# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),X2),s(t_h4s_ones_one,X1))))=>s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_ones_one,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(t_h4s_ones_one,t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_unit(s(t_fun(t_h4s_ones_one,t_bool),X2))))),s(t_h4s_ones_one,X1)))=s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_unit),s(t_h4s_ones_one,X1)))),file('i/f/Decode/dec2enc__decode__unit', ch4s_Decodes_dec2encu_u_decodeu_u_unit)).
fof(2, axiom,![X3]:![X4]:![X5]:![X6]:(![X1]:s(X4,happ(s(t_fun(X3,X4),X5),s(X3,X1)))=s(X4,happ(s(t_fun(X3,X4),X6),s(X3,X1)))=>s(t_fun(X3,X4),X5)=s(t_fun(X3,X4),X6)),file('i/f/Decode/dec2enc__decode__unit', aHLu_EXT)).
fof(7, axiom,![X12]:![X13]:(s(t_bool,X13)=s(t_bool,X12)<=>((p(s(t_bool,X13))=>p(s(t_bool,X12)))&(p(s(t_bool,X12))=>p(s(t_bool,X13))))),file('i/f/Decode/dec2enc__decode__unit', ah4s_bools_EQu_u_IMPu_u_THM)).
fof(25, axiom,![X7]:![X21]:(~(?[X1]:p(s(t_bool,happ(s(t_fun(X7,t_bool),X21),s(X7,X1)))))<=>![X1]:~(p(s(t_bool,happ(s(t_fun(X7,t_bool),X21),s(X7,X1)))))),file('i/f/Decode/dec2enc__decode__unit', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(38, axiom,![X21]:(p(s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),X21),s(t_h4s_ones_one,h4s_ones_one0))))=>![X1]:p(s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),X21),s(t_h4s_ones_one,X1))))),file('i/f/Decode/dec2enc__decode__unit', ah4s_ones_oneu_u_induction)).
fof(41, axiom,![X7]:![X24]:?[X23]:s(X7,happ(s(t_fun(t_h4s_ones_one,X7),X23),s(t_h4s_ones_one,h4s_ones_one0)))=s(X7,X24),file('i/f/Decode/dec2enc__decode__unit', ah4s_ones_oneu_u_primu_u_rec)).
fof(42, axiom,![X15]:![X7]:![X8]:![X1]:![X5]:![X25]:s(X15,happ(s(t_fun(X7,X15),X5),s(X7,h4s_bools_cond(s(t_bool,X25),s(X7,X1),s(X7,X8)))))=s(X15,h4s_bools_cond(s(t_bool,X25),s(X15,happ(s(t_fun(X7,X15),X5),s(X7,X1))),s(X15,happ(s(t_fun(X7,X15),X5),s(X7,X8))))),file('i/f/Decode/dec2enc__decode__unit', ah4s_bools_CONDu_u_RAND)).
fof(44, axiom,![X26]:s(t_h4s_ones_one,X26)=s(t_h4s_ones_one,h4s_ones_one0),file('i/f/Decode/dec2enc__decode__unit', ah4s_ones_one1)).
fof(46, axiom,![X2]:s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_unit(s(t_fun(t_h4s_ones_one,t_bool),X2)))=s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(t_h4s_ones_one,t_bool),X2),s(t_fun(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_unit))),file('i/f/Decode/dec2enc__decode__unit', ah4s_Decodes_decodeu_u_unitu_u_def)).
fof(48, axiom,![X27]:s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_unit),s(t_h4s_ones_one,X27)))=s(t_h4s_lists_list(t_bool),h4s_lists_nil),file('i/f/Decode/dec2enc__decode__unit', ah4s_Encodes_encodeu_u_unitu_u_def)).
fof(52, axiom,![X7]:![X2]:![X24]:(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X7,t_bool),X2),s(t_fun(X7,t_h4s_lists_list(t_bool)),X24))))<=>![X1]:![X8]:((p(s(t_bool,happ(s(t_fun(X7,t_bool),X2),s(X7,X1))))&(p(s(t_bool,happ(s(t_fun(X7,t_bool),X2),s(X7,X8))))&p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(t_bool),happ(s(t_fun(X7,t_h4s_lists_list(t_bool)),X24),s(X7,X8))),s(t_h4s_lists_list(t_bool),happ(s(t_fun(X7,t_h4s_lists_list(t_bool)),X24),s(X7,X1))))))))=>s(X7,X1)=s(X7,X8))),file('i/f/Decode/dec2enc__decode__unit', ah4s_Encodes_wfu_u_encoderu_u_def)).
fof(56, axiom,![X7]:![X1]:![X2]:![X24]:((p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X7,t_bool),X2),s(t_fun(X7,t_h4s_lists_list(t_bool)),X24))))&p(s(t_bool,happ(s(t_fun(X7,t_bool),X2),s(X7,X1)))))=>s(t_h4s_lists_list(t_bool),happ(s(t_fun(X7,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(X7,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X7,t_bool),X2),s(t_fun(X7,t_h4s_lists_list(t_bool)),X24))))),s(X7,X1)))=s(t_h4s_lists_list(t_bool),happ(s(t_fun(X7,t_h4s_lists_list(t_bool)),X24),s(X7,X1)))),file('i/f/Decode/dec2enc__decode__unit', ah4s_Decodes_dec2encu_u_enc2dec)).
fof(63, axiom,![X7]:![X2]:![X29]:![X24]:(s(t_h4s_options_option(t_h4s_pairs_prod(X7,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X7,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X7,t_bool),X2),s(t_fun(X7,t_h4s_lists_list(t_bool)),X24))),s(t_h4s_lists_list(t_bool),X29)))=s(t_h4s_options_option(t_h4s_pairs_prod(X7,t_h4s_lists_list(t_bool))),h4s_options_none)<=>![X1]:![X14]:(p(s(t_bool,happ(s(t_fun(X7,t_bool),X2),s(X7,X1))))=>~(s(t_h4s_lists_list(t_bool),X29)=s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),happ(s(t_fun(X7,t_h4s_lists_list(t_bool)),X24),s(X7,X1))),s(t_h4s_lists_list(t_bool),X14)))))),file('i/f/Decode/dec2enc__decode__unit', ah4s_Decodes_enc2decu_u_none)).
fof(64, axiom,![X15]:![X29]:s(t_h4s_lists_list(X15),h4s_lists_append(s(t_h4s_lists_list(X15),h4s_lists_nil),s(t_h4s_lists_list(X15),X29)))=s(t_h4s_lists_list(X15),X29),file('i/f/Decode/dec2enc__decode__unit', ah4s_richu_u_lists_APPENDu_u_NILu_c1)).
fof(70, axiom,p(s(t_bool,t)),file('i/f/Decode/dec2enc__decode__unit', aHLu_TRUTH)).
fof(72, axiom,![X14]:(s(t_bool,X14)=s(t_bool,t)<=>p(s(t_bool,X14))),file('i/f/Decode/dec2enc__decode__unit', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
