# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,t_bool),X4),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X2)))))=>s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),h4s_decodes_dec2enc(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(X1,X2))),s(t_h4s_lists_list(t_bool),X3)))))=s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_lists_list(t_bool),X3)))))),file('i/f/Decode/decode__dec2enc__append', ch4s_Decodes_decodeu_u_dec2encu_u_append)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/Decode/decode__dec2enc__append', aHLu_TRUTH)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/Decode/decode__dec2enc__append', aHLu_BOOLu_CASES)).
fof(13, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)<=>p(s(t_bool,X3))),file('i/f/Decode/decode__dec2enc__append', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(16, axiom,![X1]:![X4]:![X5]:(p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,t_bool),X4),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5))))<=>![X2]:?[X16]:((p(s(t_bool,X16))<=>?[X17]:![X18]:![X19]:(s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(t_h4s_lists_list(t_bool),X18)))=s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_lists_list(t_bool),X19)))))<=>s(t_h4s_lists_list(t_bool),X18)=s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),X17),s(t_h4s_lists_list(t_bool),X19)))))&?[X20]:((p(s(t_bool,X20))<=>![X17]:![X18]:~(s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(t_h4s_lists_list(t_bool),X17)))=s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_lists_list(t_bool),X18)))))))&p(s(t_bool,h4s_bools_cond(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X2))),s(t_bool,X16),s(t_bool,X20))))))),file('i/f/Decode/decode__dec2enc__append', ah4s_Decodes_wfu_u_decoderu_u_def)).
fof(17, axiom,![X1]:![X2]:![X4]:![X5]:((p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,t_bool),X4),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X2)))))=>s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(t_h4s_lists_list(t_bool),h4s_decodes_dec2enc(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X5),s(X1,X2)))))=s(t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(X1,X2),s(t_h4s_lists_list(t_bool),h4s_lists_nil)))))),file('i/f/Decode/decode__dec2enc__append', ah4s_Decodes_decodeu_u_dec2enc)).
fof(18, axiom,![X1]:![X21]:s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X21),s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_h4s_lists_list(X1),X21),file('i/f/Decode/decode__dec2enc__append', ah4s_richu_u_lists_APPENDu_u_NILu_c0)).
fof(20, axiom,![X1]:![X12]:![X13]:s(X1,h4s_bools_cond(s(t_bool,t0),s(X1,X13),s(X1,X12)))=s(X1,X13),file('i/f/Decode/decode__dec2enc__append', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
# SZS output end CNFRefutation
