,X1),t_fun(X1,X1)),X8))),s(t_h4s_rings_ring(X1),X3))))),file('i/f/ring/EXISTS__ring', ah4s_rings_ringu_u_fupdcanonu_c8)).
# SZS output end CNFRefutation
