%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP309_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  7 07:50:55 EDT 2024

% Result   : Theorem 142.71s 39.20s
% Output   : Refutation 143.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :  961
% Syntax   : Number of formulae    : 2427 ( 765 unt; 465 typ;   0 def)
%            Number of atoms       : 4862 (2634 equ;   0 cnn)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives : 20078 (1462   ~; 768   |; 712   &;15812   @)
%                                         ( 190 <=>;1134  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Number of types       :  151 ( 150 usr)
%            Number of type conns  :  474 ( 474   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  318 ( 315 usr;  61 con; 0-4 aty)
%            Number of variables   : 4356 (   0   ^4213   !; 143   ?;4356   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_a_element_ptr_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_a_element_ptr_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'': $tType ).

thf('\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'_type',type,
    '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'A_element_ptr_a_element_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_a_element_ptr_option_fun$\'': $tType ).

thf('\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'_type',type,
    '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'': $tType ).

thf('\'Unit_RNode_ext_RObject_ext$\'_type',type,
    '\'Unit_RNode_ext_RObject_ext$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_a_element_ptr_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_a_element_ptr_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_fun$\'': $tType ).

thf('\'D_document_ptr_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'D_document_ptr_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_option_bool_fun$\'_type',type,
    '\'A_element_ptr_option_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_k_sum$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_k_sum$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_bool_fun$\'': $tType ).

thf('\'D_document_ptr_bool_fun$\'_type',type,
    '\'D_document_ptr_bool_fun$\'': $tType ).

thf('\'B_character_data_ptr_option$\'_type',type,
    '\'B_character_data_ptr_option$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'_type',type,
    '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_a_element_ptr_option_fun_a_element_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_a_element_ptr_option_fun_a_element_ptr_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_heap_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_heap_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'B_character_data_ptr_bool_fun$\'_type',type,
    '\'B_character_data_ptr_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun$\'': $tType ).

thf('\'A_element_ptr_bool_fun$\'_type',type,
    '\'A_element_ptr_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_bool_fun$\'': $tType ).

thf('\'A_element_ptr_fset$\'_type',type,
    '\'A_element_ptr_fset$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'D_document_ptr$\'_type',type,
    '\'D_document_ptr$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_heap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_heap$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun$\'': $tType ).

thf('\'B_character_data_ptr_fset$\'_type',type,
    '\'B_character_data_ptr_fset$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'': $tType ).

thf('\'A_element_ptr_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr$\'_type',type,
    '\'A_element_ptr$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_bool_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_j_option_RDocument_ext_heap_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_j_option_RDocument_ext_heap_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_i_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_i_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'': $tType ).

thf('\'D_document_ptr_set$\'_type',type,
    '\'D_document_ptr_set$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_set$\'_type',type,
    '\'A_element_ptr_set$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_j_option_RDocument_ext_heap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_j_option_RDocument_ext_heap$\'': $tType ).

thf(tlbool_type,type,
    tlbool: $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'': $tType ).

thf('\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'_type',type,
    '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'B_character_data_ptr$\'_type',type,
    '\'B_character_data_ptr$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_bool_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'': $tType ).

thf('\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'_type',type,
    '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_heap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_heap$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_bool_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'': $tType ).

thf('\'A_element_ptr_option$\'_type',type,
    '\'A_element_ptr_option$\'': $tType ).

thf('\'D_document_ptr_a_element_ptr_option_fun$\'_type',type,
    '\'D_document_ptr_a_element_ptr_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_i_sum$\'_type',type,
    '\'H_option_RCharacterData_ext_i_sum$\'': $tType ).

thf('\'Unit_RObject_ext$\'_type',type,
    '\'Unit_RObject_ext$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_h_option_RCharacterData_ext_RNode_ext_heap_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_h_option_RCharacterData_ext_RNode_ext_heap_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'': $tType ).

thf('\'A_element_ptr_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'Bool_bool_fun$\'_type',type,
    '\'Bool_bool_fun$\'': $tType ).

thf('\'B_character_data_ptr_set$\'_type',type,
    '\'B_character_data_ptr_set$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_k_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_k_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_fmap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_fmap$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_h_option_RCharacterData_ext_RNode_ext_heap$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_h_option_RCharacterData_ext_RNode_ext_heap$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_b_character_data_ptr_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_b_character_data_ptr_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_option$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_option$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_set$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_set$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'': $tType ).

thf('\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'_type',type,
    '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_a_element_ptr_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_a_element_ptr_option_fun$\'': $tType ).

thf('\'D_document_ptr_option$\'_type',type,
    '\'D_document_ptr_option$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_heap_bool_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_heap_bool_fun$\'': $tType ).

thf('\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'D_document_ptr_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'D_document_ptr_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun$\'_type',type,
    '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun$\'': $tType ).

thf('\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'_type',type,
    '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'': $tType ).

thf('\'A_element_ptr_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'A_element_ptr_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf('\'D_document_ptr_fset$\'_type',type,
    '\'D_document_ptr_fset$\'': $tType ).

thf('\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'_type',type,
    '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'': $tType ).

thf(def_14_type,type,
    def_14: tlbool > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' > tlbool ).

thf('\'element_ptr_kinds$\'_type',type,
    '\'element_ptr_kinds$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'' ).

thf('\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'_type',type,
    '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'': '\'D_document_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' ).

thf('\'finsert$b\'_type',type,
    '\'finsert$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf('\'fun_app$au\'_type',type,
    '\'fun_app$au\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(def_24_type,type,
    def_24: tlbool > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' > tlbool ).

thf('\'fun_app$s\'_type',type,
    '\'fun_app$s\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'object_ptr_kinds$\'_type',type,
    '\'object_ptr_kinds$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'' ).

thf('\'type_wf$d\'_type',type,
    '\'type_wf$d\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$ad\'_type',type,
    '\'fun_app$ad\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun$\'' ).

thf('\'fun_app$bx\'_type',type,
    '\'fun_app$bx\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'uvi$\'_type',type,
    '\'uvi$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'fun_app$ao\'_type',type,
    '\'fun_app$ao\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'D_document_ptr_fset$\'' ).

thf('\'case_option$d\'_type',type,
    '\'case_option$d\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'get_D_o_c_u_m_e_n_t$\'_type',type,
    '\'get_D_o_c_u_m_e_n_t$\'': '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'' ).

thf('\'fmember$\'_type',type,
    '\'fmember$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'' ).

thf('\'fun_app$m\'_type',type,
    '\'fun_app$m\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$x\'_type',type,
    '\'fun_app$x\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > $o ).

thf('\'l_get_D_o_c_u_m_e_n_t_lemmas$\'_type',type,
    '\'l_get_D_o_c_u_m_e_n_t_lemmas$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > $o ).

thf('\'get_O_b_j_e_c_t$\'_type',type,
    '\'get_O_b_j_e_c_t$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'' ).

thf(def_7_type,type,
    def_7: '\'Bool_bool_fun$\'' > tlbool > tlbool ).

thf('\'l_put_M$\'_type',type,
    '\'l_put_M$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'' > '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'' > $o ).

thf('\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'_type',type,
    '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' ).

thf('\'fun_app$bw\'_type',type,
    '\'fun_app$bw\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'fmember$b\'_type',type,
    '\'fmember$b\'': '\'B_character_data_ptr$\'' > '\'B_character_data_ptr_fset$\'' > $o ).

thf('\'the$g\'_type',type,
    '\'the$g\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf('\'bind$k\'_type',type,
    '\'bind$k\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'some$a\'_type',type,
    '\'some$a\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'l_get_M$b\'_type',type,
    '\'l_get_M$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'' > $o ).

thf('\'fun_app$p\'_type',type,
    '\'fun_app$p\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bg\'_type',type,
    '\'fun_app$bg\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$al\'_type',type,
    '\'fun_app$al\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'B_character_data_ptr_fset$\'' ).

thf('\'fun_app$bl\'_type',type,
    '\'fun_app$bl\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' ).

thf('\'case_option$j\'_type',type,
    '\'case_option$j\'': tlbool > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_bool_fun$\'' ).

thf(def_22_type,type,
    def_22: tlbool > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'uvs$\'_type',type,
    '\'uvs$\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$cu\'_type',type,
    '\'fun_app$cu\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'' ).

thf(def_28_type,type,
    def_28: tlbool > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf(def_15_type,type,
    def_15: '\'Bool_bool_fun$\'' > tlbool > tlbool ).

thf('\'uvg$\'_type',type,
    '\'uvg$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'fun_app$ap\'_type',type,
    '\'fun_app$ap\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'the_elem$b\'_type',type,
    '\'the_elem$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf('\'l_get_E_l_e_m_e_n_t_lemmas$\'_type',type,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > $o ).

thf('\'combine_options$b\'_type',type,
    '\'combine_options$b\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'fset$c\'_type',type,
    '\'fset$c\'': '\'A_element_ptr_fset$\'' > '\'A_element_ptr_set$\'' ).

thf('\'put_E_l_e_m_e_n_t$\'_type',type,
    '\'put_E_l_e_m_e_n_t$\'': '\'A_element_ptr$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' ).

thf('\'more$\'_type',type,
    '\'more$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum$\'' ).

thf('\'l_put_M$b\'_type',type,
    '\'l_put_M$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'' > $o ).

thf('\'fmember$c\'_type',type,
    '\'fmember$c\'': '\'D_document_ptr$\'' > '\'D_document_ptr_fset$\'' > $o ).

thf('\'is_document_ptr_kind$\'_type',type,
    '\'is_document_ptr_kind$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > $o ).

thf('\'fmember$d\'_type',type,
    '\'fmember$d\'': '\'A_element_ptr$\'' > '\'A_element_ptr_fset$\'' > $o ).

thf('\'l_put_M$d\'_type',type,
    '\'l_put_M$d\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'' > $o ).

thf('\'put_D_o_c_u_m_e_n_t$\'_type',type,
    '\'put_D_o_c_u_m_e_n_t$\'': '\'D_document_ptr$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' ).

thf('\'fun_app$ak\'_type',type,
    '\'fun_app$ak\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'_type',type,
    '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf('\'bind$g\'_type',type,
    '\'bind$g\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'put_O_b_j_e_c_t$\'_type',type,
    '\'put_O_b_j_e_c_t$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' ).

thf('\'combine_options$c\'_type',type,
    '\'combine_options$c\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'is_character_data_kind_N_o_d_e$\'_type',type,
    '\'is_character_data_kind_N_o_d_e$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'_type',type,
    '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf('\'fthe_elem$b\'_type',type,
    '\'fthe_elem$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf('\'bind$f\'_type',type,
    '\'bind$f\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bz\'_type',type,
    '\'fun_app$bz\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'_type',type,
    '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'': '\'A_element_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf('\'fun_app$aw\'_type',type,
    '\'fun_app$aw\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > $o ).

thf('\'fun_app$bj\'_type',type,
    '\'fun_app$bj\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bk\'_type',type,
    '\'fun_app$bk\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'uvr$\'_type',type,
    '\'uvr$\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'combine_options$a\'_type',type,
    '\'combine_options$a\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'truncate$a\'_type',type,
    '\'truncate$a\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'Unit_RNode_ext_RObject_ext$\'' ).

thf('\'fun_app$aj\'_type',type,
    '\'fun_app$aj\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'cast_O_b_j_e_c_t_2_N_o_d_e$\'_type',type,
    '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'member$c\'_type',type,
    '\'member$c\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'' > $o ).

thf('\'is_element_kind_N_o_d_e$\'_type',type,
    '\'is_element_kind_N_o_d_e$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'fmember$a\'_type',type,
    '\'fmember$a\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' > $o ).

thf('\'a_type_wf$a\'_type',type,
    '\'a_type_wf$a\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$z\'_type',type,
    '\'fun_app$z\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun$\'' ).

thf(def_34_type,type,
    def_34: tlbool > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' > tlbool ).

thf('\'uu$\'_type',type,
    '\'uu$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_fun$\'' ).

thf('\'case_option$e\'_type',type,
    '\'case_option$e\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'uuh$\'_type',type,
    '\'uuh$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'type_wf$a\'_type',type,
    '\'type_wf$a\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fset$\'_type',type,
    '\'fset$\'': '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr_set$\'' ).

thf('\'case_option$c\'_type',type,
    '\'case_option$c\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'uur$\'_type',type,
    '\'uur$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'the$f\'_type',type,
    '\'the$f\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf('\'fun_app$aq\'_type',type,
    '\'fun_app$aq\'': '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'' > '\'D_document_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' ).

thf('\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'_type',type,
    '\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' ).

thf('\'uvc$\'_type',type,
    '\'uvc$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'bind$r\'_type',type,
    '\'bind$r\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'fun_app$h\'_type',type,
    '\'fun_app$h\'': '\'C_a_b_e_g_option_RElement_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$ca\'_type',type,
    '\'fun_app$ca\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'fun_app$j\'_type',type,
    '\'fun_app$j\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'pair$\'_type',type,
    '\'pair$\'': '\'A_element_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf('\'x$\'_type',type,
    '\'x$\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf('\'fun_app$bn\'_type',type,
    '\'fun_app$bn\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > $o ).

thf('\'member$a\'_type',type,
    '\'member$a\'': '\'D_document_ptr$\'' > '\'D_document_ptr_set$\'' > $o ).

thf('\'more$a\'_type',type,
    '\'more$a\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum$\'' ).

thf('\'child_nodes_update$\'_type',type,
    '\'child_nodes_update$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf('\'uvz$\'_type',type,
    '\'uvz$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$az\'_type',type,
    '\'fun_app$az\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' ).

thf('\'a_type_wf$b\'_type',type,
    '\'a_type_wf$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$y\'_type',type,
    '\'fun_app$y\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf('\'l_get_M$d\'_type',type,
    '\'l_get_M$d\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset_fun$\'' > $o ).

thf('\'fun_app$i\'_type',type,
    '\'fun_app$i\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$af\'_type',type,
    '\'fun_app$af\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun$\'' ).

thf('\'fun_app$ba\'_type',type,
    '\'fun_app$ba\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'is_node_ptr_kind$\'_type',type,
    '\'is_node_ptr_kind$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > $o ).

thf('\'fun_app$bs\'_type',type,
    '\'fun_app$bs\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'fthe_elem$a\'_type',type,
    '\'fthe_elem$a\'': '\'D_document_ptr_fset$\'' > '\'D_document_ptr$\'' ).

thf('\'h$a\'_type',type,
    '\'h$a\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' ).

thf('\'fun_app$as\'_type',type,
    '\'fun_app$as\'': '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'the$d\'_type',type,
    '\'the$d\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf(def_9_type,type,
    def_9: '\'Bool_bool_fun$\'' > tlbool > tlbool ).

thf('\'uub$\'_type',type,
    '\'uub$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'_type',type,
    '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf('\'fun_app$ag\'_type',type,
    '\'fun_app$ag\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\'' ).

thf('\'some$f\'_type',type,
    '\'some$f\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'' ).

thf('\'none$\'_type',type,
    '\'none$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf(def_19_type,type,
    def_19: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'fun_app$ck\'_type',type,
    '\'fun_app$ck\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' ).

thf(tltrue_type,type,
    tltrue: tlbool ).

thf('\'uuj$\'_type',type,
    '\'uuj$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'the$\'_type',type,
    '\'the$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf('\'fun_app$bo\'_type',type,
    '\'fun_app$bo\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > $o ).

thf('\'case_sum$a\'_type',type,
    '\'case_sum$a\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_k_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf(def_4_type,type,
    def_4: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > tlbool ).

thf('\'none$f\'_type',type,
    '\'none$f\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' ).

thf('\'uvo$\'_type',type,
    '\'uvo$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$ac\'_type',type,
    '\'fun_app$ac\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf('\'fset$a\'_type',type,
    '\'fset$a\'': '\'D_document_ptr_fset$\'' > '\'D_document_ptr_set$\'' ).

thf('\'l_put_M$c\'_type',type,
    '\'l_put_M$c\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'' > '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > $o ).

thf('\'case_sum$\'_type',type,
    '\'case_sum$\'': '\'C_a_b_e_g_option_RElement_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_i_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$cj\'_type',type,
    '\'fun_app$cj\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > $o ).

thf(def_33_type,type,
    def_33: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'fun_app$f\'_type',type,
    '\'fun_app$f\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bf\'_type',type,
    '\'fun_app$bf\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'node_ptr$\'_type',type,
    '\'node_ptr$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf('\'fun_app$bp\'_type',type,
    '\'fun_app$bp\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > $o ).

thf('\'fun_app$n\'_type',type,
    '\'fun_app$n\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'some$c\'_type',type,
    '\'some$c\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$r\'_type',type,
    '\'fun_app$r\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$am\'_type',type,
    '\'fun_app$am\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bt\'_type',type,
    '\'fun_app$bt\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'bind$a\'_type',type,
    '\'bind$a\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'none$a\'_type',type,
    '\'none$a\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'the_elem$\'_type',type,
    '\'the_elem$\'': '\'B_character_data_ptr_set$\'' > '\'B_character_data_ptr$\'' ).

thf('\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'_type',type,
    '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$at\'_type',type,
    '\'fun_app$at\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' ).

thf('\'fun_app$ci\'_type',type,
    '\'fun_app$ci\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > $o ).

thf('\'fun_app$l\'_type',type,
    '\'fun_app$l\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'bind$l\'_type',type,
    '\'bind$l\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bq\'_type',type,
    '\'fun_app$bq\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' > $o ).

thf('\'l_get_M$c\'_type',type,
    '\'l_get_M$c\'': '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'' > $o ).

thf('\'bind$i\'_type',type,
    '\'bind$i\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'extend$\'_type',type,
    '\'extend$\'': '\'Unit_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf('\'bind$\'_type',type,
    '\'bind$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'uvq$\'_type',type,
    '\'uvq$\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' ).

thf('\'element_ptr$\'_type',type,
    '\'element_ptr$\'': '\'A_element_ptr$\'' ).

thf('\'uvn$\'_type',type,
    '\'uvn$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$u\'_type',type,
    '\'fun_app$u\'': '\'Bool_bool_fun$\'' > tlbool > $o ).

thf('\'uwa$\'_type',type,
    '\'uwa$\'': '\'C_a_b_j_option_RDocument_ext_k_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'sup$b\'_type',type,
    '\'sup$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf('\'character_data_ptr_kinds$\'_type',type,
    '\'character_data_ptr_kinds$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'' ).

thf('\'v$\'_type',type,
    '\'v$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\'' ).

thf(def_29_type,type,
    def_29: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'bind$q\'_type',type,
    '\'bind$q\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'_type',type,
    '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'': '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'' ).

thf('\'uus$\'_type',type,
    '\'uus$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'bind$b\'_type',type,
    '\'bind$b\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'_type',type,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > $o ).

thf('\'the_elem$c\'_type',type,
    '\'the_elem$c\'': '\'A_element_ptr_set$\'' > '\'A_element_ptr$\'' ).

thf('\'uuw$\'_type',type,
    '\'uuw$\'': '\'Bool_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'fun_app$ar\'_type',type,
    '\'fun_app$ar\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'member$\'_type',type,
    '\'member$\'': '\'B_character_data_ptr$\'' > '\'B_character_data_ptr_set$\'' > $o ).

thf('\'bind$c\'_type',type,
    '\'bind$c\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'bind$e\'_type',type,
    '\'bind$e\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'uue$\'_type',type,
    '\'uue$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'uuu$\'_type',type,
    '\'uuu$\'': '\'Bool_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'fun_app$an\'_type',type,
    '\'fun_app$an\'': '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'B_character_data_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'l_get_N_o_d_e_lemmas$\'_type',type,
    '\'l_get_N_o_d_e_lemmas$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > $o ).

thf('\'uua$\'_type',type,
    '\'uua$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$k\'_type',type,
    '\'fun_app$k\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf(def_32_type,type,
    def_32: tlbool > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'l_get_O_b_j_e_c_t_lemmas$d\'_type',type,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > $o ).

thf('\'type_wf$\'_type',type,
    '\'type_wf$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$av\'_type',type,
    '\'fun_app$av\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_fset$\'' ).

thf('\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'_type',type,
    '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'': '\'B_character_data_ptr$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' ).

thf('\'type_wf$b\'_type',type,
    '\'type_wf$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$bi\'_type',type,
    '\'fun_app$bi\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'the$c\'_type',type,
    '\'the$c\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf('\'the$e\'_type',type,
    '\'the$e\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' ).

thf('\'bind$p\'_type',type,
    '\'bind$p\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'uuf$\'_type',type,
    '\'uuf$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf(def_12_type,type,
    def_12: tlbool > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'fun_app$bv\'_type',type,
    '\'fun_app$bv\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'the_elem$a\'_type',type,
    '\'the_elem$a\'': '\'D_document_ptr_set$\'' > '\'D_document_ptr$\'' ).

thf('\'fset$b\'_type',type,
    '\'fset$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'' ).

thf('\'is_node_kind$\'_type',type,
    '\'is_node_kind$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_bool_fun$\'' ).

thf('\'fun_app$g\'_type',type,
    '\'fun_app$g\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf(def_23_type,type,
    def_23: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'pair$b\'_type',type,
    '\'pair$b\'': '\'D_document_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf('\'l_get_M$\'_type',type,
    '\'l_get_M$\'': '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'' > $o ).

thf(tlfalse_type,type,
    tlfalse: tlbool ).

thf('\'uvu$\'_type',type,
    '\'uvu$\'': '\'H_option_RCharacterData_ext_i_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf(def_11_type,type,
    def_11: '\'Bool_bool_fun$\'' > tlbool > tlbool ).

thf('\'uui$\'_type',type,
    '\'uui$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'new_D_o_c_u_m_e_n_t$\'_type',type,
    '\'new_D_o_c_u_m_e_n_t$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf('\'new_E_l_e_m_e_n_t$\'_type',type,
    '\'new_E_l_e_m_e_n_t$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf('\'none$b\'_type',type,
    '\'none$b\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'a_type_wf$\'_type',type,
    '\'a_type_wf$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'_type',type,
    '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'' ).

thf('\'node_ptr_kinds$\'_type',type,
    '\'node_ptr_kinds$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'' ).

thf('\'fun_app$bu\'_type',type,
    '\'fun_app$bu\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'fun_app$v\'_type',type,
    '\'fun_app$v\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > $o ).

thf('\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'_type',type,
    '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' ).

thf('\'some$\'_type',type,
    '\'some$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$be\'_type',type,
    '\'fun_app$be\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'fthe_elem$c\'_type',type,
    '\'fthe_elem$c\'': '\'A_element_ptr_fset$\'' > '\'A_element_ptr$\'' ).

thf('\'is_element_ptr_kind_n_o_d_e_p_t_r$\'_type',type,
    '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'' ).

thf('\'uvl$\'_type',type,
    '\'uvl$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$ae\'_type',type,
    '\'fun_app$ae\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf('\'case_option$g\'_type',type,
    '\'case_option$g\'': tlbool > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'bind$j\'_type',type,
    '\'bind$j\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf(def_8_type,type,
    def_8: tlbool > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'uuc$\'_type',type,
    '\'uuc$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$ai\'_type',type,
    '\'fun_app$ai\'': '\'C_a_b_j_option_RDocument_ext_k_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_k_sum$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$bh\'_type',type,
    '\'fun_app$bh\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'_type',type,
    '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'': '\'B_character_data_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(def_18_type,type,
    def_18: tlbool > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > tlbool ).

thf('\'type_wf$c\'_type',type,
    '\'type_wf$c\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$bm\'_type',type,
    '\'fun_app$bm\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > $o ).

thf('\'fthe_elem$\'_type',type,
    '\'fthe_elem$\'': '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr$\'' ).

thf('\'truncate$\'_type',type,
    '\'truncate$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'Unit_RObject_ext$\'' ).

thf('\'uup$\'_type',type,
    '\'uup$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$aa\'_type',type,
    '\'fun_app$aa\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' ).

thf('\'case_option$b\'_type',type,
    '\'case_option$b\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'uvt$\'_type',type,
    '\'uvt$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$br\'_type',type,
    '\'fun_app$br\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'get_E_l_e_m_e_n_t$\'_type',type,
    '\'get_E_l_e_m_e_n_t$\'': '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'' ).

thf('\'is_document_kind$\'_type',type,
    '\'is_document_kind$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_bool_fun$\'' ).

thf('\'document_ptr_kinds$\'_type',type,
    '\'document_ptr_kinds$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'' ).

thf('\'none$c\'_type',type,
    '\'none$c\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf('\'some$b\'_type',type,
    '\'some$b\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' ).

thf('\'extend$a\'_type',type,
    '\'extend$a\'': '\'Unit_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf('\'case_option$i\'_type',type,
    '\'case_option$i\'': tlbool > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'member$b\'_type',type,
    '\'member$b\'': '\'A_element_ptr$\'' > '\'A_element_ptr_set$\'' > $o ).

thf('\'l_get_M$a\'_type',type,
    '\'l_get_M$a\'': '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'' > $o ).

thf('\'put_N_o_d_e$\'_type',type,
    '\'put_N_o_d_e$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_fun$\'' ).

thf('\'fun_app$cl\'_type',type,
    '\'fun_app$cl\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option_fun$\'' ).

thf('\'cast_N_o_d_e_2_O_b_j_e_c_t$\'_type',type,
    '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf('\'h$\'_type',type,
    '\'h$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' ).

thf('\'case_option$l\'_type',type,
    '\'case_option$l\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'bind$s\'_type',type,
    '\'bind$s\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'a_type_wf$d\'_type',type,
    '\'a_type_wf$d\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'pair$a\'_type',type,
    '\'pair$a\'': '\'B_character_data_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf('\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'_type',type,
    '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'' > '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_prod$\'' ).

thf(def_13_type,type,
    def_13: '\'Bool_bool_fun$\'' > tlbool > tlbool ).

thf('\'a_type_wf$c\'_type',type,
    '\'a_type_wf$c\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' ).

thf('\'fun_app$ab\'_type',type,
    '\'fun_app$ab\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun$\'' ).

thf('\'l_put_M$a\'_type',type,
    '\'l_put_M$a\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'' > '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'' > $o ).

thf('\'case_option$a\'_type',type,
    '\'case_option$a\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'uvm$\'_type',type,
    '\'uvm$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' ).

thf('\'fun_app$ah\'_type',type,
    '\'fun_app$ah\'': '\'H_option_RCharacterData_ext_i_sum_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_i_sum$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf('\'uvp$\'_type',type,
    '\'uvp$\'': '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' ).

thf('\'get_N_o_d_e$\'_type',type,
    '\'get_N_o_d_e$\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'' ).

thf('\'uva$\'_type',type,
    '\'uva$\'': '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'' ).

thf('\'combine_options$\'_type',type,
    '\'combine_options$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' ).

thf('\'fun_app$by\'_type',type,
    '\'fun_app$by\'': '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' ).

thf('\'bot$b\'_type',type,
    '\'bot$b\'': '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf('\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'_type',type,
    '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'': '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'' ).

thf(sk1_type,type,
    sk1: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf(sk2_type,type,
    sk2: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf(sk3_type,type,
    sk3: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf(sk4_type,type,
    sk4: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > $o ).

thf(sk5_type,type,
    sk5: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf(sk6_type,type,
    sk6: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf(sk7_type,type,
    sk7: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' ).

thf(sk9_type,type,
    sk9: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > $o ).

thf(sk10_type,type,
    sk10: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk11_type,type,
    sk11: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk12_type,type,
    sk12: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk13_type,type,
    sk13: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk14_type,type,
    sk14: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk15_type,type,
    sk15: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk16_type,type,
    sk16: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk17_type,type,
    sk17: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk18_type,type,
    sk18: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' ).

thf(sk19_type,type,
    sk19: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' ).

thf(sk20_type,type,
    sk20: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' ).

thf(sk21_type,type,
    sk21: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' ).

thf(sk22_type,type,
    sk22: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk23_type,type,
    sk23: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk24_type,type,
    sk24: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' ).

thf(sk25_type,type,
    sk25: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf(sk26_type,type,
    sk26: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'' ).

thf(sk27_type,type,
    sk27: '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr$\'' ).

thf(sk28_type,type,
    sk28: '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr_fset$\'' > '\'B_character_data_ptr$\'' ).

thf(sk29_type,type,
    sk29: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > $o ).

thf(sk30_type,type,
    sk30: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf(sk31_type,type,
    sk31: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'' ).

thf(sk43_type,type,
    sk43: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'' > $o ).

thf(sk46_type,type,
    sk46: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'' > $o ).

thf(sk53_type,type,
    sk53: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'' > $o ).

thf(sk70_type,type,
    sk70: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk71_type,type,
    sk71: '\'A_element_ptr_set$\'' > '\'A_element_ptr_fset$\'' ).

thf(sk72_type,type,
    sk72: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'A_element_ptr$\'' ).

thf(sk83_type,type,
    sk83: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_set$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'' ).

thf(sk84_type,type,
    sk84: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'' > $o ).

thf(sk93_type,type,
    sk93: '\'D_document_ptr_set$\'' > '\'D_document_ptr_fset$\'' ).

thf(sk107_type,type,
    sk107: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' > '\'B_character_data_ptr$\'' ).

thf(sk125_type,type,
    sk125: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'' ).

thf(sk138_type,type,
    sk138: '\'B_character_data_ptr_set$\'' > '\'B_character_data_ptr_fset$\'' ).

thf(sk144_type,type,
    sk144: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'' > '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'' ).

thf(sk145_type,type,
    sk145: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'' > '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'' ).

thf(97,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_8 @ B @ C @ D ) )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_9 @ A @ B ) @ ( '\'uuu$\'' @ A @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).

thf(1024,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_8 @ B @ C @ D ) )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_9 @ A @ B ) @ ( '\'uuu$\'' @ A @ C ) ) @ D ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_9 @ A @ B ) @ ( '\'uuu$\'' @ A @ C ) ) @ D )
       => ( '\'fun_app$u\'' @ A @ ( def_8 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(237,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$g\'' @ A @ C )
        = ( '\'bind$g\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).

thf(1823,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$g\'' @ A @ C )
        = ( '\'bind$g\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(52,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'D_document_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).

thf(757,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'D_document_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(758,plain,
    ~ ? [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'D_document_ptr$\''] :
        ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
        = ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(miniscope,[status(thm)],[757]) ).

thf(759,plain,
    ! [B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(cnf,[status(esa)],[758]) ).

thf(760,plain,
    ! [B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(lifteq,[status(thm)],[759]) ).

thf(410,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\''] :
      ( ( '\'fun_app$ag\'' @ '\'uu$\'' @ A )
      = '\'v$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).

thf(2778,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\''] :
      ( ( '\'fun_app$ag\'' @ '\'uu$\'' @ A )
      = '\'v$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(373,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'the$f\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).

thf(2603,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'the$f\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(2604,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'the$f\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) )
      = A ),
    inference(cnf,[status(esa)],[2603]) ).

thf(2605,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'the$f\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[2604]) ).

thf(56,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
    <=> ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).

thf(778,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
       => ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
          = A ) )
      & ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
          = A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(779,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
        ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
       => ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
          = A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
        ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
          = A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[778]) ).

thf(780,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
       != A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    inference(cnf,[status(esa)],[779]) ).

thf(782,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
       != A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[780]) ).

thf(783,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$j\'' @ '\'some$b\'' @ A )
      = ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[782]) ).

thf(4183,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'the$f\'' @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) )
      = A ),
    inference(rewrite,[status(thm)],[2605,783]) ).

thf(182,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => $false )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).

thf(1549,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$a\'' )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(485,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuf$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).

thf(3172,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuf$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(299,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
    <=> ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).

thf(2163,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) ) )
      & ( ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(35,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_29 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_727) ).

thf(645,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_29 @ A @ B )
          = tltrue )
       => ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) )
      & ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       => ( ( def_29 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(186,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).

thf(1564,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(1565,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(cnf,[status(esa)],[1564]) ).

thf(1566,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(lifteq,[status(thm)],[1565]) ).

thf(427,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).

thf(2850,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(2851,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    inference(cnf,[status(esa)],[2850]) ).

thf(2852,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    inference(lifteq,[status(thm)],[2851]) ).

thf(448,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).

thf(2952,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(2953,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(cnf,[status(esa)],[2952]) ).

thf(2954,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
      = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(lifteq,[status(thm)],[2953]) ).

thf(5434,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ B @ A )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ B ) ),
    inference(rewrite,[status(thm)],[2852,2954]) ).

thf(5437,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ '\'some$a\'' @ A )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[1566,5434]) ).

thf(143,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$g\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).

thf(1322,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$g\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(209,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\''] :
      ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
        = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).

thf(1665,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\''] :
      ( ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(99,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'D_document_ptr_fset$\''] :
      ( ( A = B )
     => ( ( '\'fmember$c\'' @ A @ C )
      <=> ( '\'fmember$c\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).

thf(1036,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'D_document_ptr_fset$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$c\'' @ A @ C )
         => ( '\'fmember$c\'' @ B @ C ) )
        & ( ( '\'fmember$c\'' @ B @ C )
         => ( '\'fmember$c\'' @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(419,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
        = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).

thf(2815,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(2816,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( A = B )
       => ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2815]) ).

thf(2818,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2816]) ).

thf(2821,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2818]) ).

thf(2822,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk145 @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_N_o_d_e_2_O_b_j_e_c_t$'),[sk145])]) ).

thf(377,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).

thf(2625,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$b\'' )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A )
       => ( A != '\'none$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(2626,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ( A != '\'none$b\'' )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A )
       => ( A != '\'none$b\'' ) ) ),
    inference(miniscope,[status(thm)],[2625]) ).

thf(2627,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ~ ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A )
      | ( A != '\'none$b\'' ) ),
    inference(cnf,[status(esa)],[2626]) ).

thf(2629,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ~ ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ A ) ),
    inference(lifteq,[status(thm)],[2627]) ).

thf(2630,plain,
    ~ ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ '\'none$b\'' ),
    inference(simp,[status(thm)],[2629]) ).

thf(286,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom647) ).

thf(2094,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(157,axiom,
    '\'l_get_M$\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).

thf(1411,plain,
    '\'l_get_M$\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(5,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != '\'none$f\'' )
     => ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).

thf(497,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != '\'none$f\'' )
     => ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(498,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) )
        = A ) ),
    inference(cnf,[status(esa)],[497]) ).

thf(499,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) )
        = A ) ),
    inference(lifteq,[status(thm)],[498]) ).

thf(90,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$s\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).

thf(1002,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$s\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(1003,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$s\'' @ B @ A ) ),
    inference(cnf,[status(esa)],[1002]) ).

thf(1004,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$s\'' @ B @ A ) ),
    inference(lifteq,[status(thm)],[1003]) ).

thf(474,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
      = ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom566) ).

thf(3078,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
      = ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(3079,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
      = ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(cnf,[status(esa)],[3078]) ).

