# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]: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_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar),s(t_h4s_integers_int,X3))),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))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1)))))=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,X3))),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),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_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar),s(t_h4s_integers_int,X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1))))),file('i/f/integerRing/int__ring__thms_c25', ch4s_integerRings_intu_u_ringu_u_thmsu_c25)).
fof(6, axiom,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar)=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(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_c25', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalaru_u_def)).
fof(8, axiom,![X4]:![X1]:![X13]:![X2]:![X3]:s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(X4,t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(X4),X13))),s(X4,X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),happ(s(t_fun(X4,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)))),h4s_canonicals_consu_u_monom),s(X4,X3))),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(X4,t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(X4),X13))),s(X4,X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))))),file('i/f/integerRing/int__ring__thms_c25', ah4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c1)).
# SZS output end CNFRefutation
