# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X2))))),file('i/f/integerRing/int__ring__thms_c6', ch4s_integerRings_intu_u_ringu_u_thmsu_c6)).
fof(4, axiom,![X8]:![X1]:![X10]:![X2]:s(X8,happ(s(t_fun(t_h4s_ringNorms_polynom(X8),X8),happ(s(t_fun(t_h4s_quotes_varmap(X8),t_fun(t_h4s_ringNorms_polynom(X8),X8)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_quotes_varmap(X8),X1))),s(t_h4s_ringNorms_polynom(X8),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(X8),X2)))))=s(X8,happ(s(t_fun(X8,X8),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X8),X10))),s(X8,happ(s(t_fun(t_h4s_ringNorms_polynom(X8),X8),happ(s(t_fun(t_h4s_quotes_varmap(X8),t_fun(t_h4s_ringNorms_polynom(X8),X8)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(X8),X10))),s(t_h4s_quotes_varmap(X8),X1))),s(t_h4s_ringNorms_polynom(X8),X2))))),file('i/f/integerRing/int__ring__thms_c6', ah4s_ringNorms_interpu_u_pu_u_defu_c4)).
fof(5, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c6', ah4s_integerRings_intu_u_interpu_u_pu_u_def)).
fof(8, axiom,![X8]:![X11]:![X12]:![X5]:![X13]:![X14]:s(t_fun(X8,X8),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X8),h4s_rings_ring0(s(X8,X14),s(X8,X13),s(t_fun(X8,t_fun(X8,X8)),X5),s(t_fun(X8,t_fun(X8,X8)),X12),s(t_fun(X8,X8),X11)))))=s(t_fun(X8,X8),X11),file('i/f/integerRing/int__ring__thms_c6', ah4s_rings_ringu_u_accessorsu_c4)).
# SZS output end CNFRefutation
