# 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]:![X4]:![X5]:s(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_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X3),s(X1,X4))),s(X1,X5)))=s(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_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X3),s(X1,X5))),s(X1,X4)))),file('i/f/semi_ring/plus__permute', ch4s_semiu_u_rings_plusu_u_permute)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/semi_ring/plus__permute', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/semi_ring/plus__permute', aHLu_FALSITY)).
fof(4, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/semi_ring/plus__permute', aHLu_BOOLu_CASES)).
fof(21, axiom,![X6]:(s(t_bool,X6)=s(t_bool,f)<=>~(p(s(t_bool,X6)))),file('i/f/semi_ring/plus__permute', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(34, 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))))<=>(![X4]:![X3]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X3)))=s(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,X4)))&(![X4]:![X3]:![X5]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(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,X5)))))=s(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_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X3))),s(X1,X5)))&(![X4]:![X3]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X3)))=s(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,X4)))&(![X4]:![X3]:![X5]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(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,X5)))))=s(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_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X3))),s(X1,X5)))&(![X4]:s(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,X4)))=s(X1,X4)&(![X4]:s(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,X4)))=s(X1,X4)&(![X4]:s(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,X4)))=s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2)))&![X4]:![X3]:![X5]:s(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_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X3))),s(X1,X5)))=s(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_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X2),s(X1,X4),s(X1,X5))),s(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,X5))))))))))))),file('i/f/semi_ring/plus__permute', ah4s_semiu_u_rings_isu_u_semiu_u_ringu_u_def)).
# SZS output end CNFRefutation
