# 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_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),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_integers_int,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_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),s(t_h4s_integers_int,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2))),file('i/f/integerRing/int__ring__thms_c50', ch4s_integerRings_intu_u_ringu_u_thmsu_c50)).
fof(6, axiom,![X10]:![X1]:![X2]:![X12]:![X3]:![X4]:s(X10,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(X10),X12))),s(t_h4s_quotes_varmap(X10),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_monom(s(X10,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2)))))=s(X10,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10),happ(s(t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(X10,t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),X10))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X10),X12))),s(t_h4s_quotes_varmap(X10),X1))),s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(X10,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(X10,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(X10),X12))),s(t_h4s_quotes_varmap(X10),X1))),s(X10,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))),file('i/f/integerRing/int__ring__thms_c50', ah4s_ringNorms_interpu_u_csu_u_defu_c2)).
fof(7, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_ringnorms_ru_u_icsu_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_c50', ah4s_integerRings_intu_u_ru_u_icsu_u_auxu_u_def)).
fof(8, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_cs(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_c50', ah4s_integerRings_intu_u_ru_u_interpu_u_csu_u_def)).
fof(10, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_interpu_u_m(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_c50', ah4s_integerRings_intu_u_ru_u_interpu_u_mu_u_def)).
# SZS output end CNFRefutation
