%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP172^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 : Wed Feb 25 08:56:08 AM UTC 2026
% Result : Theorem 3.32s 1.74s
% Output : Refutation 3.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP172^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:28:54 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP172^2 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer ShadowRootMonad problem prob_623__5857930_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : ShadowRootMonad/prob_623__5857930_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v9.1.0, 0.00 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 421 ( 182 unt; 113 typ; 0 def)
% 0.21/0.47 % Number of atoms : 596 ( 479 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 7 ( 1 avg)
% 0.21/0.47 % Number of connectives : 5645 ( 86 ~; 8 |; 41 &;5224 @)
% 0.21/0.47 % ( 0 <=>; 286 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 34 ( 7 avg)
% 0.21/0.47 % Number of types : 16 ( 15 usr)
% 0.21/0.47 % Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 99 ( 98 usr; 3 con; 0-14 aty)
% 0.21/0.47 % Number of variables : 1455 ( 16 ^;1233 !; 22 ?;1455 :)
% 0.21/0.47 % ( 184 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.47 % SPC : TH1_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:18:20.160
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (35)
% 0.21/0.47 thf(ty_t_CharacterDataClass_ORCharacterData_ORCharacterData__ext,type,
% 0.21/0.47 rCharacterData_ext: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ShadowRootClass_ORShadowRoot_ORShadowRoot__ext,type,
% 0.21/0.47 rShadowRoot_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_CharacterDataPointer_Ocharacter__data__ptr,type,
% 0.21/0.47 character_data_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_DocumentClass_ORDocument_ORDocument__ext,type,
% 0.21/0.47 rDocument_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ElementClass_ORElement_ORElement__ext,type,
% 0.21/0.47 rElement_ext: $tType > $tType > $tType > $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ShadowRootPointer_Oshadow__root__ptr,type,
% 0.21/0.47 shadow_root_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ObjectClass_ORObject_ORObject__ext,type,
% 0.21/0.47 rObject_ext: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_DocumentPointer_Odocument__ptr,type,
% 0.21/0.47 document_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_NodeClass_ORNode_ORNode__ext,type,
% 0.21/0.47 rNode_ext: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ElementPointer_Oelement__ptr,type,
% 0.21/0.47 element_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ObjectPointer_Oobject__ptr,type,
% 0.21/0.47 object_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Heap__Error__Monad_Oprog,type,
% 0.21/0.47 heap_Error_prog: $tType > $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_NodePointer_Onode__ptr,type,
% 0.21/0.47 node_ptr: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Product__Type_Ounit,type,
% 0.21/0.47 product_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Product__Type_Oprod,type,
% 0.21/0.47 product_prod: $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_ObjectClass_Oheap,type,
% 0.21/0.47 heap: $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Sum__Type_Osum,type,
% 0.21/0.47 sum_sum: $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Option_Ooption,type,
% 0.21/0.47 option: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_String_Ochar,type,
% 0.21/0.47 char: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_List_Olist,type,
% 0.21/0.47 list: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_FSet_Ofset,type,
% 0.21/0.47 fset: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Set_Oset,type,
% 0.21/0.47 set: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Nat_Onat,type,
% 0.21/0.47 nat: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_l,type,
% 0.21/0.47 l: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_k,type,
% 0.21/0.47 k: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_j,type,
% 0.21/0.47 j: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_i,type,
% 0.21/0.47 i: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_h,type,
% 0.21/0.47 h: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_g,type,
% 0.21/0.47 g: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_f,type,
% 0.21/0.47 f: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_e,type,
% 0.21/0.47 e: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_d,type,
% 0.21/0.47 d: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_c,type,
% 0.21/0.47 c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_b,type,
% 0.21/0.47 b: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_a,type,
% 0.21/0.47 a: $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (78)
% 0.21/0.47 thf(sy_cl_HOL_Otype,type,
% 0.21/0.47 type:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Nat_Osize,type,
% 0.21/0.47 size:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ozero,type,