thf(3080,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
      = ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(lifteq,[status(thm)],[3079]) ).

thf(1,conjecture,
    ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture54) ).

thf(2,negated_conjecture,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(487,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(488,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
     != ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(cnf,[status(esa)],[487]) ).

thf(489,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(lifteq,[status(thm)],[488]) ).

thf(4749,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(rewrite,[status(thm)],[489,2954]) ).

thf(8892,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,4749]) ).

thf(8893,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' )
     != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[8892:[bind(A,$thf( '\'node_ptr$\'' )),bind(B,$thf( '\'h$\'' ))]]) ).

thf(8950,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' )
     != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[8893]) ).

thf(8979,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ B @ A )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( ( '\'bind$k\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
       != ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[1004,8950]) ).

thf(8991,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( B != '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' )
      | ( A
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ A )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
      | ( B != '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[8979]) ).

thf(9011,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
     != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) ),
    inference(simp,[status(thm)],[8991]) ).

thf(9013,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[499,9011]) ).

thf(9055,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( '\'some$f\'' != '\'some$f\'' )
      | ( ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9013]) ).

thf(9077,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9055]) ).

thf(294,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).

thf(2131,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(273,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'is_node_ptr_kind$\'' @ B )
         => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).

thf(2031,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'is_node_ptr_kind$\'' @ B )
         => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(16,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$f\'' )
        <=> ( B = '\'none$f\'' ) )
        & ( ( ( A != '\'none$f\'' )
            & ( B != '\'none$f\'' ) )
         => ( ( '\'the$\'' @ A )
            = ( '\'the$\'' @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).

thf(535,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$f\'' )
         => ( B = '\'none$f\'' ) )
        & ( ( B = '\'none$f\'' )
         => ( A = '\'none$f\'' ) )
        & ( ( ( A != '\'none$f\'' )
            & ( B != '\'none$f\'' ) )
         => ( ( '\'the$\'' @ A )
            = ( '\'the$\'' @ B ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(536,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( sk4 @ A @ B )
      | ( A != '\'none$f\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[535]) ).

thf(553,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != '\'none$f\'' )
      | ( A = B )
      | ( sk4 @ A @ B ) ),
    inference(lifteq,[status(thm)],[536]) ).

thf(554,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'none$f\'' = A )
      | ( sk4 @ '\'none$f\'' @ A ) ),
    inference(simp,[status(thm)],[553]) ).

thf(3,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( '\'none$f\''
     != ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).

thf(490,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( '\'none$f\''
     != ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(491,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( '\'none$f\''
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    inference(miniscope,[status(thm)],[490]) ).

thf(492,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( '\'none$f\''
     != ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    inference(cnf,[status(esa)],[491]) ).

thf(493,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$az\'' @ '\'some$f\'' @ A )
     != '\'none$f\'' ),
    inference(lifteq,[status(thm)],[492]) ).

thf(3573,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( sk4 @ '\'none$f\'' @ A )
      | ( A
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[554,493]) ).

thf(3574,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] : ( sk4 @ '\'none$f\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[3573:[bind(A,$thf( '\'fun_app$az\'' @ '\'some$f\'' @ D )),bind(B,$thf( D ))]]) ).

thf(3666,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] : ( sk4 @ '\'none$f\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) ),
    inference(simp,[status(thm)],[3574]) ).

thf(220,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$a\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'fun_app$aa\'' @ ( '\'fun_app$ab\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).

thf(1729,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$a\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'fun_app$aa\'' @ ( '\'fun_app$ab\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(371,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'uvq$\'' @ A @ B ) @ C )
      = ( '\'case_option$b\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) @ ( '\'uvp$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).

thf(2595,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'uvq$\'' @ A @ B ) @ C )
      = ( '\'case_option$b\'' @ ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) @ ( '\'uvp$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(22,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$v\'' @ '\'uva$\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).

thf(579,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$v\'' @ '\'uva$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(580,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$v\'' @ '\'uva$\'' @ A ),
    inference(cnf,[status(esa)],[579]) ).

thf(646,plain,
    ( ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( ( def_29 @ A @ B )
          = tltrue )
       => ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) )
    & ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       => ( ( def_29 @ A @ B )
          = tltrue ) ) ),
    inference(miniscope,[status(thm)],[645]) ).

thf(647,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
      | ( ( def_29 @ A @ B )
        = tltrue ) ),
    inference(cnf,[status(esa)],[646]) ).

thf(649,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_29 @ A @ B )
        = tltrue )
      | ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[647]) ).

thf(650,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_29 @ A @ B )
        = tltrue )
      | ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(simp,[status(thm)],[649]) ).

thf(6313,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( def_29 @ B @ C )
        = tltrue )
      | ( ( '\'fun_app$v\'' @ '\'uva$\'' @ A )
       != ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,650]) ).

thf(6314,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uva$\'' @ A )
      = tltrue ),
    inference(pattern_uni,[status(thm)],[6313:[bind(A,$thf( '\'the$e\'' @ D )),bind(B,$thf( '\'uva$\'' )),bind(C,$thf( D ))]]) ).

thf(6317,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uva$\'' @ A )
      = tltrue ),
    inference(simp,[status(thm)],[6314]) ).

thf(243,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'uur$\'' )
      = '\'none$b\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).

thf(1850,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'uur$\'' )
      = '\'none$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(350,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).

thf(2480,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(263,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ? [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
          ( ( B
            = ( '\'finsert$b\'' @ A @ C ) )
          & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom609) ).

thf(1982,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ? [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
          ( ( B
            = ( '\'finsert$b\'' @ A @ C ) )
          & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(82,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
        <=> ( B = '\'none$\'' ) )
        & ( ( ( A != '\'none$\'' )
            & ( B != '\'none$\'' ) )
         => ( ( '\'the$e\'' @ A )
            = ( '\'the$e\'' @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).

thf(947,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( B = '\'none$\'' ) )
        & ( ( B = '\'none$\'' )
         => ( A = '\'none$\'' ) )
        & ( ( ( A != '\'none$\'' )
            & ( B != '\'none$\'' ) )
         => ( ( '\'the$e\'' @ A )
            = ( '\'the$e\'' @ B ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(951,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk43 @ A @ B )
      | ( B != '\'none$\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[947]) ).

thf(964,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( B != '\'none$\'' )
      | ( A = B )
      | ( sk43 @ A @ B ) ),
    inference(lifteq,[status(thm)],[951]) ).

thf(965,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$\'' )
      | ( sk43 @ A @ '\'none$\'' ) ),
    inference(simp,[status(thm)],[964]) ).

thf(348,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = '\'none$\'' )
    <=> ~ ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
            = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).

thf(2449,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = '\'none$\'' )
       => ~ ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
              = A ) )
      & ( ~ ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
              = A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(2450,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = '\'none$\'' )
       => ~ ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
              = A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ~ ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
              = A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = '\'none$\'' ) ) ),
    inference(miniscope,[status(thm)],[2449]) ).

thf(2452,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' )
      | ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
       != A ) ),
    inference(cnf,[status(esa)],[2450]) ).

thf(2455,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' )
      | ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
       != A ) ),
    inference(lifteq,[status(thm)],[2452]) ).

thf(2456,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) )
     != '\'none$\'' ),
    inference(simp,[status(thm)],[2455]) ).

thf(3982,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk43 @ A @ '\'none$\'' )
      | ( A
       != ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[965,2456]) ).

thf(3983,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) @ '\'none$\'' ),
    inference(pattern_uni,[status(thm)],[3982:[bind(A,$thf( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ E ) )),bind(B,$thf( E ))]]) ).

thf(4029,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[3983]) ).

thf(452,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$l\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).

thf(2968,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$l\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(2969,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$l\'' @ B @ A ) ),
    inference(cnf,[status(esa)],[2968]) ).

thf(2970,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$l\'' @ B @ A ) ),
    inference(lifteq,[status(thm)],[2969]) ).

thf(6036,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ B @ A )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ B ) ),
    inference(rewrite,[status(thm)],[2970,2954]) ).

thf(6042,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) @ '\'none$\'' ),
    inference(rewrite,[status(thm)],[4029,6036]) ).

thf(327,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_18 @ B @ C @ D ) )
    <=> ~ ( ( ( D = '\'none$\'' )
            & ~ ( '\'fun_app$u\'' @ A @ B ) )
          | ( ( D
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
            & ~ ( '\'fun_app$u\'' @ A @ ( def_19 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).

thf(2331,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_18 @ B @ C @ D ) )
       => ~ ( ( ( D = '\'none$\'' )
              & ~ ( '\'fun_app$u\'' @ A @ B ) )
            | ( ( D
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
              & ~ ( '\'fun_app$u\'' @ A @ ( def_19 @ C @ D ) ) ) ) )
      & ( ~ ( ( ( D = '\'none$\'' )
              & ~ ( '\'fun_app$u\'' @ A @ B ) )
            | ( ( D
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
              & ~ ( '\'fun_app$u\'' @ A @ ( def_19 @ C @ D ) ) ) )
       => ( '\'fun_app$u\'' @ A @ ( def_18 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(469,axiom,
    '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis61) ).

thf(3061,plain,
    '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(120,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).

thf(1181,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1182,plain,
    ( ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
        ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) )
       => ( A = B ) )
    & ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
        ( ( A = B )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) ) ) ),
    inference(miniscope,[status(thm)],[1181]) ).

thf(1183,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != B )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) ) ),
    inference(cnf,[status(esa)],[1182]) ).

thf(1185,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != B )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ '\'bot$b\'' ) ) ),
    inference(lifteq,[status(thm)],[1183]) ).

thf(1186,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[1185]) ).

thf(203,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ( B
                = ( '\'finsert$b\'' @ A @ C ) )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).

thf(1641,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ~ ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ~ ( ( B
                = ( '\'finsert$b\'' @ A @ C ) )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(1642,plain,
    ~ ? [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
        ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ? [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
              ( ( B
                = ( '\'finsert$b\'' @ A @ C ) )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    inference(miniscope,[status(thm)],[1641]) ).

thf(1644,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[1642]) ).

thf(4342,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( sk70 @ C @ B ) )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1186,1644]) ).

thf(4343,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) @ A ) ),
    inference(pattern_uni,[status(thm)],[4342:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( '\'finsert$b\'' @ D @ '\'bot$b\'' ))]]) ).

thf(4350,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) @ A ) ),
    inference(simp,[status(thm)],[4343]) ).

thf(4678,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3061,4350]) ).

thf(4682,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ '\'node_ptr$\'' )
       != ( '\'fmember$\'' @ A ) )
      | ( ( sk70 @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) @ A )
       != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[4678]) ).

thf(55,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$q\'' @ '\'none$\'' @ A )
      = '\'none$c\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).

thf(775,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$q\'' @ '\'none$\'' @ A )
      = '\'none$c\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(776,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$q\'' @ '\'none$\'' @ A )
      = '\'none$c\'' ),
    inference(cnf,[status(esa)],[775]) ).

thf(777,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$q\'' @ '\'none$\'' @ A )
      = '\'none$c\'' ),
    inference(lifteq,[status(thm)],[776]) ).

thf(17,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
        = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).

thf(555,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(126,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).

thf(1211,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bx\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(358,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'a_type_wf$a\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
        & ! [B: '\'B_character_data_ptr$\''] :
            ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
             != '\'none$\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).

thf(2512,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'a_type_wf$a\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
          & ! [B: '\'B_character_data_ptr$\''] :
              ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
               != '\'none$\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
          & ! [B: '\'B_character_data_ptr$\''] :
              ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
               != '\'none$\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'a_type_wf$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(91,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$a\'' @ A @ B @ C )
    <=> ( '\'l_get_M$a\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).

thf(1005,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ( '\'l_put_M$a\'' @ A @ B @ C )
       => ( '\'l_get_M$a\'' @ C @ A @ B ) )
      & ( ( '\'l_get_M$a\'' @ C @ A @ B )
       => ( '\'l_put_M$a\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(288,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_N_o_d_e$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).

thf(2102,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_N_o_d_e$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(2103,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'put_N_o_d_e$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[2102]) ).

thf(2104,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'put_N_o_d_e$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[2103]) ).

thf(54,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
         => ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
           != '\'none$a\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).

thf(771,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
         => ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
           != '\'none$a\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(772,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
      | ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
        = '\'none$a\'' )
      | ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(cnf,[status(esa)],[771]) ).

thf(774,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
        = '\'none$a\'' )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
      | ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(lifteq,[status(thm)],[772]) ).

thf(272,axiom,
    '\'type_wf$b\'' = '\'a_type_wf$b\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).

thf(2029,plain,
    '\'type_wf$b\'' = '\'a_type_wf$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(2030,plain,
    '\'type_wf$b\'' = '\'a_type_wf$b\'',
    inference(lifteq,[status(thm)],[2029]) ).

thf(15190,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
        = '\'none$a\'' )
      | ~ ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
      | ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ C ) ),
    inference(rewrite,[status(thm)],[774,2030]) ).

thf(42,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
    <=> ( ( ( C = '\'none$\'' )
         => ( A = tltrue ) )
        & ( ( C != '\'none$\'' )
         => ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).

thf(670,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
       => ( ( ( C = '\'none$\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$\'' )
           => ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ) )
      & ( ( ( ( C = '\'none$\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$\'' )
           => ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(671,plain,
    ( ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
       => ( ( ( C = '\'none$\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$\'' )
           => ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ) )
    & ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( ( ( C = '\'none$\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$\'' )
           => ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ) ),
    inference(miniscope,[status(thm)],[670]) ).

thf(672,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ( C != '\'none$\'' )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[671]) ).

thf(682,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ( C != '\'none$\'' )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[672]) ).

thf(683,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] : ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[682]) ).

thf(381,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( def_7 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$u\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_705) ).

thf(2644,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( ( def_7 @ A @ B )
          = tltrue )
       => ( '\'fun_app$u\'' @ A @ B ) )
      & ( ( '\'fun_app$u\'' @ A @ B )
       => ( ( def_7 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(334,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
    <=> ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).

thf(2381,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$\'' )
       => ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) )
      & ( ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
       => ( A != '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(197,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A = '\'bot$b\'' )
     => ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).

thf(1614,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A = '\'bot$b\'' )
     => ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1615,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( A = '\'bot$b\'' )
     => ~ ? [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ),
    inference(miniscope,[status(thm)],[1614]) ).

thf(1616,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( A != '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ),
    inference(cnf,[status(esa)],[1615]) ).

thf(1617,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( A != '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[1616]) ).

thf(1618,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' ),
    inference(simp,[status(thm)],[1617]) ).

thf(18,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
          ( A
         != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
    <=> ( A = '\'none$f\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).

thf(563,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
       => ( A = '\'none$f\'' ) )
      & ( ( A = '\'none$f\'' )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(564,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
        ( ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
              ( A
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
       => ( A = '\'none$f\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
        ( ( A = '\'none$f\'' )
       => ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
              ( A
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[563]) ).

thf(566,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk6 @ A ) ) )
      | ( A = '\'none$f\'' ) ),
    inference(cnf,[status(esa)],[564]) ).

thf(569,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk6 @ A ) )
        = A )
      | ( A = '\'none$f\'' ) ),
    inference(lifteq,[status(thm)],[566]) ).

thf(9019,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk6 @ A ) )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[569,9011]) ).

thf(9053,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( '\'some$f\'' != '\'some$f\'' )
      | ( ( sk6 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9019]) ).

thf(9075,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( ( sk6 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9053]) ).

thf(10736,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk6 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ C )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9075,3080]) ).

thf(10737,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk6 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[10736:[bind(A,$thf( A )),bind(B,$thf( '\'node_ptr$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(41,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ E ) )
           => ( ( '\'fun_app$s\'' @ C @ E )
              = ( '\'fun_app$s\'' @ D @ E ) ) ) )
     => ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).

thf(663,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ E ) )
           => ( ( '\'fun_app$s\'' @ C @ E )
              = ( '\'fun_app$s\'' @ D @ E ) ) ) )
     => ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(665,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != B )
      | ( B
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk18 @ D @ C @ B @ A ) ) )
      | ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    inference(cnf,[status(esa)],[663]) ).

thf(668,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != B )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk18 @ D @ C @ B @ A ) )
        = B )
      | ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[665]) ).

thf(669,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk18 @ C @ B @ A @ A ) )
        = A )
      | ( ( '\'bind$k\'' @ A @ B )
        = ( '\'bind$k\'' @ A @ C ) ) ),
    inference(simp,[status(thm)],[668]) ).

thf(6859,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( '\'bind$k\'' @ A @ B )
        = ( '\'bind$k\'' @ A @ C ) )
      | ( A != '\'none$f\'' )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk18 @ C @ B @ A @ A ) )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[669,493]) ).

thf(6860,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$k\'' @ C @ B )
        = ( '\'bind$k\'' @ C @ A ) )
      | ( C != '\'none$f\'' ) ),
    inference(pattern_uni,[status(thm)],[6859:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( sk18 @ E @ F @ H @ H ))]]) ).

thf(6906,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$k\'' @ '\'none$f\'' @ B )
      = ( '\'bind$k\'' @ '\'none$f\'' @ A ) ),
    inference(simp,[status(thm)],[6860]) ).

thf(421,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$k\'' @ A @ '\'uus$\'' )
      = '\'none$b\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).

thf(2827,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$k\'' @ A @ '\'uus$\'' )
      = '\'none$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(2828,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$k\'' @ A @ '\'uus$\'' )
      = '\'none$b\'' ),
    inference(cnf,[status(esa)],[2827]) ).

thf(2829,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$k\'' @ A @ '\'uus$\'' )
      = '\'none$b\'' ),
    inference(lifteq,[status(thm)],[2828]) ).

thf(6923,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$k\'' @ '\'none$f\'' @ A )
        = '\'none$b\'' )
      | ( ( '\'bind$k\'' @ '\'none$f\'' @ B )
       != ( '\'bind$k\'' @ C @ '\'uus$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6906,2829]) ).

thf(6924,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$k\'' @ '\'none$f\'' @ A )
      = '\'none$b\'' ),
    inference(pattern_uni,[status(thm)],[6923:[bind(A,$thf( A )),bind(B,$thf( '\'uus$\'' )),bind(C,$thf( '\'none$f\'' ))]]) ).

thf(13424,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk6 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[10737,6924]) ).

thf(133,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
        <=> ( B = '\'none$a\'' ) )
        & ( ( ( A != '\'none$a\'' )
            & ( B != '\'none$a\'' ) )
         => ( ( '\'the$g\'' @ A )
            = ( '\'the$g\'' @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).

thf(1256,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( B = '\'none$a\'' ) )
        & ( ( B = '\'none$a\'' )
         => ( A = '\'none$a\'' ) )
        & ( ( ( A != '\'none$a\'' )
            & ( B != '\'none$a\'' ) )
         => ( ( '\'the$g\'' @ A )
            = ( '\'the$g\'' @ B ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(1263,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk53 @ A @ B )
      | ( B != '\'none$a\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1256]) ).

thf(1268,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( B != '\'none$a\'' )
      | ( A = B )
      | ( sk53 @ A @ B ) ),
    inference(lifteq,[status(thm)],[1263]) ).

thf(1269,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$a\'' )
      | ( sk53 @ A @ '\'none$a\'' ) ),
    inference(simp,[status(thm)],[1268]) ).

thf(229,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuc$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).

thf(1791,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuc$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(1792,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuc$\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[1791]) ).

thf(1793,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuc$\'' @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[1792]) ).

thf(211,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) )
    <=> ( '\'fmember$d\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).

thf(1692,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) )
       => ( '\'fmember$d\'' @ A @ B ) )
      & ( ( '\'fmember$d\'' @ A @ B )
       => ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(162,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
        & ( ( ( C = '\'none$\'' )
            & ( A = tltrue ) )
         => $false )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( '\'fun_app$v\'' @ B @ D ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).

thf(1437,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
        & ~ ( ( C = '\'none$\'' )
            & ( A = tltrue ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ~ ( ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( '\'fun_app$v\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(472,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'some$\'' )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).

thf(3071,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'some$\'' )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(3072,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'some$\'' )
      = A ),
    inference(cnf,[status(esa)],[3071]) ).

thf(3073,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'some$\'' )
      = A ),
    inference(lifteq,[status(thm)],[3072]) ).

thf(470,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).

thf(3062,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(3063,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[3062]) ).

thf(3064,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) )
      = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[3063]) ).

thf(455,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ) @ B )
      = ( '\'fun_app$g\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).

thf(2981,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ) @ B )
      = ( '\'fun_app$g\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(2982,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ) @ B )
      = ( '\'fun_app$g\'' @ B @ A ) ),
    inference(cnf,[status(esa)],[2981]) ).

thf(2983,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ) @ B )
      = ( '\'fun_app$g\'' @ B @ A ) ),
    inference(lifteq,[status(thm)],[2982]) ).

thf(6331,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ B @ A )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ) @ B ) ),
    inference(rewrite,[status(thm)],[2983,2954]) ).

thf(7684,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
      = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B ) ),
    inference(rewrite,[status(thm)],[3064,6331]) ).

thf(7690,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A
        = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ C ) )
      | ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'some$\'' )
       != ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ C ) ) ) ) @ '\'some$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3073,7684]) ).

thf(7691,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
      = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[7690:[bind(A,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ I ) @ H ) ) )),bind(B,$thf( I )),bind(C,$thf( H ))]]) ).

thf(7704,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
      = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ),
    inference(simp,[status(thm)],[7691]) ).

thf(7688,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
        = C )
      | ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
       != ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ C ) @ '\'some$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[7684,3073]) ).

thf(7689,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
      = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[7688:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ I ) @ H ) ) ))]]) ).

thf(7703,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
      = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) ) ),
    inference(simp,[status(thm)],[7689]) ).

thf(461,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).

thf(3023,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(3024,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      = A ),
    inference(cnf,[status(esa)],[3023]) ).

thf(3025,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[3024]) ).

thf(4751,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$d\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) )
      = A ),
    inference(rewrite,[status(thm)],[3025,2954]) ).

thf(8104,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) )
        = C )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,4751]) ).

thf(8105,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A )
      = ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[8104:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8191,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A )
      = ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[8105]) ).

thf(8650,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ) ) )
      = ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ),
    inference(rewrite,[status(thm)],[7704,8191]) ).

thf(8952,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
       != ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8650,8950]) ).

thf(8953,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(pattern_uni,[status(thm)],[8952:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ G ) @ F ) ))]]) ).

thf(9003,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[8953]) ).

thf(119,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( A = B )
     => ( ( '\'fmember$a\'' @ C @ A )
      <=> ( '\'fmember$a\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).

thf(1173,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$a\'' @ C @ A )
         => ( '\'fmember$a\'' @ C @ B ) )
        & ( ( '\'fmember$a\'' @ C @ B )
         => ( '\'fmember$a\'' @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(330,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( ( '\'finsert$b\'' @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).

thf(2363,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( ( '\'finsert$b\'' @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(280,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).

thf(2077,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(50,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_fset$\''] :
      ( ( A = B )
     => ( ( '\'fmember$d\'' @ A @ C )
      <=> ( '\'fmember$d\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).

thf(730,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_fset$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$d\'' @ A @ C )
         => ( '\'fmember$d\'' @ B @ C ) )
        & ( ( '\'fmember$d\'' @ B @ C )
         => ( '\'fmember$d\'' @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(138,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
     => ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).

thf(1290,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
     => ( ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(255,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A )
    <=> ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).

thf(1939,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
         != '\'none$\'' ) )
      & ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
         != '\'none$\'' )
       => ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(314,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$e\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ ( '\'uuh$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).

thf(2248,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$e\'' @ ( '\'bind$g\'' @ A @ B ) @ C )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ ( '\'uuh$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(38,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$j\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$p\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).

thf(655,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$j\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$p\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(8,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$f\'' )
         => $false )
        & ( ( A
            = ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).

thf(511,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$f\'' )
        & ( A
         != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'the$\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(58,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_19 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_717) ).

thf(788,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_19 @ A @ B )
          = tltrue )
       => ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) )
      & ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       => ( ( def_19 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(789,plain,
    ( ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( ( def_19 @ A @ B )
          = tltrue )
       => ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) )
    & ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       => ( ( def_19 @ A @ B )
          = tltrue ) ) ),
    inference(miniscope,[status(thm)],[788]) ).

thf(791,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_19 @ A @ B )
       != tltrue )
      | ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(cnf,[status(esa)],[789]) ).

thf(794,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_19 @ A @ B )
       != tltrue )
      | ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[791]) ).

thf(61,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$v\'' @ '\'uvg$\'' @ A )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).

thf(819,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ~ ( '\'fun_app$v\'' @ '\'uvg$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(820,plain,
    ~ ? [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$v\'' @ '\'uvg$\'' @ A ),
    inference(miniscope,[status(thm)],[819]) ).

thf(821,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ~ ( '\'fun_app$v\'' @ '\'uvg$\'' @ A ),
    inference(cnf,[status(esa)],[820]) ).

thf(17090,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_19 @ A @ B )
       != tltrue )
      | ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       != ( '\'fun_app$v\'' @ '\'uvg$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[794,821]) ).

thf(17091,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(pattern_uni,[status(thm)],[17090:[bind(A,$thf( '\'uvg$\'' )),bind(B,$thf( D )),bind(C,$thf( '\'the$e\'' @ D ))]]) ).

thf(17113,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(simp,[status(thm)],[17091]) ).

thf(114,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
    <=> ~ ( ( ( B = '\'none$\'' )
            & ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
          | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).

thf(1137,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
       => ~ ( ( ( B = '\'none$\'' )
              & ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
            | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
                ( ( B
                  = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
                & ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) ) )
      & ( ~ ( ( ( B = '\'none$\'' )
              & ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
            | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
                ( ( B
                  = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
                & ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) )
       => ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(389,axiom,
    '\'l_get_D_o_c_u_m_e_n_t_lemmas$\'' @ '\'type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).

thf(2686,plain,
    '\'l_get_D_o_c_u_m_e_n_t_lemmas$\'' @ '\'type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(14,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = '\'none$c\'' )
    <=> ~ ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
            = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).

thf(526,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = '\'none$c\'' )
       => ~ ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
              ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
              = A ) )
      & ( ~ ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
              ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
              = A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = '\'none$c\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(527,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = '\'none$c\'' )
       => ~ ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
              ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
              = A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ~ ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
              ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
              = A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
          = '\'none$c\'' ) ) ),
    inference(miniscope,[status(thm)],[526]) ).

thf(529,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != '\'none$c\'' )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
       != A ) ),
    inference(cnf,[status(esa)],[527]) ).

thf(532,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != '\'none$c\'' )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
       != A ) ),
    inference(lifteq,[status(thm)],[529]) ).

thf(533,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
     != '\'none$c\'' ),
    inference(simp,[status(thm)],[532]) ).

thf(267,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$j\'' @ '\'some$b\'' @ A )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).

thf(1999,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$j\'' @ '\'some$b\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$j\'' @ '\'some$b\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(129,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$c\'' @ A @ B @ C )
      = ( '\'case_option$a\'' @ C @ ( '\'uvs$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).

thf(1233,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$c\'' @ A @ B @ C )
      = ( '\'case_option$a\'' @ C @ ( '\'uvs$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(173,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
     => ( A != '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).

thf(1507,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
     => ( A != '\'none$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(213,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
        = '\'none$a\'' )
    <=> ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
            = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).

thf(1705,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
          = '\'none$a\'' )
       => ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
              = A ) )
      & ( ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
              = A )
       => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
          = '\'none$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(459,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
     => ( ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).

thf(3017,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
     => ( ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(105,axiom,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\'',C: '\'A_element_ptr$\''] :
      ( ( A = B )
     => ( ( '\'fmember$d\'' @ C @ A )
      <=> ( '\'fmember$d\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).

thf(1078,plain,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\'',C: '\'A_element_ptr$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$d\'' @ C @ A )
         => ( '\'fmember$d\'' @ C @ B ) )
        & ( ( '\'fmember$d\'' @ C @ B )
         => ( '\'fmember$d\'' @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(147,axiom,
    '\'l_get_M$c\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).

thf(1345,plain,
    '\'l_get_M$c\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(300,axiom,
    '\'type_wf$a\'' = '\'a_type_wf$a\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).

thf(2168,plain,
    '\'type_wf$a\'' = '\'a_type_wf$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(2169,plain,
    '\'type_wf$a\'' = '\'a_type_wf$a\'',
    inference(lifteq,[status(thm)],[2168]) ).

thf(3217,plain,
    '\'l_get_M$c\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ '\'a_type_wf$a\'' @ '\'character_data_ptr_kinds$\'',
    inference(rewrite,[status(thm)],[1345,2169]) ).

thf(195,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).

thf(1608,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(245,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
        <=> ( B = '\'none$b\'' ) )
        & ( ( ( A != '\'none$b\'' )
            & ( B != '\'none$b\'' ) )
         => ( ( '\'the$d\'' @ A )
            = ( '\'the$d\'' @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).

thf(1857,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => ( B = '\'none$b\'' ) )
        & ( ( B = '\'none$b\'' )
         => ( A = '\'none$b\'' ) )
        & ( ( ( A != '\'none$b\'' )
            & ( B != '\'none$b\'' ) )
         => ( ( '\'the$d\'' @ A )
            = ( '\'the$d\'' @ B ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(1861,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ A @ B )
      | ( A != '\'none$b\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1857]) ).

thf(1869,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ( A = B )
      | ( sk84 @ A @ B ) ),
    inference(lifteq,[status(thm)],[1861]) ).

thf(1870,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'none$b\'' = A )
      | ( sk84 @ '\'none$b\'' @ A ) ),
    inference(simp,[status(thm)],[1869]) ).

thf(4541,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( A
       != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1870,489]) ).

thf(4542,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(pattern_uni,[status(thm)],[4541:[bind(A,$thf( '\'fun_app$g\'' @ '\'some$\'' @ D )),bind(B,$thf( D ))]]) ).

thf(4574,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(simp,[status(thm)],[4542]) ).

thf(4576,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( '\'none$b\'' != '\'none$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1870,4574]) ).

thf(4577,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(pattern_uni,[status(thm)],[4576:[]]) ).

thf(5056,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[4577,2954]) ).

thf(8096,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ C )
      | ( sk84 @ C @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,5056]) ).

thf(8097,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ C ) @ B ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(pattern_uni,[status(thm)],[8096:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ G ) @ F ))]]) ).

thf(8182,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ C ) @ B ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(simp,[status(thm)],[8097]) ).

thf(480,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
        & ( ( ( C = '\'none$b\'' )
            & ( A = tltrue ) )
         => $false )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( ( C
                = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
              & ( '\'fun_app$x\'' @ B @ D ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).

thf(3120,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
        & ~ ( ( C = '\'none$b\'' )
            & ( A = tltrue ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ~ ( ( C
                = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
              & ( '\'fun_app$x\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(39,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).

thf(658,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(659,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(cnf,[status(esa)],[658]) ).

thf(6505,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ C ) ),
    inference(rewrite,[status(thm)],[659,2030]) ).

thf(6,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != '\'none$f\'' )
    <=> ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).

thf(500,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( A != '\'none$f\'' )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) )
      & ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
       => ( A != '\'none$f\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(486,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).

thf(3175,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$ca\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(43,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
          ( ( '\'fmember$a\'' @ C @ A )
        <=> ( '\'fmember$a\'' @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).

thf(689,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
          ( ( ( '\'fmember$a\'' @ C @ A )
           => ( '\'fmember$a\'' @ C @ B ) )
          & ( ( '\'fmember$a\'' @ C @ B )
           => ( '\'fmember$a\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(690,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
            ( ( '\'fmember$a\'' @ C @ A )
           => ( '\'fmember$a\'' @ C @ B ) )
        & ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
            ( ( '\'fmember$a\'' @ C @ B )
           => ( '\'fmember$a\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(miniscope,[status(thm)],[689]) ).

thf(694,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ A )
      | ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[690]) ).

thf(698,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
      | ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ A )
      | ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[694]) ).

thf(239,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( '\'none$\''
     != ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).

thf(1835,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( '\'none$\''
     != ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(477,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_22 @ B @ C @ D ) )
    <=> ~ ( ( ( D = '\'none$b\'' )
            & ~ ( '\'fun_app$u\'' @ A @ B ) )
          | ( ( D
              = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
            & ~ ( '\'fun_app$u\'' @ A @ ( def_23 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).

thf(3088,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_22 @ B @ C @ D ) )
       => ~ ( ( ( D = '\'none$b\'' )
              & ~ ( '\'fun_app$u\'' @ A @ B ) )
            | ( ( D
                = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
              & ~ ( '\'fun_app$u\'' @ A @ ( def_23 @ C @ D ) ) ) ) )
      & ( ~ ( ( ( D = '\'none$b\'' )
              & ~ ( '\'fun_app$u\'' @ A @ B ) )
            | ( ( D
                = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
              & ~ ( '\'fun_app$u\'' @ A @ ( def_23 @ C @ D ) ) ) )
       => ( '\'fun_app$u\'' @ A @ ( def_22 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(253,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'uvo$\'' @ A @ B ) @ C )
      = ( '\'case_option$c\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) @ ( '\'uvn$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).

thf(1935,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'uvo$\'' @ A @ B ) @ C )
      = ( '\'case_option$c\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) @ ( '\'uvn$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(151,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).

thf(1359,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$bs\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(184,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).

thf(1560,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(1561,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
      = '\'none$\'' ),
    inference(cnf,[status(esa)],[1560]) ).

thf(1562,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
      = '\'none$\'' ),
    inference(lifteq,[status(thm)],[1561]) ).

thf(259,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).

thf(1965,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(1966,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$a\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[1965]) ).

thf(1967,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$a\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[1966]) ).

thf(13559,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ D )
        = ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ C @ D ) ) )
      | ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
       != ( '\'bind$f\'' @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1562,1967]) ).

thf(13560,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ B )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(pattern_uni,[status(thm)],[13559:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'uup$\'' ))]]) ).

thf(13579,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ B )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(simp,[status(thm)],[13560]) ).

thf(437,axiom,
    ( '\'h$a\''
    = ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'h$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis58) ).

thf(2897,plain,
    ( '\'h$a\''
    = ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'h$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(2898,plain,
    ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'h$\'' )
    = '\'h$a\'' ),
    inference(lifteq,[status(thm)],[2897]) ).

thf(291,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).

thf(2120,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(2121,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[2120]) ).

thf(2122,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'put_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
      = ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) ),
    inference(lifteq,[status(thm)],[2121]) ).

thf(5420,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) )
      = ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) ),
    inference(rewrite,[status(thm)],[2122,2104]) ).

thf(5421,plain,
    ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) @ '\'h$\'' )
    = '\'h$a\'' ),
    inference(rewrite,[status(thm)],[2898,5420]) ).

thf(149,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).

