# 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_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,X4))),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))),h4s_canonicals_consu_u_varlist),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_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_add),s(t_h4s_integers_int,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_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_quotes_varmap(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_vl),s(t_h4s_quotes_varmap(t_h4s_integers_int),X1))),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_c46', ch4s_integerRings_intu_u_ringu_u_thmsu_c46)).
fof(5, axiom,s(t_fun(t_h4s_quotes_varmap(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_vl)=s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_vl(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_c46', ah4s_integerRings_intu_u_ru_u_interpu_u_vlu_u_def)).
fof(8, 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_c46', ah4s_integerRings_intu_u_ru_u_icsu_u_auxu_u_def)).
fof(12, axiom,![X5]:![X1]:![X2]:![X13]:![X3]:![X4]:s(X5,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5),happ(s(t_fun(X5,t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5)),happ(s(t_fun(t_h4s_quotes_varmap(X5),t_fun(X5,t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X5),X13))),s(t_h4s_quotes_varmap(X5),X1))),s(X5,X4))),s(t_h4s_canonicals_canonicalu_u_sum(X5),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2)))))=s(X5,happ(s(t_fun(X5,X5),happ(s(t_fun(X5,t_fun(X5,X5)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X5),X13))),s(X5,X4))),s(X5,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5),happ(s(t_fun(X5,t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5)),happ(s(t_fun(t_h4s_quotes_varmap(X5),t_fun(X5,t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),X5))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(X5),X13))),s(t_h4s_quotes_varmap(X5),X1))),s(X5,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X5),happ(s(t_fun(t_h4s_quotes_varmap(X5),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X5)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(X5),X13))),s(t_h4s_quotes_varmap(X5),X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2))))),file('i/f/integerRing/int__ring__thms_c46', ah4s_ringNorms_icsu_u_auxu_u_defu_c1)).
fof(26, axiom,![X5]:![X17]:![X18]:![X10]:![X19]:![X4]:s(t_fun(X5,t_fun(X5,X5)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X5),h4s_rings_ring0(s(X5,X4),s(X5,X19),s(t_fun(X5,t_fun(X5,X5)),X10),s(t_fun(X5,t_fun(X5,X5)),X18),s(t_fun(X5,X5),X17)))))=s(t_fun(X5,t_fun(X5,X5)),X10),file('i/f/integerRing/int__ring__thms_c46', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
