# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_numrings_numu_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_nums_num),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil)))=s(t_h4s_nums_num,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X1),s(t_h4s_quotes_varmap(t_h4s_nums_num),X2))),file('i/f/numRing/num__ring__thms_c38', ch4s_numRings_numu_u_ringu_u_thmsu_c38)).
fof(8, axiom,![X3]:![X1]:![X2]:![X18]:s(X3,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X3),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X3)),happ(s(t_fun(t_h4s_quotes_varmap(X3),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X3))),h4s_canonicals_ivlu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X3),X18))),s(t_h4s_quotes_varmap(X3),X2))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil)))=s(X3,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X1),s(t_h4s_quotes_varmap(X3),X2))),file('i/f/numRing/num__ring__thms_c38', ah4s_canonicals_ivlu_u_auxu_u_defu_c0)).
fof(10, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_numrings_numu_u_ivlu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num))),h4s_canonicals_ivlu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a))))),file('i/f/numRing/num__ring__thms_c38', ah4s_numRings_numu_u_ivlu_u_auxu_u_def)).
fof(30, axiom,![X34]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X34)))=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,X34))),file('i/f/numRing/num__ring__thms_c38', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(31, axiom,![X34]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,X34))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X34),file('i/f/numRing/num__ring__thms_c38', ah4s_numerals_numeralu_u_distribu_c1)).
# SZS output end CNFRefutation