thf(1353,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(1354,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ),
    inference(cnf,[status(esa)],[1353]) ).

thf(1355,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ),
    inference(lifteq,[status(thm)],[1354]) ).

thf(476,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).

thf(3085,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(3086,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(cnf,[status(esa)],[3085]) ).

thf(3087,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(lifteq,[status(thm)],[3086]) ).

thf(9635,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[1355,5437,3087]) ).

thf(9652,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[5421,9635]) ).

thf(9653,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(pattern_uni,[status(thm)],[9652:[bind(A,$thf( '\'element_ptr$\'' )),bind(B,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(1508,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
     => ( A != '\'none$a\'' ) ),
    inference(miniscope,[status(thm)],[1507]) ).

thf(1509,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A
       != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
      | ( A != '\'none$a\'' ) ),
    inference(cnf,[status(esa)],[1508]) ).

thf(1510,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A
       != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
      | ( A != '\'none$a\'' ) ),
    inference(lifteq,[status(thm)],[1509]) ).

thf(1511,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ '\'some$a\'' @ A )
     != '\'none$a\'' ),
    inference(simp,[status(thm)],[1510]) ).

thf(5603,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' ),
    inference(rewrite,[status(thm)],[1511,5437]) ).

thf(9702,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[9653,5603]) ).

thf(9703,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[9702:[bind(A,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(9784,plain,
    ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' )
    | ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[9653,9703]) ).

thf(9785,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[9784:[]]) ).

thf(1323,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$g\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) )
      = A ),
    inference(cnf,[status(esa)],[1322]) ).

thf(1324,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$g\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[1323]) ).

thf(5604,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      = A ),
    inference(rewrite,[status(thm)],[1324,5437]) ).

thf(9692,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
        = A )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[9653,5604]) ).

thf(9693,plain,
    ( ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' )
    = ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[9692:[bind(A,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(10060,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(rewrite,[status(thm)],[9785,9693]) ).

thf(10427,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,10060]) ).

thf(10428,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[10427:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(13644,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ B )
       != '\'none$a\'' )
      | ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[13579,10428]) ).

thf(13654,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ B )
       != '\'none$a\'' )
      | ( A
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) )
      | ( ( '\'uub$\'' @ '\'uup$\'' @ B )
       != '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(simp,[status(thm)],[13644]) ).

thf(13704,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ A )
       != '\'none$a\'' )
      | ( ( '\'uub$\'' @ '\'uup$\'' @ A )
       != '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(simp,[status(thm)],[13654]) ).

thf(13750,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
       != '\'none$a\'' )
      | ( ( '\'uub$\'' @ '\'uup$\'' @ C )
       != '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ B )
       != ( '\'bind$a\'' @ '\'none$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13579,13704]) ).

thf(13751,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
       != '\'none$a\'' )
      | ( ( '\'uub$\'' @ '\'uup$\'' @ B )
       != '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(pattern_uni,[status(thm)],[13750:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(145,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuc$\'' @ A @ B ) @ C )
      = ( '\'bind$c\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).

thf(1335,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuc$\'' @ A @ B ) @ C )
      = ( '\'bind$c\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1336,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuc$\'' @ A @ B ) @ C )
      = ( '\'bind$c\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[1335]) ).

thf(1337,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uuc$\'' @ A @ B ) @ C )
      = ( '\'bind$c\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(lifteq,[status(thm)],[1336]) ).

thf(12770,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uuc$\'' @ A @ B ) )
      = ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ A ) @ B ) ),
    inference(rewrite,[status(thm)],[1337,6036,5434]) ).

thf(790,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
      | ( ( def_19 @ A @ B )
        = tltrue ) ),
    inference(cnf,[status(esa)],[789]) ).

thf(792,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_19 @ A @ B )
        = tltrue )
      | ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[790]) ).

thf(793,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_19 @ A @ B )
        = tltrue )
      | ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(simp,[status(thm)],[792]) ).

thf(16975,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( def_19 @ B @ C )
        = tltrue )
      | ( ( '\'fun_app$v\'' @ '\'uva$\'' @ A )
       != ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,793]) ).

thf(16976,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uva$\'' @ A )
      = tltrue ),
    inference(pattern_uni,[status(thm)],[16975:[bind(A,$thf( '\'the$e\'' @ D )),bind(B,$thf( '\'uva$\'' )),bind(C,$thf( D ))]]) ).

thf(16979,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uva$\'' @ A )
      = tltrue ),
    inference(simp,[status(thm)],[16976]) ).

thf(176,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( def_15 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$u\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_713) ).

thf(1518,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( ( def_15 @ A @ B )
          = tltrue )
       => ( '\'fun_app$u\'' @ A @ B ) )
      & ( ( '\'fun_app$u\'' @ A @ B )
       => ( ( def_15 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(338,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ '\'uvi$\'' @ A )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).

thf(2405,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ~ ( '\'fun_app$x\'' @ '\'uvi$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(110,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
        <=> ( B = '\'none$c\'' ) )
        & ( ( ( A != '\'none$c\'' )
            & ( B != '\'none$c\'' ) )
         => ( ( '\'the$f\'' @ A )
            = ( '\'the$f\'' @ B ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).

thf(1107,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( B = '\'none$c\'' ) )
        & ( ( B = '\'none$c\'' )
         => ( A = '\'none$c\'' ) )
        & ( ( ( A != '\'none$c\'' )
            & ( B != '\'none$c\'' ) )
         => ( ( '\'the$f\'' @ A )
            = ( '\'the$f\'' @ B ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(1113,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk46 @ A @ B )
      | ( B != '\'none$c\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1107]) ).

thf(1123,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( B != '\'none$c\'' )
      | ( A = B )
      | ( sk46 @ A @ B ) ),
    inference(lifteq,[status(thm)],[1113]) ).

thf(1124,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ( sk46 @ A @ '\'none$c\'' ) ),
    inference(simp,[status(thm)],[1123]) ).

thf(4207,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk46 @ A @ '\'none$c\'' )
      | ( A
       != ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1124,533]) ).

thf(4208,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( sk46 @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'none$c\'' ),
    inference(pattern_uni,[status(thm)],[4207:[bind(A,$thf( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ E ) )),bind(B,$thf( E ))]]) ).

thf(4249,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( sk46 @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'none$c\'' ),
    inference(simp,[status(thm)],[4208]) ).

thf(648,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_29 @ A @ B )
       != tltrue )
      | ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(cnf,[status(esa)],[646]) ).

thf(651,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_29 @ A @ B )
       != tltrue )
      | ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[648]) ).

thf(773,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
      | ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C ) ),
    inference(cnf,[status(esa)],[771]) ).

thf(14292,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C )
      | ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
      | ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ C ) ),
    inference(rewrite,[status(thm)],[773,2030]) ).

thf(108,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A )
    <=> ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != '\'none$c\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).

thf(1095,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
         != '\'none$c\'' ) )
      & ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
         != '\'none$c\'' )
       => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(223,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).

thf(1744,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(1745,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ),
    inference(cnf,[status(esa)],[1744]) ).

thf(1746,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ),
    inference(lifteq,[status(thm)],[1745]) ).

thf(74,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B )
    <=> ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
        | ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).

thf(898,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B )
       => ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          | ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          | ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(353,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).

thf(2491,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(111,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).

thf(1127,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(206,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).

thf(1650,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(127,axiom,
    ! [A: '\'H_option_RCharacterData_ext_i_sum$\''] :
      ( ( '\'fun_app$ah\'' @ '\'uvu$\'' @ A )
      = '\'none$a\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).

thf(1228,plain,
    ! [A: '\'H_option_RCharacterData_ext_i_sum$\''] :
      ( ( '\'fun_app$ah\'' @ '\'uvu$\'' @ A )
      = '\'none$a\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(167,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).

thf(1482,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(230,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
    <=> ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).

thf(1794,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
       => ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
          = A ) )
      & ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
          = A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(1795,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
       => ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
          = A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
          = A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1794]) ).

thf(1796,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
       != A )
      | ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    inference(cnf,[status(esa)],[1795]) ).

thf(1798,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B )
       != A )
      | ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[1796]) ).

thf(1799,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ '\'some$c\'' @ A )
      = ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ),
    inference(simp,[status(thm)],[1798]) ).

thf(6039,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ '\'some$c\'' @ A )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(rewrite,[status(thm)],[1799,6036]) ).

thf(57,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$c\'' )
     => ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).

thf(785,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$c\'' )
     => ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(356,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A )
    <=> ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
       != '\'none$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).

thf(2501,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A )
       => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
         != '\'none$b\'' ) )
      & ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
         != '\'none$b\'' )
       => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(346,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).

thf(2444,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(45,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).

thf(702,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(60,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).

thf(802,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(304,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( A
         != ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
    <=> ( A = '\'none$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).

thf(2185,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
       => ( A = '\'none$\'' ) )
      & ( ( A = '\'none$\'' )
       => ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(365,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$c\'' )
    <=> ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).

thf(2562,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$c\'' )
       => ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) )
      & ( ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
       => ( A != '\'none$c\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(158,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$b\'' )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).

thf(1412,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A = '\'none$b\'' )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A )
       => ( A = '\'none$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(1413,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ( A = '\'none$b\'' )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A )
       => ( A = '\'none$b\'' ) ) ),
    inference(miniscope,[status(thm)],[1412]) ).

thf(1415,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A ) ),
    inference(cnf,[status(esa)],[1413]) ).

thf(1418,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ A ) ),
    inference(lifteq,[status(thm)],[1415]) ).

thf(1419,plain,
    '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ '\'none$b\'',
    inference(simp,[status(thm)],[1418]) ).

thf(3246,plain,
    ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ '\'none$b\'' )
   != ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) @ '\'none$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1419,2630]) ).

thf(3247,plain,
    ( ( ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' )
     != ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) )
    | ( '\'none$b\'' != '\'none$b\'' ) ),
    inference(simp,[status(thm)],[3246]) ).

thf(3248,plain,
    ( ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' )
   != ( '\'case_option$i\'' @ tltrue @ '\'uvi$\'' ) ),
    inference(simp,[status(thm)],[3247]) ).

thf(102,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).

thf(1055,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(12399,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'fun_app$az\'' @ '\'some$f\'' @ B )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[1746,9011]) ).

thf(12426,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'some$f\'' != '\'some$f\'' )
      | ( B
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) )
      | ( ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A )
       != ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C )
       != '\'h$\'' ) ),
    inference(simp,[status(thm)],[12399]) ).

thf(12450,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A )
       != ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ B )
       != '\'h$\'' ) ),
    inference(simp,[status(thm)],[12426]) ).

thf(17056,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'get_O_b_j_e_c_t$\'' != '\'get_O_b_j_e_c_t$\'' )
      | ( A
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ B )
       != '\'h$\'' ) ),
    inference(simp,[status(thm)],[12450]) ).

thf(17075,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
     != '\'h$\'' ),
    inference(simp,[status(thm)],[17056]) ).

thf(296,axiom,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$a\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).

thf(2150,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(3195,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'a_type_wf$a\'',
    inference(rewrite,[status(thm)],[2150,2169]) ).

thf(19,axiom,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$d\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).

thf(570,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$d\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(393,axiom,
    '\'l_put_M$c\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).

thf(2698,plain,
    '\'l_put_M$c\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(207,axiom,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( ( '\'fset$c\'' @ A )
        = ( '\'fset$c\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).

thf(1653,plain,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( ( ( '\'fset$c\'' @ A )
          = ( '\'fset$c\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fset$c\'' @ A )
          = ( '\'fset$c\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(1654,plain,
    ( ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
        ( ( ( '\'fset$c\'' @ A )
          = ( '\'fset$c\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
        ( ( A = B )
       => ( ( '\'fset$c\'' @ A )
          = ( '\'fset$c\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1653]) ).

thf(1656,plain,
    ! [B: '\'A_element_ptr_fset$\'',A: '\'A_element_ptr_fset$\''] :
      ( ( ( '\'fset$c\'' @ A )
       != ( '\'fset$c\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1654]) ).

thf(1659,plain,
    ! [B: '\'A_element_ptr_fset$\'',A: '\'A_element_ptr_fset$\''] :
      ( ( ( '\'fset$c\'' @ A )
       != ( '\'fset$c\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1656]) ).

thf(1660,plain,
    ! [A: '\'A_element_ptr_fset$\''] :
      ( ( sk71 @ ( '\'fset$c\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('fset$c'),[sk71])]) ).

thf(48,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B )
    <=> ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
        & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).

thf(719,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B )
       => ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) )
       => ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(379,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).

thf(2640,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(2641,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[2640]) ).

thf(2642,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) )
      = ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[2641]) ).

thf(6518,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
      = ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) ),
    inference(rewrite,[status(thm)],[2642,5437]) ).

thf(1259,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk53 @ A @ B )
      | ( A != '\'none$a\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1256]) ).

thf(1266,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$a\'' )
      | ( A = B )
      | ( sk53 @ A @ B ) ),
    inference(lifteq,[status(thm)],[1259]) ).

thf(1267,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'none$a\'' = A )
      | ( sk53 @ '\'none$a\'' @ A ) ),
    inference(simp,[status(thm)],[1266]) ).

thf(4259,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk53 @ '\'none$a\'' @ A )
      | ( A
       != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1267,1511]) ).

thf(4260,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ '\'none$a\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[4259:[bind(A,$thf( '\'fun_app$i\'' @ '\'some$a\'' @ D )),bind(B,$thf( D ))]]) ).

thf(4287,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ '\'none$a\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(simp,[status(thm)],[4260]) ).

thf(5606,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ '\'none$a\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[4287,5437]) ).

thf(6536,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk53 @ '\'none$a\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ C ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,5606]) ).

thf(6537,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] : ( sk53 @ '\'none$a\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[6536:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( '\'extend$a\'' @ ( '\'truncate$a\'' @ F ) @ E ))]]) ).

thf(6547,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] : ( sk53 @ '\'none$a\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) ),
    inference(simp,[status(thm)],[6537]) ).

thf(298,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).

thf(2159,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(2160,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ D ) ) ),
    inference(cnf,[status(esa)],[2159]) ).

thf(2161,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ D ) ) ),
    inference(lifteq,[status(thm)],[2160]) ).

thf(2162,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C ) ) ),
    inference(simp,[status(thm)],[2161]) ).

thf(6423,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ C ) ) ),
    inference(rewrite,[status(thm)],[2162,2104]) ).

thf(24,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ '\'none$\'' ) @ A )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).

thf(587,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ '\'none$\'' ) @ A )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(482,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$l\'' @ C @ E )
              = ( '\'fun_app$l\'' @ D @ E ) ) ) )
     => ( ( '\'bind$f\'' @ A @ C )
        = ( '\'bind$f\'' @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).

thf(3148,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$l\'' @ C @ E )
              = ( '\'fun_app$l\'' @ D @ E ) ) ) )
     => ( ( '\'bind$f\'' @ A @ C )
        = ( '\'bind$f\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(8129,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,4749]) ).

thf(8130,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(pattern_uni,[status(thm)],[8129:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8168,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(simp,[status(thm)],[8130]) ).

thf(8232,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
       != ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ D ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[7684,8168]) ).

thf(8233,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(pattern_uni,[status(thm)],[8232:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(8319,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(rewrite,[status(thm)],[8233,3073]) ).

thf(8413,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B ) ) ) )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(rewrite,[status(thm)],[8319,8191]) ).

thf(8654,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
     != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ),
    inference(rewrite,[status(thm)],[8413,8650]) ).

thf(142,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$c\'' @ A @ B )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
    <=> ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
          & ( ( '\'fun_app$bg\'' @ B @ D )
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).

thf(1313,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$c\'' @ A @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
       => ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
            & ( ( '\'fun_app$bg\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) )
      & ( ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
            & ( ( '\'fun_app$bg\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) )
       => ( ( '\'bind$c\'' @ A @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(135,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => $false )
        & ( ( A != '\'none$a\'' )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).

thf(1279,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(5064,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ '\'none$b\'' @ B )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( A
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[1870,5056]) ).

thf(5065,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[5064:[bind(A,$thf( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(5072,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(simp,[status(thm)],[5065]) ).

thf(5278,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
      | ( ( sk84 @ '\'none$b\'' @ A )
       != ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5072]) ).

thf(5284,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[5278:[bind(A,$thf( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )),bind(B,$thf( B ))]]) ).

thf(5289,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ) ),
    inference(simp,[status(thm)],[5284]) ).

thf(351,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uub$\'' @ A @ B ) @ C )
      = ( '\'bind$a\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).

thf(2484,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uub$\'' @ A @ B ) @ C )
      = ( '\'bind$a\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(2485,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uub$\'' @ A @ B ) @ C )
      = ( '\'bind$a\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[2484]) ).

thf(2486,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B )
      = ( '\'fun_app$n\'' @ ( '\'uub$\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[2485]) ).

thf(14110,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ A ) @ B )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uub$\'' @ A @ B ) ) ),
    inference(rewrite,[status(thm)],[2486,6036,5434]) ).

thf(14143,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ C )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ ( '\'uub$\'' @ B @ C ) ) )
      | ( ( '\'bind$f\'' @ A @ '\'uup$\'' )
       != ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1562,14110]) ).

thf(14144,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ A )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[14143:[bind(A,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ G ) )),bind(B,$thf( '\'uup$\'' )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).

thf(14165,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ A )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(simp,[status(thm)],[14144]) ).

thf(14404,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
        = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ D ) ) )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ A )
       != ( '\'bind$a\'' @ '\'none$\'' @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[14165,13579]) ).

thf(14405,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[14404:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(14726,plain,
    ! [E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
        = ( '\'bind$a\'' @ '\'none$\'' @ E ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
       != ( '\'bind$g\'' @ D @ ( '\'uub$\'' @ '\'uup$\'' @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14405,13579]) ).

thf(14727,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$a\'' @ '\'none$\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[14726:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ H ) )),bind(E,$thf( A ))]]) ).

thf(14904,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$a\'' @ '\'none$\'' @ A ) ),
    inference(simp,[status(thm)],[14727]) ).

thf(14982,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
        = ( '\'bind$g\'' @ D @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ B )
       != ( '\'bind$a\'' @ '\'none$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13579,14904]) ).

thf(14983,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
      = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(pattern_uni,[status(thm)],[14982:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(15092,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
      = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(simp,[status(thm)],[14983]) ).

thf(34,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C )
        & ( ( '\'is_node_ptr_kind$\'' @ A )
         => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).

thf(642,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C )
        & ( ( '\'is_node_ptr_kind$\'' @ A )
         => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(643,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C )
      | ~ ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(cnf,[status(esa)],[642]) ).

thf(283,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).

thf(2086,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(2087,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ),
    inference(cnf,[status(esa)],[2086]) ).

thf(6070,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ $true
      | ~ ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(rewrite,[status(thm)],[643,2087]) ).

thf(6071,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(simp,[status(thm)],[6070]) ).

thf(644,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C )
      | ( '\'is_node_ptr_kind$\'' @ A )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(cnf,[status(esa)],[642]) ).

thf(6239,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ $true
      | ( '\'is_node_ptr_kind$\'' @ A )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(rewrite,[status(thm)],[644,2087]) ).

thf(6240,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ( '\'is_node_ptr_kind$\'' @ A )
      | ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(simp,[status(thm)],[6239]) ).

thf(33,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ D @ E ) ) @ '\'bot$b\'' ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ D @ E ) ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',F: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',G: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ E ) @ G )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ F ) @ G ) )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ D @ E ) ) @ ( '\'finsert$b\'' @ F @ G ) ) ) )
     => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).

thf(630,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ D @ E ) ) @ '\'bot$b\'' ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ D @ E ) ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',F: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',G: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ E ) @ G )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ F ) @ G ) )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ D @ E ) ) @ ( '\'finsert$b\'' @ F @ G ) ) ) )
     => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(631,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ B @ C ) ) @ '\'bot$b\'' ) )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ B @ C ) ) )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ C ) @ E )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C )
              & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ E ) )
           => ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ B @ C ) ) @ ( '\'finsert$b\'' @ D @ E ) ) ) )
     => ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] : ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(miniscope,[status(thm)],[630]) ).

thf(638,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk12 @ A ) ) @ ( sk13 @ A ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk14 @ A ) ) @ ( sk15 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(363,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom651) ).

thf(2552,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(781,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
        = A ) ),
    inference(cnf,[status(esa)],[779]) ).

thf(784,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
        = A ) ),
    inference(lifteq,[status(thm)],[781]) ).

thf(15742,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B )
        = A ) ),
    inference(rewrite,[status(thm)],[784,783]) ).

thf(30,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( A = B )
        & ( ( ( '\'fmember$a\'' @ C @ A )
            & ( '\'fmember$a\'' @ C @ B ) )
         => $false )
        & ( ( ~ ( '\'fmember$a\'' @ C @ A )
            & ~ ( '\'fmember$a\'' @ C @ B ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).

thf(606,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ~ ( ( A = B )
        & ~ ( ( '\'fmember$a\'' @ C @ A )
            & ( '\'fmember$a\'' @ C @ B ) )
        & ~ ( ~ ( '\'fmember$a\'' @ C @ A )
            & ~ ( '\'fmember$a\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(9724,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,9653]) ).

thf(9725,plain,
    ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(pattern_uni,[status(thm)],[9724:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(10830,plain,
    ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[9725,9693]) ).

thf(10919,plain,
    ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' )
    | ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[10830,10428]) ).

thf(10920,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[10919:[]]) ).

thf(12229,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(rewrite,[status(thm)],[10920,5604]) ).

thf(188,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
    <=> ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).

thf(1568,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
       => ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
          = A ) )
      & ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B )
          = A )
       => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(335,axiom,
    ! [A: '\'A_element_ptr_fset$\''] :
      ( ( '\'fthe_elem$c\'' @ A )
      = ( '\'the_elem$c\'' @ ( '\'fset$c\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom645) ).

thf(2388,plain,
    ! [A: '\'A_element_ptr_fset$\''] :
      ( ( '\'fthe_elem$c\'' @ A )
      = ( '\'the_elem$c\'' @ ( '\'fset$c\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(128,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'is_node_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).

thf(1231,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'is_node_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(1232,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'is_node_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(cnf,[status(esa)],[1231]) ).

thf(242,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'pair$b\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom686) ).

thf(1847,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'pair$b\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(175,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom656) ).

thf(1514,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(465,axiom,
    ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' ) @ '\'h$\'' )
    = ( '\'fun_app$i\'' @ '\'some$a\'' @ '\'x$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis57) ).

thf(3039,plain,
    ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' ) @ '\'h$\'' )
    = ( '\'fun_app$i\'' @ '\'some$a\'' @ '\'x$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(3040,plain,
    ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' ) @ '\'h$\'' )
    = ( '\'fun_app$i\'' @ '\'some$a\'' @ '\'x$\'' ) ),
    inference(lifteq,[status(thm)],[3039]) ).

thf(5601,plain,
    ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' ) @ '\'h$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[3040,5437]) ).

thf(9290,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[5601,3087]) ).

thf(12945,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ C )
        = ( '\'bind$f\'' @ A @ ( '\'uuc$\'' @ B @ C ) ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9290,1793]) ).

thf(12946,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ A )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[12945:[bind(A,$thf( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' )),bind(B,$thf( '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )),bind(C,$thf( C ))]]) ).

thf(12997,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ A )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[12946]) ).

thf(13058,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) )
        = ( '\'bind$f\'' @ B @ ( '\'uuc$\'' @ C @ D ) ) )
      | ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ A )
       != ( '\'bind$c\'' @ ( '\'bind$g\'' @ B @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[12997,1793]) ).

thf(13059,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[13058:[bind(A,$thf( A )),bind(B,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) )),bind(C,$thf( '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )),bind(D,$thf( A ))]]) ).

thf(13183,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$c\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ A )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ ( '\'uuc$\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) ) ),
    inference(rewrite,[status(thm)],[12997,13059]) ).

thf(93,axiom,
    ! [A: tlbool,B: '\'A_element_ptr$\'',C: '\'A_element_ptr$\'',D: '\'A_element_ptr_fset$\''] :
      ( ( ( ( A = tltrue )
         => ( '\'fmember$d\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$d\'' @ C @ D ) ) )
    <=> ( ( ( A = tltrue )
         => ( '\'fmember$d\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$d\'' @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).

thf(1013,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(53,axiom,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ! [C: '\'B_character_data_ptr$\''] :
          ( ( '\'fmember$b\'' @ C @ A )
        <=> ( '\'fmember$b\'' @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).

thf(761,plain,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ! [C: '\'B_character_data_ptr$\''] :
          ( ( ( '\'fmember$b\'' @ C @ A )
           => ( '\'fmember$b\'' @ C @ B ) )
          & ( ( '\'fmember$b\'' @ C @ B )
           => ( '\'fmember$b\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(762,plain,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ! [C: '\'B_character_data_ptr$\''] :
            ( ( '\'fmember$b\'' @ C @ A )
           => ( '\'fmember$b\'' @ C @ B ) )
        & ! [C: '\'B_character_data_ptr$\''] :
            ( ( '\'fmember$b\'' @ C @ B )
           => ( '\'fmember$b\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(miniscope,[status(thm)],[761]) ).

thf(766,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ A )
      | ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[762]) ).

thf(770,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
      | ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ A )
      | ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[766]) ).

thf(3253,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[3061,1618]) ).

thf(3254,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ '\'node_ptr$\'' )
       != ( '\'fmember$\'' @ A ) )
      | ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[3253]) ).

thf(3787,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'node_ptr$\'' != A )
      | ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[3254]) ).

thf(3788,plain,
    ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' )
   != '\'bot$b\'' ),
    inference(simp,[status(thm)],[3787]) ).

thf(302,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).

thf(2178,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(77,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
     != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).

thf(921,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
     != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(922,plain,
    ~ ? [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
        ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
        = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ),
    inference(miniscope,[status(thm)],[921]) ).

thf(923,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
     != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ),
    inference(cnf,[status(esa)],[922]) ).

thf(924,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
     != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ),
    inference(lifteq,[status(thm)],[923]) ).

thf(256,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B )
    <=> ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
        & ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).

thf(1946,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B )
       => ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
          & ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
          & ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) )
       => ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(803,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) )
        & ( ( ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
                ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
            & ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
                ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) ) )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(miniscope,[status(thm)],[802]) ).

thf(811,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk29 @ C @ B @ A )
      | ( C = '\'none$c\'' )
      | ( C
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk31 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(cnf,[status(esa)],[803]) ).

thf(816,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( C = '\'none$c\'' )
      | ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk31 @ C @ B @ A ) )
        = C )
      | ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(lifteq,[status(thm)],[811]) ).

thf(17899,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( C = '\'none$c\'' )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk31 @ C @ B @ A ) ) )
        = C )
      | ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(rewrite,[status(thm)],[816,783]) ).

thf(238,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
         != '\'none$\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).

thf(1828,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
           != '\'none$\'' ) )
        & ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
           != '\'none$\'' )
         => ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(20,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).

thf(571,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(572,plain,
    ~ ? [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
        = ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(miniscope,[status(thm)],[571]) ).

thf(573,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(cnf,[status(esa)],[572]) ).

thf(574,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(lifteq,[status(thm)],[573]) ).

thf(274,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom606) ).

thf(2034,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(364,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( A
         != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
    <=> ( A = '\'none$c\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).

thf(2555,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
       => ( A = '\'none$c\'' ) )
      & ( ( A = '\'none$c\'' )
       => ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(169,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$j\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).

thf(1487,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$j\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(1488,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ B )
      = ( '\'bind$j\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' ) ),
    inference(cnf,[status(esa)],[1487]) ).

thf(1489,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'bind$j\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' )
      = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[1488]) ).

thf(14980,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
        = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ D ) ) )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ A )
       != ( '\'bind$a\'' @ '\'none$\'' @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[14904,13579]) ).

thf(14981,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$g\'' @ C @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[14980:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).

thf(208,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ~ ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom691) ).

thf(1661,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ~ ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(1662,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\''] :
      ( ? [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
          ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
          = ( '\'pair$b\'' @ B @ C ) )
     => ~ ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ),
    inference(miniscope,[status(thm)],[1661]) ).

thf(1663,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'pair$b\'' @ B @ C ) )
      | ~ ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ),
    inference(cnf,[status(esa)],[1662]) ).

thf(1664,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'pair$b\'' @ B @ C ) )
      | ~ ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ),
    inference(lifteq,[status(thm)],[1663]) ).

thf(413,axiom,
    '\'type_wf$\'' = '\'a_type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).

thf(2794,plain,
    '\'type_wf$\'' = '\'a_type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(289,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_12 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_710) ).

thf(2105,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_12 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
       => ( ( def_12 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(233,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fset$b\'' @ A )
        = ( '\'fset$b\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).

thf(1804,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( ( '\'fset$b\'' @ A )
          = ( '\'fset$b\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fset$b\'' @ A )
          = ( '\'fset$b\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(1805,plain,
    ( ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
        ( ( ( '\'fset$b\'' @ A )
          = ( '\'fset$b\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
        ( ( A = B )
       => ( ( '\'fset$b\'' @ A )
          = ( '\'fset$b\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1804]) ).

thf(1807,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fset$b\'' @ A )
       != ( '\'fset$b\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1805]) ).

thf(1810,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fset$b\'' @ A )
       != ( '\'fset$b\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1807]) ).

thf(1811,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( sk83 @ ( '\'fset$b\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('fset$b'),[sk83])]) ).

thf(10062,plain,
    ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) @ '\'h$\'' )
    = '\'h$a\'' ),
    inference(rewrite,[status(thm)],[5421,9693]) ).

thf(4,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'is_node_ptr_kind$\'' @ A )
     => ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).

thf(494,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'is_node_ptr_kind$\'' @ A )
     => ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(495,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
        = A ) ),
    inference(cnf,[status(esa)],[494]) ).

thf(496,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
        = A )
      | ~ ( '\'is_node_ptr_kind$\'' @ A ) ),
    inference(lifteq,[status(thm)],[495]) ).

thf(17062,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A )
       != ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ C )
       != '\'h$\'' )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[496,12450]) ).

thf(17074,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( '\'get_O_b_j_e_c_t$\'' != '\'get_O_b_j_e_c_t$\'' )
      | ( A != B )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ C )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
       != '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[17062]) ).

thf(17087,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ B )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
       != '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[17074]) ).

thf(17195,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ C )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
       != '\'node_ptr$\'' )
      | ( ( '\'is_node_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       != ( '\'is_node_ptr_kind$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1232,17087]) ).

thf(17196,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) ) )
       != '\'node_ptr$\'' ) ),
    inference(pattern_uni,[status(thm)],[17195:[bind(A,$thf( E )),bind(B,$thf( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ E ))]]) ).

thf(17212,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) ) )
       != '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[17196]) ).

thf(3241,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) )
        = B )
      | ( ( '\'is_node_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       != ( '\'is_node_ptr_kind$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1232,496]) ).

thf(3242,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ) )
      = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[3241:[bind(A,$thf( C )),bind(B,$thf( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ))]]) ).

thf(3245,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ) )
      = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(simp,[status(thm)],[3242]) ).

thf(412,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
        = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).

thf(2786,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(2787,plain,
    ( ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
        ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
        ( ( A = B )
       => ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2786]) ).

thf(2789,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2787]) ).

thf(2792,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2789]) ).

thf(2793,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk144 @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$'),[sk144])]) ).

thf(4876,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( sk144 @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
        = B )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ) )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3245,2793]) ).

thf(4877,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk144 @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
      = ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[4876:[bind(A,$thf( E )),bind(B,$thf( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ E ) ) ))]]) ).

thf(4895,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk144 @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
      = ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ) ),
    inference(simp,[status(thm)],[4877]) ).

thf(4897,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) )
      = A ),
    inference(rewrite,[status(thm)],[4895,2793]) ).

thf(17281,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
       != '\'h$\'' )
      | ( C != '\'node_ptr$\'' ) ),
    inference(rewrite,[status(thm)],[17212,4897]) ).

thf(17286,plain,
    ! [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C )
       != '\'h$\'' )
      | ( E != '\'node_ptr$\'' )
      | ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) )
       != ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ E ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5420,17281]) ).

thf(17287,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A )
       != '\'h$\'' )
      | ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B )
       != '\'node_ptr$\'' ) ),
    inference(pattern_uni,[status(thm)],[17286:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ G )),bind(E,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ F ))]]) ).

thf(17296,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A )
       != '\'h$\'' )
      | ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B )
       != '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[17287]) ).

thf(17746,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'h$\'' != '\'h$a\'' )
      | ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B )
       != '\'node_ptr$\'' )
      | ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) @ '\'h$\'' )
       != ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10062,17296]) ).

thf(17747,plain,
    ( ( '\'h$\'' != '\'h$a\'' )
    | ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
     != '\'node_ptr$\'' ) ),
    inference(pattern_uni,[status(thm)],[17746:[bind(A,$thf( '\'h$\'' )),bind(B,$thf( '\'element_ptr$\'' )),bind(C,$thf( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ))]]) ).

thf(673,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ~ ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[671]) ).

thf(686,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ~ ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[673]) ).

thf(687,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ B ) ),
    inference(simp,[status(thm)],[686]) ).

thf(7419,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ B ) @ C )
      | ( ( '\'fun_app$v\'' @ '\'uva$\'' @ A )
       != ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,687]) ).

thf(7420,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) @ A ),
    inference(pattern_uni,[status(thm)],[7419:[bind(A,$thf( '\'the$e\'' @ D )),bind(B,$thf( '\'uva$\'' )),bind(C,$thf( D ))]]) ).

thf(7425,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) @ A ),
    inference(simp,[status(thm)],[7420]) ).

thf(677,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
      | ( C != '\'none$\'' )
      | ( A = tltrue ) ),
    inference(cnf,[status(esa)],[671]) ).

thf(678,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( C != '\'none$\'' )
      | ( A = tltrue )
      | ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[677]) ).

thf(679,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A = tltrue )
      | ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' ) ),
    inference(simp,[status(thm)],[678]) ).

thf(6343,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( def_29 @ A @ B )
       != tltrue )
      | ( ( '\'fun_app$v\'' @ A @ ( '\'the$e\'' @ B ) )
       != ( '\'fun_app$v\'' @ '\'uvg$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[651,821]) ).

thf(6344,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(pattern_uni,[status(thm)],[6343:[bind(A,$thf( '\'uvg$\'' )),bind(B,$thf( D )),bind(C,$thf( '\'the$e\'' @ D ))]]) ).

thf(6354,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(simp,[status(thm)],[6344]) ).

thf(7146,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
      | ( A
       != ( def_29 @ '\'uvg$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[679,6354]) ).

thf(7147,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ B ) @ A ) @ '\'none$\'' ),
    inference(pattern_uni,[status(thm)],[7146:[bind(A,$thf( def_29 @ '\'uvg$\'' @ E )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(7161,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ B ) @ A ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[7147]) ).

