# 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_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_sp),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(t_h4s_canonicals_spolynom(t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(t_h4s_nums_num)),h4s_canonicals_spvar),s(t_h4s_quotes_index,X2)))))=s(t_h4s_nums_num,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X2),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),file('i/f/numRing/num__ring__thms_c3', ch4s_numRings_numu_u_ringu_u_thmsu_c3)).
fof(3, axiom,![X3]:![X1]:![X6]:![X2]:s(X3,happ(s(t_fun(t_h4s_canonicals_spolynom(X3),X3),happ(s(t_fun(t_h4s_quotes_varmap(X3),t_fun(t_h4s_canonicals_spolynom(X3),X3)),h4s_canonicals_interpu_u_sp(s(t_h4s_semiu_u_rings_semiu_u_ring(X3),X6))),s(t_h4s_quotes_varmap(X3),X1))),s(t_h4s_canonicals_spolynom(X3),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(X3)),h4s_canonicals_spvar),s(t_h4s_quotes_index,X2)))))=s(X3,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X2),s(t_h4s_quotes_varmap(X3),X1))),file('i/f/numRing/num__ring__thms_c3', ah4s_canonicals_interpu_u_spu_u_defu_c1)).
fof(8, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_sp)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_canonicals_interpu_u_sp(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_c3', ah4s_numRings_numu_u_interpu_u_spu_u_def)).
fof(12, axiom,![X17]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=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,X17))),file('i/f/numRing/num__ring__thms_c3', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(14, axiom,![X17]: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,X17))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X17),file('i/f/numRing/num__ring__thms_c3', ah4s_numerals_numeralu_u_distribu_c1)).
# SZS output end CNFRefutation
