# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_semiu_u_rings_isu_u_semiu_u_ring(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))=>![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))),s(X1,X3)))=s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2)))),file('i/f/semi_ring/mult__zero__left', ch4s_semiu_u_rings_multu_u_zerou_u_left)).
fof(12, axiom,![X1]:![X2]:(p(s(t_bool,h4s_semiu_u_rings_isu_u_semiu_u_ring(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))<=>(![X3]:![X20]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X20)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X20))),s(X1,X3)))&(![X3]:![X20]:![X21]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X20))),s(X1,X21)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X20))))),s(X1,X21)))&(![X3]:![X20]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X20)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X20))),s(X1,X3)))&(![X3]:![X20]:![X21]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X20))),s(X1,X21)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X20))))),s(X1,X21)))&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))))),s(X1,X3)))=s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2)))&![X3]:![X20]:![X21]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X20))))),s(X1,X21)))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X3))),s(X1,X21))))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2))),s(X1,X20))),s(X1,X21))))))))))))),file('i/f/semi_ring/mult__zero__left', ah4s_semiu_u_rings_isu_u_semiu_u_ringu_u_def)).
fof(14, axiom,![X1]:![X22]:![X6]:![X23]:![X15]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1))),happ(s(t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)))),happ(s(t_fun(X1,t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1))))),h4s_semiu_u_rings_semiu_u_ring0),s(X1,X15))),s(X1,X23))),s(t_fun(X1,t_fun(X1,X1)),X6))),s(t_fun(X1,t_fun(X1,X1)),X22)))))=s(X1,X15),file('i/f/semi_ring/mult__zero__left', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c0)).
fof(25, axiom,![X1]:![X28]:?[X15]:?[X23]:?[X6]:?[X22]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X28)=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1))),happ(s(t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1)))),happ(s(t_fun(X1,t_fun(X1,t_fun(t_fun(X1,t_fun(X1,X1)),t_fun(t_fun(X1,t_fun(X1,X1)),t_h4s_semiu_u_rings_semiu_u_ring(X1))))),h4s_semiu_u_rings_semiu_u_ring0),s(X1,X15))),s(X1,X23))),s(t_fun(X1,t_fun(X1,X1)),X6))),s(t_fun(X1,t_fun(X1,X1)),X22))),file('i/f/semi_ring/mult__zero__left', ah4s_semiu_u_rings_semiu_u_ringu_u_nchotomy)).
fof(72, axiom,p(s(t_bool,t)),file('i/f/semi_ring/mult__zero__left', aHLu_TRUTH)).
fof(77, axiom,![X14]:(s(t_bool,t)=s(t_bool,X14)<=>p(s(t_bool,X14))),file('i/f/semi_ring/mult__zero__left', ah4s_bools_EQu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