thf(7428,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) @ A )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ C ) @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[7425,7161]) ).

thf(7438,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ C ) @ B )
       != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) )
      | ( A != '\'none$\'' ) ),
    inference(simp,[status(thm)],[7428]) ).

thf(7441,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ B ) @ A )
     != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) ),
    inference(simp,[status(thm)],[7438]) ).

thf(6526,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
       != '\'none$a\'' )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ C ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,5603]) ).

thf(6527,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A )
     != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[6526:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( '\'extend$a\'' @ ( '\'truncate$a\'' @ F ) @ E ))]]) ).

thf(6554,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A )
     != '\'none$a\'' ),
    inference(simp,[status(thm)],[6527]) ).

thf(6557,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
       != ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ D ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,6554]) ).

thf(6558,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[6557:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(6523,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$g\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) )
        = C )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ C ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,5604]) ).

thf(6524,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'extend$a\'' @ ( '\'truncate$a\'' @ B ) @ A )
      = ( '\'the$g\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[6523:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( '\'extend$a\'' @ ( '\'truncate$a\'' @ F ) @ E ))]]) ).

thf(6553,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] :
      ( ( '\'extend$a\'' @ ( '\'truncate$a\'' @ B ) @ A )
      = ( '\'the$g\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[6524]) ).

thf(6745,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' ),
    inference(rewrite,[status(thm)],[6558,6553]) ).

thf(113,axiom,
    ! [A: tlbool,B: '\'B_character_data_ptr$\'',C: '\'B_character_data_ptr$\'',D: '\'B_character_data_ptr_fset$\''] :
      ( ( ( ( A = tltrue )
         => ( '\'fmember$b\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$b\'' @ C @ D ) ) )
    <=> ( ( ( A = tltrue )
         => ( '\'fmember$b\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$b\'' @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).

thf(1136,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(124,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ '\'uvc$\'' @ A )
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).

thf(1202,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$x\'' @ '\'uvc$\'' @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(1203,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$x\'' @ '\'uvc$\'' @ A ),
    inference(cnf,[status(esa)],[1202]) ).

thf(1940,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A )
       => ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
         != '\'none$\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
         != '\'none$\'' )
       => ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A ) ) ),
    inference(miniscope,[status(thm)],[1939]) ).

thf(1942,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ~ ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A )
      | ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' ) ),
    inference(cnf,[status(esa)],[1940]) ).

thf(1945,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' )
      | ~ ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A ) ),
    inference(lifteq,[status(thm)],[1942]) ).

thf(3926,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B )
       != '\'none$\'' )
      | ( ( '\'fun_app$x\'' @ '\'uvc$\'' @ A )
       != ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1203,1945]) ).

thf(3928,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' )
      | ( A != B ) ),
    inference(simp,[status(thm)],[3926]) ).

thf(3931,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[3928]) ).

thf(6038,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' ) ),
    inference(rewrite,[status(thm)],[3931,6036]) ).

thf(8118,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,6038]) ).

thf(8119,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' ) ),
    inference(pattern_uni,[status(thm)],[8118:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8196,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
       != '\'none$\'' )
      | ( '\'uvc$\'' != '\'is_character_data_kind_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[8119]) ).

thf(137,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ E ) )
           => ( ( '\'fun_app$p\'' @ C @ E )
              = ( '\'fun_app$p\'' @ D @ E ) ) ) )
     => ( ( '\'bind$j\'' @ A @ C )
        = ( '\'bind$j\'' @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).

thf(1283,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ E ) )
           => ( ( '\'fun_app$p\'' @ C @ E )
              = ( '\'fun_app$p\'' @ D @ E ) ) ) )
     => ( ( '\'bind$j\'' @ A @ C )
        = ( '\'bind$j\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(270,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ C ) )
    <=> ( ( A = B )
        | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).

thf(2017,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ C ) )
       => ( ( A = B )
          | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) )
      & ( ( ( A = B )
          | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(75,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
    <=> ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
          & ( ( '\'fun_app$k\'' @ B @ D )
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).

thf(905,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
       => ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$k\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) )
      & ( ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$k\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) )
       => ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(634,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ ( sk12 @ A ) @ ( sk13 @ A ) ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ ( sk14 @ A ) @ ( sk15 @ A ) ) ) @ ( '\'finsert$b\'' @ ( sk16 @ A ) @ ( sk17 @ A ) ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(199,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fmember$b\'' @ A @ B )
    <=> ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).

thf(1622,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ( '\'fmember$b\'' @ A @ B )
       => ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) ) )
      & ( ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) )
       => ( '\'fmember$b\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(40,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uua$\'' @ A @ B ) @ C )
      = ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'fun_app$l\'' @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).

thf(660,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uua$\'' @ A @ B ) @ C )
      = ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'fun_app$l\'' @ A @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(193,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'bind$k\'' @ A @ B ) @ C )
      = ( '\'bind$l\'' @ A @ ( '\'uuj$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).

thf(1600,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'bind$k\'' @ A @ B ) @ C )
      = ( '\'bind$l\'' @ A @ ( '\'uuj$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(212,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A = B )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
      <=> ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).

thf(1697,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A = B )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
        & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(400,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( def_4 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$x\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_702) ).

thf(2718,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( def_4 @ A @ B )
          = tltrue )
       => ( '\'fun_app$x\'' @ A @ B ) )
      & ( ( '\'fun_app$x\'' @ A @ B )
       => ( ( def_4 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(435,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
         != '\'none$b\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).

thf(2884,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' ) )
        & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(357,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom658) ).

thf(2508,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(5058,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ B )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( '\'none$b\'' != '\'none$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1870,5056]) ).

thf(5059,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ B )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' ) ),
    inference(pattern_uni,[status(thm)],[5058:[]]) ).

thf(284,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).

thf(2088,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(2089,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ D ) ) ),
    inference(cnf,[status(esa)],[2088]) ).

thf(2090,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ D ) ) ),
    inference(lifteq,[status(thm)],[2089]) ).

thf(2091,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] : ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) ) ),
    inference(simp,[status(thm)],[2090]) ).

thf(268,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).

thf(2006,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(2007,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B )
      = ( '\'put_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[2006]) ).

thf(2008,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'put_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
      = ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) ),
    inference(lifteq,[status(thm)],[2007]) ).

thf(5419,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(rewrite,[status(thm)],[2008,2104]) ).

thf(7707,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] : ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) @ C ) ) ),
    inference(rewrite,[status(thm)],[2091,5419]) ).

thf(6452,plain,
    ! [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ E ) ) )
      | ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) )
       != ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5420,6423]) ).

thf(6453,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[6452:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ F )),bind(D,$thf( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ G ))]]) ).

thf(6499,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(simp,[status(thm)],[6453]) ).

thf(7880,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5421,6499]) ).

thf(7881,plain,
    '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ),
    inference(pattern_uni,[status(thm)],[7880:[bind(A,$thf( '\'h$\'' )),bind(B,$thf( '\'element_ptr$\'' )),bind(C,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(7930,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ B @ A ) )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[7881,1644]) ).

thf(7931,plain,
    ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[7930:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ))]]) ).

thf(423,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ~ ( '\'fmember$d\'' @ A @ B )
    <=> ~ ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).

thf(2833,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( ~ ( '\'fmember$d\'' @ A @ B )
       => ~ ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) ) )
      & ( ~ ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) )
       => ~ ( '\'fmember$d\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(163,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( A = B )
        & ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
            & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
         => $false )
        & ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
            & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).

thf(1447,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( ( A = B )
        & ~ ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
            & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
        & ~ ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
            & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(2481,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ),
    inference(cnf,[status(esa)],[2480]) ).

thf(2482,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ),
    inference(lifteq,[status(thm)],[2481]) ).

thf(2483,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] : ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) ) ),
    inference(simp,[status(thm)],[2482]) ).

thf(949,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk43 @ A @ B )
      | ( A != '\'none$\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[947]) ).

thf(955,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
      | ( A = B )
      | ( sk43 @ A @ B ) ),
    inference(lifteq,[status(thm)],[949]) ).

thf(956,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'none$\'' = A )
      | ( sk43 @ '\'none$\'' @ A ) ),
    inference(simp,[status(thm)],[955]) ).

thf(415,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).

thf(2799,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(417,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
         != '\'none$c\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).

thf(2804,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
           != '\'none$c\'' ) )
        & ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
           != '\'none$c\'' )
         => ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(451,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uue$\'' @ A @ B ) @ C )
      = ( '\'bind$b\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).

thf(2965,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uue$\'' @ A @ B ) @ C )
      = ( '\'bind$b\'' @ ( '\'fun_app$l\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(7,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$f\'' )
         => $false )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).

thf(507,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$f\'' )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(116,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).

thf(1163,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(1164,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ D ) ) ),
    inference(cnf,[status(esa)],[1163]) ).

thf(1165,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ D ) ) ),
    inference(lifteq,[status(thm)],[1164]) ).

thf(1166,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] : ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) ) ),
    inference(simp,[status(thm)],[1165]) ).

thf(6280,plain,
    ! [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fmember$a\'' @ C @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ E ) ) )
      | ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) )
       != ( '\'put_O_b_j_e_c_t$\'' @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[5420,1166]) ).

thf(6281,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[6280:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ G ) )),bind(D,$thf( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ I ) )),bind(E,$thf( E ))]]) ).

thf(6287,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(simp,[status(thm)],[6281]) ).

thf(7721,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ '\'h$a\'' ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5421,6287]) ).

thf(7722,plain,
    '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ '\'h$a\'' ),
    inference(pattern_uni,[status(thm)],[7721:[bind(A,$thf( '\'h$\'' )),bind(B,$thf( '\'element_ptr$\'' )),bind(C,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(261,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
    <=> ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).

thf(1975,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) ) )
      & ( ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(439,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
             != '\'none$b\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).

thf(2910,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
          & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
               != '\'none$b\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
          & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
               != '\'none$b\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(703,plain,
    ~ ? [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
        ( ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
        = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(miniscope,[status(thm)],[702]) ).

thf(704,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(cnf,[status(esa)],[703]) ).

thf(705,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A )
     != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ),
    inference(lifteq,[status(thm)],[704]) ).

thf(3565,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( A
       != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[496,705]) ).

thf(3566,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',A: '\'D_document_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ B )
      | ( B
       != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3565:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ E ) ))]]) ).

thf(3567,plain,
    ! [A: '\'D_document_ptr$\''] :
      ~ ( '\'is_node_ptr_kind$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(simp,[status(thm)],[3566]) ).

thf(9307,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,9290]) ).

thf(9308,plain,
    ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ '\'x$\'' ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(pattern_uni,[status(thm)],[9307:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$\'' ))]]) ).

thf(78,axiom,
    ! [A: '\'D_document_ptr$\'',B: tlbool,C: '\'D_document_ptr_fset$\'',D: '\'D_document_ptr_fset$\''] :
      ( ( ( ( B = tltrue )
         => ( '\'fmember$c\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$c\'' @ A @ D ) ) )
    <=> ( ( ( B = tltrue )
         => ( '\'fmember$c\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$c\'' @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).

thf(925,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(146,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_18 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_716) ).

thf(1338,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_18 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
       => ( ( def_18 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(251,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'is_document_ptr_kind$\'' @ B )
         => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).

thf(1915,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'is_document_ptr_kind$\'' @ B )
         => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(15,axiom,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$b\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).

thf(534,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(328,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
      = ( '\'case_sum$\'' @ ( '\'uvt$\'' @ A ) @ '\'uvu$\'' @ ( '\'more$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).

thf(2349,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
      = ( '\'case_sum$\'' @ ( '\'uvt$\'' @ A ) @ '\'uvu$\'' @ ( '\'more$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(2350,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
      = ( '\'case_sum$\'' @ ( '\'uvt$\'' @ A ) @ '\'uvu$\'' @ ( '\'more$\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2349]) ).

thf(2351,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'case_sum$\'' @ ( '\'uvt$\'' @ A ) @ '\'uvu$\'' @ ( '\'more$\'' @ A ) )
      = ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A ) ),
    inference(lifteq,[status(thm)],[2350]) ).

thf(5438,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'case_sum$\'' @ ( '\'uvt$\'' @ A ) @ '\'uvu$\'' @ ( '\'more$\'' @ A ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[2351,5434]) ).

thf(508,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
        ( ( A != '\'none$f\'' )
        & ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
              ( A
              = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ),
    inference(miniscope,[status(thm)],[507]) ).

thf(509,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk2 @ A ) ) ) ),
    inference(cnf,[status(esa)],[508]) ).

thf(510,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk2 @ A ) )
        = A ) ),
    inference(lifteq,[status(thm)],[509]) ).

thf(9048,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk2 @ A ) )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[510,9011]) ).

thf(9057,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( '\'some$f\'' != '\'some$f\'' )
      | ( ( sk2 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9048]) ).

thf(9079,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( ( sk2 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9057]) ).

thf(11443,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk2 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ C )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9079,3080]) ).

thf(11444,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk2 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[11443:[bind(A,$thf( A )),bind(B,$thf( '\'node_ptr$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(15642,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk2 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[11444,6924]) ).

thf(807,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk29 @ C @ B @ A )
      | ( C = '\'none$c\'' )
      | ( A
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk30 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(cnf,[status(esa)],[803]) ).

thf(818,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( C = '\'none$c\'' )
      | ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk30 @ C @ B @ A ) )
        = A )
      | ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(lifteq,[status(thm)],[807]) ).

thf(18664,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( C = '\'none$c\'' )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk30 @ C @ B @ A ) ) )
        = A )
      | ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(rewrite,[status(thm)],[818,783]) ).

thf(355,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) )
    <=> ( '\'fmember$b\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).

thf(2496,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) )
       => ( '\'fmember$b\'' @ A @ B ) )
      & ( ( '\'fmember$b\'' @ A @ B )
       => ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(376,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).

thf(2621,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(384,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'uvn$\'' @ A @ B ) @ C )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'fun_app$aa\'' @ ( '\'fun_app$ab\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).

thf(2660,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$k\'' @ ( '\'uvn$\'' @ A @ B ) @ C )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'fun_app$aa\'' @ ( '\'fun_app$ab\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(47,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
        & ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D )
              & ( '\'fun_app$aw\'' @ A @ D ) )
           => ( '\'fun_app$aw\'' @ A @ ( '\'finsert$b\'' @ C @ D ) ) ) )
     => ( '\'fun_app$aw\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).

thf(714,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
        & ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D )
              & ( '\'fun_app$aw\'' @ A @ D ) )
           => ( '\'fun_app$aw\'' @ A @ ( '\'finsert$b\'' @ C @ D ) ) ) )
     => ( '\'fun_app$aw\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(217,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).

thf(1723,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(73,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'B_character_data_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$b\'' @ B @ C ) )
     => ( '\'fmember$b\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).

thf(894,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'B_character_data_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$b\'' @ B @ C ) )
     => ( '\'fmember$b\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(26,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'is_document_ptr_kind$\'' @ A )
     => ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).

thf(598,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'is_document_ptr_kind$\'' @ A )
     => ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(556,plain,
    ( ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
        ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
        ( ( A = B )
       => ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
          = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[555]) ).

thf(558,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
       != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[556]) ).

thf(561,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A )
       != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[558]) ).

thf(402,axiom,
    '\'l_put_M$a\'' @ '\'type_wf$b\'' @ '\'element_ptr_kinds$\'' @ '\'get_E_l_e_m_e_n_t$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).

thf(2726,plain,
    '\'l_put_M$a\'' @ '\'type_wf$b\'' @ '\'element_ptr_kinds$\'' @ '\'get_E_l_e_m_e_n_t$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(3239,plain,
    '\'l_put_M$a\'' @ '\'a_type_wf$b\'' @ '\'element_ptr_kinds$\'' @ '\'get_E_l_e_m_e_n_t$\'',
    inference(rewrite,[status(thm)],[2726,2030]) ).

thf(374,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
        = '\'none$b\'' )
    <=> ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
            = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).

thf(2606,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = '\'none$b\'' )
       => ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
              = A ) )
      & ( ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
              = A )
       => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = '\'none$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(804,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ~ ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(cnf,[status(esa)],[803]) ).

thf(815,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ~ ( sk29 @ C @ B @ A )
      | ( '\'fun_app$bm\'' @ ( '\'fun_app$bv\'' @ B @ A ) @ C ) ),
    inference(lifteq,[status(thm)],[804]) ).

thf(49,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
    <=> ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).

thf(725,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) ) )
      & ( ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(726,plain,
    ( ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
        ( ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) ) )
    & ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
        ( ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[725]) ).

thf(727,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ~ ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
      | ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[726]) ).

thf(729,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ~ ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
      | ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ),
    inference(simp,[status(thm)],[727]) ).

thf(3205,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$v\'' @ '\'uva$\'' @ A )
     != ( '\'fun_app$v\'' @ '\'uvg$\'' @ B ) ),
    inference(paramod_ordered,[status(thm)],[580,821]) ).

thf(3206,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'uva$\'' != '\'uvg$\'' )
      | ( A != B ) ),
    inference(simp,[status(thm)],[3205]) ).

thf(3207,plain,
    '\'uva$\'' != '\'uvg$\'',
    inference(simp,[status(thm)],[3206]) ).

thf(387,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
     => ( ( ( '\'finsert$b\'' @ A @ B )
          = ( '\'finsert$b\'' @ A @ C ) )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom612) ).

thf(2673,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
     => ( ( ( ( '\'finsert$b\'' @ A @ B )
            = ( '\'finsert$b\'' @ A @ C ) )
         => ( B = C ) )
        & ( ( B = C )
         => ( ( '\'finsert$b\'' @ A @ B )
            = ( '\'finsert$b\'' @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(661,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uua$\'' @ A @ B ) @ C )
      = ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'fun_app$l\'' @ A @ C ) ) @ B ) ),
    inference(cnf,[status(esa)],[660]) ).

thf(662,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$l\'' @ ( '\'uua$\'' @ A @ B ) @ C )
      = ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'fun_app$l\'' @ A @ C ) ) @ B ) ),
    inference(lifteq,[status(thm)],[661]) ).

thf(6652,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uua$\'' @ A @ B ) )
      = ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ A ) ) @ B ) ),
    inference(rewrite,[status(thm)],[662,6036]) ).

thf(404,axiom,
    ! [A: '\'D_document_ptr_fset$\''] :
      ( ( '\'fthe_elem$a\'' @ A )
      = ( '\'the_elem$a\'' @ ( '\'fset$a\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom643) ).

thf(2731,plain,
    ! [A: '\'D_document_ptr_fset$\''] :
      ( ( '\'fthe_elem$a\'' @ A )
      = ( '\'the_elem$a\'' @ ( '\'fset$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(2732,plain,
    ! [A: '\'D_document_ptr_fset$\''] :
      ( ( '\'fthe_elem$a\'' @ A )
      = ( '\'the_elem$a\'' @ ( '\'fset$a\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2731]) ).

thf(2733,plain,
    ! [A: '\'D_document_ptr_fset$\''] :
      ( ( '\'the_elem$a\'' @ ( '\'fset$a\'' @ A ) )
      = ( '\'fthe_elem$a\'' @ A ) ),
    inference(lifteq,[status(thm)],[2732]) ).

thf(64,axiom,
    ! [A: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$c\'' @ A @ B @ C )
     => ( '\'l_put_M$c\'' @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).

thf(825,plain,
    ! [A: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$c\'' @ A @ B @ C )
     => ( '\'l_put_M$c\'' @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(96,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'is_document_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).

thf(1021,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'is_document_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(295,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).

thf(2133,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$br\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(172,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
    <=> ~ ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).

thf(1502,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ~ ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) ) )
      & ( ~ ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) )
       => ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(198,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom626) ).

thf(1619,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(1601,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$f\'' @ ( '\'bind$k\'' @ A @ B ) @ C )
      = ( '\'bind$l\'' @ A @ ( '\'uuj$\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[1600]) ).

thf(1602,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( '\'bind$l\'' @ A @ ( '\'uuj$\'' @ B @ C ) )
      = ( '\'bind$f\'' @ ( '\'bind$k\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[1601]) ).

thf(9727,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( sk53 @ '\'none$a\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[9653,5606]) ).

thf(9728,plain,
    sk53 @ '\'none$a\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ),
    inference(pattern_uni,[status(thm)],[9727:[bind(A,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(10037,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk53 @ '\'none$a\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,9728]) ).

thf(10038,plain,
    sk53 @ '\'none$a\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ),
    inference(pattern_uni,[status(thm)],[10037:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(471,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B )
    <=> ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).

thf(3065,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B )
       => ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(72,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$c\'' @ A @ B @ C )
    <=> ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).

thf(889,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ( '\'l_put_M$c\'' @ A @ B @ C )
       => ( '\'l_get_M$c\'' @ C @ A @ B ) )
      & ( ( '\'l_get_M$c\'' @ C @ A @ B )
       => ( '\'l_put_M$c\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(303,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
          ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
         => $false )
     => ( A = '\'bot$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).

thf(2181,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
          ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
     => ( A = '\'bot$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(309,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'B_character_data_ptr$\''] :
      ( ( ( '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( '\'fmember$b\'' @ C @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) )
      <=> ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ C ) @ B )
         != '\'none$\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).

thf(2213,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'B_character_data_ptr$\''] :
      ( ( ( '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( ( '\'fmember$b\'' @ C @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) )
         => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ C ) @ B )
           != '\'none$\'' ) )
        & ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ C ) @ B )
           != '\'none$\'' )
         => ( '\'fmember$b\'' @ C @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(123,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).

thf(1195,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(312,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'uus$\'' @ A )
      = '\'none$b\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).

thf(2226,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'uus$\'' @ A )
      = '\'none$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(2227,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'uus$\'' @ A )
      = '\'none$b\'' ),
    inference(cnf,[status(esa)],[2226]) ).

thf(2228,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'uus$\'' @ A )
      = '\'none$b\'' ),
    inference(lifteq,[status(thm)],[2227]) ).

thf(290,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( A = B )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C )
      <=> ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).

thf(2112,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( A = B )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C ) )
        & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(463,axiom,
    '\'l_get_M$b\'' @ '\'get_N_o_d_e$\'' @ '\'type_wf$c\'' @ '\'node_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).

thf(3033,plain,
    '\'l_get_M$b\'' @ '\'get_N_o_d_e$\'' @ '\'type_wf$c\'' @ '\'node_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(254,axiom,
    '\'l_put_M$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'' @ '\'get_D_o_c_u_m_e_n_t$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).

thf(1938,plain,
    '\'l_put_M$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'' @ '\'get_D_o_c_u_m_e_n_t$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(68,axiom,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\'',C: '\'B_character_data_ptr$\''] :
      ( ( A = B )
     => ( ( '\'fmember$b\'' @ C @ A )
      <=> ( '\'fmember$b\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).

thf(847,plain,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\'',C: '\'B_character_data_ptr$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$b\'' @ C @ A )
         => ( '\'fmember$b\'' @ C @ B ) )
        & ( ( '\'fmember$b\'' @ C @ B )
         => ( '\'fmember$b\'' @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(408,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
        & ! [B: '\'A_element_ptr$\''] :
            ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
             != '\'none$a\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).

thf(2758,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
          & ! [B: '\'A_element_ptr$\''] :
              ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
               != '\'none$a\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
          & ! [B: '\'A_element_ptr$\''] :
              ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
               != '\'none$a\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'a_type_wf$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(260,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'D_document_ptr$\''] :
      ( ( ( '\'l_get_D_o_c_u_m_e_n_t_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
      <=> ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ C ) @ B )
         != '\'none$c\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).

thf(1968,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'D_document_ptr$\''] :
      ( ( ( '\'l_get_D_o_c_u_m_e_n_t_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) )
         => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ C ) @ B )
           != '\'none$c\'' ) )
        & ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ C ) @ B )
           != '\'none$c\'' )
         => ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(345,axiom,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$a\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).

thf(2443,plain,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(3198,plain,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'a_type_wf$a\'',
    inference(rewrite,[status(thm)],[2443,2169]) ).

thf(385,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).

thf(2663,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(219,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).

thf(1726,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(1727,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) )
      = A ),
    inference(cnf,[status(esa)],[1726]) ).

thf(1728,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[1727]) ).

thf(4659,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) )
      = A ),
    inference(rewrite,[status(thm)],[1728,1799]) ).

thf(6043,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'the$e\'' @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) )
      = A ),
    inference(rewrite,[status(thm)],[4659,6036]) ).

thf(307,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).

thf(2200,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(12,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'the$\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).

thf(522,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'the$\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(66,axiom,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
      ( ! [C: '\'D_document_ptr$\''] :
          ( ( '\'fmember$c\'' @ C @ A )
        <=> ( '\'fmember$c\'' @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).

thf(830,plain,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
      ( ! [C: '\'D_document_ptr$\''] :
          ( ( ( '\'fmember$c\'' @ C @ A )
           => ( '\'fmember$c\'' @ C @ B ) )
          & ( ( '\'fmember$c\'' @ C @ B )
           => ( '\'fmember$c\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(7921,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[7881,1618]) ).

thf(7969,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
       != ( '\'fmember$\'' @ A ) )
      | ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[7921]) ).

thf(8030,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
       != A )
      | ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[7969]) ).

thf(8031,plain,
    ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' )
   != '\'bot$b\'' ),
    inference(simp,[status(thm)],[8030]) ).

thf(92,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ '\'some$c\'' )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).

thf(1010,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ '\'some$c\'' )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1011,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ '\'some$c\'' )
      = A ),
    inference(cnf,[status(esa)],[1010]) ).

thf(1012,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ '\'some$c\'' )
      = A ),
    inference(lifteq,[status(thm)],[1011]) ).

thf(5280,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ A )
      | ( ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
       != ( sk84 @ '\'none$b\'' @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5072]) ).

thf(5285,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ A )
      | ( ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
       != ( sk84 @ '\'none$b\'' @ A ) ) ),
    inference(simp,[status(thm)],[5280]) ).

thf(21,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).

thf(575,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(576,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
        ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
        = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(miniscope,[status(thm)],[575]) ).

thf(577,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(cnf,[status(esa)],[576]) ).

thf(578,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A )
     != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ),
    inference(lifteq,[status(thm)],[577]) ).

thf(693,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ A )
      | ~ ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[690]) ).

thf(697,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
      | ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ A )
      | ~ ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[693]) ).

thf(425,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
          ( A
         != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
    <=> ( A = '\'none$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).

thf(2840,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A = '\'none$b\'' ) )
      & ( ( A = '\'none$b\'' )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(447,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).

thf(2949,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(2950,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ),
    inference(cnf,[status(esa)],[2949]) ).

thf(2951,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ),
    inference(lifteq,[status(thm)],[2950]) ).

thf(12538,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ C ) )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) @ '\'some$\'' ) ),
    inference(rewrite,[status(thm)],[2951,2104,6331]) ).

thf(6602,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
       != '\'none$a\'' )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ C ) @ D ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,6558]) ).

thf(6603,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B )
     != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[6602:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(397,axiom,
    ! [A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fthe_elem$\'' @ A )
      = ( '\'the_elem$\'' @ ( '\'fset$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom642) ).

thf(2707,plain,
    ! [A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fthe_elem$\'' @ A )
      = ( '\'the_elem$\'' @ ( '\'fset$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(2708,plain,
    ! [A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fthe_elem$\'' @ A )
      = ( '\'the_elem$\'' @ ( '\'fset$\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2707]) ).

thf(2709,plain,
    ! [A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fthe_elem$\'' @ A )
      = ( '\'the_elem$\'' @ ( '\'fset$\'' @ A ) ) ),
    inference(lifteq,[status(thm)],[2708]) ).

thf(160,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( def_11 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$u\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_709) ).

thf(1425,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( ( def_11 @ A @ B )
          = tltrue )
       => ( '\'fun_app$u\'' @ A @ B ) )
      & ( ( '\'fun_app$u\'' @ A @ B )
       => ( ( def_11 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(1666,plain,
    ( ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\''] :
        ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\''] :
        ( ( A = B )
       => ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1665]) ).

thf(1668,plain,
    ! [B: '\'A_element_ptr$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
       != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1666]) ).

thf(1671,plain,
    ! [B: '\'A_element_ptr$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
       != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1668]) ).

thf(1672,plain,
    ! [A: '\'A_element_ptr$\''] :
      ( ( sk72 @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$'),[sk72])]) ).

thf(450,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uui$\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).

thf(2962,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uui$\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(2963,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uui$\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[2962]) ).

thf(2964,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uui$\'' @ A @ B ) @ C )
      = ( '\'bind$g\'' @ ( '\'fun_app$g\'' @ A @ C ) @ B ) ),
    inference(lifteq,[status(thm)],[2963]) ).

thf(18035,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uui$\'' @ A @ B ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) @ A ) @ B ) ),
    inference(rewrite,[status(thm)],[2964,5434,6331]) ).

thf(18074,plain,
    ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uui$\'' @ A @ B ) )
        = ( '\'bind$a\'' @ '\'none$\'' @ D ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) @ A ) @ B )
       != ( '\'bind$g\'' @ E @ ( '\'uub$\'' @ '\'uup$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18035,14904]) ).

thf(18075,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uui$\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
      = ( '\'bind$a\'' @ '\'none$\'' @ C ) ),
    inference(pattern_uni,[status(thm)],[18074:[bind(A,$thf( G )),bind(B,$thf( '\'uub$\'' @ '\'uup$\'' @ M )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ K ) ) ) @ G ))]]) ).

thf(18431,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uui$\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
      = ( '\'bind$a\'' @ '\'none$\'' @ C ) ),
    inference(simp,[status(thm)],[18075]) ).

thf(1851,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'uur$\'' )
      = '\'none$b\'' ),
    inference(cnf,[status(esa)],[1850]) ).

thf(1852,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'uur$\'' )
      = '\'none$b\'' ),
    inference(lifteq,[status(thm)],[1851]) ).

thf(18123,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ ( '\'uui$\'' @ B @ C ) )
        = ( '\'bind$g\'' @ '\'none$b\'' @ C ) )
      | ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ '\'uur$\'' )
       != ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1852,18035]) ).

thf(18124,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uui$\'' @ '\'uur$\'' @ A ) )
      = ( '\'bind$g\'' @ '\'none$b\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[18123:[bind(A,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ G ) )),bind(B,$thf( '\'uur$\'' )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).

thf(18454,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uui$\'' @ '\'uur$\'' @ A ) )
      = ( '\'bind$g\'' @ '\'none$b\'' @ A ) ),
    inference(simp,[status(thm)],[18124]) ).

thf(19057,plain,
    ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$a\'' @ '\'none$\'' @ C )
        = ( '\'bind$g\'' @ '\'none$b\'' @ D ) )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ ( '\'uui$\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ E ) ) @ ( '\'uui$\'' @ '\'uur$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18431,18454]) ).

thf(19058,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ A )
      = ( '\'bind$g\'' @ '\'none$b\'' @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[19057:[bind(A,$thf( '\'uur$\'' )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( '\'uub$\'' @ '\'uup$\'' @ G )),bind(E,$thf( B ))]]) ).

thf(19167,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$a\'' @ '\'none$\'' @ A )
      = ( '\'bind$g\'' @ '\'none$b\'' @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(simp,[status(thm)],[19058]) ).

thf(19258,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$g\'' @ '\'none$b\'' @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
      = ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(rewrite,[status(thm)],[13579,19167]) ).

thf(95,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'D_document_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$c\'' @ B @ C ) )
     => ( '\'fmember$c\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).

thf(1017,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr$\'',C: '\'D_document_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$c\'' @ B @ C ) )
     => ( '\'fmember$c\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(7985,plain,
    ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) )
   != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3061,7931]) ).

thf(8009,plain,
    ( ( ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
     != ( '\'fmember$\'' @ '\'node_ptr$\'' ) )
    | ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[7985]) ).

thf(247,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
          ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
    <=> ( A = '\'bot$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom605) ).

thf(1878,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
       => ( A = '\'bot$b\'' ) )
      & ( ( A = '\'bot$b\'' )
       => ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(318,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).

thf(2268,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(187,axiom,
    '\'l_get_M$d\'' @ '\'get_O_b_j_e_c_t$\'' @ '\'type_wf$d\'' @ '\'object_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).

thf(1567,plain,
    '\'l_get_M$d\'' @ '\'get_O_b_j_e_c_t$\'' @ '\'type_wf$d\'' @ '\'object_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(94,axiom,
    tltrue != tlfalse,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_735) ).

thf(1014,plain,
    tltrue != tlfalse,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(1015,plain,
    tltrue != tlfalse,
    inference(polarity_switch,[status(thm)],[1014]) ).

thf(1016,plain,
    tlfalse != tltrue,
    inference(lifteq,[status(thm)],[1015]) ).

thf(7121,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
      | ( A != tlfalse ) ),
    inference(paramod_ordered,[status(thm)],[679,1016]) ).

thf(7122,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ A ) @ '\'none$\'' ),
    inference(pattern_uni,[status(thm)],[7121:[bind(A,$thf( tlfalse ))]]) ).

thf(7165,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ A ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[7122]) ).

thf(7172,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[683,7165]) ).

thf(7187,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ A )
       != ( '\'case_option$g\'' @ tlfalse @ B ) )
      | ( '\'none$\'' != '\'none$\'' ) ),
    inference(simp,[status(thm)],[7172]) ).

thf(7189,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tltrue @ A )
     != ( '\'case_option$g\'' @ tlfalse @ B ) ),
    inference(simp,[status(thm)],[7187]) ).

thf(326,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ? [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
    <=> ( A != '\'bot$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).

thf(2323,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ? [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A )
       => ( A != '\'bot$b\'' ) )
      & ( ( A != '\'bot$b\'' )
       => ? [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(422,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
      = ( '\'case_sum$a\'' @ ( '\'uvz$\'' @ A ) @ '\'uwa$\'' @ ( '\'more$a\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom692) ).

thf(2830,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
      = ( '\'case_sum$a\'' @ ( '\'uvz$\'' @ A ) @ '\'uwa$\'' @ ( '\'more$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(164,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A )
    <=> ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
       != '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).

thf(1461,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A )
       => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
         != '\'none$a\'' ) )
      & ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
         != '\'none$a\'' )
       => ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(159,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( A = C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom604) ).

thf(1420,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( A = C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(1422,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != C )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    inference(cnf,[status(esa)],[1420]) ).

thf(1423,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != C )
      | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[1422]) ).

thf(1424,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'finsert$b\'' @ B @ A ) ),
    inference(simp,[status(thm)],[1423]) ).

thf(637,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk10 @ A ) ) @ ( sk11 @ A ) )
      | ~ ( sk9 @ A )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(2607,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = '\'none$b\'' )
       => ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
              = A ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
              = A )
       => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = '\'none$b\'' ) ) ),
    inference(miniscope,[status(thm)],[2606]) ).

