# 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_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,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_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil)))=s(t_h4s_integers_int,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X1),s(t_h4s_quotes_varmap(t_h4s_integers_int),X2))),file('i/f/integerRing/int__ring__thms_c39', ch4s_integerRings_intu_u_ringu_u_thmsu_c39)).
fof(8, axiom,![X8]:![X1]:![X2]:![X14]:s(X8,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X8),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X8)),happ(s(t_fun(t_h4s_quotes_varmap(X8),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X8))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(X8),X14))),s(t_h4s_quotes_varmap(X8),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil)))=s(X8,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X1),s(t_h4s_quotes_varmap(X8),X2))),file('i/f/integerRing/int__ring__thms_c39', ah4s_ringNorms_ivlu_u_auxu_u_defu_c0)).
fof(10, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_ivlu_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_c39', ah4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def)).
# SZS output end CNFRefutation
