# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X2)))))=>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)))),h4s_decodes_enc2dec(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))),s(X1,X2)))=s(t_h4s_lists_list(t_bool),happ(s(t_fun(X1,t_h4s_lists_list(t_bool)),X4),s(X1,X2)))),file('i/f/Decode/dec2enc__enc2dec', ch4s_Decodes_dec2encu_u_enc2dec)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/Decode/dec2enc__enc2dec', aHLu_TRUTH)).
fof(11, axiom,![X9]:(s(t_bool,t)=s(t_bool,X9)<=>p(s(t_bool,X9))),file('i/f/Decode/dec2enc__enc2dec', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(15, axiom,![X1]:![X2]:![X9]:![X3]:![X16]:![X4]:(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))))=>(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)))),h4s_decodes_enc2dec(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))),s(t_h4s_lists_list(t_bool),X16)))=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),X9)))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X2))))&s(t_h4s_lists_list(t_bool),X16)=s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),happ(s(t_fun(X1,t_h4s_lists_list(t_bool)),X4),s(X1,X2))),s(t_h4s_lists_list(t_bool),X9)))))),file('i/f/Decode/dec2enc__enc2dec', ah4s_Decodes_enc2decu_u_some)).
fof(16, axiom,![X1]:![X2]:![X3]:![X16]:![X17]:(p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,t_bool),X3),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_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)))),X17),s(X1,X2)))=s(t_h4s_lists_list(t_bool),X16)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),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)))),X17),s(t_h4s_lists_list(t_bool),X16)))=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/dec2enc__enc2dec', ah4s_Decodes_dec2encu_u_some)).
fof(17, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))))=>p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,t_bool),X3),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),X3),s(t_fun(X1,t_h4s_lists_list(t_bool)),X4))))))),file('i/f/Decode/dec2enc__enc2dec', ah4s_Decodes_wfu_u_enc2dec)).
fof(18, axiom,![X1]:![X16]:s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X16),s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_h4s_lists_list(X1),X16),file('i/f/Decode/dec2enc__enc2dec', ah4s_richu_u_lists_APPENDu_u_NILu_c0)).
# SZS output end CNFRefutation
