# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool))),happ(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),X1))),s(t_h4s_lists_list(t_bool),X2)))=s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool))),h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),X1),s(t_h4s_ones_one,h4s_ones_one0))),s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_ones_one,h4s_ones_one0),s(t_h4s_lists_list(t_bool),X2))))),s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_ones_one,t_h4s_lists_list(t_bool))),h4s_options_none))),file('i/f/Decode/decode__unit0', ch4s_Decodes_decodeu_u_unit0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/Decode/decode__unit0', aHLu_TRUTH)).
fof(4, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/Decode/decode__unit0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/Decode/decode__unit0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X4),s(X6,X3)))=s(X6,X4),file('i/f/Decode/decode__unit0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(14, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/Decode/decode__unit0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(15, axiom,![X6]:![X1]:![X2]:![X12]:(s(t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X6,t_bool),X1),s(t_fun(X6,t_h4s_lists_list(t_bool)),X12))),s(t_h4s_lists_list(t_bool),X2)))=s(t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool))),h4s_options_none)<=>![X7]:![X5]:(p(s(t_bool,happ(s(t_fun(X6,t_bool),X1),s(X6,X7))))=>~(s(t_h4s_lists_list(t_bool),X2)=s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),happ(s(t_fun(X6,t_h4s_lists_list(t_bool)),X12),s(X6,X7))),s(t_h4s_lists_list(t_bool),X5)))))),file('i/f/Decode/decode__unit0', ah4s_Decodes_enc2decu_u_none)).
fof(16, axiom,![X6]:![X7]:![X5]:![X1]:![X2]:![X12]:(p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(X6,t_bool),X1),s(t_fun(X6,t_h4s_lists_list(t_bool)),X12))))=>(s(t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool)))),h4s_decodes_enc2dec(s(t_fun(X6,t_bool),X1),s(t_fun(X6,t_h4s_lists_list(t_bool)),X12))),s(t_h4s_lists_list(t_bool),X2)))=s(t_h4s_options_option(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool))),h4s_options_some(s(t_h4s_pairs_prod(X6,t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(X6,X7),s(t_h4s_lists_list(t_bool),X5)))))<=>(p(s(t_bool,happ(s(t_fun(X6,t_bool),X1),s(X6,X7))))&s(t_h4s_lists_list(t_bool),X2)=s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),happ(s(t_fun(X6,t_h4s_lists_list(t_bool)),X12),s(X6,X7))),s(t_h4s_lists_list(t_bool),X5)))))),file('i/f/Decode/decode__unit0', ah4s_Decodes_enc2decu_u_some)).
fof(17, axiom,![X1]: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),X1)))=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),X1),s(t_fun(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_unit))),file('i/f/Decode/decode__unit0', ah4s_Decodes_decodeu_u_unitu_u_def)).
fof(18, axiom,![X6]:![X2]:s(t_h4s_lists_list(X6),h4s_lists_append(s(t_h4s_lists_list(X6),h4s_lists_nil),s(t_h4s_lists_list(X6),X2)))=s(t_h4s_lists_list(X6),X2),file('i/f/Decode/decode__unit0', ah4s_lists_APPEND0u_c0)).
fof(19, axiom,![X13]: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,X13)))=s(t_h4s_lists_list(t_bool),h4s_lists_nil),file('i/f/Decode/decode__unit0', ah4s_Encodes_encodeu_u_unitu_u_def)).
fof(20, axiom,![X1]:p(s(t_bool,h4s_encodes_wfu_u_encoder(s(t_fun(t_h4s_ones_one,t_bool),X1),s(t_fun(t_h4s_ones_one,t_h4s_lists_list(t_bool)),h4s_encodes_encodeu_u_unit)))),file('i/f/Decode/decode__unit0', ah4s_Encodes_wfu_u_encodeu_u_unit)).
fof(21, axiom,~(p(s(t_bool,f))),file('i/f/Decode/decode__unit0', aHLu_FALSITY)).
fof(25, axiom,![X14]:s(t_h4s_ones_one,X14)=s(t_h4s_ones_one,h4s_ones_one0),file('i/f/Decode/decode__unit0', ah4s_ones_one1)).
# SZS output end CNFRefutation
