# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]: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),X3))),s(t_h4s_quotes_index,X2))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X4)))))=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_2a),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),X3))))),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),X3))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))))),file('i/f/numRing/num__ring__thms_c39', ch4s_numRings_numu_u_ringu_u_thmsu_c39)).
fof(7, axiom,![X10]:![X12]:![X8]:![X13]:![X14]:s(t_fun(X10,t_fun(X10,X10)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),h4s_semiu_u_rings_semiu_u_ring0(s(X10,X14),s(X10,X13),s(t_fun(X10,t_fun(X10,X10)),X8),s(t_fun(X10,t_fun(X10,X10)),X12)))))=s(t_fun(X10,t_fun(X10,X10)),X12),file('i/f/numRing/num__ring__thms_c39', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c3)).
fof(8, axiom,![X10]:![X1]:![X2]:![X3]:![X4]:![X15]:s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10))),h4s_canonicals_ivlu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X15))),s(t_h4s_quotes_varmap(X10),X3))),s(t_h4s_quotes_index,X2))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,X1),s(t_h4s_lists_list(t_h4s_quotes_index),X4)))))=s(X10,happ(s(t_fun(X10,X10),happ(s(t_fun(X10,t_fun(X10,X10)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X15))),s(X10,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,X2),s(t_h4s_quotes_varmap(X10),X3))))),s(X10,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10)),happ(s(t_fun(t_h4s_quotes_varmap(X10),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),X10))),h4s_canonicals_ivlu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X10),X15))),s(t_h4s_quotes_varmap(X10),X3))),s(t_h4s_quotes_index,X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))))),file('i/f/numRing/num__ring__thms_c39', ah4s_canonicals_ivlu_u_auxu_u_defu_c1)).
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_c39', ah4s_numRings_numu_u_ivlu_u_auxu_u_def)).
# SZS output end CNFRefutation