% 0.21/0.47 zero:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.21/0.47 bot:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.47 ord:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.21/0.47 group_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Omonoid__add,type,
% 0.21/0.47 monoid_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.47 linorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.21/0.47 semigroup_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.21/0.47 comm_monoid_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.21/0.47 ab_semigroup_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.21/0.47 cancel_semigroup_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.21/0.47 cancel1352612707id_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.21/0.47 linord219039673up_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.21/0.47 ordere779506340up_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.21/0.47 canoni770627133id_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.21/0.47 semiri456707255roduct:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_ORDocument__ext,type,
% 0.21/0.47 rDocument_ext2:
% 0.21/0.47 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( product_unit > ( list @ char ) > ( option @ ( element_ptr @ Element_ptr ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > Z > ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes,type,
% 0.21/0.47 disconnected_nodes:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes__update,type,
% 0.21/0.47 discon1635973971update:
% 0.21/0.47 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( ( ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odoctype,type,
% 0.21/0.47 doctype:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ char ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odoctype__update,type,
% 0.21/0.47 doctype_update:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( list @ char ) > ( list @ char ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odocument__element,type,
% 0.21/0.47 document_element:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Odocument__element__update,type,
% 0.21/0.47 docume446011358update:
% 0.21/0.47 !>[Element_ptr: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Omore,type,
% 0.21/0.47 more:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > Z ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Omore__update,type,
% 0.21/0.47 more_update:
% 0.21/0.47 !>[Z: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType] : ( ( Z > Z ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Onothing,type,
% 0.21/0.47 nothing:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > product_unit ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_ORDocument_Onothing__update,type,
% 0.21/0.47 nothing_update:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( product_unit > product_unit ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 0.21/0.47 cast_D42511940_e_c_t:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.21/0.47 cast_O1159777348_e_n_t:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Odocument__ptrs,type,
% 0.21/0.47 document_ptrs:
% 0.21/0.47 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Shadow_root_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Oget_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.21/0.47 get_D_o_c_u_m_e_n_t:
% 0.21/0.47 !>[Shadow_root_ptr: $tType,Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Ois__document__kind,type,
% 0.21/0.47 is_document_kind:
% 0.21/0.47 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentClass_Oput_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.21/0.47 put_D_o_c_u_m_e_n_t:
% 0.21/0.47 !>[Shadow_root_ptr: $tType,Document_ptr: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 0.21/0.47 cast_d1427782271_p_t_r:
% 0.21/0.47 !>[Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 0.21/0.47 cast_o823910367_p_t_r:
% 0.21/0.47 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType] : ( ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) > ( option @ ( document_ptr @ Document_ptr ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Odocument__ptr_OExt,type,
% 0.21/0.47 document_Ext:
% 0.21/0.47 !>[Document_ptr: $tType] : ( Document_ptr > ( document_ptr @ Document_ptr ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Odocument__ptr_ORef,type,
% 0.21/0.47 document_Ref:
% 0.21/0.47 !>[Document_ptr: $tType] : ( nat > ( document_ptr @ Document_ptr ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Odocument__ptr_Osize__document__ptr,type,
% 0.21/0.47 docume1907984069nt_ptr:
% 0.21/0.47 !>[Document_ptr: $tType] : ( ( Document_ptr > nat ) > ( document_ptr @ Document_ptr ) > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_DocumentPointer_Ois__document__ptr_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 0.21/0.47 is_doc697300620_p_t_r:
% 0.21/0.47 !>[Document_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.21/0.47 plus_plus:
% 0.21/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.21/0.47 zero_zero:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Heap__Error__Monad_Oprog_OProg,type,
% 0.21/0.47 heap_Error_Prog:
