# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]: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),X3))),s(t_h4s_quotes_index,X2))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X4)))))=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_mul),s(t_h4s_integers_int,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X2),s(t_h4s_quotes_varmap(t_h4s_integers_int),X3))))),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),X3))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))))),file('i/f/integerRing/int__ring__thms_c40', ch4s_integerRings_intu_u_ringu_u_thmsu_c40)).
fof(7, axiom,![X10]:![X12]:![X13]:![X8]:![X14]:![X15]:s(t_fun(X10,t_fun(X10,X10)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X10),h4s_rings_ring0(s(X10,X15),s(X10,X14),s(t_fun(X10,t_fun(X10,X10)),X8),s(t_fun(X10,t_fun(X10,X10)),X13),s(t_fun(X10,X10),X12)))))=s(t_fun(X10,t_fun(X10,X10)),X13),file('i/f/integerRing/int__ring__thms_c40', ah4s_rings_ringu_u_accessorsu_c3)).
fof(8, axiom,![X10]:![X1]:![X2]:![X3]:![X4]:![X16]:s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(X10),X16))),s(t_h4s_quotes_varmap(X10),X3))),s(t_h4s_quotes_index,X2))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X4)))))=s(X10,happ(s(t_fun(X10,X10),happ(s(t_fun(X10,t_fun(X10,X10)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X10),X16))),s(X10,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X2),s(t_h4s_quotes_varmap(X10),X3))))),s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(X10),X16))),s(t_h4s_quotes_varmap(X10),X3))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))))),file('i/f/integerRing/int__ring__thms_c40', ah4s_ringNorms_ivlu_u_auxu_u_defu_c1)).
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_c40', ah4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def)).
# SZS output end CNFRefutation