thf(2609,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
       != '\'none$b\'' )
      | ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
       != A ) ),
    inference(cnf,[status(esa)],[2607]) ).

thf(2612,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
       != '\'none$b\'' )
      | ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
       != A ) ),
    inference(lifteq,[status(thm)],[2609]) ).

thf(2613,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
     != '\'none$b\'' ),
    inference(simp,[status(thm)],[2612]) ).

thf(386,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_28 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_726) ).

thf(2666,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_28 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
       => ( ( def_28 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(46,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
        = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).

thf(706,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
          = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
          = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(411,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
     => ( A != '\'none$c\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).

thf(2781,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
     => ( A != '\'none$c\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(278,axiom,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$b\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).

thf(2069,plain,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(3194,plain,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'a_type_wf$b\'',
    inference(rewrite,[status(thm)],[2069,2030]) ).

thf(25,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
     => ( ( '\'fmember$b\'' @ A @ C )
      <=> ( '\'fmember$b\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).

thf(590,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$b\'' @ A @ C )
         => ( '\'fmember$b\'' @ B @ C ) )
        & ( ( '\'fmember$b\'' @ B @ C )
         => ( '\'fmember$b\'' @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(282,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).

thf(2085,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(454,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'uur$\'' @ A )
      = '\'none$b\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).

thf(2978,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'uur$\'' @ A )
      = '\'none$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(17122,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
      | ( A
       != ( def_19 @ '\'uvg$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[679,17113]) ).

thf(17123,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ B ) @ A ) @ '\'none$\'' ),
    inference(pattern_uni,[status(thm)],[17122:[bind(A,$thf( def_19 @ '\'uvg$\'' @ E )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).

thf(17128,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ B ) @ A ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[17123]) ).

thf(17153,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) @ A )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ C ) @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[7425,17128]) ).

thf(17166,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ C ) @ B )
       != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) )
      | ( A != '\'none$\'' ) ),
    inference(simp,[status(thm)],[17153]) ).

thf(17172,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ B ) @ A )
     != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) ),
    inference(simp,[status(thm)],[17166]) ).

thf(17222,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ B )
       != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) )
      | ( ( def_19 @ '\'uva$\'' @ A )
       != ( def_19 @ '\'uvg$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[16979,17172]) ).

thf(17229,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( tltrue != tltrue )
      | ( B != '\'uva$\'' )
      | ( ( def_19 @ '\'uva$\'' @ A )
       != ( def_19 @ '\'uvg$\'' @ C ) ) ),
    inference(simp,[status(thm)],[17222]) ).

thf(17236,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uva$\'' @ A )
     != ( def_19 @ '\'uvg$\'' @ B ) ),
    inference(simp,[status(thm)],[17229]) ).

thf(17239,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_19 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(rewrite,[status(thm)],[17236,16979]) ).

thf(324,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).

thf(2317,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(32,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
     => ( ( '\'fmember$a\'' @ A @ C )
      <=> ( '\'fmember$a\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).

thf(622,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$a\'' @ A @ C )
         => ( '\'fmember$a\'' @ B @ C ) )
        & ( ( '\'fmember$a\'' @ B @ C )
         => ( '\'fmember$a\'' @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(17132,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ C ) @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[683,17128]) ).

thf(17164,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ A )
       != ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ C ) @ B ) )
      | ( '\'none$\'' != '\'none$\'' ) ),
    inference(simp,[status(thm)],[17132]) ).

thf(17170,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tltrue @ A )
     != ( '\'case_option$g\'' @ ( def_19 @ '\'uvg$\'' @ C ) @ B ) ),
    inference(simp,[status(thm)],[17164]) ).

thf(139,axiom,
    ! [A: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$\'' @ A @ B @ C )
     => ( '\'l_put_M$\'' @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).

thf(1297,plain,
    ! [A: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$\'' @ A @ B @ C )
     => ( '\'l_put_M$\'' @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(51,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
    <=> ( ( ( B = '\'none$\'' )
         => ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
           => ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).

thf(738,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
       => ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) ) )
      & ( ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) )
       => ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(179,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).

thf(1539,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(37,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => $false )
        & ( ( A != '\'none$c\'' )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).

thf(654,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(7210,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ C ) @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[683,7161]) ).

thf(7226,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ A )
       != ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ C ) @ B ) )
      | ( '\'none$\'' != '\'none$\'' ) ),
    inference(simp,[status(thm)],[7210]) ).

thf(7232,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tltrue @ A )
     != ( '\'case_option$g\'' @ ( def_29 @ '\'uvg$\'' @ C ) @ B ) ),
    inference(simp,[status(thm)],[7226]) ).

thf(7235,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ C )
       != ( '\'case_option$g\'' @ tltrue @ B ) )
      | ( ( def_29 @ '\'uva$\'' @ A )
       != ( def_29 @ '\'uvg$\'' @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[6317,7232]) ).

thf(7247,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( tltrue != tltrue )
      | ( C != B )
      | ( ( def_29 @ '\'uva$\'' @ A )
       != ( def_29 @ '\'uvg$\'' @ D ) ) ),
    inference(simp,[status(thm)],[7235]) ).

thf(7257,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uva$\'' @ A )
     != ( def_29 @ '\'uvg$\'' @ B ) ),
    inference(simp,[status(thm)],[7247]) ).

thf(7385,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( def_29 @ '\'uvg$\'' @ A )
     != tltrue ),
    inference(rewrite,[status(thm)],[7257,6317]) ).

thf(322,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) )
     => ( ( ( '\'finsert$b\'' @ A @ B )
          = ( '\'finsert$b\'' @ C @ D ) )
      <=> ( ( ( A = C )
           => ( B = D ) )
          & ( ( A != C )
           => ? [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
                ( ( B
                  = ( '\'finsert$b\'' @ C @ E ) )
                & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ E )
                & ( D
                  = ( '\'finsert$b\'' @ A @ E ) )
                & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom610) ).

thf(2285,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) )
     => ( ( ( ( '\'finsert$b\'' @ A @ B )
            = ( '\'finsert$b\'' @ C @ D ) )
         => ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
                  ( ( B
                    = ( '\'finsert$b\'' @ C @ E ) )
                  & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ E )
                  & ( D
                    = ( '\'finsert$b\'' @ A @ E ) )
                  & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ E ) ) ) ) )
        & ( ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
                  ( ( B
                    = ( '\'finsert$b\'' @ C @ E ) )
                  & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ E )
                  & ( D
                    = ( '\'finsert$b\'' @ A @ E ) )
                  & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ E ) ) ) )
         => ( ( '\'finsert$b\'' @ A @ B )
            = ( '\'finsert$b\'' @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(442,axiom,
    ! [A: '\'D_document_ptr$\''] :
      ( ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ '\'h$\'' )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis56) ).

thf(2932,plain,
    ! [A: '\'D_document_ptr$\''] :
      ( ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ '\'h$\'' )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(191,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$s\'' @ A @ B )
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
    <=> ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
          & ( ( '\'fun_app$bj\'' @ B @ D )
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).

thf(1588,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$s\'' @ A @ B )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
       => ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
            & ( ( '\'fun_app$bj\'' @ B @ D )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) )
      & ( ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
            & ( ( '\'fun_app$bj\'' @ B @ D )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) )
       => ( ( '\'bind$s\'' @ A @ B )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(85,axiom,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( ( ( A = tltrue )
         => ( '\'fmember$a\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$a\'' @ C @ D ) ) )
    <=> ( ( ( A = tltrue )
         => ( '\'fmember$a\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$a\'' @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).

thf(985,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(9,axiom,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).

thf(515,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(166,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).

thf(1478,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C )
        = D )
     => ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(352,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).

thf(2487,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(372,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
     => ( A != '\'none$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).

thf(2598,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
     => ( A != '\'none$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(4909,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ ( sk70 @ D @ C ) )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'finsert$b\'' @ B @ A ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1424,1644]) ).

thf(4910,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[4909:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( '\'finsert$b\'' @ E @ F ))]]) ).

thf(4937,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A ) ),
    inference(simp,[status(thm)],[4910]) ).

thf(5877,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3061,4937]) ).

thf(5900,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ '\'node_ptr$\'' )
       != ( '\'fmember$\'' @ A ) )
      | ( ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A )
       != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[5877]) ).

thf(240,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' )
    <=> ( A = tltrue ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).

thf(1839,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' )
       => ( A = tltrue ) )
      & ( ( A = tltrue )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(1840,plain,
    ( ! [A: tlbool] :
        ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] : ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' )
       => ( A = tltrue ) )
    & ! [A: tlbool] :
        ( ( A = tltrue )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] : ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' ) ) ),
    inference(miniscope,[status(thm)],[1839]) ).

thf(1841,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' ) ),
    inference(cnf,[status(esa)],[1840]) ).

thf(1843,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( A != tltrue )
      | ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ '\'none$b\'' ) ),
    inference(lifteq,[status(thm)],[1841]) ).

thf(1844,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] : ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ A ) @ '\'none$b\'' ),
    inference(simp,[status(thm)],[1843]) ).

thf(3425,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tltrue @ A ) @ '\'none$b\'' )
     != ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) @ '\'none$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1844,2630]) ).

thf(3426,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'case_option$i\'' @ tltrue @ A )
       != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) )
      | ( '\'none$b\'' != '\'none$b\'' ) ),
    inference(simp,[status(thm)],[3425]) ).

thf(3427,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$i\'' @ tltrue @ A )
     != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) ),
    inference(simp,[status(thm)],[3426]) ).

thf(7136,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
      | ( ( '\'case_option$i\'' @ tltrue @ C )
       != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) )
      | ( A != tltrue ) ),
    inference(paramod_ordered,[status(thm)],[679,3427]) ).

thf(7137,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
      | ( ( '\'case_option$i\'' @ tltrue @ B )
       != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[7136:[bind(A,$thf( tltrue ))]]) ).

thf(7155,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
      | ( ( '\'case_option$i\'' @ tltrue @ B )
       != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) ) ),
    inference(simp,[status(thm)],[7137]) ).

thf(11359,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ $true
      | ( ( '\'case_option$i\'' @ tltrue @ A )
       != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) ) ),
    inference(rewrite,[status(thm)],[7155,683]) ).

thf(11360,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$i\'' @ tltrue @ A )
     != ( '\'case_option$i\'' @ tlfalse @ '\'uvc$\'' ) ),
    inference(simp,[status(thm)],[11359]) ).

thf(2406,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$x\'' @ '\'uvi$\'' @ A ),
    inference(miniscope,[status(thm)],[2405]) ).

thf(2407,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ~ ( '\'fun_app$x\'' @ '\'uvi$\'' @ A ),
    inference(cnf,[status(esa)],[2406]) ).

thf(3220,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ '\'uvc$\'' @ A )
     != ( '\'fun_app$x\'' @ '\'uvi$\'' @ B ) ),
    inference(paramod_ordered,[status(thm)],[1203,2407]) ).

thf(3221,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'uvc$\'' != '\'uvi$\'' )
      | ( A != B ) ),
    inference(simp,[status(thm)],[3220]) ).

thf(3222,plain,
    '\'uvc$\'' != '\'uvi$\'',
    inference(simp,[status(thm)],[3221]) ).

thf(14408,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ B )
       != ( '\'bind$a\'' @ '\'none$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13579,14165]) ).

thf(14409,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(pattern_uni,[status(thm)],[14408:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(14516,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'bind$g\'' @ A @ ( '\'uub$\'' @ '\'uup$\'' @ B ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ B ) ) ),
    inference(simp,[status(thm)],[14409]) ).

thf(192,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$r\'' @ ( '\'uuj$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).

thf(1597,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$r\'' @ ( '\'uuj$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(1598,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$r\'' @ ( '\'uuj$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[1597]) ).

thf(1599,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$r\'' @ ( '\'uuj$\'' @ A @ B ) @ C )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ A @ C ) @ B ) ),
    inference(lifteq,[status(thm)],[1598]) ).

thf(132,axiom,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr$\''] :
          ( ( '\'fmember$d\'' @ C @ A )
        <=> ( '\'fmember$d\'' @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).

thf(1246,plain,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr$\''] :
          ( ( ( '\'fmember$d\'' @ C @ A )
           => ( '\'fmember$d\'' @ C @ B ) )
          & ( ( '\'fmember$d\'' @ C @ B )
           => ( '\'fmember$d\'' @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(215,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( def_13 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$u\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_711) ).

thf(1715,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( ( def_13 @ A @ B )
          = tltrue )
       => ( '\'fun_app$u\'' @ A @ B ) )
      & ( ( '\'fun_app$u\'' @ A @ B )
       => ( ( def_13 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(728,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ~ ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
      | ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[726]) ).

thf(10570,plain,
    ! [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ E ) )
      | ( ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) ) )
       != ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ D ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1166,728]) ).

thf(10571,plain,
    ! [C: '\'D_document_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ B ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[10570:[bind(A,$thf( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ K )),bind(B,$thf( J )),bind(C,$thf( H )),bind(D,$thf( K )),bind(E,$thf( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ K ) @ J ) @ H ))]]) ).

thf(10588,plain,
    ! [C: '\'D_document_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[10571]) ).

thf(473,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).

thf(3074,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_N_o_d_e$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(4339,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ B @ A ) )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3061,1644]) ).

thf(4340,plain,
    ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ),
    inference(pattern_uni,[status(thm)],[4339:[bind(A,$thf( '\'node_ptr$\'' )),bind(B,$thf( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ))]]) ).

thf(4353,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[1186,4340]) ).

thf(4355,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ A )
       != ( '\'fmember$\'' @ '\'node_ptr$\'' ) )
      | ( ( '\'finsert$b\'' @ A @ '\'bot$b\'' )
       != ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(simp,[status(thm)],[4353]) ).

thf(4688,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != '\'node_ptr$\'' )
      | ( ( '\'finsert$b\'' @ A @ '\'bot$b\'' )
       != ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(simp,[status(thm)],[4355]) ).

thf(4689,plain,
    ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' )
   != ( '\'finsert$b\'' @ '\'node_ptr$\'' @ '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[4688]) ).

thf(484,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'a_type_wf$c\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
             != '\'none$b\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).

thf(3162,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'a_type_wf$c\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
          & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
               != '\'none$b\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
          & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( '\'member$c\'' @ B @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
               != '\'none$b\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'a_type_wf$c\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(1022,plain,
    ~ ? [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] : ( '\'is_document_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(miniscope,[status(thm)],[1021]) ).

thf(1023,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'is_document_ptr_kind$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ),
    inference(cnf,[status(esa)],[1022]) ).

thf(3199,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ~ ( '\'is_document_ptr_kind$\'' @ A )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[496,1023]) ).

thf(3200,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ~ ( '\'is_document_ptr_kind$\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[3199:[bind(A,$thf( D )),bind(B,$thf( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ D ) ))]]) ).

thf(3201,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ~ ( '\'is_document_ptr_kind$\'' @ A ) ),
    inference(simp,[status(thm)],[3200]) ).

thf(29,axiom,
    ! [A: '\'A_element_ptr$\'',B: tlbool,C: '\'A_element_ptr_fset$\'',D: '\'A_element_ptr_fset$\''] :
      ( ( ( ( B = tltrue )
         => ( '\'fmember$d\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$d\'' @ A @ D ) ) )
    <=> ( ( ( B = tltrue )
         => ( '\'fmember$d\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$d\'' @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).

thf(605,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(200,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom688) ).

thf(1627,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(177,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( A
         != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
    <=> ( A = '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom221) ).

thf(1525,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
       => ( A = '\'none$a\'' ) )
      & ( ( A = '\'none$a\'' )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(106,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$\'' @ A @ B @ C )
     => ( '\'l_get_M$\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).

thf(1086,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$\'' @ A @ B @ C )
     => ( '\'l_get_M$\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(633,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ ( sk12 @ A ) @ ( sk13 @ A ) ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk14 @ A ) ) @ ( sk15 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(112,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).

thf(1129,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$\'' )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A )
       => ( A != '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1130,plain,
    ( ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( A != '\'none$\'' )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A ) )
    & ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A )
       => ( A != '\'none$\'' ) ) ),
    inference(miniscope,[status(thm)],[1129]) ).

thf(1131,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A )
      | ( A != '\'none$\'' ) ),
    inference(cnf,[status(esa)],[1130]) ).

thf(1133,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
      | ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ A ) ),
    inference(lifteq,[status(thm)],[1131]) ).

thf(1134,plain,
    ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ '\'none$\'' ),
    inference(simp,[status(thm)],[1133]) ).

thf(3418,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[683,1134]) ).

thf(3419,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'case_option$g\'' @ tltrue @ A )
       != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) )
      | ( '\'none$\'' != '\'none$\'' ) ),
    inference(simp,[status(thm)],[3418]) ).

thf(3420,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tltrue @ A )
     != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) ),
    inference(simp,[status(thm)],[3419]) ).

thf(7148,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
      | ( ( '\'case_option$g\'' @ tltrue @ C )
       != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) )
      | ( A != tltrue ) ),
    inference(paramod_ordered,[status(thm)],[679,3420]) ).

thf(7149,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
      | ( ( '\'case_option$g\'' @ tltrue @ B )
       != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[7148:[bind(A,$thf( tltrue ))]]) ).

thf(7162,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ A ) @ '\'none$\'' )
      | ( ( '\'case_option$g\'' @ tltrue @ B )
       != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) ) ),
    inference(simp,[status(thm)],[7149]) ).

thf(12205,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ~ $true
      | ( ( '\'case_option$g\'' @ tltrue @ A )
       != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) ) ),
    inference(rewrite,[status(thm)],[7162,683]) ).

thf(12206,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tltrue @ A )
     != ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) ),
    inference(simp,[status(thm)],[12205]) ).

thf(241,axiom,
    '\'l_put_M$d\'' @ '\'type_wf$d\'' @ '\'object_ptr_kinds$\'' @ '\'get_O_b_j_e_c_t$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).

thf(1846,plain,
    '\'l_put_M$d\'' @ '\'type_wf$d\'' @ '\'object_ptr_kinds$\'' @ '\'get_O_b_j_e_c_t$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(118,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).

thf(1170,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(117,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'bind$f\'' @ A @ B ) ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uua$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).

thf(1167,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ ( '\'bind$f\'' @ A @ B ) ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uua$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(221,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ~ ( '\'fmember$c\'' @ A @ B )
    <=> ~ ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).

thf(1732,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( ~ ( '\'fmember$c\'' @ A @ B )
       => ~ ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) ) )
      & ( ~ ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) )
       => ~ ( '\'fmember$c\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(79,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$a\'' @ A @ B @ C )
      = ( '\'case_option$c\'' @ C @ ( '\'uvo$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).

thf(926,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$a\'' @ A @ B @ C )
      = ( '\'case_option$c\'' @ C @ ( '\'uvo$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(18468,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ ( '\'uui$\'' @ '\'uur$\'' @ C ) )
        = ( '\'bind$g\'' @ '\'none$b\'' @ C ) )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8650,18454]) ).

thf(18469,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ C ) @ B ) @ ( '\'uui$\'' @ '\'uur$\'' @ A ) )
      = ( '\'bind$g\'' @ '\'none$b\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[18468:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ H ) @ G ) ))]]) ).

thf(18640,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ C ) @ B ) @ ( '\'uui$\'' @ '\'uur$\'' @ A ) )
      = ( '\'bind$g\'' @ '\'none$b\'' @ A ) ),
    inference(simp,[status(thm)],[18469]) ).

thf(501,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
        ( ( A != '\'none$f\'' )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
        ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
       => ( A != '\'none$f\'' ) ) ),
    inference(miniscope,[status(thm)],[500]) ).

thf(503,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[501]) ).

thf(506,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk1 @ A ) )
        = A ) ),
    inference(lifteq,[status(thm)],[503]) ).

thf(9049,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( A
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
      | ( ( '\'fun_app$az\'' @ '\'some$f\'' @ ( sk1 @ A ) )
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[506,9011]) ).

thf(9059,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( '\'some$f\'' != '\'some$f\'' )
      | ( ( sk1 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9049]) ).

thf(9081,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
        = '\'none$f\'' )
      | ( ( sk1 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[9059]) ).

thf(10365,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) @ '\'h$\'' )
        = '\'h$a\'' )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,10062]) ).

thf(10366,plain,
    ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) @ '\'h$\'' )
    = '\'h$a\'' ),
    inference(pattern_uni,[status(thm)],[10365:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(4543,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( A
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1870,2613]) ).

thf(4544,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4543:[bind(A,$thf( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ E ) )),bind(B,$thf( E ))]]) ).

thf(4567,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[4544]) ).

thf(308,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ~ ( '\'fmember$b\'' @ A @ B )
    <=> ~ ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).

thf(2208,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ~ ( '\'fmember$b\'' @ A @ B )
       => ~ ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) ) )
      & ( ~ ( '\'member$\'' @ A @ ( '\'fset$\'' @ B ) )
       => ~ ( '\'fmember$b\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(15039,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
        = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ D ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ C ) ) )
      | ( ( '\'bind$a\'' @ '\'none$\'' @ A )
       != ( '\'bind$a\'' @ '\'none$\'' @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14904,14165]) ).

thf(15040,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[15039:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).

thf(15101,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(simp,[status(thm)],[15040]) ).

thf(185,axiom,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$c\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).

thf(1563,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$c\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(656,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'bind$j\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$p\'' @ B @ A ) ),
    inference(cnf,[status(esa)],[655]) ).

thf(657,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'bind$j\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ B )
      = ( '\'fun_app$p\'' @ B @ A ) ),
    inference(lifteq,[status(thm)],[656]) ).

thf(339,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
    <=> ( '\'fun_app$v\'' @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).

thf(2408,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
       => ( '\'fun_app$v\'' @ B @ C ) )
      & ( ( '\'fun_app$v\'' @ B @ C )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(715,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\''] :
      ( ( ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
            ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ C )
              & ( '\'fun_app$aw\'' @ A @ C ) )
           => ( '\'fun_app$aw\'' @ A @ ( '\'finsert$b\'' @ B @ C ) ) ) )
     => ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] : ( '\'fun_app$aw\'' @ A @ B ) ),
    inference(miniscope,[status(thm)],[714]) ).

thf(718,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk22 @ A ) ) @ ( sk23 @ A ) )
      | ( '\'fun_app$aw\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[715]) ).

thf(71,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$p\'' @ '\'none$c\'' @ A )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).

thf(886,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$p\'' @ '\'none$c\'' @ A )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(887,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$p\'' @ '\'none$c\'' @ A )
      = '\'none$\'' ),
    inference(cnf,[status(esa)],[886]) ).

thf(888,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$p\'' @ '\'none$c\'' @ A )
      = '\'none$\'' ),
    inference(lifteq,[status(thm)],[887]) ).

thf(336,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).

thf(2391,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'D_document_ptr$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(168,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => $false )
        & ( ( A
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'the$g\'' @ A ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).

thf(1483,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$a\'' )
        & ( A
         != ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'the$g\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(224,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).

thf(1747,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(359,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fthe_elem$b\'' @ A )
      = ( '\'the_elem$b\'' @ ( '\'fset$b\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom644) ).

thf(2522,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fthe_elem$b\'' @ A )
      = ( '\'the_elem$b\'' @ ( '\'fset$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(2523,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fthe_elem$b\'' @ A )
      = ( '\'the_elem$b\'' @ ( '\'fset$b\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2522]) ).

thf(2524,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fthe_elem$b\'' @ A )
      = ( '\'the_elem$b\'' @ ( '\'fset$b\'' @ A ) ) ),
    inference(lifteq,[status(thm)],[2523]) ).

thf(201,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$k\'' @ '\'some$c\'' @ A )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).

thf(1631,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$k\'' @ '\'some$c\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$k\'' @ '\'some$c\'' @ A )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(739,plain,
    ( ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
        ( ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
       => ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) ) )
    & ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
        ( ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ) )
       => ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ) ),
    inference(miniscope,[status(thm)],[738]) ).

thf(741,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ( B
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[739]) ).

thf(746,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) )
        = B )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[741]) ).

thf(747,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) )
        = B )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(simp,[status(thm)],[746]) ).

thf(11165,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ ( sk26 @ C @ B @ A ) ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
        = B )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(rewrite,[status(thm)],[747,6039]) ).

thf(134,axiom,
    ! [A: tlbool] :
      ( ( A = tltrue )
      | ( A = tlfalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_734) ).

thf(1276,plain,
    ! [A: tlbool] :
      ( ( A = tltrue )
      | ( A = tlfalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(1277,plain,
    ! [A: tlbool] :
      ( ( A = tltrue )
      | ( A = tlfalse ) ),
    inference(cnf,[status(esa)],[1276]) ).

thf(1278,plain,
    ! [A: tlbool] :
      ( ( A = tltrue )
      | ( A = tlfalse ) ),
    inference(lifteq,[status(thm)],[1277]) ).

thf(745,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[739]) ).

thf(749,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[745]) ).

thf(750,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B = '\'none$\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(simp,[status(thm)],[749]) ).

thf(10839,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
        = A )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[10830,5604]) ).

thf(10840,plain,
    ( ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) )
    = ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[10839:[bind(A,$thf( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ))]]) ).

thf(340,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) )
    <=> ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).

thf(2413,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) )
      & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(481,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_32 @ B @ C @ D ) )
    <=> ( ( ( D = '\'none$b\'' )
         => ( '\'fun_app$u\'' @ A @ B ) )
        & ( ( D
            = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
         => ( '\'fun_app$u\'' @ A @ ( def_33 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom557) ).

thf(3130,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_32 @ B @ C @ D ) )
       => ( ( ( D = '\'none$b\'' )
           => ( '\'fun_app$u\'' @ A @ B ) )
          & ( ( D
              = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
           => ( '\'fun_app$u\'' @ A @ ( def_33 @ C @ D ) ) ) ) )
      & ( ( ( ( D = '\'none$b\'' )
           => ( '\'fun_app$u\'' @ A @ B ) )
          & ( ( D
              = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ D ) ) )
           => ( '\'fun_app$u\'' @ A @ ( def_33 @ C @ D ) ) ) )
       => ( '\'fun_app$u\'' @ A @ ( def_32 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(8116,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,4567]) ).

thf(8117,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[8116:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8195,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) ),
    inference(simp,[status(thm)],[8117]) ).

thf(63,axiom,
    ! [A: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$a\'' @ A @ B @ C )
     => ( '\'l_put_M$a\'' @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).

thf(823,plain,
    ! [A: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$a\'' @ A @ B @ C )
     => ( '\'l_put_M$a\'' @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(824,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',A: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ~ ( '\'l_get_M$a\'' @ A @ B @ C )
      | ( '\'l_put_M$a\'' @ B @ C @ A ) ),
    inference(cnf,[status(esa)],[823]) ).

thf(4365,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk53 @ A @ '\'none$a\'' )
      | ( A
       != ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1269,1511]) ).

thf(4366,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) @ '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[4365:[bind(A,$thf( '\'fun_app$i\'' @ '\'some$a\'' @ D )),bind(B,$thf( D ))]]) ).

thf(4419,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) @ '\'none$a\'' ),
    inference(simp,[status(thm)],[4366]) ).

thf(5608,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( sk53 @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ '\'none$a\'' ),
    inference(rewrite,[status(thm)],[4419,5437]) ).

thf(405,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( '\'none$a\''
     != ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).

thf(2734,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( '\'none$a\''
     != ( '\'fun_app$i\'' @ '\'some$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(23,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B )
    <=> ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).

thf(581,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B )
       => ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(582,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
        ( ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B )
       => ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
        ( ( ( '\'fun_app$bo\'' @ A @ '\'none$a\'' )
          & ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bo\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
       => ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bo\'' @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[581]) ).

thf(584,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bo\'' @ A @ ( sk7 @ A ) )
      | ( '\'fun_app$bo\'' @ A @ '\'none$a\'' ) ),
    inference(cnf,[status(esa)],[582]) ).

thf(562,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( sk5 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$'),[sk5])]) ).

thf(403,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
         => ( ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) )
           != '\'none$\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).

thf(2727,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
         => ( ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) )
           != '\'none$\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(181,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'uup$\'' @ A )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).

thf(1546,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'uup$\'' @ A )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(1547,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'uup$\'' @ A )
      = '\'none$\'' ),
    inference(cnf,[status(esa)],[1546]) ).

thf(1548,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'uup$\'' @ A )
      = '\'none$\'' ),
    inference(lifteq,[status(thm)],[1547]) ).

thf(3317,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$l\'' @ '\'uup$\'' @ A )
     != ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1548,2456]) ).

thf(3318,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' != '\'uup$\'' )
      | ( A
       != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ),
    inference(simp,[status(thm)],[3317]) ).

thf(3319,plain,
    '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' != '\'uup$\'',
    inference(simp,[status(thm)],[3318]) ).

thf(360,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$a\'' )
    <=> ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).

thf(2525,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$a\'' )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
      & ( ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
       => ( A != '\'none$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(226,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( ( A = '\'bot$b\'' )
         => $false )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B )
              & ( A
                = ( '\'finsert$b\'' @ C @ B ) ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).

thf(1752,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ~ ( ( A != '\'bot$b\'' )
        & ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ~ ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B )
              & ( A
                = ( '\'finsert$b\'' @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(269,axiom,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( ( '\'fset$a\'' @ A )
        = ( '\'fset$a\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).

thf(2009,plain,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( ( ( '\'fset$a\'' @ A )
          = ( '\'fset$a\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fset$a\'' @ A )
          = ( '\'fset$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(2010,plain,
    ( ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
        ( ( ( '\'fset$a\'' @ A )
          = ( '\'fset$a\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\''] :
        ( ( A = B )
       => ( ( '\'fset$a\'' @ A )
          = ( '\'fset$a\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2009]) ).

thf(2012,plain,
    ! [B: '\'D_document_ptr_fset$\'',A: '\'D_document_ptr_fset$\''] :
      ( ( ( '\'fset$a\'' @ A )
       != ( '\'fset$a\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2010]) ).

thf(2015,plain,
    ! [B: '\'D_document_ptr_fset$\'',A: '\'D_document_ptr_fset$\''] :
      ( ( ( '\'fset$a\'' @ A )
       != ( '\'fset$a\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2012]) ).

thf(2016,plain,
    ! [A: '\'D_document_ptr_fset$\''] :
      ( ( sk93 @ ( '\'fset$a\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('fset$a'),[sk93])]) ).

thf(457,axiom,
    ! [A: '\'B_character_data_ptr$\''] :
      ( ( '\'member$\'' @ A @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ '\'h$\'' )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis55) ).

thf(2991,plain,
    ! [A: '\'B_character_data_ptr$\''] :
      ( ( '\'member$\'' @ A @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ '\'h$\'' )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(1462,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A )
       => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
         != '\'none$a\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
         != '\'none$a\'' )
       => ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A ) ) ),
    inference(miniscope,[status(thm)],[1461]) ).

thf(1464,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ~ ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A )
      | ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
       != '\'none$a\'' ) ),
    inference(cnf,[status(esa)],[1462]) ).

thf(1467,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
       != '\'none$a\'' )
      | ~ ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A ) ),
    inference(lifteq,[status(thm)],[1464]) ).

thf(3849,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ B )
       != '\'none$a\'' )
      | ( ( '\'fun_app$x\'' @ '\'uvc$\'' @ A )
       != ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1203,1467]) ).

thf(3850,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ B )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' )
      | ( A != B ) ),
    inference(simp,[status(thm)],[3849]) ).

thf(3851,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ A )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[3850]) ).

thf(5435,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' ) ),
    inference(rewrite,[status(thm)],[3851,5434]) ).

thf(8127,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,5435]) ).

thf(8128,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' ) ),
    inference(pattern_uni,[status(thm)],[8127:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8167,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( '\'uvc$\'' != '\'is_element_kind_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[8128]) ).

thf(276,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).

thf(2048,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$bw\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(430,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => $false )
        & ( ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ A ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).

thf(2859,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$b\'' )
        & ( A
         != ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'the$d\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(5066,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
       != ( sk84 @ '\'none$b\'' @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5056]) ).

thf(5067,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
       != '\'none$b\'' )
      | ( ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) )
       != ( sk84 @ '\'none$b\'' @ A ) ) ),
    inference(simp,[status(thm)],[5066]) ).

thf(7436,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) @ A )
     != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ B ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[7425,7165]) ).

thf(7437,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'case_option$g\'' @ tlfalse @ B )
       != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) )
      | ( A != '\'none$\'' ) ),
    inference(simp,[status(thm)],[7436]) ).

thf(7440,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'case_option$g\'' @ tlfalse @ A )
     != ( '\'case_option$g\'' @ tltrue @ '\'uva$\'' ) ),
    inference(simp,[status(thm)],[7437]) ).

thf(475,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( '\'none$b\''
     != ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).

thf(3081,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( '\'none$b\''
     != ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(9705,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( sk53 @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ '\'none$a\'' )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[9653,5608]) ).

thf(9706,plain,
    sk53 @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ '\'none$a\'',
    inference(pattern_uni,[status(thm)],[9705:[bind(A,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ))]]) ).

thf(542,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( sk4 @ A @ B )
      | ( ( '\'the$\'' @ A )
       != ( '\'the$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[535]) ).

thf(545,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( '\'the$\'' @ A )
       != ( '\'the$\'' @ B ) )
      | ( A = B )
      | ( sk4 @ A @ B ) ),
    inference(lifteq,[status(thm)],[542]) ).

thf(392,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'pair$\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom648) ).

thf(2695,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'pair$\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(641,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ ( sk10 @ A ) @ ( sk11 @ A ) ) ) @ '\'bot$b\'' )
      | ~ ( sk9 @ A )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(310,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'uvp$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'fun_app$y\'' @ ( '\'fun_app$z\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).

thf(2220,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'uvp$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'fun_app$y\'' @ ( '\'fun_app$z\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(406,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) )
    <=> ( ( ( B = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
           => ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).

thf(2738,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) )
       => ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) ) )
      & ( ( ( ( B = '\'none$\'' )
           => ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
          & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
             => ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) )
       => ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(707,plain,
    ( ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
          = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
        ( ( A = B )
       => ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
          = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[706]) ).

thf(709,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
       != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[707]) ).

thf(712,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A )
       != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[709]) ).

thf(713,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( sk21 @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$'),[sk21])]) ).

thf(443,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).

thf(2935,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(266,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).

thf(1997,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(344,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
        = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).

thf(2435,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
          = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
          = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(2436,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
        ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
          = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
        ( ( A = B )
       => ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
          = ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2435]) ).

thf(2438,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
       != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2436]) ).

thf(2441,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
       != ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2438]) ).

thf(2442,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( sk125 @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_E_l_e_m_e_n_t_2_N_o_d_e$'),[sk125])]) ).