% 0.21/0.47 !>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) ) ) > ( heap_Error_prog @ Heap @ E @ Result ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Heap__Error__Monad_Oprog_Osize__prog,type,
% 0.21/0.47 heap_Error_size_prog:
% 0.21/0.47 !>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > nat ) > ( E > nat ) > ( Result > nat ) > ( heap_Error_prog @ Heap @ E @ Result ) > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oappend,type,
% 0.21/0.47 append:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Ocount__list,type,
% 0.21/0.47 count_list:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Ogen__length,type,
% 0.21/0.47 gen_length:
% 0.21/0.47 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oinsert,type,
% 0.21/0.47 insert:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_OCons,type,
% 0.21/0.47 cons:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil,type,
% 0.21/0.47 nil:
% 0.21/0.47 !>[A: $tType] : ( list @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist__ex1,type,
% 0.21/0.47 list_ex1:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_On__lists,type,
% 0.21/0.47 n_lists:
% 0.21/0.47 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Onths,type,
% 0.21/0.47 nths:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oproduct__lists,type,
% 0.21/0.47 product_lists:
% 0.21/0.47 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Osplice,type,
% 0.21/0.47 splice:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Osubseqs,type,
% 0.21/0.47 subseqs:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat_OSuc,type,
% 0.21/0.47 suc: nat > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.21/0.47 size_size:
% 0.21/0.47 !>[A: $tType] : ( A > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 0.21/0.47 nat_set_decode: nat > ( set @ nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 0.21/0.47 nat_set_encode: ( set @ nat ) > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.21/0.47 nat_triangle: nat > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_ORObject_ORObject__ext,type,
% 0.21/0.47 rObject_ext2:
% 0.21/0.47 !>[Z: $tType] : ( product_unit > Z > ( rObject_ext @ Z ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_ORObject_Oextend,type,
% 0.21/0.47 extend:
% 0.21/0.47 !>[Z: $tType] : ( ( rObject_ext @ product_unit ) > Z > ( rObject_ext @ Z ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_ORObject_Omore,type,
% 0.21/0.47 more2:
% 0.21/0.47 !>[Z: $tType] : ( ( rObject_ext @ Z ) > Z ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_ORObject_Onothing,type,
% 0.21/0.47 nothing2:
% 0.21/0.47 !>[Z: $tType] : ( ( rObject_ext @ Z ) > product_unit ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_Oget_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 0.21/0.47 get_O_b_j_e_c_t:
% 0.21/0.47 !>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( heap @ Object_ptr @ Object ) > ( option @ ( rObject_ext @ Object ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ObjectClass_Oput_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 0.21/0.47 put_O_b_j_e_c_t:
% 0.21/0.47 !>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( rObject_ext @ Object ) > ( heap @ Object_ptr @ Object ) > ( heap @ Object_ptr @ Object ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Option_Obind,type,
% 0.21/0.47 bind:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( option @ A ) > ( A > ( option @ B ) ) > ( option @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Option_Ooption_ONone,type,
% 0.21/0.47 none:
% 0.21/0.47 !>[A: $tType] : ( option @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Option_Ooption_OSome,type,
% 0.21/0.47 some:
% 0.21/0.47 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Option_Ooption_Osize__option,type,
% 0.21/0.47 size_option:
% 0.21/0.47 !>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.21/0.47 bot_bot:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Product__Type_OUnity,type,
% 0.21/0.47 product_Unity: product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect,type,
% 0.21/0.47 collect:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ShadowRootClass_Otype__wf,type,
% 0.21/0.47 type_wf:
% 0.21/0.47 !>[A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,L: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ A ) @ ( sum_sum @ ( character_data_ptr @ B ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ D ) @ E ) ) @ F ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ A @ B @ D @ ( option @ G ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ H ) ) @ I ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ A @ B @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ C @ A @ B @ ( option @ J ) ) @ K ) ) ) @ L ) ) ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_h,type,
% 0.21/0.47 h2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_h_H,type,
% 0.21/0.47 h3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (251)
% 0.21/0.47 thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject,axiom,
% 0.21/0.47 ! [I: $tType,G: $tType,F: $tType,E: $tType,D: $tType,H: $tType,C: $tType,B: $tType,A: $tType,X: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) ),Y: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) )] :
