# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((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)))),X6))))&p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X2,t_bool),X3),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X2,t_h4s_lists_list(t_bool)))),X5)))))=>p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_encodes_liftu_u_prod(s(t_fun(X1,t_bool),X4),s(t_fun(X2,t_bool),X3))),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_pairs_prod(X1,X2),t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_prod(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_encodes_liftu_u_prod(s(t_fun(X1,t_bool),X4),s(t_fun(X2,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)))),X6),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X2,t_h4s_lists_list(t_bool)))),X5))))))),file('i/f/Decode/wf__decode__prod', ch4s_Decodes_wfu_u_decodeu_u_prod)).
fof(4, axiom,![X12]:![X13]:((p(s(t_bool,X13))=>p(s(t_bool,X12)))=>((p(s(t_bool,X12))=>p(s(t_bool,X13)))=>s(t_bool,X13)=s(t_bool,X12))),file('i/f/Decode/wf__decode__prod', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, axiom,![X1]:![X2]:![X17]:![X5]:![X6]:s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_pairs_prod(X1,X2),t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_prod(s(t_fun(t_h4s_pairs_prod(X1,X2),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)))),X6),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X2,t_h4s_lists_list(t_bool)))),X5)))=s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_pairs_prod(X1,X2),t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),X17),s(t_fun(t_h4s_pairs_prod(X1,X2),t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_prod(s(t_fun(X1,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)))),X6))),s(t_fun(X2,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(X2,t_h4s_lists_list(t_bool)))),X5))))))),file('i/f/Decode/wf__decode__prod', ah4s_Decodes_decodeu_u_produ_u_def)).
fof(27, axiom,![X1]:![X2]:![X3]:![X4]:![X21]:![X22]:((p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_lists_list(t_bool)),X22))))&p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X2,t_bool),X3),s(t_fun(X2,t_h4s_lists_list(t_bool)),X21)))))=>p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_encodes_liftu_u_prod(s(t_fun(X1,t_bool),X4),s(t_fun(X2,t_bool),X3))),s(t_fun(t_h4s_pairs_prod(X1,X2),t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_prod(s(t_fun(X1,t_h4s_lists_list(t_bool)),X22),s(t_fun(X2,t_h4s_lists_list(t_bool)),X21))))))),file('i/f/Decode/wf__decode__prod', ah4s_Encodes_wfu_u_encodeu_u_prod)).
fof(30, axiom,![X1]:![X17]:![X24]:(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X17),s(t_fun(X1,t_h4s_lists_list(t_bool)),X24))))=>p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,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),X17),s(t_fun(X1,t_h4s_lists_list(t_bool)),X24))))))),file('i/f/Decode/wf__decode__prod', ah4s_Decodes_wfu_u_enc2dec)).
fof(34, axiom,![X1]:![X17]:![X23]:(p(s(t_bool,h4s_decodes_wfu_u_decoder(s(t_fun(X1,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)))),X23))))=>p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X1,t_bool),X17),s(t_fun(X1,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)))),X23))))))),file('i/f/Decode/wf__decode__prod', ah4s_Decodes_wfu_u_dec2enc)).
fof(66, axiom,![X1]:![X12]:![X13]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X13),s(X1,X12)))=s(X1,X13),file('i/f/Decode/wf__decode__prod', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(67, axiom,![X12]:![X13]:![X39]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X39),s(t_bool,X13),s(t_bool,X12))))<=>((~(p(s(t_bool,X39)))|p(s(t_bool,X13)))&(p(s(t_bool,X39))|p(s(t_bool,X12))))),file('i/f/Decode/wf__decode__prod', ah4s_bools_CONDu_u_EXPAND)).
fof(72, axiom,![X1]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))),file('i/f/Decode/wf__decode__prod', ah4s_predu_u_sets_FINITEu_u_EMPTY)).
# SZS output end CNFRefutation
