# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/ring/mult__zero__right', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/ring/mult__zero__right', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/ring/mult__zero__right', aHLu_BOOLu_CASES)).
fof(9, axiom,![X7]:![X10]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X7),X10))))<=>(![X11]:![X12]:s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X12)))=s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X12),s(X7,X11)))&(![X11]:![X12]:![X13]:s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X12),s(X7,X13)))))=s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X12))),s(X7,X13)))&(![X11]:![X12]:s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X12)))=s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X12),s(X7,X11)))&(![X11]:![X12]:![X13]:s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X12),s(X7,X13)))))=s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X12))),s(X7,X13)))&(![X11]:s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X7),X10))),s(X7,X11)))=s(X7,X11)&(![X11]:s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X7),X10))),s(X7,X11)))=s(X7,X11)&(![X11]:s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X7),X10),s(X7,X11)))))=s(X7,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X7),X10)))&![X11]:![X12]:![X13]:s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X12))),s(X7,X13)))=s(X7,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X7),X10),s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,X13))),s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X12),s(X7,X13))))))))))))),file('i/f/ring/mult__zero__right', ah4s_rings_isu_u_ringu_u_def)).
fof(10, conjecture,![X7]:![X10]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X7),X10))))=>![X11]:s(X7,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X7),X10),s(X7,X11),s(X7,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X7),X10)))))=s(X7,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X7),X10)))),file('i/f/ring/mult__zero__right', ch4s_rings_multu_u_zerou_u_right)).
# SZS output end CNFRefutation
