# 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_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_popp(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)),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_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg),s(t_h4s_integers_int,h4s_integers_intu_u_1))))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),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_c55', ch4s_integerRings_intu_u_ringu_u_thmsu_c55)).
fof(4, axiom,![X7]:![X9]:![X1]:s(t_h4s_canonicals_canonicalu_u_sum(X7),happ(s(t_fun(t_h4s_ringNorms_polynom(X7),t_h4s_canonicals_canonicalu_u_sum(X7)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X7),X9))),s(t_h4s_ringNorms_polynom(X7),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(X7),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(t_h4s_lists_list(t_h4s_quotes_index),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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(X7),X9))),s(X7,happ(s(t_fun(X7,X7),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X7),X9))),s(X7,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X7),X9))))))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(X7),happ(s(t_fun(t_h4s_ringNorms_polynom(X7),t_h4s_canonicals_canonicalu_u_sum(X7)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X7),X9))),s(t_h4s_ringNorms_polynom(X7),X1))))),file('i/f/integerRing/int__ring__thms_c55', ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c4)).
fof(5, 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_c55', ah4s_integerRings_intu_u_polynomu_u_normalizeu_u_def)).
fof(7, axiom,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_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3)=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_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(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_c55', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def)).
fof(11, axiom,![X7]:![X12]:![X13]:![X4]:![X14]:![X15]:s(X7,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X7),h4s_rings_ring0(s(X7,X15),s(X7,X14),s(t_fun(X7,t_fun(X7,X7)),X4),s(t_fun(X7,t_fun(X7,X7)),X13),s(t_fun(X7,X7),X12)))))=s(X7,X14),file('i/f/integerRing/int__ring__thms_c55', ah4s_rings_ringu_u_accessorsu_c1)).
fof(12, axiom,![X7]:![X12]:![X13]:![X4]:![X14]:![X15]:s(t_fun(X7,X7),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(X7),h4s_rings_ring0(s(X7,X15),s(X7,X14),s(t_fun(X7,t_fun(X7,X7)),X4),s(t_fun(X7,t_fun(X7,X7)),X13),s(t_fun(X7,X7),X12)))))=s(t_fun(X7,X7),X12),file('i/f/integerRing/int__ring__thms_c55', ah4s_rings_ringu_u_accessorsu_c4)).
# SZS output end CNFRefutation