% 0.21/0.47 ( ( ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ X )
% 0.21/0.47 = ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ Y ) )
% 0.21/0.47 = ( X = Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % cast\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_inject
% 0.21/0.47 thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject,axiom,
% 0.21/0.47 ! [E: $tType,C: $tType,B: $tType,A: $tType,D: $tType,X: document_ptr @ D,Y: document_ptr @ D] :
% 0.21/0.47 ( ( ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ X )
% 0.21/0.47 = ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ Y ) )
% 0.21/0.47 = ( X = Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_inject
% 0.21/0.47 thf(fact_2_document__ptr_Oinject_I1_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X1: nat,Y1: nat] :
% 0.21/0.47 ( ( ( document_Ref @ Document_ptr @ X1 )
% 0.21/0.47 = ( document_Ref @ Document_ptr @ Y1 ) )
% 0.21/0.47 = ( X1 = Y1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.inject(1)
% 0.21/0.47 thf(fact_3_RDocument_Oext__inject,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z,Nothinga2: product_unit,Doctype2: list @ char,Document_element2: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More2: Z] :
% 0.21/0.47 ( ( ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
% 0.21/0.47 = ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga2 @ Doctype2 @ Document_element2 @ Disconnected_nodes2 @ More2 ) )
% 0.21/0.47 = ( ( Nothinga = Nothinga2 )
% 0.21/0.47 & ( Doctype = Doctype2 )
% 0.21/0.47 & ( Document_element = Document_element2 )
% 0.21/0.47 & ( Disconnected_nodes = Disconnected_nodes2 )
% 0.21/0.47 & ( More = More2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.ext_inject
% 0.21/0.47 thf(fact_4_RObject_Oext__inject,axiom,
% 0.21/0.47 ! [Z: $tType,Nothing: product_unit,More: Z,Nothing2: product_unit,More2: Z] :
% 0.21/0.47 ( ( ( rObject_ext2 @ Z @ Nothing @ More )
% 0.21/0.47 = ( rObject_ext2 @ Z @ Nothing2 @ More2 ) )
% 0.21/0.47 = ( ( Nothing = Nothing2 )
% 0.21/0.47 & ( More = More2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.ext_inject
% 0.21/0.47 thf(fact_5_nat_Oinject,axiom,
% 0.21/0.47 ! [X2: nat,Y2: nat] :
% 0.21/0.47 ( ( ( suc @ X2 )
% 0.21/0.47 = ( suc @ Y2 ) )
% 0.21/0.47 = ( X2 = Y2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat.inject
% 0.21/0.47 thf(fact_6_old_Onat_Oinject,axiom,
% 0.21/0.47 ! [Nat: nat,Nat2: nat] :
% 0.21/0.47 ( ( ( suc @ Nat )
% 0.21/0.47 = ( suc @ Nat2 ) )
% 0.21/0.47 = ( Nat = Nat2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.inject
% 0.21/0.47 thf(fact_7_bot__apply,axiom,
% 0.21/0.47 ! [C: $tType,D: $tType] :
% 0.21/0.47 ( ( bot @ C )
% 0.21/0.47 => ( ( bot_bot @ ( D > C ) )
% 0.21/0.47 = ( ^ [X3: D] : ( bot_bot @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_apply
% 0.21/0.47 thf(fact_8_RDocument_Ocases__scheme,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 0.21/0.47 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] :
% 0.21/0.47 ( R
% 0.21/0.47 != ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.cases_scheme
% 0.21/0.47 thf(fact_9_RDocument_Oinduct__scheme,axiom,
% 0.21/0.47 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 0.21/0.47 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
% 0.21/0.47 => ( P @ R ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.induct_scheme
% 0.21/0.47 thf(fact_10_RDocument_Oinduct,axiom,
% 0.21/0.47 ! [Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
% 0.21/0.47 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) )
% 0.21/0.47 => ( P @ R ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.induct
% 0.21/0.47 thf(fact_11_RDocument_Ocases,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
% 0.21/0.47 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] :
% 0.21/0.47 ( R
% 0.21/0.47 != ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.cases
% 0.21/0.47 thf(fact_12_bot__nat__def,axiom,
% 0.21/0.47 ( ( bot_bot @ nat )
% 0.21/0.47 = ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_nat_def
% 0.21/0.47 thf(fact_13_RObject_Oinduct,axiom,
% 0.21/0.47 ! [P: ( rObject_ext @ product_unit ) > $o,R: rObject_ext @ product_unit] :
% 0.21/0.47 ( ! [Nothing3: product_unit] : ( P @ ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) )
% 0.21/0.47 => ( P @ R ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.induct
% 0.21/0.47 thf(fact_14_RObject_Ocases,axiom,
% 0.21/0.47 ! [R: rObject_ext @ product_unit] :
% 0.21/0.47 ~ ! [Nothing3: product_unit] :
% 0.21/0.47 ( R
% 0.21/0.47 != ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.cases
% 0.21/0.47 thf(fact_15_zero__reorient,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( zero @ A )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ( ( ( zero_zero @ A )
% 0.21/0.47 = X )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % zero_reorient
% 0.21/0.47 thf(fact_16_bot__fun__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( bot @ B )
% 0.21/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.21/0.47 = ( ^ [X3: A] : ( bot_bot @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_fun_def
