# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(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_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(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),X2)))))=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),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_nums_num)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_numrings_numu_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),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_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_vl),s(t_h4s_quotes_varmap(t_h4s_nums_num),X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),X2))),file('i/f/numRing/num__ring__thms_c48', ch4s_numRings_numu_u_ringu_u_thmsu_c48)).
fof(5, axiom,![X9]:![X1]:![X2]:![X11]:![X3]:s(X9,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),X9),happ(s(t_fun(t_h4s_quotes_varmap(X9),t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),X9)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X11))),s(t_h4s_quotes_varmap(X9),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X9),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X9),X2)))))=s(X9,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),X9),happ(s(t_fun(X9,t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),X9)),happ(s(t_fun(t_h4s_quotes_varmap(X9),t_fun(X9,t_fun(t_h4s_canonicals_canonicalu_u_sum(X9),X9))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X11))),s(t_h4s_quotes_varmap(X9),X1))),s(X9,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9),happ(s(t_fun(t_h4s_quotes_varmap(X9),t_fun(t_h4s_lists_list(t_h4s_quotes_index),X9)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(X9),X11))),s(t_h4s_quotes_varmap(X9),X1))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))))),s(t_h4s_canonicals_canonicalu_u_sum(X9),X2))),file('i/f/numRing/num__ring__thms_c48', ah4s_canonicals_interpu_u_csu_u_defu_c1)).
fof(7, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_cs)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num)),h4s_canonicals_interpu_u_cs(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_c48', ah4s_numRings_numu_u_interpu_u_csu_u_def)).
fof(8, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_numrings_numu_u_icsu_u_aux)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_nums_num))),h4s_canonicals_icsu_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_c48', ah4s_numRings_numu_u_icsu_u_auxu_u_def)).
fof(10, axiom,s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_vl)=s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_nums_num)),h4s_canonicals_interpu_u_vl(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_c48', ah4s_numRings_numu_u_interpu_u_vlu_u_def)).
# SZS output end CNFRefutation
