# 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_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),X2))),s(t_h4s_integers_int,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X3)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_h4s_integers_int,X4))),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_quotes_index,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_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),file('i/f/integerRing/int__ring__thms_c44', ch4s_integerRings_intu_u_ringu_u_thmsu_c44)).
fof(5, axiom,![X9]:![X1]:![X2]:![X3]:![X11]:![X4]:s(X9,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9),happ(s(t_fun(X9,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9)),happ(s(t_fun(t_h4s_quotes_varmap(X9),t_fun(X9,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(X9),X11))),s(t_h4s_quotes_varmap(X9),X2))),s(X9,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X3)))))=s(X9,happ(s(t_fun(X9,X9),happ(s(t_fun(X9,t_fun(X9,X9)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X9),X11))),s(X9,X4))),s(X9,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9)),happ(s(t_fun(t_h4s_quotes_varmap(X9),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(X9),X11))),s(t_h4s_quotes_varmap(X9),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),file('i/f/integerRing/int__ring__thms_c44', ah4s_ringNorms_interpu_u_mu_u_defu_c1)).
fof(6, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_ivlu_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_c44', ah4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def)).
fof(7, 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_c44', ah4s_integerRings_intu_u_ru_u_interpu_u_mu_u_def)).
fof(8, axiom,![X9]:![X12]:![X13]:![X7]:![X14]:![X15]:s(t_fun(X9,t_fun(X9,X9)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X9),h4s_rings_ring0(s(X9,X15),s(X9,X14),s(t_fun(X9,t_fun(X9,X9)),X7),s(t_fun(X9,t_fun(X9,X9)),X13),s(t_fun(X9,X9),X12)))))=s(t_fun(X9,t_fun(X9,X9)),X13),file('i/f/integerRing/int__ring__thms_c44', ah4s_rings_ringu_u_accessorsu_c3)).
# SZS output end CNFRefutation
