# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))=>p(s(t_bool,h4s_coders_wfu_u_coder(s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))))),h4s_coders_bnumu_u_coder(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))))),file('i/f/Coder/wf__coder__bnum', ch4s_Coders_wfu_u_coderu_u_bnum)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/Coder/wf__coder__bnum', aHLu_TRUTH)).
fof(7, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/Coder/wf__coder__bnum', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X4]:![X1]:![X12]:![X13]:(p(s(t_bool,h4s_coders_wfu_u_coder(s(t_h4s_pairs_prod(t_fun(X4,t_bool),t_h4s_pairs_prod(t_fun(X4,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X4,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(X4,t_bool),X1),s(t_h4s_pairs_prod(t_fun(X4,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X4,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(X4,t_h4s_lists_list(t_bool)),X12),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X4,t_h4s_lists_list(t_bool)))),X13))))))))<=>(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(X4,t_bool),X1))))&(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X4,t_bool),X1),s(t_fun(X4,t_h4s_lists_list(t_bool)),X12))))&s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X4,t_h4s_lists_list(t_bool)))),X13)=s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X4,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X4,t_bool),X1),s(t_fun(X4,t_h4s_lists_list(t_bool)),X12)))))),file('i/f/Coder/wf__coder__bnum', ah4s_Coders_wfu_u_coderu_u_def)).
fof(12, axiom,![X1]:![X2]:s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))))),h4s_coders_bnumu_u_coder(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1)))=s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))))),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool))))),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_bnum(s(t_h4s_nums_num,X2))),s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))))),file('i/f/Coder/wf__coder__bnum', ah4s_Coders_bnumu_u_coderu_u_def)).
fof(14, axiom,![X1]:![X2]:(p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))=>p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_bnum(s(t_h4s_nums_num,X2))))))),file('i/f/Coder/wf__coder__bnum', ah4s_Encodes_wfu_u_encodeu_u_bnum)).
fof(15, axiom,![X1]:![X2]:s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),h4s_decodes_decodeu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1)))=s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_bnum(s(t_h4s_nums_num,X2))))),file('i/f/Coder/wf__coder__bnum', ah4s_Decodes_decodeu_u_bnumu_u_def)).
fof(16, axiom,![X1]:![X2]:(p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))<=>(p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(t_h4s_nums_num,t_bool),X1))))&![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X5))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))))))))),file('i/f/Coder/wf__coder__bnum', ah4s_Encodes_wfu_u_predu_u_bnumu_u_def)).
fof(17, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/Coder/wf__coder__bnum', aHLu_BOOLu_CASES)).
fof(18, axiom,~(p(s(t_bool,f))),file('i/f/Coder/wf__coder__bnum', aHLu_FALSITY)).
# SZS output end CNFRefutation