thf(396,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_k_sum$\''] :
      ( ( '\'fun_app$ai\'' @ '\'uwa$\'' @ A )
      = '\'none$b\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).

thf(2704,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_k_sum$\''] :
      ( ( '\'fun_app$ai\'' @ '\'uwa$\'' @ A )
      = '\'none$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(2705,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_k_sum$\''] :
      ( ( '\'fun_app$ai\'' @ '\'uwa$\'' @ A )
      = '\'none$b\'' ),
    inference(cnf,[status(esa)],[2704]) ).

thf(2706,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_k_sum$\''] :
      ( ( '\'fun_app$ai\'' @ '\'uwa$\'' @ A )
      = '\'none$b\'' ),
    inference(lifteq,[status(thm)],[2705]) ).

thf(349,axiom,
    ! [A: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$c\'' @ A @ B @ C )
    <=> ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'B_character_data_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ B @ D )
              & ( '\'fmember$b\'' @ E @ ( '\'fun_app$al\'' @ C @ D ) ) )
           => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ E ) @ D )
             != '\'none$\'' ) )
        & ! [D: '\'B_character_data_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ D ) @ E )
             != '\'none$\'' )
           => ( '\'fmember$b\'' @ D @ ( '\'fun_app$al\'' @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).

thf(2457,plain,
    ! [A: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\''] :
      ( ( ( '\'l_get_M$c\'' @ A @ B @ C )
       => ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'B_character_data_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$b\'' @ E @ ( '\'fun_app$al\'' @ C @ D ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ E ) @ D )
               != '\'none$\'' ) )
          & ! [D: '\'B_character_data_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ D ) @ E )
               != '\'none$\'' )
             => ( '\'fmember$b\'' @ D @ ( '\'fun_app$al\'' @ C @ E ) ) ) ) )
      & ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'B_character_data_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$b\'' @ E @ ( '\'fun_app$al\'' @ C @ D ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ E ) @ D )
               != '\'none$\'' ) )
          & ! [D: '\'B_character_data_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ A @ D ) @ E )
               != '\'none$\'' )
             => ( '\'fmember$b\'' @ D @ ( '\'fun_app$al\'' @ C @ E ) ) ) )
       => ( '\'l_get_M$c\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(150,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$b\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ ( '\'uue$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).

thf(1356,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$b\'' @ ( '\'bind$f\'' @ A @ B ) @ C )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ ( '\'uue$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(306,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
         != '\'none$a\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).

thf(2193,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' ) )
        & ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' )
         => ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(436,axiom,
    ! [A: '\'A_element_ptr$\''] :
      ( ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( ( ( '\'element_ptr$\'' = A )
           => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
          & ( ( '\'element_ptr$\'' != A )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ '\'h$\'' )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis60) ).

thf(2891,plain,
    ! [A: '\'A_element_ptr$\''] :
      ( ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( ( ( '\'element_ptr$\'' = A )
           => ( ( '\'fun_app$n\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) )
          & ( ( '\'element_ptr$\'' != A )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ '\'h$\'' )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(323,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'bind$r\'' @ A @ B )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
    <=> ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
          & ( ( '\'fun_app$bi\'' @ B @ D )
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).

thf(2308,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$r\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
       => ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
            & ( ( '\'fun_app$bi\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) )
      & ( ? [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
            & ( ( '\'fun_app$bi\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) )
       => ( ( '\'bind$r\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(202,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom608) ).

thf(1638,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(28,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: tlbool,C: '\'B_character_data_ptr_fset$\'',D: '\'B_character_data_ptr_fset$\''] :
      ( ( ( ( B = tltrue )
         => ( '\'fmember$b\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$b\'' @ A @ D ) ) )
    <=> ( ( ( B = tltrue )
         => ( '\'fmember$b\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$b\'' @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).

thf(604,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(388,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
         != '\'none$a\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).

thf(2679,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' ) )
        & ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' )
         => ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(3238,plain,
    '\'l_put_M$c\'' @ '\'a_type_wf$a\'' @ '\'character_data_ptr_kinds$\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'',
    inference(rewrite,[status(thm)],[2698,2169]) ).

thf(342,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => $false )
        & ( ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ A ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).

thf(2422,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$\'' )
        & ( A
         != ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(101,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B )
    <=> ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
        | ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).

thf(1048,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B )
       => ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          | ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          | ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) )
       => ? [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(87,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$b\'' @ A @ B @ C )
      = ( '\'case_option$b\'' @ C @ ( '\'uvq$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).

thf(990,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$b\'' @ A @ B @ C )
      = ( '\'case_option$b\'' @ C @ ( '\'uvq$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(478,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
    <=> ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
          ( A
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).

thf(3106,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A != '\'none$b\'' )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
      & ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A != '\'none$b\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(445,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uvl$\'' @ A @ B ) @ C )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).

thf(2945,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uvl$\'' @ A @ B ) @ C )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(429,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'pair$a\'' @ B @ C ) )
        & ( D
         != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom659) ).

thf(2856,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'pair$a\'' @ B @ C ) )
        & ( D
         != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(1112,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk46 @ A @ B )
      | ( A != '\'none$c\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1107]) ).

thf(1121,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$c\'' )
      | ( A = B )
      | ( sk46 @ A @ B ) ),
    inference(lifteq,[status(thm)],[1112]) ).

thf(1122,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( '\'none$c\'' = A )
      | ( sk46 @ '\'none$c\'' @ A ) ),
    inference(simp,[status(thm)],[1121]) ).

thf(5266,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ B )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( '\'none$b\'' != '\'none$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1870,5072]) ).

thf(5267,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ '\'none$b\'' @ B )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(pattern_uni,[status(thm)],[5266:[]]) ).

thf(277,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom646) ).

thf(2065,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(674,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( C = '\'none$\'' )
      | ~ ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[671]) ).

thf(680,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( C = '\'none$\'' )
      | ~ ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[674]) ).

thf(681,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( C = '\'none$\'' )
      | ~ ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[680]) ).

thf(244,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ~ ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom660) ).

thf(1853,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ~ ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(156,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) )
        & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
         => $false )
        & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom627) ).

thf(1408,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ~ ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(136,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).

thf(1280,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(1281,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B )
      = ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[1280]) ).

thf(1282,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
      = ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) ),
    inference(lifteq,[status(thm)],[1281]) ).

thf(258,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$\'' )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).

thf(1957,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( A = '\'none$\'' )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A )
       => ( A = '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1958,plain,
    ( ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( A = '\'none$\'' )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A ) )
    & ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
        ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A )
       => ( A = '\'none$\'' ) ) ),
    inference(miniscope,[status(thm)],[1957]) ).

thf(1960,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A ) ),
    inference(cnf,[status(esa)],[1958]) ).

thf(1963,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
      | ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ A ) ),
    inference(lifteq,[status(thm)],[1960]) ).

thf(1964,plain,
    '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ '\'none$\'',
    inference(simp,[status(thm)],[1963]) ).

thf(3249,plain,
    ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' ) @ '\'none$\'' )
   != ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) @ '\'none$\'' ) ),
    inference(paramod_ordered,[status(thm)],[1964,1134]) ).

thf(3250,plain,
    ( ( ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' )
     != ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) )
    | ( '\'none$\'' != '\'none$\'' ) ),
    inference(simp,[status(thm)],[3249]) ).

thf(3251,plain,
    ( ( '\'case_option$g\'' @ tlfalse @ '\'uva$\'' )
   != ( '\'case_option$g\'' @ tltrue @ '\'uvg$\'' ) ),
    inference(simp,[status(thm)],[3250]) ).

thf(297,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).

thf(2151,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(483,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
         != '\'none$b\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).

thf(3155,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' ) )
        & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(313,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
    <=> ( ( ( C = '\'none$b\'' )
         => ( A = tltrue ) )
        & ( ( C != '\'none$b\'' )
         => ( '\'fun_app$x\'' @ B @ ( '\'the$d\'' @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).

thf(2229,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
       => ( ( ( C = '\'none$b\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$b\'' )
           => ( '\'fun_app$x\'' @ B @ ( '\'the$d\'' @ C ) ) ) ) )
      & ( ( ( ( C = '\'none$b\'' )
           => ( A = tltrue ) )
          & ( ( C != '\'none$b\'' )
           => ( '\'fun_app$x\'' @ B @ ( '\'the$d\'' @ C ) ) ) )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(449,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'l_get_N_o_d_e_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
      <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ C ) @ B )
         != '\'none$b\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).

thf(2955,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'l_get_N_o_d_e_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
         => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ C ) @ B )
           != '\'none$b\'' ) )
        & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ C ) @ B )
           != '\'none$b\'' )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(194,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( '\'fmember$d\'' @ A @ B )
    <=> ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).

thf(1603,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr_fset$\''] :
      ( ( ( '\'fmember$d\'' @ A @ B )
       => ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) ) )
      & ( ( '\'member$b\'' @ A @ ( '\'fset$c\'' @ B ) )
       => ( '\'fmember$d\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(216,axiom,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$b\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).

thf(1722,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$b\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(4905,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'finsert$b\'' @ B @ A ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ '\'bot$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1424,1618]) ).

thf(4928,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fmember$\'' @ B )
       != ( '\'fmember$\'' @ C ) )
      | ( ( '\'finsert$b\'' @ B @ A )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[4905]) ).

thf(5053,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( B != C )
      | ( ( '\'finsert$b\'' @ B @ A )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[4928]) ).

thf(5054,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'finsert$b\'' @ B @ A )
     != '\'bot$b\'' ),
    inference(simp,[status(thm)],[5053]) ).

thf(154,axiom,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ '\'type_wf$a\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).

thf(1384,plain,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ '\'type_wf$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(3197,plain,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ '\'a_type_wf$a\'',
    inference(rewrite,[status(thm)],[1384,2169]) ).

thf(231,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).

thf(1801,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(599,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_document_ptr_kind$\'' @ A )
      | ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) ),
    inference(cnf,[status(esa)],[598]) ).

thf(433,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ C )
        = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).

thf(2871,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$g\'' @ C @ E )
              = ( '\'fun_app$g\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ C )
        = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(152,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$b\'' @ A @ B @ C )
    <=> ( '\'l_get_M$b\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).

thf(1376,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ( '\'l_put_M$b\'' @ A @ B @ C )
       => ( '\'l_get_M$b\'' @ C @ A @ B ) )
      & ( ( '\'l_get_M$b\'' @ C @ A @ B )
       => ( '\'l_put_M$b\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(218,axiom,
    '\'l_get_M$a\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'type_wf$b\'' @ '\'element_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).

thf(1725,plain,
    '\'l_get_M$a\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'type_wf$b\'' @ '\'element_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(3219,plain,
    '\'l_get_M$a\'' @ '\'get_E_l_e_m_e_n_t$\'' @ '\'a_type_wf$b\'' @ '\'element_ptr_kinds$\'',
    inference(rewrite,[status(thm)],[1725,2030]) ).

thf(246,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: tlbool,C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( ( B = tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
        & ( ( B != tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ D ) ) )
    <=> ( ( ( B = tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
        & ( ( B != tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).

thf(1877,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(539,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( sk4 @ A @ B )
      | ( B != '\'none$f\'' )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[535]) ).

thf(551,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( B != '\'none$f\'' )
      | ( A = B )
      | ( sk4 @ A @ B ) ),
    inference(lifteq,[status(thm)],[539]) ).

thf(552,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( sk4 @ A @ '\'none$f\'' ) ),
    inference(simp,[status(thm)],[551]) ).

thf(265,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ~ ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom650) ).

thf(1993,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
        = ( '\'pair$\'' @ B @ C ) )
     => ~ ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(3192,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'a_type_wf$b\'',
    inference(rewrite,[status(thm)],[534,2030]) ).

thf(98,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).

thf(1029,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(321,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
         != '\'none$a\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).

thf(2278,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' ) )
        & ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
           != '\'none$a\'' )
         => ( '\'fmember$d\'' @ B @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(257,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ C )
        = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).

thf(1952,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ C )
        = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(19256,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ '\'none$b\'' @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
       != '\'none$a\'' )
      | ( ( '\'uub$\'' @ '\'uup$\'' @ A )
       != '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[13704,19167]) ).

thf(378,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B = A )
       => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$az\'' @ '\'some$f\'' @ C ) ) )
      & ( ( B != A )
       => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).

thf(2632,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B = A )
       => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$az\'' @ '\'some$f\'' @ C ) ) )
      & ( ( B != A )
       => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(2779,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\''] :
      ( ( '\'fun_app$ag\'' @ '\'uu$\'' @ A )
      = '\'v$\'' ),
    inference(cnf,[status(esa)],[2778]) ).

thf(2780,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_list$\''] :
      ( ( '\'fun_app$ag\'' @ '\'uu$\'' @ A )
      = '\'v$\'' ),
    inference(lifteq,[status(thm)],[2779]) ).

thf(317,axiom,
    '\'type_wf$c\'' = '\'a_type_wf$c\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).

thf(2266,plain,
    '\'type_wf$c\'' = '\'a_type_wf$c\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(2267,plain,
    '\'a_type_wf$c\'' = '\'type_wf$c\'',
    inference(lifteq,[status(thm)],[2266]) ).

thf(347,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom661) ).

thf(2446,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
        = ( '\'pair$a\'' @ B @ C ) )
     => ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(31,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).

thf(620,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(621,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(cnf,[status(esa)],[620]) ).

thf(407,axiom,
    '\'l_get_M$c\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).

thf(2757,plain,
    '\'l_get_M$c\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ '\'type_wf$a\'' @ '\'character_data_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(464,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
     => ( A != '\'none$b\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).

thf(3034,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
     => ( A != '\'none$b\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(144,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
        & ! [B: '\'B_character_data_ptr$\''] :
            ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
             != '\'none$\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).

thf(1325,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
          & ! [B: '\'B_character_data_ptr$\''] :
              ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
               != '\'none$\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
          & ! [B: '\'B_character_data_ptr$\''] :
              ( ( '\'member$\'' @ B @ ( '\'fset$\'' @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
               != '\'none$\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(765,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ A )
      | ~ ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[762]) ).

thf(769,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
      | ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ A )
      | ~ ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[765]) ).

thf(6044,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
       != '\'none$\'' )
      | ~ ( '\'fun_app$x\'' @ '\'is_character_data_kind_N_o_d_e$\'' @ A ) ),
    inference(rewrite,[status(thm)],[1945,6036]) ).

thf(441,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => $false )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).

thf(2928,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$b\'' )
        & ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(153,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
     => ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).

thf(1381,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$\'' )
     => ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(398,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
    <=> ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).

thf(2710,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) ) )
      & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$a\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(236,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'combine_options$b\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) @ ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'fun_app$y\'' @ ( '\'fun_app$z\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).

thf(1820,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'combine_options$b\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) @ ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'fun_app$y\'' @ ( '\'fun_app$z\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(11,axiom,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$a\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).

thf(521,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$a\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(401,axiom,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).

thf(2725,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(225,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).

thf(1749,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(1750,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ),
    inference(cnf,[status(esa)],[1749]) ).

thf(1751,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ),
    inference(lifteq,[status(thm)],[1750]) ).

thf(444,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ B )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).

thf(2942,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ B )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(2943,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ B )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(cnf,[status(esa)],[2942]) ).

thf(2944,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ B )
      = ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(lifteq,[status(thm)],[2943]) ).

thf(12465,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A @ B ) @ C ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
      = ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(rewrite,[status(thm)],[1751,2944,6039]) ).

thf(19257,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ B @ ( '\'uub$\'' @ '\'uup$\'' @ A ) )
      = ( '\'bind$g\'' @ '\'none$b\'' @ ( '\'uub$\'' @ '\'uup$\'' @ A ) ) ),
    inference(rewrite,[status(thm)],[14904,19167]) ).

thf(332,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( '\'fmember$c\'' @ A @ B )
    <=> ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).

thf(2369,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( ( '\'fmember$c\'' @ A @ B )
       => ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) ) )
      & ( ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) )
       => ( '\'fmember$c\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(86,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$a\'' @ B @ C ) )
     => ( '\'fmember$a\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).

thf(986,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$a\'' @ B @ C ) )
     => ( '\'fmember$a\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(720,plain,
    ( ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
        ( ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B )
       => ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ) )
    & ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
        ( ( ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
          & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) )
       => ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] : ( '\'fun_app$bm\'' @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[719]) ).

thf(723,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( sk24 @ A ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    inference(cnf,[status(esa)],[720]) ).

thf(10119,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( sk24 @ A ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(rewrite,[status(thm)],[723,783]) ).

thf(36,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$c\'' @ A @ B @ C )
     => ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).

thf(652,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$c\'' @ A @ B @ C )
     => ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(653,plain,
    ! [C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\''] :
      ( ~ ( '\'l_put_M$c\'' @ A @ B @ C )
      | ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    inference(cnf,[status(esa)],[652]) ).

thf(456,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B )
    <=> ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
        | ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).

thf(2984,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B )
       => ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
          | ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bp\'' @ A @ '\'none$b\'' )
          | ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bp\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
       => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bp\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(341,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).

thf(2418,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr$\''] :
      ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(4915,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'finsert$b\'' @ B @ A ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[1424,4340]) ).

thf(4933,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fmember$\'' @ B )
       != ( '\'fmember$\'' @ '\'node_ptr$\'' ) )
      | ( ( '\'finsert$b\'' @ B @ A )
       != ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(simp,[status(thm)],[4915]) ).

thf(764,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ~ ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ B )
      | ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[762]) ).

thf(768,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
      | ~ ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ B )
      | ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[764]) ).

thf(65,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$a\'' )
     => ( ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'the$g\'' @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).

thf(827,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$a\'' )
     => ( ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'the$g\'' @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(691,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ~ ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ B )
      | ~ ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[690]) ).

thf(695,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
      | ~ ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ B )
      | ~ ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[691]) ).

thf(636,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk12 @ A ) ) @ ( sk13 @ A ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk16 @ A ) ) @ ( sk17 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(100,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
         => ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) )
           != '\'none$a\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).

thf(1044,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
        & ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_element_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
         => ( ( '\'case_option$e\'' @ '\'none$a\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) )
           != '\'none$a\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(370,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).

thf(2592,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
      = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(9794,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,9703]) ).

thf(9795,plain,
    ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
   != '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[9794:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(10093,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ '\'none$b\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'bind$k\'' @ '\'none$f\'' @ A )
       != ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6924,9795]) ).

thf(10098,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'bind$g\'' @ '\'none$b\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' )
       != '\'none$f\'' )
      | ( A != '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ),
    inference(simp,[status(thm)],[10093]) ).

thf(10108,plain,
    ( ( ( '\'bind$g\'' @ '\'none$b\'' @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
     != '\'none$a\'' )
    | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' )
     != '\'none$f\'' ) ),
    inference(simp,[status(thm)],[10098]) ).

thf(89,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).

thf(1000,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(362,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).

thf(2535,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$\'' )
         => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',E: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
              & ( C
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ E ) ) )
           => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bn\'' @ ( '\'fun_app$bt\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(2389,plain,
    ! [A: '\'A_element_ptr_fset$\''] :
      ( ( '\'fthe_elem$c\'' @ A )
      = ( '\'the_elem$c\'' @ ( '\'fset$c\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2388]) ).

thf(2390,plain,
    ! [A: '\'A_element_ptr_fset$\''] :
      ( ( '\'fthe_elem$c\'' @ A )
      = ( '\'the_elem$c\'' @ ( '\'fset$c\'' @ A ) ) ),
    inference(lifteq,[status(thm)],[2389]) ).

thf(744,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
      | ( B
       != ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ),
    inference(cnf,[status(esa)],[739]) ).

thf(753,plain,
    ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( B
       != ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ D ) ) ),
    inference(lifteq,[status(thm)],[744]) ).

thf(754,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) @ B ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ B @ C ) ) ),
    inference(simp,[status(thm)],[753]) ).

thf(12308,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ C ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) @ B ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ B @ C ) ) ),
    inference(rewrite,[status(thm)],[754,6039]) ).

thf(109,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$j\'' @ A @ C )
        = ( '\'bind$j\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).

thf(1102,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$j\'' @ A @ C )
        = ( '\'bind$j\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(104,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).

thf(1076,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(722,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ ( sk24 @ A ) )
      | ( '\'fun_app$bm\'' @ A @ '\'none$c\'' ) ),
    inference(cnf,[status(esa)],[720]) ).

thf(375,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_23 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_721) ).

thf(2614,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_23 @ A @ B )
          = tltrue )
       => ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) ) )
      & ( ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) )
       => ( ( def_23 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(528,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ A ) )
        = A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = '\'none$c\'' ) ),
    inference(cnf,[status(esa)],[527]) ).

thf(530,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ A ) )
        = A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = '\'none$c\'' ) ),
    inference(lifteq,[status(thm)],[528]) ).

thf(531,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ A ) )
        = A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
        = '\'none$c\'' ) ),
    inference(simp,[status(thm)],[530]) ).

thf(275,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ B @ D ) ) )
           => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ C @ E ) @ D )
             != '\'none$c\'' ) )
        & ! [D: '\'D_document_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ C @ D ) @ E )
             != '\'none$c\'' )
           => ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).

thf(2037,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ B @ D ) ) )
           => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ C @ E ) @ D )
             != '\'none$c\'' ) )
        & ! [D: '\'D_document_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ C @ D ) @ E )
             != '\'none$c\'' )
           => ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(434,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
          ( ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
              = A )
           => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
          & ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
             != A )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ '\'h$\'' )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis59) ).

thf(2878,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'member$c\'' @ A @ ( '\'fset$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) )
     => ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
          ( ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
              = A )
           => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) ) )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
          & ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
             != A )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ '\'h$\'' )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(2841,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( A
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A = '\'none$b\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
        ( ( A = '\'none$b\'' )
       => ~ ? [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
              ( A
              = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2840]) ).

thf(2842,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ( A
       != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(cnf,[status(esa)],[2841]) ).

thf(2844,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( A != '\'none$b\'' )
      | ( A
       != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(lifteq,[status(thm)],[2842]) ).

thf(2845,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
     != '\'none$b\'' ),
    inference(simp,[status(thm)],[2844]) ).

thf(4545,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( A
       != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1870,2845]) ).

thf(4546,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[4545:[bind(A,$thf( '\'fun_app$g\'' @ '\'some$\'' @ D )),bind(B,$thf( D ))]]) ).

thf(4568,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] : ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(simp,[status(thm)],[4546]) ).

thf(4640,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ '\'none$b\'' @ '\'none$b\'' )
      | ( A
       != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1870,4568]) ).

thf(4641,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      | ( sk84 @ '\'none$b\'' @ '\'none$b\'' ) ),
    inference(pattern_uni,[status(thm)],[4640:[bind(A,$thf( '\'fun_app$g\'' @ '\'some$\'' @ D )),bind(B,$thf( D ))]]) ).

thf(4645,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) )
      | ( sk84 @ '\'none$b\'' @ '\'none$b\'' ) ),
    inference(simp,[status(thm)],[4641]) ).

thf(15152,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk84 @ '\'none$b\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) ) @ '\'some$\'' ) )
      | ( sk84 @ '\'none$b\'' @ '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[4645,6331]) ).

thf(10,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
     => ( A != '\'none$f\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).

thf(516,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( A
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
     => ( A != '\'none$f\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(2979,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'uur$\'' @ A )
      = '\'none$b\'' ),
    inference(cnf,[status(esa)],[2978]) ).

thf(2980,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'uur$\'' @ A )
      = '\'none$b\'' ),
    inference(lifteq,[status(thm)],[2979]) ).

thf(3274,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ '\'uur$\'' @ A )
     != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ),
    inference(paramod_ordered,[status(thm)],[2980,2845]) ).

thf(3276,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'some$\'' != '\'uur$\'' )
      | ( A != B ) ),
    inference(simp,[status(thm)],[3274]) ).

thf(3278,plain,
    '\'some$\'' != '\'uur$\'',
    inference(simp,[status(thm)],[3276]) ).

thf(438,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ E ) @ ( '\'fun_app$au\'' @ B @ D ) ) )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ C @ E ) @ D )
             != '\'none$b\'' ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ C @ D ) @ E )
             != '\'none$b\'' )
           => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ ( '\'fun_app$au\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$b\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).

thf(2899,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ E ) @ ( '\'fun_app$au\'' @ B @ D ) ) )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ C @ E ) @ D )
             != '\'none$b\'' ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ C @ D ) @ E )
             != '\'none$b\'' )
           => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ ( '\'fun_app$au\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$b\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(190,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$x\'' @ ( '\'uuw$\'' @ A @ B ) @ C )
    <=> ( '\'fun_app$u\'' @ A @ ( def_4 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).

thf(1583,plain,
    ! [A: '\'Bool_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$x\'' @ ( '\'uuw$\'' @ A @ B ) @ C )
       => ( '\'fun_app$u\'' @ A @ ( def_4 @ B @ C ) ) )
      & ( ( '\'fun_app$u\'' @ A @ ( def_4 @ B @ C ) )
       => ( '\'fun_app$x\'' @ ( '\'uuw$\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(3193,plain,
    '\'l_get_N_o_d_e_lemmas$\'' @ '\'a_type_wf$b\'',
    inference(rewrite,[status(thm)],[1722,2030]) ).

thf(227,axiom,
    ! [A: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$\'' @ A @ B @ C )
    <=> ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ B @ D )
              & ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ C @ D ) ) )
           => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ E ) @ D )
             != '\'none$c\'' ) )
        & ! [D: '\'D_document_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ D ) @ E )
             != '\'none$c\'' )
           => ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).

thf(1758,plain,
    ! [A: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\''] :
      ( ( ( '\'l_get_M$\'' @ A @ B @ C )
       => ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ C @ D ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ E ) @ D )
               != '\'none$c\'' ) )
          & ! [D: '\'D_document_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ D ) @ E )
               != '\'none$c\'' )
             => ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ C @ E ) ) ) ) )
      & ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ C @ D ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ E ) @ D )
               != '\'none$c\'' ) )
          & ! [D: '\'D_document_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ A @ D ) @ E )
               != '\'none$c\'' )
             => ( '\'fmember$c\'' @ D @ ( '\'fun_app$ao\'' @ C @ E ) ) ) )
       => ( '\'l_get_M$\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(588,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ '\'none$\'' ) @ A )
      = '\'none$\'' ),
    inference(cnf,[status(esa)],[587]) ).

thf(589,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ '\'none$\'' ) @ A )
      = '\'none$\'' ),
    inference(lifteq,[status(thm)],[588]) ).

thf(7936,plain,
    ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) )
   != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[7881,4340]) ).

thf(7975,plain,
    ( ( ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
     != ( '\'fmember$\'' @ '\'node_ptr$\'' ) )
    | ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) ) ),
    inference(simp,[status(thm)],[7936]) ).

thf(458,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$b\'' @ A @ B @ C )
    <=> ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ B @ D )
              & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ E ) @ ( '\'fun_app$au\'' @ C @ D ) ) )
           => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ E ) @ D )
             != '\'none$b\'' ) )
        & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ D ) @ E )
             != '\'none$b\'' )
           => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ ( '\'fun_app$au\'' @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).

thf(2994,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\''] :
      ( ( ( '\'l_get_M$b\'' @ A @ B @ C )
       => ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ E ) @ ( '\'fun_app$au\'' @ C @ D ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ E ) @ D )
               != '\'none$b\'' ) )
          & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ D ) @ E )
               != '\'none$b\'' )
             => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ ( '\'fun_app$au\'' @ C @ E ) ) ) ) )
      & ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ E ) @ ( '\'fun_app$au\'' @ C @ D ) ) )
             => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ E ) @ D )
               != '\'none$b\'' ) )
          & ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ A @ D ) @ E )
               != '\'none$b\'' )
             => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ D ) @ ( '\'fun_app$au\'' @ C @ E ) ) ) )
       => ( '\'l_get_M$b\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(59,axiom,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( def_34 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_732) ).

thf(795,plain,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( ( def_34 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C )
       => ( ( def_34 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(320,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$i\'' @ '\'some$a\'' @ A )
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).

thf(2271,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$i\'' @ '\'some$a\'' @ A )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$i\'' @ '\'some$a\'' @ A )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(541,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( B = '\'none$f\'' )
      | ~ ( sk4 @ A @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[535]) ).

thf(548,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A = '\'none$f\'' )
      | ( B = '\'none$f\'' )
      | ( A = B )
      | ~ ( sk4 @ A @ B ) ),
    inference(lifteq,[status(thm)],[541]) ).

thf(316,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
        & ! [B: '\'A_element_ptr$\''] :
            ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
             != '\'none$a\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).

thf(2256,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
          & ! [B: '\'A_element_ptr$\''] :
              ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
               != '\'none$a\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A )
          & ! [B: '\'A_element_ptr$\''] :
              ( ( '\'member$b\'' @ B @ ( '\'fset$c\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ B ) @ A )
               != '\'none$a\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(8113,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
       != '\'none$b\'' )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ B ) @ A ) ) )
       != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7703,2613]) ).

thf(8114,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != '\'none$b\'' ),
    inference(pattern_uni,[status(thm)],[8113:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( '\'extend$\'' @ ( '\'truncate$\'' @ F ) @ E ))]]) ).

thf(8194,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ B ) @ A )
     != '\'none$b\'' ),
    inference(simp,[status(thm)],[8114]) ).

thf(13,axiom,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$c\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).

thf(525,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'type_wf$c\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(431,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).

thf(2863,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$\'' @ A @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
      = ( '\'fun_app$g\'' @ '\'some$\'' @ ( '\'fun_app$ae\'' @ ( '\'fun_app$af\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(640,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ ( sk12 @ A ) @ ( sk13 @ A ) ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk16 @ A ) ) @ ( sk17 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(4938,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'node_ptr$\'' != A )
      | ( ( sk70 @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) @ A )
       != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[4682]) ).

thf(4939,plain,
    ( ( sk70 @ ( '\'finsert$b\'' @ '\'node_ptr$\'' @ '\'bot$b\'' ) @ '\'node_ptr$\'' )
   != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ),
    inference(simp,[status(thm)],[4938]) ).

thf(305,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).

thf(2192,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(84,axiom,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\'',C: '\'B_character_data_ptr$\''] :
      ( ( ( A = B )
        & ( ( ( '\'fmember$b\'' @ C @ A )
            & ( '\'fmember$b\'' @ C @ B ) )
         => $false )
        & ( ( ~ ( '\'fmember$b\'' @ C @ A )
            & ~ ( '\'fmember$b\'' @ C @ B ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).

thf(971,plain,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\'',C: '\'B_character_data_ptr$\''] :
      ~ ( ( A = B )
        & ~ ( ( '\'fmember$b\'' @ C @ A )
            & ( '\'fmember$b\'' @ C @ B ) )
        & ~ ( ~ ( '\'fmember$b\'' @ C @ A )
            & ~ ( '\'fmember$b\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(10059,plain,
    ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'the$g\'' @ ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[9653,9693]) ).

thf(205,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuf$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).

thf(1647,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ B ) @ C )
      = ( '\'bind$f\'' @ A @ ( '\'uuf$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(88,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'is_node_ptr_kind$\'' @ A )
       => ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
          = ( '\'sup$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ C ) @ ( '\'finsert$b\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ '\'bot$b\'' ) ) ) )
      & ( ~ ( '\'is_node_ptr_kind$\'' @ A )
       => ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
          = ( '\'sup$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ C ) @ '\'bot$b\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).

thf(993,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'is_node_ptr_kind$\'' @ A )
       => ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
          = ( '\'sup$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ C ) @ ( '\'finsert$b\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ '\'bot$b\'' ) ) ) )
      & ( ~ ( '\'is_node_ptr_kind$\'' @ A )
       => ( ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
          = ( '\'sup$b\'' @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ C ) @ '\'bot$b\'' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(69,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).

thf(855,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$c\'' )
         => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$j\'' @ '\'some$b\'' @ E ) ) )
           => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bm\'' @ ( '\'fun_app$by\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(399,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).

thf(2715,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ '\'bot$b\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(5249,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( B != '\'node_ptr$\'' )
      | ( ( '\'finsert$b\'' @ B @ A )
       != ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ) ),
    inference(simp,[status(thm)],[4933]) ).

thf(5250,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'finsert$b\'' @ '\'node_ptr$\'' @ A )
     != ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[5249]) ).

thf(70,axiom,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\'',C: '\'A_element_ptr$\''] :
      ( ( ( A = B )
        & ( ( ( '\'fmember$d\'' @ C @ A )
            & ( '\'fmember$d\'' @ C @ B ) )
         => $false )
        & ( ( ~ ( '\'fmember$d\'' @ C @ A )
            & ~ ( '\'fmember$d\'' @ C @ B ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).

thf(872,plain,
    ! [A: '\'A_element_ptr_fset$\'',B: '\'A_element_ptr_fset$\'',C: '\'A_element_ptr$\''] :
      ~ ( ( A = B )
        & ~ ( ( '\'fmember$d\'' @ C @ A )
            & ( '\'fmember$d\'' @ C @ B ) )
        & ~ ( ~ ( '\'fmember$d\'' @ C @ A )
            & ~ ( '\'fmember$d\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(115,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$az\'' @ '\'some$f\'' @ A )
        = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).

thf(1156,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$az\'' @ '\'some$f\'' @ A )
          = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$az\'' @ '\'some$f\'' @ A )
          = ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(10674,plain,
    ! [F: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'D_document_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ D )
       != ( '\'pair$b\'' @ E @ F ) )
      | ( ( '\'fmember$c\'' @ C @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ C ) @ B ) @ A ) ) )
       != ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10588,1664]) ).

thf(10675,plain,
    ! [D: '\'D_document_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ D ) @ C ) @ B ) )
     != ( '\'pair$b\'' @ D @ A ) ),
    inference(pattern_uni,[status(thm)],[10674:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ K ) @ J ) @ H )),bind(E,$thf( K )),bind(F,$thf( F ))]]) ).

thf(10684,plain,
    ! [D: '\'D_document_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ D ) @ C ) @ B ) )
     != ( '\'pair$b\'' @ D @ A ) ),
    inference(simp,[status(thm)],[10675]) ).

thf(3947,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ '\'bot$b\'' ) )
     != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ '\'bot$b\'' ) ),
    inference(paramod_ordered,[status(thm)],[1186,1618]) ).

thf(3948,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'fmember$\'' @ A )
       != ( '\'fmember$\'' @ B ) )
      | ( ( '\'finsert$b\'' @ A @ '\'bot$b\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[3947]) ).

thf(4199,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( A != B )
      | ( ( '\'finsert$b\'' @ A @ '\'bot$b\'' )
       != '\'bot$b\'' ) ),
    inference(simp,[status(thm)],[3948]) ).

