# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_prod),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_consu_u_monom(s(t_h4s_nums_num,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X2)))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)))),h4s_numrings_numu_u_canonicalu_u_sumu_u_scalar3),s(t_h4s_nums_num,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_prod),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X2))))),file('i/f/numRing/num__ring__thms_c32', ch4s_numRings_numu_u_ringu_u_thmsu_c32)).
fof(4, axiom,![X10]:![X1]:![X12]:![X2]:![X3]:![X4]:s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),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),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2)))=s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),happ(s(t_fun(X10,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)))),h4s_canonicals_canonicalu_u_sumu_u_scalar3(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(X10,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),file('i/f/numRing/num__ring__thms_c32', ah4s_canonicals_canonicalu_u_sumu_u_produ_u_defu_c0)).
fof(7, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_prod)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_canonicalu_u_sumu_u_prod(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_c32', ah4s_numRings_numu_u_canonicalu_u_sumu_u_produ_u_def)).
fof(8, axiom,s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)))),h4s_numrings_numu_u_canonicalu_u_sumu_u_scalar3)=s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)))),h4s_canonicals_canonicalu_u_sumu_u_scalar3(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_c32', ah4s_numRings_numu_u_canonicalu_u_sumu_u_scalar3u_u_def)).
fof(9, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_merge)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_canonicalu_u_sumu_u_merge(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_c32', ah4s_numRings_numu_u_canonicalu_u_sumu_u_mergeu_u_def)).
# SZS output end CNFRefutation
