# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_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_scalar),s(t_h4s_nums_num,X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom),file('i/f/numRing/num__ring__thms_c25', ch4s_numRings_numu_u_ringu_u_thmsu_c25)).
fof(4, axiom,![X7]:![X9]:![X1]:s(t_h4s_canonicals_canonicalu_u_sum(X7),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7)),happ(s(t_fun(X7,t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7))),h4s_canonicals_canonicalu_u_sumu_u_scalar(s(t_h4s_semiu_u_rings_semiu_u_ring(X7),X9))),s(X7,X1))),s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom),file('i/f/numRing/num__ring__thms_c25', ah4s_canonicals_canonicalu_u_sumu_u_scalaru_u_defu_c2)).
fof(7, axiom,s(t_fun(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_scalar)=s(t_fun(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_scalar(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_c25', ah4s_numRings_numu_u_canonicalu_u_sumu_u_scalaru_u_def)).
# SZS output end CNFRefutation