% 0.21/0.47 thf(fact_17_n__not__Suc__n,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( N
% 0.21/0.47 != ( suc @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % n_not_Suc_n
% 0.21/0.47 thf(fact_18_Suc__inject,axiom,
% 0.21/0.47 ! [X: nat,Y: nat] :
% 0.21/0.47 ( ( ( suc @ X )
% 0.21/0.47 = ( suc @ Y ) )
% 0.21/0.47 => ( X = Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_inject
% 0.21/0.47 thf(fact_19_RObject_Oinduct__scheme,axiom,
% 0.21/0.47 ! [Z: $tType,P: ( rObject_ext @ Z ) > $o,R: rObject_ext @ Z] :
% 0.21/0.47 ( ! [Nothing3: product_unit,More3: Z] : ( P @ ( rObject_ext2 @ Z @ Nothing3 @ More3 ) )
% 0.21/0.47 => ( P @ R ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.induct_scheme
% 0.21/0.47 thf(fact_20_RObject_Ocases__scheme,axiom,
% 0.21/0.47 ! [Z: $tType,R: rObject_ext @ Z] :
% 0.21/0.47 ~ ! [Nothing3: product_unit,More3: Z] :
% 0.21/0.47 ( R
% 0.21/0.47 != ( rObject_ext2 @ Z @ Nothing3 @ More3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.cases_scheme
% 0.21/0.47 thf(fact_21_RDocument_Oext__induct,axiom,
% 0.21/0.47 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) > $o,R: rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z] :
% 0.21/0.47 ( ! [Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
% 0.21/0.47 => ( P @ R ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.ext_induct
% 0.21/0.47 thf(fact_22_not0__implies__Suc,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( ( N
% 0.21/0.47 != ( zero_zero @ nat ) )
% 0.21/0.47 => ? [M: nat] :
% 0.21/0.47 ( N
% 0.21/0.47 = ( suc @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not0_implies_Suc
% 0.21/0.47 thf(fact_23_old_Onat_Oinducts,axiom,
% 0.21/0.47 ! [P: nat > $o,Nat: nat] :
% 0.21/0.47 ( ( P @ ( zero_zero @ nat ) )
% 0.21/0.47 => ( ! [Nat3: nat] :
% 0.21/0.47 ( ( P @ Nat3 )
% 0.21/0.47 => ( P @ ( suc @ Nat3 ) ) )
% 0.21/0.47 => ( P @ Nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.inducts
% 0.21/0.47 thf(fact_24_old_Onat_Oexhaust,axiom,
% 0.21/0.47 ! [Y: nat] :
% 0.21/0.47 ( ( Y
% 0.21/0.47 != ( zero_zero @ nat ) )
% 0.21/0.47 => ~ ! [Nat3: nat] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( suc @ Nat3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.exhaust
% 0.21/0.47 thf(fact_25_Zero__not__Suc,axiom,
% 0.21/0.47 ! [M2: nat] :
% 0.21/0.47 ( ( zero_zero @ nat )
% 0.21/0.47 != ( suc @ M2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Zero_not_Suc
% 0.21/0.47 thf(fact_26_Zero__neq__Suc,axiom,
% 0.21/0.47 ! [M2: nat] :
% 0.21/0.47 ( ( zero_zero @ nat )
% 0.21/0.47 != ( suc @ M2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Zero_neq_Suc
% 0.21/0.47 thf(fact_27_Suc__neq__Zero,axiom,
% 0.21/0.47 ! [M2: nat] :
% 0.21/0.47 ( ( suc @ M2 )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_neq_Zero
% 0.21/0.47 thf(fact_28_zero__induct,axiom,
% 0.21/0.47 ! [P: nat > $o,K2: nat] :
% 0.21/0.47 ( ( P @ K2 )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( P @ ( suc @ N2 ) )
% 0.21/0.47 => ( P @ N2 ) )
% 0.21/0.47 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % zero_induct
% 0.21/0.47 thf(fact_29_diff__induct,axiom,
% 0.21/0.47 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 0.21/0.47 ( ! [X4: nat] : ( P @ X4 @ ( zero_zero @ nat ) )
% 0.21/0.47 => ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
% 0.21/0.47 => ( ! [X4: nat,Y3: nat] :
% 0.21/0.47 ( ( P @ X4 @ Y3 )
% 0.21/0.47 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 0.21/0.47 => ( P @ M2 @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_induct
% 0.21/0.47 thf(fact_30_nat__induct,axiom,
% 0.21/0.47 ! [P: nat > $o,N: nat] :
% 0.21/0.47 ( ( P @ ( zero_zero @ nat ) )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( P @ N2 )
% 0.21/0.47 => ( P @ ( suc @ N2 ) ) )
% 0.21/0.47 => ( P @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_induct
% 0.21/0.47 thf(fact_31_nat_OdiscI,axiom,
% 0.21/0.47 ! [Nat: nat,X2: nat] :
% 0.21/0.47 ( ( Nat
% 0.21/0.47 = ( suc @ X2 ) )
% 0.21/0.47 => ( Nat
% 0.21/0.47 != ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat.discI
% 0.21/0.47 thf(fact_32_old_Onat_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [Nat2: nat] :
% 0.21/0.47 ( ( zero_zero @ nat )
% 0.21/0.47 != ( suc @ Nat2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.distinct(1)
% 0.21/0.47 thf(fact_33_old_Onat_Odistinct_I2_J,axiom,
% 0.21/0.47 ! [Nat4: nat] :
% 0.21/0.47 ( ( suc @ Nat4 )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.distinct(2)
% 0.21/0.47 thf(fact_34_nat_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [X2: nat] :
% 0.21/0.47 ( ( zero_zero @ nat )
% 0.21/0.47 != ( suc @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat.distinct(1)
% 0.21/0.47 thf(fact_35_document__ptr_Osize__gen_I1_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X: Document_ptr > nat,X1: nat] :
% 0.21/0.47 ( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ref @ Document_ptr @ X1 ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.size_gen(1)
% 0.21/0.47 thf(fact_36_document__ptr_Osize_I3_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X1: nat] :
% 0.21/0.47 ( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ref @ Document_ptr @ X1 ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.size(3)
