# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_coders_wfu_u_coder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),X2))))=>![X3]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_coders_domain(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),X2))),s(X1,X3))))=>s(X1,happ(s(t_fun(t_h4s_lists_list(t_bool),X1),h4s_coders_decoder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),X2))),s(t_h4s_lists_list(t_bool),happ(s(t_fun(X1,t_h4s_lists_list(t_bool)),h4s_coders_encoder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),X2))),s(X1,X3)))))=s(X1,X3))),file('i/f/Coder/wf__coder0', ch4s_Coders_wfu_u_coder0)).
fof(7, axiom,![X1]:![X3]:![X15]:![X16]:((p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X15),s(t_fun(X1,t_h4s_lists_list(t_bool)),X16))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X15),s(X1,X3)))))=>s(X1,happ(s(t_fun(t_h4s_lists_list(t_bool),X1),h4s_coders_decode(s(t_fun(X1,t_bool),X15),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X1,t_bool),X15),s(t_fun(X1,t_h4s_lists_list(t_bool)),X16))))),s(t_h4s_lists_list(t_bool),happ(s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),s(X1,X3)))))=s(X1,X3)),file('i/f/Coder/wf__coder0', ah4s_Coders_decodeu_u_encode)).
fof(8, axiom,![X1]:![X15]:![X16]:![X17]:s(t_fun(X1,t_h4s_lists_list(t_bool)),h4s_coders_encoder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X15),s(t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17)))))))=s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),file('i/f/Coder/wf__coder0', ah4s_Coders_encoderu_u_def)).
fof(9, axiom,![X1]:![X18]:![X3]:?[X19]:?[X20]:s(t_h4s_pairs_prod(X1,X18),X3)=s(t_h4s_pairs_prod(X1,X18),h4s_pairs_u_2c(s(X1,X19),s(X18,X20))),file('i/f/Coder/wf__coder0', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(10, axiom,![X1]:![X15]:![X16]:![X17]:s(t_fun(t_h4s_lists_list(t_bool),X1),h4s_coders_decoder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X15),s(t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17)))))))=s(t_fun(t_h4s_lists_list(t_bool),X1),h4s_coders_decode(s(t_fun(X1,t_bool),X15),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17))),file('i/f/Coder/wf__coder0', ah4s_Coders_decoderu_u_def)).
fof(11, axiom,p(s(t_bool,t)),file('i/f/Coder/wf__coder0', aHLu_TRUTH)).
fof(16, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/Coder/wf__coder0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X1]:![X15]:![X16]:![X17]:s(t_fun(X1,t_bool),h4s_coders_domain(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X15),s(t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17)))))))=s(t_fun(X1,t_bool),X15),file('i/f/Coder/wf__coder0', ah4s_Coders_domainu_u_def)).
fof(18, axiom,![X1]:![X15]:![X16]:![X17]:(p(s(t_bool,h4s_coders_wfu_u_coder(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X15),s(t_h4s_pairs_prod(t_fun(X1,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(X1,t_h4s_lists_list(t_bool)),X16),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17))))))))<=>(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(X1,t_bool),X15))))&(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X15),s(t_fun(X1,t_h4s_lists_list(t_bool)),X16))))&s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),X17)=s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X1,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X1,t_bool),X15),s(t_fun(X1,t_h4s_lists_list(t_bool)),X16)))))),file('i/f/Coder/wf__coder0', ah4s_Coders_wfu_u_coderu_u_def)).
# SZS output end CNFRefutation
