# 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_semiu_u_rings_semiu_u_ring(X1),t_bool),X2),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X3))))<=>![X4]:![X5]:![X6]:![X7]:p(s(t_bool,happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_bool),X2),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X4))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X5))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),h4s_bools_arb))))))))))))),file('i/f/semi_ring/FORALL__semi__ring', ch4s_semiu_u_rings_FORALLu_u_semiu_u_ring)).
fof(31, axiom,![X1]:![X3]:?[X4]:?[X5]:?[X6]:?[X7]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X3)=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X4))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X5))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),h4s_bools_arb))))))))),file('i/f/semi_ring/FORALL__semi__ring', ah4s_semiu_u_rings_semiu_u_ringu_u_literalu_u_nchotomy)).
fof(32, axiom,![X1]:![X3]:![X6]:![X7]:![X4]:![X5]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X4))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X5))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),X3)))))))))=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X4))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_combins_k),s(X1,X5))))),s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(X1),t_h4s_semiu_u_rings_semiu_u_ring(X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_u_fupd(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(X1,t_fun(X1,X1))),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),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_semiu_u_rings_semiu_u_ring(X1),h4s_bools_arb))))))))),file('i/f/semi_ring/FORALL__semi__ring', ah4s_semiu_u_rings_semiu_u_ringu_u_updatesu_u_equ_u_literal)).
# SZS output end CNFRefutation