% 0.21/0.47 thf(fact_37_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 0.21/0.47 ! [Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
% 0.21/0.47 ( ( put_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Object_ptr @ Element @ CharacterData @ Node @ Object )
% 0.21/0.47 = ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),Document2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) )] : ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ ( cast_D42511940_e_c_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Object @ Document2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
% 0.21/0.47 thf(fact_38_exists__least__lemma,axiom,
% 0.21/0.47 ! [P: nat > $o] :
% 0.21/0.47 ( ~ ( P @ ( zero_zero @ nat ) )
% 0.21/0.47 => ( ? [X_1: nat] : ( P @ X_1 )
% 0.21/0.47 => ? [N2: nat] :
% 0.21/0.47 ( ~ ( P @ N2 )
% 0.21/0.47 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % exists_least_lemma
% 0.21/0.47 thf(fact_39_dependent__nat__choice,axiom,
% 0.21/0.47 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 0.21/0.47 ( ? [X_1: A] : ( P @ ( zero_zero @ nat ) @ X_1 )
% 0.21/0.47 => ( ! [X4: A,N2: nat] :
% 0.21/0.47 ( ( P @ N2 @ X4 )
% 0.21/0.47 => ? [Y4: A] :
% 0.21/0.47 ( ( P @ ( suc @ N2 ) @ Y4 )
% 0.21/0.47 & ( Q @ N2 @ X4 @ Y4 ) ) )
% 0.21/0.47 => ? [F2: nat > A] :
% 0.21/0.47 ! [N3: nat] :
% 0.21/0.47 ( ( P @ N3 @ ( F2 @ N3 ) )
% 0.21/0.47 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dependent_nat_choice
% 0.21/0.47 thf(fact_40_list__decode_Ocases,axiom,
% 0.21/0.47 ! [X: nat] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( zero_zero @ nat ) )
% 0.21/0.47 => ~ ! [N2: nat] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( suc @ N2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_decode.cases
% 0.21/0.47 thf(fact_41_object__empty,axiom,
% 0.21/0.47 ! [A: $tType,X: rObject_ext @ A] :
% 0.21/0.47 ( ( rObject_ext2 @ A @ product_Unity @ ( more2 @ A @ X ) )
% 0.21/0.47 = X ) ).
% 0.21/0.47
% 0.21/0.47 % object_empty
% 0.21/0.47 thf(fact_42_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_43_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: $tType,A3: set @ A] :
% 0.21/0.47 ( ( collect @ A
% 0.21/0.47 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.21/0.47 = A3 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_44_Collect__cong,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X4: A] :
% 0.21/0.47 ( ( P @ X4 )
% 0.21/0.47 = ( Q @ X4 ) )
% 0.21/0.47 => ( ( collect @ A @ P )
% 0.21/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_45_ext,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 0.21/0.47 ( ! [X4: A] :
% 0.21/0.47 ( ( F3 @ X4 )
% 0.21/0.47 = ( G2 @ X4 ) )
% 0.21/0.47 => ( F3 = G2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ext
% 0.21/0.47 thf(fact_46_RDocument_Oupdate__convs_I1_J,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( nothing_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Nothing2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.update_convs(1)
% 0.21/0.47 thf(fact_47_RDocument_Oupdate__convs_I2_J,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Doctype2: ( list @ char ) > ( list @ char ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( doctype_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Doctype2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.update_convs(2)
% 0.21/0.47 thf(fact_48_RDocument_Oupdate__convs_I3_J,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Document_element2: ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( docume446011358update @ Element_ptr @ Node_ptr @ Character_data_ptr @ Z @ Document_element2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.update_convs(3)
% 0.21/0.47 thf(fact_49_RDocument_Oupdate__convs_I4_J,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Disconnected_nodes2: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( discon1635973971update @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Disconnected_nodes2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.update_convs(4)
% 0.21/0.47 thf(fact_50_size__neq__size__imp__neq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( size @ A )
% 0.21/0.47 => ! [X: A,Y: A] :
% 0.21/0.47 ( ( ( size_size @ A @ X )
% 0.21/0.47 != ( size_size @ A @ Y ) )
% 0.21/0.47 => ( X != Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % size_neq_size_imp_neq
% 0.21/0.47 thf(fact_51_RObject_Oselect__convs_I2_J,axiom,
% 0.21/0.47 ! [Z: $tType,Nothing: product_unit,More: Z] :
% 0.21/0.47 ( ( more2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
% 0.21/0.47 = More ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.select_convs(2)
% 0.21/0.47 thf(fact_52_document__ptr_Osize__neq,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X: document_ptr @ Document_ptr] :
% 0.21/0.47 ( ( size_size @ ( document_ptr @ Document_ptr ) @ X )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.size_neq
% 0.21/0.47 thf(fact_53_object__more__extend__id,axiom,
% 0.21/0.47 ! [A: $tType,X: rObject_ext @ product_unit,Y: A] :
% 0.21/0.47 ( ( more2 @ A @ ( extend @ A @ X @ Y ) )
% 0.21/0.47 = Y ) ).
