# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_integers_int,X5))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_canonicals_consu_u_monom),s(t_h4s_integers_int,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_h4s_integers_int,X5))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_integers_int,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2))))),file('i/f/integerRing/int__ring__thms_c47', ch4s_integerRings_intu_u_ringu_u_thmsu_c47)).
fof(5, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_interpu_u_m(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_c47', ah4s_integerRings_intu_u_ru_u_interpu_u_mu_u_def)).
fof(8, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_ringnorms_ru_u_icsu_u_aux(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_c47', ah4s_integerRings_intu_u_ru_u_icsu_u_auxu_u_def)).
fof(13, axiom,![X6]:![X1]:![X2]:![X14]:![X3]:![X4]:![X5]:s(X6,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6),happ(s(t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,X5))),s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6))),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)))),h4s_canonicals_consu_u_monom),s(X6,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X6),X2)))))=s(X6,happ(s(t_fun(X6,X6),happ(s(t_fun(X6,t_fun(X6,X6)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X6),X14))),s(X6,X5))),s(X6,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6),happ(s(t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),X6))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6)),happ(s(t_fun(t_h4s_quotes_varmap(X6),t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X6))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(X6),X14))),s(t_h4s_quotes_varmap(X6),X1))),s(X6,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X6),X2))))),file('i/f/integerRing/int__ring__thms_c47', ah4s_ringNorms_icsu_u_auxu_u_defu_c2)).
fof(27, axiom,![X6]:![X17]:![X18]:![X11]:![X19]:![X5]:s(t_fun(X6,t_fun(X6,X6)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X6),h4s_rings_ring0(s(X6,X5),s(X6,X19),s(t_fun(X6,t_fun(X6,X6)),X11),s(t_fun(X6,t_fun(X6,X6)),X18),s(t_fun(X6,X6),X17)))))=s(t_fun(X6,t_fun(X6,X6)),X11),file('i/f/integerRing/int__ring__thms_c47', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