thf(4200,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'finsert$b\'' @ A @ '\'bot$b\'' )
     != '\'bot$b\'' ),
    inference(simp,[status(thm)],[4199]) ).

thf(1229,plain,
    ! [A: '\'H_option_RCharacterData_ext_i_sum$\''] :
      ( ( '\'fun_app$ah\'' @ '\'uvu$\'' @ A )
      = '\'none$a\'' ),
    inference(cnf,[status(esa)],[1228]) ).

thf(1230,plain,
    ! [A: '\'H_option_RCharacterData_ext_i_sum$\''] :
      ( ( '\'fun_app$ah\'' @ '\'uvu$\'' @ A )
      = '\'none$a\'' ),
    inference(lifteq,[status(thm)],[1229]) ).

thf(285,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).

thf(2092,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$c\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(161,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_12 @ B @ C @ D ) )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ ( def_13 @ A @ B ) @ ( '\'uuw$\'' @ A @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).

thf(1432,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_12 @ B @ C @ D ) )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ ( def_13 @ A @ B ) @ ( '\'uuw$\'' @ A @ C ) ) @ D ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ ( def_13 @ A @ B ) @ ( '\'uuw$\'' @ A @ C ) ) @ D )
       => ( '\'fun_app$u\'' @ A @ ( def_12 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(235,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( def_9 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$u\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_707) ).

thf(1813,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool] :
      ( ( ( ( def_9 @ A @ B )
          = tltrue )
       => ( '\'fun_app$u\'' @ A @ B ) )
      & ( ( '\'fun_app$u\'' @ A @ B )
       => ( ( def_9 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(440,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).

thf(2920,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ C ) ) )
      & ( ( B
         != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(717,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
      | ( '\'fun_app$aw\'' @ A @ ( sk23 @ A ) )
      | ( '\'fun_app$aw\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[715]) ).

thf(67,axiom,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( def_24 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_722) ).

thf(840,plain,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( ( def_24 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C )
       => ( ( def_24 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(462,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
    <=> ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).

thf(3026,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
          = A ) )
      & ( ( ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B )
          = A )
       => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(4345,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( sk70 @ B @ A ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[1644]) ).

thf(4349,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
      | ( ( '\'fmember$\'' @ A )
       != ( '\'fmember$\'' @ A ) )
      | ( ( sk70 @ B @ A )
       != B ) ),
    inference(simp,[status(thm)],[4345]) ).

thf(4351,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
      | ( ( sk70 @ B @ A )
       != B ) ),
    inference(simp,[status(thm)],[4349]) ).

thf(7946,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( sk70 @ B @ A )
       != B )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[7881,4351]) ).

thf(7947,plain,
    ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
   != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) ),
    inference(pattern_uni,[status(thm)],[7946:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ))]]) ).

thf(262,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).

thf(1980,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(3270,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ A ) )
        = A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[531,533]) ).

thf(3271,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) )
      = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ),
    inference(pattern_uni,[status(thm)],[3270:[bind(A,$thf( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ C )),bind(B,$thf( C ))]]) ).

thf(3272,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) )
      = ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ),
    inference(simp,[status(thm)],[3271]) ).

thf(4105,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( sk5 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
        = B )
      | ( ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) )
       != ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3272,562]) ).

thf(4106,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( sk5 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4105:[bind(A,$thf( D )),bind(B,$thf( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ D ) ))]]) ).

thf(4114,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( sk5 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[4106]) ).

thf(4117,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( sk3 @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) )
      = A ),
    inference(rewrite,[status(thm)],[4114,562]) ).

thf(466,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom689) ).

thf(3041,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(786,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) )
        = A ) ),
    inference(cnf,[status(esa)],[785]) ).

thf(787,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ( ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) )
        = A ) ),
    inference(lifteq,[status(thm)],[786]) ).

thf(16811,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( A = '\'none$c\'' )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( '\'the$f\'' @ A ) ) )
        = A ) ),
    inference(rewrite,[status(thm)],[787,783]) ).

thf(171,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).

thf(1499,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(366,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$\'' @ A @ B @ C )
      = ( '\'case_option$d\'' @ C @ ( '\'uvm$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).

thf(2569,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'combine_options$\'' @ A @ B @ C )
      = ( '\'case_option$d\'' @ C @ ( '\'uvm$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(721,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk25 @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[720]) ).

thf(724,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$j\'' @ '\'some$b\'' @ ( sk25 @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ B ) ),
    inference(simp,[status(thm)],[721]) ).

thf(10307,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ ( sk25 @ A ) ) ) )
      | ( '\'fun_app$bm\'' @ A @ B ) ),
    inference(rewrite,[status(thm)],[724,783]) ).

thf(6037,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
     != '\'none$\'' ),
    inference(rewrite,[status(thm)],[2456,6036]) ).

thf(121,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$\'' @ A @ B @ C )
    <=> ( '\'l_get_M$\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).

thf(1188,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_d_document_ptr_fset_fun$\'',C: '\'D_document_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ( '\'l_put_M$\'' @ A @ B @ C )
       => ( '\'l_get_M$\'' @ C @ A @ B ) )
      & ( ( '\'l_get_M$\'' @ C @ A @ B )
       => ( '\'l_put_M$\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(395,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => $false )
        & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).

thf(2700,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$c\'' )
        & ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(446,axiom,
    '\'l_put_M$b\'' @ '\'type_wf$c\'' @ '\'node_ptr_kinds$\'' @ '\'get_N_o_d_e$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).

thf(2948,plain,
    '\'l_put_M$b\'' @ '\'type_wf$c\'' @ '\'node_ptr_kinds$\'' @ '\'get_N_o_d_e$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(424,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom615) ).

thf(2838,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] : ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(343,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$p\'' @ A @ B )
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
    <=> ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
          & ( ( '\'fun_app$be\'' @ B @ D )
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).

thf(2426,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$p\'' @ A @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) )
       => ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
            & ( ( '\'fun_app$be\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) )
      & ( ? [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ D ) )
            & ( ( '\'fun_app$be\'' @ B @ D )
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) )
       => ( ( '\'bind$p\'' @ A @ B )
          = ( '\'fun_app$k\'' @ '\'some$c\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(9850,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk53 @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) ) @ B ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ '\'none$a\'' )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ A ) @ B )
       != ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3080,9706]) ).

thf(9851,plain,
    sk53 @ ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) @ '\'none$a\'',
    inference(pattern_uni,[status(thm)],[9850:[bind(A,$thf( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )),bind(B,$thf( '\'h$a\'' ))]]) ).

thf(325,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uui$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).

thf(2320,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$g\'' @ ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ A ) @ B ) @ C )
      = ( '\'bind$g\'' @ A @ ( '\'uui$\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(368,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
    <=> ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).

thf(2579,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) )
       => ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) ) )
      & ( ( '\'fmember$b\'' @ A @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ B ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(369,axiom,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ( '\'fset$\'' @ A )
        = ( '\'fset$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).

thf(2584,plain,
    ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
      ( ( ( ( '\'fset$\'' @ A )
          = ( '\'fset$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fset$\'' @ A )
          = ( '\'fset$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(180,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).

thf(1543,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(8316,plain,
    ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
     != '\'node_ptr$\'' )
    | ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[8009]) ).

thf(232,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).

thf(1802,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(27,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
     != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).

thf(600,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
     != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(6278,plain,
    ! [E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'fmember$a\'' @ C @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ E ) ) )
      | ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
       != ( '\'put_O_b_j_e_c_t$\'' @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1282,1166]) ).

thf(6279,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[6278:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ F )),bind(D,$thf( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ G ))]]) ).

thf(6286,plain,
    ! [C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',B: '\'D_document_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] : ( '\'fmember$a\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ B @ C ) @ A ) ) ),
    inference(simp,[status(thm)],[6279]) ).

thf(228,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
          ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
        <=> ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).

thf(1781,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
          ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A )
           => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B ) )
          & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ B )
           => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(252,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).

thf(1918,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) )
        & ! [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bu\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(329,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$d\'' @ E @ ( '\'fun_app$av\'' @ B @ D ) ) )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ C @ E ) @ D )
             != '\'none$a\'' ) )
        & ! [D: '\'A_element_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ C @ D ) @ E )
             != '\'none$a\'' )
           => ( '\'fmember$d\'' @ D @ ( '\'fun_app$av\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$a\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).

thf(2352,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$d\'' @ E @ ( '\'fun_app$av\'' @ B @ D ) ) )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ C @ E ) @ D )
             != '\'none$a\'' ) )
        & ! [D: '\'A_element_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ C @ D ) @ E )
             != '\'none$a\'' )
           => ( '\'fmember$d\'' @ D @ ( '\'fun_app$av\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$a\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(3868,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( sk43 @ '\'none$\'' @ A )
      | ( A
       != ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[956,2456]) ).

thf(3869,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ '\'none$\'' @ ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3868:[bind(A,$thf( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ E ) )),bind(B,$thf( E ))]]) ).

thf(3896,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ '\'none$\'' @ ( '\'fun_app$l\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ),
    inference(simp,[status(thm)],[3869]) ).

thf(6041,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( sk43 @ '\'none$\'' @ ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ A ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' ) ),
    inference(rewrite,[status(thm)],[3896,6036]) ).

thf(183,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_22 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_720) ).

thf(1553,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_22 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
       => ( ( def_22 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(676,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
      | ( C = '\'none$\'' )
      | ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ),
    inference(cnf,[status(esa)],[671]) ).

thf(688,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',A: tlbool] :
      ( ( C = '\'none$\'' )
      | ~ ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
      | ( '\'fun_app$v\'' @ B @ ( '\'the$e\'' @ C ) ) ),
    inference(lifteq,[status(thm)],[676]) ).

thf(523,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'the$\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) )
      = A ),
    inference(cnf,[status(esa)],[522]) ).

thf(524,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'the$\'' @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[523]) ).

thf(2488,plain,
    ~ ? [A: '\'A_element_ptr$\'',B: '\'B_character_data_ptr$\''] :
        ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
        = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(miniscope,[status(thm)],[2487]) ).

thf(2489,plain,
    ! [B: '\'B_character_data_ptr$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(cnf,[status(esa)],[2488]) ).

thf(2490,plain,
    ! [B: '\'B_character_data_ptr$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(lifteq,[status(thm)],[2489]) ).

thf(8228,plain,
    ( ( ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' )
     != '\'node_ptr$\'' )
    | ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$a\'' ) ) ),
    inference(simp,[status(thm)],[7975]) ).

thf(189,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ C ) ) )
      & ( ( B
         != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).

thf(1575,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( B
          = ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ C ) ) )
      & ( ( B
         != ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) )
       => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ B @ C ) @ D ) )
          = ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(6528,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( sk53 @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ A ) @ B ) @ '\'none$a\'' )
      | ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ ( '\'extend$a\'' @ ( '\'truncate$a\'' @ A ) @ B ) ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ C ) ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[6518,5608]) ).

thf(6529,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] : ( sk53 @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) @ '\'none$a\'' ),
    inference(pattern_uni,[status(thm)],[6528:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( '\'extend$a\'' @ ( '\'truncate$a\'' @ F ) @ E ))]]) ).

thf(6543,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext$\''] : ( sk53 @ ( '\'fun_app$h\'' @ ( '\'uvt$\'' @ B ) @ A ) @ '\'none$a\'' ),
    inference(simp,[status(thm)],[6529]) ).

thf(380,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$b\'' )
         => $false )
        & ( ( A != '\'none$b\'' )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).

thf(2643,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(155,axiom,
    ! [A: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$a\'' @ A @ B @ C )
    <=> ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ B @ D )
              & ( '\'fmember$d\'' @ E @ ( '\'fun_app$av\'' @ C @ D ) ) )
           => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ E ) @ D )
             != '\'none$a\'' ) )
        & ! [D: '\'A_element_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ D ) @ E )
             != '\'none$a\'' )
           => ( '\'fmember$d\'' @ D @ ( '\'fun_app$av\'' @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).

thf(1385,plain,
    ! [A: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\''] :
      ( ( ( '\'l_get_M$a\'' @ A @ B @ C )
       => ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$d\'' @ E @ ( '\'fun_app$av\'' @ C @ D ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ E ) @ D )
               != '\'none$a\'' ) )
          & ! [D: '\'A_element_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ D ) @ E )
               != '\'none$a\'' )
             => ( '\'fmember$d\'' @ D @ ( '\'fun_app$av\'' @ C @ E ) ) ) ) )
      & ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'A_element_ptr$\''] :
              ( ( ( '\'fun_app$ci\'' @ B @ D )
                & ( '\'fmember$d\'' @ E @ ( '\'fun_app$av\'' @ C @ D ) ) )
             => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ E ) @ D )
               != '\'none$a\'' ) )
          & ! [D: '\'A_element_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
              ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ A @ D ) @ E )
               != '\'none$a\'' )
             => ( '\'fmember$d\'' @ D @ ( '\'fun_app$av\'' @ C @ E ) ) ) )
       => ( '\'l_get_M$a\'' @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(249,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( '\'bind$q\'' @ A @ B )
        = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
    <=> ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
          & ( ( '\'fun_app$bf\'' @ B @ D )
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).

thf(1903,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$q\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) )
       => ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bf\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) )
      & ( ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bf\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) )
       => ( ( '\'bind$q\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$b\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1479,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ D ) ) ),
    inference(cnf,[status(esa)],[1478]) ).

thf(1480,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C )
       != D )
      | ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ D ) ) ),
    inference(lifteq,[status(thm)],[1479]) ).

thf(1481,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] : ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) ) ),
    inference(simp,[status(thm)],[1480]) ).

thf(420,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( '\'none$c\''
     != ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).

thf(2823,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] :
      ( '\'none$c\''
     != ( '\'fun_app$j\'' @ '\'some$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(418,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom687) ).

thf(2811,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ A )
        = ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(293,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => $false )
        & ( ( A != '\'none$\'' )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).

thf(2130,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(2585,plain,
    ( ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
        ( ( ( '\'fset$\'' @ A )
          = ( '\'fset$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'B_character_data_ptr_fset$\'',B: '\'B_character_data_ptr_fset$\''] :
        ( ( A = B )
       => ( ( '\'fset$\'' @ A )
          = ( '\'fset$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2584]) ).

thf(2587,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( ( '\'fset$\'' @ A )
       != ( '\'fset$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2585]) ).

thf(2590,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( ( '\'fset$\'' @ A )
       != ( '\'fset$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2587]) ).

thf(2591,plain,
    ! [A: '\'B_character_data_ptr_fset$\''] :
      ( ( sk138 @ ( '\'fset$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('fset$'),[sk138])]) ).

thf(204,axiom,
    '\'l_get_M$\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).

thf(1646,plain,
    '\'l_get_M$\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ '\'type_wf$\'' @ '\'document_ptr_kinds$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(44,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C )
        & ( ( '\'is_document_ptr_kind$\'' @ A )
         => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).

thf(699,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C )
        & ( ( '\'is_document_ptr_kind$\'' @ A )
         => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(287,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$\'' )
         => $false )
        & ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).

thf(2098,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$\'' )
        & ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( A
           != ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(742,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[739]) ).

thf(748,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ~ ( '\'fun_app$bm\'' @ A @ ( '\'fun_app$bf\'' @ C @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(simp,[status(thm)],[742]) ).

thf(428,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uuh$\'' @ A @ B ) @ C )
      = ( '\'bind$e\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).

thf(2853,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uuh$\'' @ A @ B ) @ C )
      = ( '\'bind$e\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(315,axiom,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) )
    <=> ( '\'fmember$c\'' @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).

thf(2251,plain,
    ! [A: '\'D_document_ptr$\'',B: '\'D_document_ptr_fset$\''] :
      ( ( ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) )
       => ( '\'fmember$c\'' @ A @ B ) )
      & ( ( '\'fmember$c\'' @ A @ B )
       => ( '\'member$a\'' @ A @ ( '\'fset$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(103,axiom,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\'',C: '\'D_document_ptr$\''] :
      ( ( ( A = B )
        & ( ( ( '\'fmember$c\'' @ C @ A )
            & ( '\'fmember$c\'' @ C @ B ) )
         => $false )
        & ( ( ~ ( '\'fmember$c\'' @ C @ A )
            & ~ ( '\'fmember$c\'' @ C @ B ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).

thf(1062,plain,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\'',C: '\'D_document_ptr$\''] :
      ~ ( ( A = B )
        & ~ ( ( '\'fmember$c\'' @ C @ A )
            & ( '\'fmember$c\'' @ C @ B ) )
        & ~ ( ~ ( '\'fmember$c\'' @ C @ A )
            & ~ ( '\'fmember$c\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(361,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom690) ).

thf(2532,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'D_document_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ A )
        = ( '\'pair$b\'' @ B @ C ) )
     => ( '\'fmember$c\'' @ B @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(81,axiom,
    ! [A: tlbool,B: '\'D_document_ptr$\'',C: '\'D_document_ptr$\'',D: '\'D_document_ptr_fset$\''] :
      ( ( ( ( A = tltrue )
         => ( '\'fmember$c\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$c\'' @ C @ D ) ) )
    <=> ( ( ( A = tltrue )
         => ( '\'fmember$c\'' @ B @ D ) )
        & ( ( A != tltrue )
         => ( '\'fmember$c\'' @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).

thf(946,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(1096,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A )
       => ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
         != '\'none$c\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
         != '\'none$c\'' )
       => ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A ) ) ),
    inference(miniscope,[status(thm)],[1095]) ).

thf(1098,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ~ ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A )
      | ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != '\'none$c\'' ) ),
    inference(cnf,[status(esa)],[1096]) ).

thf(1101,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ A )
       != '\'none$c\'' )
      | ~ ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ A ) ),
    inference(lifteq,[status(thm)],[1098]) ).

thf(271,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom625) ).

thf(2026,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(632,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk12 @ A ) ) @ ( sk13 @ A ) )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( '\'finsert$b\'' @ ( sk14 @ A ) @ ( sk15 @ A ) ) ) @ ( '\'finsert$b\'' @ ( sk16 @ A ) @ ( sk17 @ A ) ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(453,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
         != '\'none$b\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).

thf(2971,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' ) )
        & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(131,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$a\'' @ A @ B @ C )
     => ( '\'l_get_M$a\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).

thf(1244,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_fset_fun$\'',C: '\'A_element_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$a\'' @ A @ B @ C )
     => ( '\'l_get_M$a\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(11567,plain,
    ( ( '\'bind$g\'' @ ( '\'bind$k\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) ) @ '\'h$a\'' ) @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
    = ( '\'bind$g\'' @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ '\'element_ptr$\'' ) ) @ '\'h$a\'' ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' ) ),
    inference(rewrite,[status(thm)],[10830,10059]) ).

thf(337,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'B_character_data_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$b\'' @ E @ ( '\'fun_app$al\'' @ B @ D ) ) )
           => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ C @ E ) @ D )
             != '\'none$\'' ) )
        & ! [D: '\'B_character_data_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ C @ D ) @ E )
             != '\'none$\'' )
           => ( '\'fmember$b\'' @ D @ ( '\'fun_app$al\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).

thf(2394,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_b_character_data_ptr_fset_fun$\'',C: '\'B_character_data_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'B_character_data_ptr$\''] :
            ( ( ( '\'fun_app$ci\'' @ A @ D )
              & ( '\'fmember$b\'' @ E @ ( '\'fun_app$al\'' @ B @ D ) ) )
           => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ C @ E ) @ D )
             != '\'none$\'' ) )
        & ! [D: '\'B_character_data_ptr$\'',E: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
            ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ C @ D ) @ E )
             != '\'none$\'' )
           => ( '\'fmember$b\'' @ D @ ( '\'fun_app$al\'' @ B @ E ) ) ) )
     => ( '\'l_get_M$c\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(281,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ C ) )
        & ( ( A = B )
         => $false )
        & ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).

thf(2081,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ~ ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ B @ C ) )
        & ( A != B )
        & ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(6373,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( sk70 @ D @ C )
       != D )
      | ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'finsert$b\'' @ B @ A ) )
       != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1424,4351]) ).

thf(6374,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A )
     != ( '\'finsert$b\'' @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[6373:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( '\'finsert$b\'' @ E @ F ))]]) ).

thf(6397,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A )
     != ( '\'finsert$b\'' @ A @ B ) ),
    inference(simp,[status(thm)],[6374]) ).

thf(3428,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'uus$\'' @ A )
     != ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2228,2613]) ).

thf(3429,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'uus$\'' != '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' )
      | ( A
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(simp,[status(thm)],[3428]) ).

thf(3430,plain,
    '\'uus$\'' != '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'',
    inference(simp,[status(thm)],[3429]) ).

thf(664,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != B )
      | ( ( '\'fun_app$s\'' @ C @ ( sk18 @ D @ C @ B @ A ) )
       != ( '\'fun_app$s\'' @ D @ ( sk18 @ D @ C @ B @ A ) ) )
      | ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    inference(cnf,[status(esa)],[663]) ).

thf(666,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( A != B )
      | ( ( '\'fun_app$s\'' @ C @ ( sk18 @ D @ C @ B @ A ) )
       != ( '\'fun_app$s\'' @ D @ ( sk18 @ D @ C @ B @ A ) ) )
      | ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[664]) ).

thf(667,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$s\'' @ B @ ( sk18 @ C @ B @ A @ A ) )
       != ( '\'fun_app$s\'' @ C @ ( sk18 @ C @ B @ A @ A ) ) )
      | ( ( '\'bind$k\'' @ A @ B )
        = ( '\'bind$k\'' @ A @ C ) ) ),
    inference(simp,[status(thm)],[666]) ).

thf(80,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).

thf(929,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_bool_fun_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) )
        & ( ( C = '\'none$a\'' )
         => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) )
        & ! [D: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',E: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
            ( ( ( A
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ D ) )
              & ( C
                = ( '\'fun_app$i\'' @ '\'some$a\'' @ E ) ) )
           => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) ) )
     => ( '\'fun_app$bo\'' @ ( '\'fun_app$bz\'' @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(122,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).

thf(1193,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$d\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(141,axiom,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$d\'' @ B @ C ) )
     => ( '\'fmember$d\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).

thf(1309,plain,
    ! [A: '\'A_element_ptr$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_fset$\''] :
      ( ( ( A = B )
        & ( '\'fmember$d\'' @ B @ C ) )
     => ( '\'fmember$d\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(354,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$b\'' @ A @ B @ C )
     => ( '\'l_get_M$b\'' @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).

thf(2494,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\''] :
      ( ( '\'l_put_M$b\'' @ A @ B @ C )
     => ( '\'l_get_M$b\'' @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(414,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).

thf(2796,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
     => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'finsert$b\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(76,axiom,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( def_14 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_712) ).

thf(914,plain,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
      ( ( ( ( def_14 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C )
       => ( ( def_14 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(4133,plain,
    ! [B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( sk46 @ '\'none$c\'' @ A )
      | ( A
       != ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1122,533]) ).

thf(4134,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( sk46 @ '\'none$c\'' @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(pattern_uni,[status(thm)],[4133:[bind(A,$thf( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ E ) )),bind(B,$thf( E ))]]) ).

thf(4153,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\''] : ( sk46 @ '\'none$c\'' @ ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ A ) ) ),
    inference(simp,[status(thm)],[4134]) ).

thf(6289,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr$\''] :
      ( ( '\'fmember$d\'' @ A @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ '\'h$a\'' ) )
      | ( ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ '\'element_ptr$\'' @ ( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$at\'' @ ( '\'put_E_l_e_m_e_n_t$\'' @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[5421,1481]) ).

thf(6290,plain,
    '\'fmember$d\'' @ '\'element_ptr$\'' @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ '\'h$a\'' ),
    inference(pattern_uni,[status(thm)],[6289:[bind(A,$thf( '\'element_ptr$\'' )),bind(B,$thf( '\'child_nodes_update$\'' @ '\'uu$\'' @ '\'x$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(174,axiom,
    '\'type_wf$d\'' = '\'a_type_wf$d\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).

thf(1512,plain,
    '\'type_wf$d\'' = '\'a_type_wf$d\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(1513,plain,
    '\'a_type_wf$d\'' = '\'type_wf$d\'',
    inference(lifteq,[status(thm)],[1512]) ).

thf(716,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ A @ '\'bot$b\'' )
      | ~ ( '\'fun_app$aw\'' @ A @ ( '\'finsert$b\'' @ ( sk22 @ A ) @ ( sk23 @ A ) ) )
      | ( '\'fun_app$aw\'' @ A @ B ) ),
    inference(cnf,[status(esa)],[715]) ).

thf(2419,plain,
    ~ ? [A: '\'B_character_data_ptr$\'',B: '\'A_element_ptr$\''] :
        ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
        = ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(miniscope,[status(thm)],[2418]) ).

thf(2420,plain,
    ! [B: '\'A_element_ptr$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(cnf,[status(esa)],[2419]) ).

thf(2421,plain,
    ! [B: '\'A_element_ptr$\'',A: '\'B_character_data_ptr$\''] :
      ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
     != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ),
    inference(lifteq,[status(thm)],[2420]) ).

thf(796,plain,
    ( ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
        ( ( ( def_34 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) )
    & ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\''] :
        ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C )
       => ( ( def_34 @ A @ B @ C )
          = tltrue ) ) ),
    inference(miniscope,[status(thm)],[795]) ).

thf(797,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',A: tlbool] :
      ( ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C )
      | ( ( def_34 @ A @ B @ C )
        = tltrue ) ),
    inference(cnf,[status(esa)],[796]) ).

thf(799,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',A: tlbool] :
      ( ( ( def_34 @ A @ B @ C )
        = tltrue )
      | ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[797]) ).

thf(800,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',A: tlbool] :
      ( ( ( def_34 @ A @ B @ C )
        = tltrue )
      | ~ ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[799]) ).

thf(333,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_8 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_706) ).

thf(2374,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_8 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ C )
       => ( ( def_8 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(4352,plain,
    ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' ) )
   != ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ '\'node_ptr$\'' ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(paramod_ordered,[status(thm)],[3061,4340]) ).

thf(4354,plain,
    ( ( ( '\'fmember$\'' @ '\'node_ptr$\'' )
     != ( '\'fmember$\'' @ '\'node_ptr$\'' ) )
    | ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[4352]) ).

thf(4356,plain,
    ( ( sk70 @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) @ '\'node_ptr$\'' )
   != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ),
    inference(simp,[status(thm)],[4354]) ).

thf(2854,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uuh$\'' @ A @ B ) @ C )
      = ( '\'bind$e\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(cnf,[status(esa)],[2853]) ).

thf(2855,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uuh$\'' @ A @ B ) @ C )
      = ( '\'bind$e\'' @ ( '\'fun_app$n\'' @ A @ C ) @ B ) ),
    inference(lifteq,[status(thm)],[2854]) ).

thf(17956,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'bind$e\'' @ ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ A ) @ B )
      = ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) ) @ ( '\'uuh$\'' @ A @ B ) ) ),
    inference(rewrite,[status(thm)],[2855,5434,6331]) ).

thf(210,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) )
    <=> ~ ( ( ( B = '\'none$\'' )
            & ~ ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
          | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
              ( ( B
                = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
              & ~ ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).

thf(1673,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) )
       => ~ ( ( ( B = '\'none$\'' )
              & ~ ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
            | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
                ( ( B
                  = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
                & ~ ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) ) )
      & ( ~ ( ( ( B = '\'none$\'' )
              & ~ ( '\'fun_app$bn\'' @ A @ '\'none$\'' ) )
            | ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
                ( ( B
                  = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
                & ~ ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ C @ D ) ) ) )
       => ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$m\'' @ ( '\'bind$\'' @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(701,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C )
      | ( '\'is_document_ptr_kind$\'' @ A )
      | ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(cnf,[status(esa)],[699]) ).

thf(8589,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'a_type_wf$a\'' @ C )
      | ( '\'is_document_ptr_kind$\'' @ A )
      | ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(rewrite,[status(thm)],[701,2169]) ).

thf(292,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B )
    <=> ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
        | ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).

thf(2123,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B )
       => ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
          | ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) ) )
      & ( ( ( '\'fun_app$bn\'' @ A @ '\'none$\'' )
          | ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] : ( '\'fun_app$bn\'' @ A @ ( '\'fun_app$k\'' @ '\'some$c\'' @ B ) ) )
       => ? [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] : ( '\'fun_app$bn\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(7513,plain,
    ! [C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ B @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) )
      | ( ( sk84 @ '\'none$b\'' @ B )
       != ( sk84 @ '\'none$b\'' @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[5267]) ).

thf(7527,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[7513:[bind(A,$thf( B ))]]) ).

thf(7542,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( sk84 @ '\'none$b\'' @ A )
      | ( sk84 @ A @ ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' ) )
      | ( sk84 @ A @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) ) ),
    inference(simp,[status(thm)],[7527]) ).

thf(83,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
         => ( ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
           != '\'none$\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).

thf(967,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
        & ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
        & ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ C )
        & ( ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ tlfalse @ '\'is_character_data_ptr_kind_n_o_d_e_p_t_r$\'' ) @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
         => ( ( '\'case_option$l\'' @ '\'none$\'' @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) ) )
           != '\'none$\'' ) ) )
     => ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(17288,plain,
    ! [D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ A )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ C ) ) @ B )
       != '\'h$\'' )
      | ( D != '\'node_ptr$\'' )
      | ( ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) ) )
       != ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[496,17281]) ).

thf(17289,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ C )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ C @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ C ) )
       != '\'node_ptr$\'' ) ),
    inference(pattern_uni,[status(thm)],[17288:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ F ) ))]]) ).

thf(17297,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ~ ( '\'is_node_ptr_kind$\'' @ C )
      | ( ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ C @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ B ) ) @ A )
       != '\'h$\'' )
      | ( ( '\'the$c\'' @ ( '\'cast_o_b_j_e_c_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ C ) )
       != '\'node_ptr$\'' ) ),
    inference(simp,[status(thm)],[17289]) ).

thf(1500,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ),
    inference(cnf,[status(esa)],[1499]) ).

thf(1501,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$j\'' @ '\'some$b\'' @ B ) ),
    inference(lifteq,[status(thm)],[1500]) ).

thf(12292,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) )
      = ( '\'fun_app$p\'' @ '\'cast_O_b_j_e_c_t_2_D_o_c_u_m_e_n_t$\'' @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) ) ),
    inference(rewrite,[status(thm)],[1501,783]) ).

thf(264,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_32 @ A @ B @ C )
        = tltrue )
    <=> ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_730) ).

thf(1986,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_32 @ A @ B @ C )
          = tltrue )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C ) )
      & ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ C )
       => ( ( def_32 @ A @ B @ C )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(409,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
        & ! [B: '\'D_document_ptr$\''] :
            ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
             != '\'none$c\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).

thf(2768,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
          & ! [B: '\'D_document_ptr$\''] :
              ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
               != '\'none$c\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
          & ! [B: '\'D_document_ptr$\''] :
              ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
               != '\'none$c\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(601,plain,
    ~ ? [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
        ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
        = ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ),
    inference(miniscope,[status(thm)],[600]) ).

thf(602,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
     != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ),
    inference(cnf,[status(esa)],[601]) ).

thf(603,plain,
    ! [B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'cast_E_l_e_m_e_n_t_2_N_o_d_e$\'' @ A )
     != ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ B ) ),
    inference(lifteq,[status(thm)],[602]) ).

thf(6410,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'node_ptr$\'' != A )
      | ( ( sk70 @ ( '\'finsert$b\'' @ A @ B ) @ A )
       != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ) ),
    inference(simp,[status(thm)],[5900]) ).

thf(6411,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( sk70 @ ( '\'finsert$b\'' @ '\'node_ptr$\'' @ A ) @ '\'node_ptr$\'' )
     != ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ '\'h$\'' ) ),
    inference(simp,[status(thm)],[6410]) ).

thf(798,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',A: tlbool] :
      ( ( ( def_34 @ A @ B @ C )
       != tltrue )
      | ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[796]) ).

thf(801,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_option$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_bool_fun$\'',A: tlbool] :
      ( ( ( def_34 @ A @ B @ C )
       != tltrue )
      | ( '\'fun_app$bq\'' @ ( '\'case_option$j\'' @ A @ B ) @ C ) ),
    inference(lifteq,[status(thm)],[798]) ).

thf(8202,plain,
    ! [D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
       != '\'none$b\'' )
      | ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
       != ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ D ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[7684,8194]) ).

thf(8203,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$ba\'' @ ( '\'bind$i\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) ) ) @ '\'some$\'' )
     != '\'none$b\'' ),
    inference(pattern_uni,[status(thm)],[8202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(8307,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'extend$\'' @ ( '\'truncate$\'' @ A ) @ B ) ) )
     != '\'none$b\'' ),
    inference(rewrite,[status(thm)],[8203,3073]) ).

thf(8414,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'the$d\'' @ ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B ) ) ) )
     != '\'none$b\'' ),
    inference(rewrite,[status(thm)],[8307,8191]) ).

thf(8653,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$f\'' @ ( '\'uvz$\'' @ A ) @ B )
     != '\'none$b\'' ),
    inference(rewrite,[status(thm)],[8414,8650]) ).

thf(11551,plain,
    ! [F: '\'D_document_ptr$\'',E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ D ) )
       != ( '\'pair$b\'' @ F @ C ) )
      | ( ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ A ) @ ( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ B ) )
       != ( '\'put_O_b_j_e_c_t$\'' @ ( '\'cast_d_o_c_u_m_e_n_t_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ F ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[1282,10684]) ).

thf(11552,plain,
    ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ D ) @ C ) )
     != ( '\'pair$b\'' @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[11551:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( '\'cast_D_o_c_u_m_e_n_t_2_O_b_j_e_c_t$\'' @ G )),bind(F,$thf( A ))]]) ).

thf(11557,plain,
    ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'D_document_ptr$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ D ) @ C ) )
     != ( '\'pair$b\'' @ A @ B ) ),
    inference(simp,[status(thm)],[11552]) ).

thf(763,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ~ ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ B )
      | ~ ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ A )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[762]) ).

thf(767,plain,
    ! [B: '\'B_character_data_ptr_fset$\'',A: '\'B_character_data_ptr_fset$\''] :
      ( ( A = B )
      | ~ ( '\'fmember$b\'' @ ( sk27 @ B @ A ) @ B )
      | ~ ( '\'fmember$b\'' @ ( sk28 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[763]) ).

thf(11122,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ C )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9077,3080]) ).

thf(11123,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[11122:[bind(A,$thf( A )),bind(B,$thf( '\'node_ptr$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(14191,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[11123,6924]) ).

thf(3196,plain,
    '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ '\'a_type_wf$a\'',
    inference(rewrite,[status(thm)],[521,2169]) ).

thf(692,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ~ ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ B )
      | ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ B )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[690]) ).

