# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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_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,X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom),file('i/f/integerRing/int__ring__thms_c26', ch4s_integerRings_intu_u_ringu_u_thmsu_c26)).
fof(4, axiom,![X7]:![X9]:![X1]:s(t_h4s_canonicals_canonicalu_u_sum(X7),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7)),happ(s(t_fun(X7,t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(X7),X9))),s(X7,X1))),s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom),file('i/f/integerRing/int__ring__thms_c26', ah4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c2)).
fof(7, 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_c26', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalaru_u_def)).
# SZS output end CNFRefutation
