# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X1),X2))))=>![X3]:![X4]:s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4)))=s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X3)))),file('i/f/ring/plus__sym', ch4s_rings_plusu_u_sym)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/ring/plus__sym', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/ring/plus__sym', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/ring/plus__sym', aHLu_BOOLu_CASES)).
fof(5, axiom,![X1]:![X2]:(p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(X1),X2))))<=>(![X3]:![X4]:s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4)))=s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X3)))&(![X3]:![X4]:![X6]:s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X6)))))=s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4))),s(X1,X6)))&(![X3]:![X4]:s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4)))=s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X3)))&(![X3]:![X4]:![X6]:s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X6)))))=s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4))),s(X1,X6)))&(![X3]:s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X2))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X2))),s(X1,X3)))=s(X1,X3)&(![X3]:s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X1),X2),s(X1,X3)))))=s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X2)))&![X3]:![X4]:![X6]:s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X4))),s(X1,X6)))=s(X1,h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X2),s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X3),s(X1,X6))),s(X1,h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X2),s(X1,X4),s(X1,X6))))))))))))),file('i/f/ring/plus__sym', ah4s_rings_isu_u_ringu_u_def)).
# SZS output end CNFRefutation