% 0.21/0.47
% 0.21/0.47 % object_more_extend_id
% 0.21/0.47 thf(fact_54_RDocument_Oupdate__convs_I5_J,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,More2: Z > Z,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( more_update @ Z @ Node_ptr @ Element_ptr @ Character_data_ptr @ More2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.update_convs(5)
% 0.21/0.47 thf(fact_55_is__document__ptr__ref,axiom,
% 0.21/0.47 ! [A: $tType,N: nat] : ( is_doc697300620_p_t_r @ A @ ( document_Ref @ A @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_document_ptr_ref
% 0.21/0.47 thf(fact_56_RDocument_Oselect__convs_I5_J,axiom,
% 0.21/0.47 ! [Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Z: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = More ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.select_convs(5)
% 0.21/0.47 thf(fact_57_RDocument_Oselect__convs_I4_J,axiom,
% 0.21/0.47 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = Disconnected_nodes ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.select_convs(4)
% 0.21/0.47 thf(fact_58_RDocument_Oselect__convs_I3_J,axiom,
% 0.21/0.47 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = Document_element ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.select_convs(3)
% 0.21/0.47 thf(fact_59_RDocument_Oselect__convs_I2_J,axiom,
% 0.21/0.47 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = Doctype ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.select_convs(2)
% 0.21/0.47 thf(fact_60_RDocument_Oselect__convs_I1_J,axiom,
% 0.21/0.47 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 0.21/0.47 ( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 0.21/0.47 = Nothinga ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.select_convs(1)
% 0.21/0.47 thf(fact_61_RDocument_Ounfold__congs_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: A] :
% 0.21/0.47 ( ( V2 = V )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
% 0.21/0.47 = ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.unfold_congs(6)
% 0.21/0.47 thf(fact_62_RDocument_Ofold__congs_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: A] :
% 0.21/0.47 ( ( V = V2 )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
% 0.21/0.47 = ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.fold_congs(6)
% 0.21/0.47 thf(fact_63_heap_Osize__neq,axiom,
% 0.21/0.47 ! [Object_ptr: $tType,Object: $tType,X: heap @ Object_ptr @ Object] :
% 0.21/0.47 ( ( size_size @ ( heap @ Object_ptr @ Object ) @ X )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % heap.size_neq
% 0.21/0.47 thf(fact_64_RDocument_Ounfold__congs_I3_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: list @ char] :
% 0.21/0.47 ( ( V2 = V )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.unfold_congs(3)
% 0.21/0.47 thf(fact_65_RDocument_Ounfold__congs_I4_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
% 0.21/0.47 ( ( V2 = V )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.unfold_congs(4)
% 0.21/0.47 thf(fact_66_RDocument_Ounfold__congs_I5_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
% 0.21/0.47 ( ( V2 = V )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.unfold_congs(5)
% 0.21/0.47 thf(fact_67_RDocument_Ofold__congs_I3_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: list @ char] :
% 0.21/0.47 ( ( V = V2 )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.fold_congs(3)
% 0.21/0.47 thf(fact_68_RDocument_Ofold__congs_I4_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
% 0.21/0.47 ( ( V = V2 )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.fold_congs(4)
% 0.21/0.47 thf(fact_69_RDocument_Ofold__congs_I5_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
% 0.21/0.47 ( ( V = V2 )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.fold_congs(5)
% 0.21/0.47 thf(fact_70_RDocument_Ounfold__congs_I2_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: product_unit] :
% 0.21/0.47 ( ( V2 = V )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.unfold_congs(2)
% 0.21/0.47 thf(fact_71_RDocument_Ofold__congs_I2_J,axiom,
% 0.21/0.47 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
% 0.21/0.47 ( ( R = R2 )
% 0.21/0.47 => ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 0.21/0.47 = V )
% 0.21/0.47 => ( ! [V2: product_unit] :
% 0.21/0.47 ( ( V = V2 )
% 0.21/0.47 => ( ( F3 @ V2 )
% 0.21/0.47 = ( F4 @ V2 ) ) )
% 0.21/0.47 => ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 0.21/0.47 = ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.fold_congs(2)
% 0.21/0.47 thf(fact_72_length__0__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 = ( Xs
% 0.21/0.47 = ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_0_conv
% 0.21/0.47 thf(fact_73_RDocument_Osurjective,axiom,
% 0.21/0.47 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 0.21/0.47 ( R
% 0.21/0.47 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R ) @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.surjective
% 0.21/0.47 thf(fact_74_RDocument_Oequality,axiom,