thf(696,plain,
    ! [B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( A = B )
      | ~ ( '\'fmember$a\'' @ ( sk19 @ B @ A ) @ B )
      | ( '\'fmember$a\'' @ ( sk20 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[692]) ).

thf(467,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
         != '\'none$b\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).

thf(3045,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' ) )
        & ( ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ A )
           != '\'none$b\'' )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ ( '\'fun_app$au\'' @ '\'node_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(382,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).

thf(2651,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\'',C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( A != B )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ ( '\'fun_app$at\'' @ ( '\'put_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B @ C ) @ D ) )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(279,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( def_33 @ A @ B )
        = tltrue )
    <=> ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_731) ).

thf(2070,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\''] :
      ( ( ( ( def_33 @ A @ B )
          = tltrue )
       => ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) ) )
      & ( ( '\'fun_app$x\'' @ A @ ( '\'the$d\'' @ B ) )
       => ( ( def_33 @ A @ B )
          = tltrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(367,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr$\''] :
      ( ( ( '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( '\'fmember$d\'' @ C @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) )
      <=> ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ C ) @ B )
         != '\'none$a\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).

thf(2572,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr$\''] :
      ( ( ( '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( ( '\'fmember$d\'' @ C @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) )
         => ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ C ) @ B )
           != '\'none$a\'' ) )
        & ( ( ( '\'fun_app$ar\'' @ ( '\'fun_app$as\'' @ '\'get_E_l_e_m_e_n_t$\'' @ C ) @ B )
           != '\'none$a\'' )
         => ( '\'fmember$d\'' @ C @ ( '\'fun_app$av\'' @ '\'element_ptr_kinds$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(331,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ ( '\'uvs$\'' @ A @ B ) @ C )
      = ( '\'case_option$a\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) @ ( '\'uvr$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).

thf(2366,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ ( '\'uvs$\'' @ A @ B ) @ C )
      = ( '\'case_option$a\'' @ ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) @ ( '\'uvr$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(311,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$c\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) @ ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom600) ).

thf(2223,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'combine_options$c\'' @ A @ ( '\'fun_app$i\'' @ '\'some$a\'' @ B ) @ ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(635,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ ( sk12 @ A ) ) @ ( sk13 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( sk15 @ A ) ) @ ( sk17 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(2795,plain,
    '\'a_type_wf$\'' = '\'type_wf$\'',
    inference(lifteq,[status(thm)],[2794]) ).

thf(148,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
         != '\'none$\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).

thf(1346,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
     => ( ( ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
           != '\'none$\'' ) )
        & ( ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ B ) @ A )
           != '\'none$\'' )
         => ( '\'fmember$b\'' @ B @ ( '\'fun_app$al\'' @ '\'character_data_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(196,axiom,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ( ( ( ( A = '\'none$c\'' )
         => $false )
        & ( ( A
            = ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) ) )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).

thf(1610,plain,
    ! [A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option$\''] :
      ~ ( ( A != '\'none$c\'' )
        & ( A
         != ( '\'fun_app$j\'' @ '\'some$b\'' @ ( '\'the$f\'' @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(6501,plain,
    ! [F: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',E: '\'D_document_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',A: '\'D_document_ptr$\''] :
      ( ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ D )
       != ( '\'pair$b\'' @ E @ F ) )
      | ( ( '\'fmember$c\'' @ A @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ A @ B ) @ C ) ) )
       != ( '\'fmember$c\'' @ E @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2483,1664]) ).

thf(6502,plain,
    ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ C @ D ) @ B ) )
     != ( '\'pair$b\'' @ C @ A ) ),
    inference(pattern_uni,[status(thm)],[6501:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( H )),bind(D,$thf( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ I @ J ) @ H )),bind(E,$thf( I )),bind(F,$thf( F ))]]) ).

thf(6503,plain,
    ! [D: '\'C_a_b_j_option_RDocument_ext_RObject_ext$\'',C: '\'D_document_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'new_D_o_c_u_m_e_n_t$\'' @ ( '\'fun_app$at\'' @ ( '\'put_D_o_c_u_m_e_n_t$\'' @ C @ D ) @ B ) )
     != ( '\'pair$b\'' @ C @ A ) ),
    inference(simp,[status(thm)],[6502]) ).

thf(130,axiom,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\'',C: '\'D_document_ptr$\''] :
      ( ( A = B )
     => ( ( '\'fmember$c\'' @ C @ A )
      <=> ( '\'fmember$c\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).

thf(1236,plain,
    ! [A: '\'D_document_ptr_fset$\'',B: '\'D_document_ptr_fset$\'',C: '\'D_document_ptr$\''] :
      ( ( A = B )
     => ( ( ( '\'fmember$c\'' @ C @ A )
         => ( '\'fmember$c\'' @ C @ B ) )
        & ( ( '\'fmember$c\'' @ C @ B )
         => ( '\'fmember$c\'' @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(700,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ C )
      | ~ ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(cnf,[status(esa)],[699]) ).

thf(8444,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ~ ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ ( '\'fun_app$at\'' @ ( '\'put_O_b_j_e_c_t$\'' @ A @ B ) @ C ) )
      | ~ ( '\'fmember$a\'' @ A @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ C ) )
      | ~ ( '\'fun_app$ci\'' @ '\'a_type_wf$a\'' @ C )
      | ~ ( '\'fun_app$cj\'' @ '\'is_document_kind$\'' @ ( '\'the$\'' @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ A ) @ C ) ) )
      | ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ C ) ),
    inference(rewrite,[status(thm)],[700,2169]) ).

thf(3431,plain,
    ! [B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\''] :
      ( ( sk4 @ A @ '\'none$f\'' )
      | ( A
       != ( '\'fun_app$az\'' @ '\'some$f\'' @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[552,493]) ).

thf(3432,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] : ( sk4 @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ '\'none$f\'' ),
    inference(pattern_uni,[status(thm)],[3431:[bind(A,$thf( '\'fun_app$az\'' @ '\'some$f\'' @ D )),bind(B,$thf( D ))]]) ).

thf(3489,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] : ( sk4 @ ( '\'fun_app$az\'' @ '\'some$f\'' @ A ) @ '\'none$f\'' ),
    inference(simp,[status(thm)],[3432]) ).

thf(460,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uvm$\'' @ A @ B ) @ C )
      = ( '\'case_option$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) @ ( '\'uvl$\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).

thf(3020,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$g\'' @ ( '\'uvm$\'' @ A @ B ) @ C )
      = ( '\'case_option$d\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) @ ( '\'uvl$\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(214,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$b\'' @ A @ B @ C )
     => ( '\'l_put_M$b\'' @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).

thf(1713,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_fun$\''] :
      ( ( '\'l_get_M$b\'' @ A @ B @ C )
     => ( '\'l_put_M$b\'' @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(140,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
        = '\'none$\'' )
    <=> ( ( A = '\'none$\'' )
        | ( ( '\'fun_app$k\'' @ B @ ( '\'the$e\'' @ A ) )
          = '\'none$\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).

thf(1299,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
          = '\'none$\'' )
       => ( ( A = '\'none$\'' )
          | ( ( '\'fun_app$k\'' @ B @ ( '\'the$e\'' @ A ) )
            = '\'none$\'' ) ) )
      & ( ( ( A = '\'none$\'' )
          | ( ( '\'fun_app$k\'' @ B @ ( '\'the$e\'' @ A ) )
            = '\'none$\'' ) )
       => ( ( '\'fun_app$m\'' @ ( '\'bind$\'' @ A ) @ B )
          = '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(479,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$n\'' @ C @ E )
              = ( '\'fun_app$n\'' @ D @ E ) ) ) )
     => ( ( '\'bind$g\'' @ A @ C )
        = ( '\'bind$g\'' @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).

thf(3113,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',D: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$n\'' @ C @ E )
              = ( '\'fun_app$n\'' @ D @ E ) ) ) )
     => ( ( '\'bind$g\'' @ A @ C )
        = ( '\'bind$g\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(319,axiom,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ '\'type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).

thf(2270,plain,
    '\'l_get_C_h_a_r_a_c_t_e_r_D_a_t_a_lemmas$\'' @ '\'type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(11750,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk1 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ B ) @ C )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) )
      | ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' )
       != ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ B ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9081,3080]) ).

thf(11751,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk1 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = ( '\'bind$k\'' @ '\'none$f\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' ) ) ),
    inference(pattern_uni,[status(thm)],[11750:[bind(A,$thf( A )),bind(B,$thf( '\'node_ptr$\'' )),bind(C,$thf( '\'h$\'' ))]]) ).

thf(16859,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( sk1 @ ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ ( '\'cast_n_o_d_e_p_t_r_2_o_b_j_e_c_t_p_t_r$\'' @ '\'node_ptr$\'' ) ) @ '\'h$\'' ) )
       != ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) )
      | ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ '\'node_ptr$\'' ) @ '\'h$\'' )
        = '\'none$b\'' ) ),
    inference(rewrite,[status(thm)],[11751,6924]) ).

thf(416,axiom,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).

thf(2803,plain,
    '\'l_get_E_l_e_m_e_n_t_lemmas$\'' @ '\'type_wf$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(178,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) )
    <=> ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
        | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).

thf(1532,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) )
       => ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
          | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) ) )
      & ( ( ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ B )
          | ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ C ) )
       => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ A ) @ ( '\'sup$b\'' @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(426,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'pair$\'' @ B @ C ) )
        & ( D
         != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom649) ).

thf(2847,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\''] :
      ( ( ( ( '\'new_E_l_e_m_e_n_t$\'' @ A )
          = ( '\'pair$\'' @ B @ C ) )
        & ( D
         != ( '\'cast_e_l_e_m_e_n_t_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) )
     => ( ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ A )
        = ( '\'fun_app$aj\'' @ ( '\'fun_app$ak\'' @ '\'get_N_o_d_e$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(62,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\'',B: tlbool,C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr_fset$\''] :
      ( ( ( ( B = tltrue )
         => ( '\'fmember$a\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$a\'' @ A @ D ) ) )
    <=> ( ( ( B = tltrue )
         => ( '\'fmember$a\'' @ A @ C ) )
        & ( ( B != tltrue )
         => ( '\'fmember$a\'' @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).

thf(822,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(2502,plain,
    ( ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A )
       => ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
         != '\'none$b\'' ) )
    & ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
        ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
         != '\'none$b\'' )
       => ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A ) ) ),
    inference(miniscope,[status(thm)],[2501]) ).

thf(2504,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ~ ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A )
      | ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
       != '\'none$b\'' ) ),
    inference(cnf,[status(esa)],[2502]) ).

thf(2507,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
       != '\'none$b\'' )
      | ~ ( '\'fun_app$cj\'' @ '\'is_node_kind$\'' @ A ) ),
    inference(lifteq,[status(thm)],[2504]) ).

thf(390,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'pair$a\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom657) ).

thf(2687,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'B_character_data_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',D: '\'B_character_data_ptr$\''] :
      ( ( ( ( '\'new_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ A )
          = ( '\'pair$a\'' @ B @ C ) )
        & ( D != B ) )
     => ( ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ A )
        = ( '\'fun_app$am\'' @ ( '\'fun_app$an\'' @ '\'get_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(248,axiom,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( '\'fun_app$u\'' @ A @ ( def_28 @ B @ C @ D ) )
    <=> ( ( ( D = '\'none$\'' )
         => ( '\'fun_app$u\'' @ A @ B ) )
        & ( ( D
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
         => ( '\'fun_app$u\'' @ A @ ( def_29 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).

thf(1885,plain,
    ! [A: '\'Bool_bool_fun$\'',B: tlbool,C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\'',D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\''] :
      ( ( ( '\'fun_app$u\'' @ A @ ( def_28 @ B @ C @ D ) )
       => ( ( ( D = '\'none$\'' )
           => ( '\'fun_app$u\'' @ A @ B ) )
          & ( ( D
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
           => ( '\'fun_app$u\'' @ A @ ( def_29 @ C @ D ) ) ) ) )
      & ( ( ( ( D = '\'none$\'' )
           => ( '\'fun_app$u\'' @ A @ B ) )
          & ( ( D
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( '\'the$e\'' @ D ) ) )
           => ( '\'fun_app$u\'' @ A @ ( def_29 @ C @ D ) ) ) )
       => ( '\'fun_app$u\'' @ A @ ( def_28 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(394,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A )
     => ( '\'fun_app$ci\'' @ '\'type_wf$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).

thf(2699,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(222,axiom,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
    <=> ( A = tltrue ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).

thf(1737,plain,
    ! [A: tlbool,B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_bool_fun$\''] :
      ( ( ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' )
       => ( A = tltrue ) )
      & ( ( A = tltrue )
       => ( '\'fun_app$bn\'' @ ( '\'case_option$g\'' @ A @ B ) @ '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(391,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$f\'' @ A @ C )
        = ( '\'bind$f\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).

thf(2690,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_h_option_RCharacterData_ext_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$f\'' @ A @ C )
        = ( '\'bind$f\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(5436,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$g\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ A ) ) @ '\'cast_N_o_d_e_2_E_l_e_m_e_n_t$\'' )
       != '\'none$a\'' )
      | ~ ( '\'fun_app$x\'' @ '\'is_element_kind_N_o_d_e$\'' @ A ) ),
    inference(rewrite,[status(thm)],[1467,5434]) ).

thf(740,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ( B
        = ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) ) )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(cnf,[status(esa)],[739]) ).

thf(755,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) )
        = B )
      | ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[740]) ).

thf(756,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ( '\'fun_app$k\'' @ '\'some$c\'' @ ( sk26 @ C @ B @ A ) )
        = B )
      | ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(simp,[status(thm)],[755]) ).

thf(12637,plain,
    ! [C: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_j_option_RDocument_ext_RObject_ext_option_fun$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',A: '\'C_a_b_j_option_RDocument_ext_RObject_ext_option_bool_fun$\''] :
      ( ( ( '\'bind$f\'' @ ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ ( '\'cast_N_o_d_e_2_O_b_j_e_c_t$\'' @ ( '\'cast_C_h_a_r_a_c_t_e_r_D_a_t_a_2_N_o_d_e$\'' @ ( sk26 @ C @ B @ A ) ) ) ) @ '\'cast_N_o_d_e_2_C_h_a_r_a_c_t_e_r_D_a_t_a$\'' )
        = B )
      | ~ ( '\'fun_app$bm\'' @ A @ '\'none$c\'' )
      | ( '\'fun_app$bm\'' @ A @ ( '\'bind$q\'' @ B @ C ) ) ),
    inference(rewrite,[status(thm)],[756,6039]) ).

thf(639,plain,
    ! [C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\'',A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_a_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset_bool_fun_fun$\''] :
      ( ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ '\'bot$b\'' )
      | ( sk9 @ A )
      | ~ ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ '\'bot$b\'' ) @ ( '\'finsert$b\'' @ ( sk12 @ A ) @ ( sk13 @ A ) ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ ( sk15 @ A ) ) @ ( sk17 @ A ) )
      | ( '\'fun_app$aw\'' @ ( '\'fun_app$cu\'' @ A @ B ) @ C ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(468,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$b\'' @ A @ B )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
    <=> ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
          & ( ( '\'fun_app$bk\'' @ B @ D )
            = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).

thf(3052,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$b\'' @ A @ B )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
       => ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bk\'' @ B @ D )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) ) ) )
      & ( ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bk\'' @ B @ D )
              = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) ) )
       => ( ( '\'bind$b\'' @ A @ B )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(165,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( '\'fun_app$ci\'' @ '\'a_type_wf$\'' @ A )
    <=> ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
        & ! [B: '\'D_document_ptr$\''] :
            ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
           => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
             != '\'none$c\'' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).

thf(1468,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\''] :
      ( ( ( '\'fun_app$ci\'' @ '\'a_type_wf$\'' @ A )
       => ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
          & ! [B: '\'D_document_ptr$\''] :
              ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
               != '\'none$c\'' ) ) ) )
      & ( ( ( '\'fun_app$ci\'' @ '\'type_wf$a\'' @ A )
          & ! [B: '\'D_document_ptr$\''] :
              ( ( '\'member$a\'' @ B @ ( '\'fset$a\'' @ ( '\'fun_app$ao\'' @ '\'document_ptr_kinds$\'' @ A ) ) )
             => ( ( '\'fun_app$ap\'' @ ( '\'fun_app$aq\'' @ '\'get_D_o_c_u_m_e_n_t$\'' @ B ) @ A )
               != '\'none$c\'' ) ) )
       => ( '\'fun_app$ci\'' @ '\'a_type_wf$\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(250,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ ( '\'uvr$\'' @ A @ B ) @ C )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).

thf(1912,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_fun_fun$\'',B: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$i\'' @ ( '\'uvr$\'' @ A @ B ) @ C )
      = ( '\'fun_app$i\'' @ '\'some$a\'' @ ( '\'fun_app$ac\'' @ ( '\'fun_app$ad\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(432,axiom,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
    <=> ( '\'fun_app$x\'' @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).

thf(2866,plain,
    ! [A: tlbool,B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_bool_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
       => ( '\'fun_app$x\'' @ B @ C ) )
      & ( ( '\'fun_app$x\'' @ B @ C )
       => ( '\'fun_app$bp\'' @ ( '\'case_option$i\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(2831,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A )
      = ( '\'case_sum$a\'' @ ( '\'uvz$\'' @ A ) @ '\'uwa$\'' @ ( '\'more$a\'' @ A ) ) ),
    inference(cnf,[status(esa)],[2830]) ).

thf(2832,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext$\''] :
      ( ( '\'case_sum$a\'' @ ( '\'uvz$\'' @ A ) @ '\'uwa$\'' @ ( '\'more$a\'' @ A ) )
      = ( '\'fun_app$s\'' @ '\'cast_O_b_j_e_c_t_2_N_o_d_e$\'' @ A ) ),
    inference(lifteq,[status(thm)],[2831]) ).

thf(170,axiom,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( '\'bind$a\'' @ A @ B )
        = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
    <=> ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
          ( ( A
            = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
          & ( ( '\'fun_app$bh\'' @ B @ D )
            = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).

thf(1490,plain,
    ! [A: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_option$\'',B: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext_c_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext_option_fun$\'',C: '\'C_a_b_e_g_option_RElement_ext_RNode_ext_RObject_ext$\''] :
      ( ( ( ( '\'bind$a\'' @ A @ B )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) )
       => ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bh\'' @ B @ D )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) )
      & ( ? [D: '\'H_option_RCharacterData_ext_RNode_ext_RObject_ext$\''] :
            ( ( A
              = ( '\'fun_app$k\'' @ '\'some$c\'' @ D ) )
            & ( ( '\'fun_app$bh\'' @ B @ D )
              = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) )
       => ( ( '\'bind$a\'' @ A @ B )
          = ( '\'fun_app$i\'' @ '\'some$a\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(301,axiom,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\''] :
      ( ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
        = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).

thf(2170,plain,
    ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\''] :
      ( ( ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(107,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( '\'fmember$a\'' @ C @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ C ) @ B )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).

thf(1088,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap_bool_fun$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( ( '\'l_get_O_b_j_e_c_t_lemmas$d\'' @ A )
        & ( '\'fun_app$ci\'' @ A @ B ) )
     => ( ( ( '\'fmember$a\'' @ C @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ C ) @ B )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ C ) @ B )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ C @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(125,axiom,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
      <=> ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
         != '\'none$f\'' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom561) ).

thf(1204,plain,
    ! [A: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_heap$\'',B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_d_document_ptr_e_shadow_root_ptr_f_sum_sum_sum_object_ptr$\''] :
      ( ( '\'fun_app$ci\'' @ '\'type_wf$\'' @ A )
     => ( ( ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) )
         => ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' ) )
        & ( ( ( '\'fun_app$ck\'' @ ( '\'fun_app$cl\'' @ '\'get_O_b_j_e_c_t$\'' @ B ) @ A )
           != '\'none$f\'' )
         => ( '\'fmember$a\'' @ B @ ( '\'fun_app$bl\'' @ '\'object_ptr_kinds$\'' @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(234,axiom,
    ! [A: tlbool,B: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',C: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr$\'',D: '\'A_element_ptr_b_character_data_ptr_c_sum_sum_node_ptr_fset$\''] :
      ( ( ( ( A = tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ D ) )
        & ( ( A != tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) ) )
    <=> ( ( ( A = tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ B ) @ D ) )
        & ( ( A != tltrue )
         => ( '\'fun_app$aw\'' @ ( '\'fmember$\'' @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).

thf(1812,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(2171,plain,
    ( ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\''] :
        ( ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
       => ( A = B ) )
    & ! [A: '\'B_character_data_ptr$\'',B: '\'B_character_data_ptr$\''] :
        ( ( A = B )
       => ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
          = ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) ) ) ),
    inference(miniscope,[status(thm)],[2170]) ).

thf(2173,plain,
    ! [B: '\'B_character_data_ptr$\'',A: '\'B_character_data_ptr$\''] :
      ( ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
       != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[2171]) ).

thf(2176,plain,
    ! [B: '\'B_character_data_ptr$\'',A: '\'B_character_data_ptr$\''] :
      ( ( ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A )
       != ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[2173]) ).

thf(2177,plain,
    ! [A: '\'B_character_data_ptr$\''] :
      ( ( sk107 @ ( '\'cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$\'' @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse('cast_c_h_a_r_a_c_t_e_r_d_a_t_a_p_t_r_2_n_o_d_e_p_t_r$'),[sk107])]) ).

thf(383,axiom,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).

thf(2655,plain,
    ! [A: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',B: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_option$\'',C: '\'C_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_c_a_b_j_option_RDocument_ext_k_sum_sum_RObject_ext_c_a_b_e_g_option_RElement_ext_h_option_RCharacterData_ext_i_sum_sum_RNode_ext_RObject_ext_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$k\'' @ A @ C )
        = ( '\'bind$k\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(48058,plain,
    $false,
    inference(cvc4,[status(thm)],[1024,1823,760,2778,4183,1549,3172,2163,645,5437,1322,1665,1036,2822,2630,2094,1411,9077,2131,2031,3666,1729,2595,6317,1850,2480,1982,6042,2331,4682,777,555,1211,2512,1005,2104,15190,683,2644,2381,1618,13424,1269,1793,1692,1437,9003,1173,2363,2077,730,1290,1939,2248,655,511,17113,1137,2686,533,1999,1233,8650,1507,670,1705,3017,1078,3217,1608,8182,3120,6505,500,3175,2168,698,1835,3088,1935,1359,13751,12770,16979,1967,1518,2405,4249,651,14292,1095,1746,898,2491,1127,1650,5056,1228,1482,2603,6039,785,2501,2444,702,802,2185,2562,2897,3248,1055,17075,3195,570,2698,1660,719,6547,9693,3061,6423,587,3148,8654,1313,1279,5289,15092,6071,6240,638,2552,15742,606,12229,1568,1641,2388,1232,1847,2169,1514,5604,13183,1013,770,2829,3788,2178,924,1946,17899,1828,574,2034,2555,821,1489,14981,1664,2794,2105,1811,17747,7441,6745,1136,8196,1283,2017,905,634,1622,660,1600,1697,2718,2884,2508,5059,7707,4751,687,7931,2833,1447,2483,956,1345,2799,2804,2965,507,7722,1975,1564,9703,10062,2910,3567,9308,793,925,1338,1915,534,13059,1163,5438,761,15642,18664,2496,2621,2660,714,1723,894,9075,598,561,1487,3239,630,2606,815,729,3207,1560,2673,6652,2733,825,8168,1021,778,7881,2133,1502,7161,788,1619,2150,1602,10038,3065,889,2181,493,2213,757,1195,2228,2112,3033,12450,1938,847,2758,1968,3198,2663,6043,2200,522,830,17296,8031,1012,5285,578,697,2840,12538,650,6603,2709,725,1425,1672,3078,19258,783,3087,1794,1017,1804,8009,1878,2726,2268,499,1567,14405,7189,2323,554,2830,1461,669,1424,642,637,2613,1791,2666,1644,706,2781,526,14110,3194,2349,1016,590,2085,2978,17239,679,2317,1744,622,17170,1297,738,1539,654,7385,569,5603,2968,2285,2932,1588,985,515,1478,2487,2598,6331,1231,5900,11360,3222,2006,1002,1852,8191,14516,1599,1246,1715,10588,3074,4689,3162,3201,605,1627,1525,1202,1086,633,12206,921,1846,1170,5434,5419,1167,6038,794,1732,926,18640,1857,9081,10366,4567,2208,15101,1563,657,2408,2793,718,888,2391,1483,1747,689,2524,1631,11165,1278,965,750,10840,2413,3130,8195,824,5608,9635,4340,7165,2734,584,819,562,2727,3319,2525,1752,2016,579,2991,8167,1965,1124,2827,2048,2859,2981,5067,7440,3081,9706,545,2695,1256,641,7425,2220,2029,2738,713,2935,1107,1997,2442,2706,2457,9290,1356,2193,3023,2891,2308,18035,947,1638,17128,604,2679,3238,2422,1048,990,3106,2945,2856,1122,5267,2065,681,1853,1408,1282,3251,2151,3155,2229,2955,1603,1722,5054,3197,1801,599,2871,1376,3219,1877,552,9079,3073,1993,4897,3192,1029,2278,1952,494,19256,2632,535,2625,2780,2267,2446,621,2757,3034,1325,769,6044,2928,6553,1381,2710,1820,521,2962,2725,2086,12465,19257,2369,986,563,10119,653,7232,2984,1562,2418,4933,768,827,695,636,1044,2592,10108,1000,2535,9011,1726,2390,12308,1102,2069,658,1076,5435,722,2952,2614,531,1420,2037,2878,487,2449,15152,516,3278,4355,2899,490,1583,3193,3427,1758,1166,1203,589,7975,2994,795,2271,663,548,2256,17281,8194,1181,823,2942,4749,525,2863,640,4939,2192,971,10059,1647,993,712,19167,580,855,2715,5250,872,4937,17087,705,1156,10684,4200,2407,1267,1230,2850,2092,1432,1813,2920,717,840,3026,7947,1980,4351,4117,3041,16811,3080,1499,2569,10307,5420,6036,6037,1188,2700,2948,2838,2426,9851,2320,2579,1749,2949,2030,2584,1543,8316,1802,1023,1353,600,3071,571,497,2266,2435,6286,1839,2088,1412,1781,771,3039,1918,2352,6041,1553,1844,688,524,581,2490,8228,1010,1575,6543,2226,2643,1385,1903,1481,652,2823,2811,2130,18454,1276,2591,1646,2443,699,2707,2098,748,2853,2251,1062,2532,946,1101,10428,2026,632,2971,1244,11567,6354,2394,3085,2944,2009,2081,2786,6397,3430,6554,667,929,1193,1661,2120,1309,2494,6499,2796,914,4153,6290,510,5072,1513,716,3420,1614,2421,800,2374,620,1512,1957,5606,4356,1546,2522,17956,1673,8589,6924,2123,2102,7542,1725,1280,967,17297,2815,12292,1986,9728,2768,603,3062,6411,801,8653,11557,506,2704,767,14191,3196,9795,696,3045,2651,1335,2070,2572,2366,6287,2223,635,2795,1346,1610,886,6503,728,1236,1129,17172,575,8444,1384,3489,3020,1713,1299,3113,2270,2159,2731,16859,2803,1532,2847,822,2507,1597,2687,1004,2484,1885,2699,1653,1737,2690,5436,12637,639,3052,2087,1468,496,1912,8950,2640,2866,2832,1490,775,2170,1088,1204,1812,2177,2655,1014,1870]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP309_1 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May  6 14:43:09 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.58/1.25  % [INFO] 	 Parsing done (385ms). 
% 2.58/1.25  % [INFO] 	 Running in sequential loop mode. 
% 3.04/1.45  % [INFO] 	 eprover registered as external prover. 
% 3.04/1.46  % [INFO] 	 cvc4 registered as external prover. 
% 3.04/1.46  % [INFO] 	 Scanning for conjecture ... 
% 3.41/1.63  % [INFO] 	 Found a conjecture and 734 axioms. Running axiom selection ... 
% 4.44/1.82  % [INFO] 	 Axiom selection finished. Selected 484 axioms (removed 250 axioms). 
% 5.16/2.04  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.16/2.06  % [INFO] 	 Type checking passed. 
% 5.16/2.06  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 8.52/3.07  % [INFO] 	 [Domain constraints] Detected constraint on tlbool 
% 8.52/3.07  % [INFO] 	 [Domain constraints] dom(tlbool) ⊆ {tltrue,tlfalse} 
% 142.71/39.19  % External prover 'cvc4' found a proof!
% 142.71/39.19  % [INFO] 	 Killing All external provers ... 
% 142.71/39.20  % Time passed: 38667ms (effective reasoning time: 37938ms)
% 142.71/39.20  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 142.71/39.20  % Axioms used in derivation (484): axiom32, axiom260, axiom280, axiom127, axiom626, axiom116, axiom452, axiom491, axiom241, axiom28, axiom611, hypothesis57, axiom230, axiom100, axiom6, axiom564, axiom503, axiom295, axiom396, hypothesis60, axiom404, axiom474, axiom221, axiom214, axiom516, formula_730, axiom203, axiom496, axiom284, axiom423, axiom65, axiom142, axiom311, axiom169, axiom622, axiom531, axiom291, axiom441, axiom507, axiom430, axiom600, axiom158, axiom131, axiom10, axiom386, axiom597, axiom580, axiom344, axiom508, axiom392, axiom119, axiom210, formula_734, axiom460, axiom692, axiom17, axiom401, axiom397, axiom407, formula_706, axiom467, axiom257, axiom579, axiom22, axiom619, axiom412, axiom445, axiom147, axiom524, axiom434, axiom341, axiom504, axiom173, axiom109, axiom350, axiom348, axiom561, axiom376, axiom172, axiom535, axiom513, axiom239, axiom162, axiom632, axiom616, axiom123, axiom383, axiom605, axiom134, axiom104, axiom33, axiom150, axiom87, axiom568, axiom130, axiom557, axiom235, axiom98, axiom112, axiom488, axiom473, axiom365, axiom39, axiom499, axiom330, axiom650, axiom418, axiom643, axiom225, formula_712, axiom608, axiom687, axiom64, axiom247, axiom578, axiom530, axiom352, axiom283, axiom126, axiom289, axiom427, axiom625, axiom642, axiom217, axiom343, axiom411, axiom294, axiom179, axiom363, axiom437, axiom236, axiom115, axiom623, axiom94, axiom336, axiom308, axiom35, axiom647, axiom78, axiom24, axiom661, axiom228, axiom405, axiom5, axiom101, axiom475, axiom121, hypothesis58, axiom132, axiom490, axiom137, axiom563, axiom206, axiom416, axiom240, axiom290, axiom433, axiom143, axiom489, axiom108, axiom395, axiom387, axiom16, axiom459, axiom400, axiom9, axiom258, axiom75, axiom385, axiom478, axiom658, axiom90, axiom168, formula_707, axiom448, formula_717, axiom552, axiom612, axiom366, formula_711, axiom207, axiom133, axiom80, axiom371, axiom252, axiom567, axiom355, axiom422, axiom185, axiom472, axiom146, axiom97, formula_722, axiom391, axiom604, axiom263, axiom415, axiom254, axiom444, axiom657, axiom82, axiom45, axiom483, axiom174, axiom398, axiom382, axiom426, axiom347, axiom646, axiom180, axiom450, axiom523, axiom232, axiom615, axiom463, axiom72, axiom461, axiom449, axiom438, axiom91, axiom105, axiom267, axiom89, axiom224, axiom122, axiom419, axiom377, axiom218, axiom86, axiom163, axiom408, axiom111, axiom120, axiom660, axiom297, axiom447, axiom432, axiom390, axiom37, axiom342, axiom212, axiom205, axiom34, axiom630, axiom79, axiom152, axiom425, axiom167, axiom607, axiom454, axiom190, axiom573, axiom443, axiom96, axiom149, axiom189, axiom375, axiom560, axiom93, axiom476, axiom595, axiom562, axiom41, axiom394, formula_721, axiom227, axiom182, axiom409, formula_732, axiom313, axiom618, axiom118, axiom275, hypothesis59, axiom63, axiom458, axiom613, axiom102, axiom8, axiom410, axiom320, axiom30, axiom178, axiom370, axiom659, axiom428, axiom259, axiom74, axiom276, axiom451, axiom85, axiom509, axiom233, axiom220, axiom598, formula_726, axiom378, axiom599, axiom566, axiom145, axiom471, axiom506, axiom186, axiom497, axiom164, axiom374, axiom614, axiom440, axiom581, axiom282, axiom114, axiom287, axiom255, axiom153, axiom324, axiom71, axiom462, axiom15, axiom129, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom268, axiom181, axiom403, axiom522, axiom436, axiom482, axiom555, axiom346, formula_710, axiom645, axiom262, axiom68, axiom686, axiom335, axiom170, axiom656, axiom175, axiom237, axiom219, axiom439, axiom469, axiom421, axiom110, axiom125, axiom603, axiom49, axiom577, axiom690, axiom298, axiom547, axiom18, axiom338, axiom242, axiom691, axiom510, axiom389, axiom226, axiom166, axiom559, axiom457, axiom521, axiom651, axiom88, axiom442, axiom92, axiom399, axiom66, hypothesis56, axiom345, axiom596, axiom204, axiom296, axiom141, axiom357, axiom274, axiom117, axiom393, axiom621, axiom446, axiom269, axiom453, axiom81, axiom103, axiom7, axiom515, formula_709, axiom84, hypothesis61, axiom349, axiom211, axiom689, axiom550, axiom565, axiom99, axiom537, axiom183, axiom649, axiom361, axiom429, axiom532, axiom177, axiom31, axiom431, axiom208, axiom20, axiom627, formula_720, axiom159, axiom609, axiom384, axiom73, axiom107, axiom171, axiom417, axiom339, axiom154, axiom40, formula_731, axiom270, axiom113, axiom176, axiom402, formula_716, formula_705, axiom165, axiom305, axiom424, axiom187, axiom288, axiom135, formula_702, axiom529, axiom144, axiom435, axiom281, axiom593, axiom245, axiom644, axiom69, hypothesis55, axiom277, axiom95, axiom70, axiom238, axiom617, axiom299, axiom351, axiom261, axiom606, axiom413, axiom256, axiom334, formula_735, axiom582, axiom514, axiom43, axiom124, axiom505, axiom406, axiom388, formula_727, axiom420, axiom62, axiom468, axiom21, axiom140, axiom624, axiom525, axiom234, axiom340, axiom51, axiom309, axiom610, axiom470, formula_713, axiom648, axiom209, axiom250, axiom688
% 142.71/39.20  % No. of inferences in proof: 1962
% 142.71/39.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38667 ms resp. 37938 ms w/o parsing
% 143.62/39.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 143.62/39.59  % [INFO] 	 Killing All external provers ... 
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