# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]: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),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))),h4s_canonicals_consu_u_varlist),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))),h4s_numrings_numu_u_canonicalu_u_sumu_u_scalar2),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_c33', ch4s_numRings_numu_u_ringu_u_thmsu_c33)).
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_c33', ah4s_numRings_numu_u_canonicalu_u_sumu_u_produ_u_def)).
fof(8, axiom,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))),h4s_numrings_numu_u_canonicalu_u_sumu_u_scalar2)=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))),h4s_canonicals_canonicalu_u_sumu_u_scalar2(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_c33', ah4s_numRings_numu_u_canonicalu_u_sumu_u_scalar2u_u_def)).
fof(12, 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_c33', ah4s_numRings_numu_u_canonicalu_u_sumu_u_mergeu_u_def)).
fof(25, axiom,![X4]:![X1]:![X32]:![X2]:![X3]:s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X4),X32))),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X2)))=s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(X4),X32))),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_canonicalu_u_sumu_u_scalar2(s(t_h4s_semiu_u_rings_semiu_u_ring(X4),X32))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X4),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_fun(t_h4s_canonicals_canonicalu_u_sum(X4),t_h4s_canonicals_canonicalu_u_sum(X4))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X4),X32))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X4),X2))))),file('i/f/numRing/num__ring__thms_c33', ah4s_canonicals_canonicalu_u_sumu_u_produ_u_defu_c1)).
# SZS output end CNFRefutation
