# 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_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify),s(t_h4s_ringNorms_polynom(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)),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_simplify),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),X1))))),file('i/f/integerRing/int__ring__thms_c56', ch4s_integerRings_intu_u_ringu_u_thmsu_c56)).
fof(13, axiom,s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize)=s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_normalize(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_c56', ah4s_integerRings_intu_u_polynomu_u_normalizeu_u_def)).
fof(15, axiom,s(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_simplify)=s(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_simplify(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_c56', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_simplifyu_u_def)).
fof(30, axiom,s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify)=s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_simplify(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_c56', ah4s_integerRings_intu_u_polynomu_u_simplifyu_u_def)).
fof(58, axiom,![X6]:![X1]:![X31]:s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_ringNorms_polynom(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),h4s_ringnorms_polynomu_u_simplify(s(t_h4s_rings_ring(X6),X31))),s(t_h4s_ringNorms_polynom(X6),X1)))=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)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X6),X31))),s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_ringNorms_polynom(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X6),X31))),s(t_h4s_ringNorms_polynom(X6),X1))))),file('i/f/integerRing/int__ring__thms_c56', ah4s_ringNorms_polynomu_u_simplifyu_u_def)).
# SZS output end CNFRefutation