% 0.21/0.47 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 0.21/0.47 ( ( ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R )
% 0.21/0.47 = ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R2 ) )
% 0.21/0.47 => ( ( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 0.21/0.47 = ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 0.21/0.47 => ( ( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 0.21/0.47 = ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 0.21/0.47 => ( ( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 0.21/0.47 = ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 0.21/0.47 => ( ( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 0.21/0.47 = ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 0.21/0.47 => ( ( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 0.21/0.47 = ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 0.21/0.47 => ( R = R2 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RDocument.equality
% 0.21/0.47 thf(fact_75_option_Osize_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( size_size @ ( option @ A ) @ ( none @ A ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.size(3)
% 0.21/0.47 thf(fact_76_list_Osize_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.21/0.47 = ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.size(3)
% 0.21/0.47 thf(fact_77_document__ptr_Osize_I4_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X2: Document_ptr] :
% 0.21/0.47 ( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ext @ Document_ptr @ X2 ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.size(4)
% 0.21/0.47 thf(fact_78_RObject_Osurjective,axiom,
% 0.21/0.47 ! [Z: $tType,R: rObject_ext @ Z] :
% 0.21/0.47 ( R
% 0.21/0.47 = ( rObject_ext2 @ Z @ ( nothing2 @ Z @ R ) @ ( more2 @ Z @ R ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.surjective
% 0.21/0.47 thf(fact_79_document__ptr_Oinject_I2_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X2: Document_ptr,Y2: Document_ptr] :
% 0.21/0.47 ( ( ( document_Ext @ Document_ptr @ X2 )
% 0.21/0.47 = ( document_Ext @ Document_ptr @ Y2 ) )
% 0.21/0.47 = ( X2 = Y2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.inject(2)
% 0.21/0.47 thf(fact_80_neq__if__length__neq,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.21/0.47 => ( Xs != Ys ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_if_length_neq
% 0.21/0.47 thf(fact_81_Ex__list__of__length,axiom,
% 0.21/0.47 ! [A: $tType,N: nat] :
% 0.21/0.47 ? [Xs2: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % Ex_list_of_length
% 0.21/0.47 thf(fact_82_document__ptr_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X1: nat,X2: Document_ptr] :
% 0.21/0.47 ( ( document_Ref @ Document_ptr @ X1 )
% 0.21/0.47 != ( document_Ext @ Document_ptr @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.distinct(1)
% 0.21/0.47 thf(fact_83_document__ptr_Oinduct,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,P: ( document_ptr @ Document_ptr ) > $o,Document_ptr3: document_ptr @ Document_ptr] :
% 0.21/0.47 ( ! [X4: nat] : ( P @ ( document_Ref @ Document_ptr @ X4 ) )
% 0.21/0.47 => ( ! [X4: Document_ptr] : ( P @ ( document_Ext @ Document_ptr @ X4 ) )
% 0.21/0.47 => ( P @ Document_ptr3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.induct
% 0.21/0.47 thf(fact_84_document__ptr_Oexhaust,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,Y: document_ptr @ Document_ptr] :
% 0.21/0.47 ( ! [X12: nat] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( document_Ref @ Document_ptr @ X12 ) )
% 0.21/0.47 => ~ ! [X22: Document_ptr] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( document_Ext @ Document_ptr @ X22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.exhaust
% 0.21/0.47 thf(fact_85_RObject_Oselect__convs_I1_J,axiom,
% 0.21/0.47 ! [Z: $tType,Nothing: product_unit,More: Z] :
% 0.21/0.47 ( ( nothing2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
% 0.21/0.47 = Nothing ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.select_convs(1)
% 0.21/0.47 thf(fact_86_RObject_Oequality,axiom,
% 0.21/0.47 ! [Z: $tType,R: rObject_ext @ Z,R2: rObject_ext @ Z] :
% 0.21/0.47 ( ( ( nothing2 @ Z @ R )
% 0.21/0.47 = ( nothing2 @ Z @ R2 ) )
% 0.21/0.47 => ( ( ( more2 @ Z @ R )
% 0.21/0.47 = ( more2 @ Z @ R2 ) )
% 0.21/0.47 => ( R = R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % RObject.equality
% 0.21/0.47 thf(fact_87_option_Osize__neq,axiom,
% 0.21/0.47 ! [A: $tType,X: option @ A] :
% 0.21/0.47 ( ( size_size @ ( option @ A ) @ X )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.size_neq
% 0.21/0.47 thf(fact_88_option_Osize__gen_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X: A > nat] :
% 0.21/0.47 ( ( size_option @ A @ X @ ( none @ A ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.size_gen(1)
% 0.21/0.47 thf(fact_89_length__code,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) )
% 0.21/0.47 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_code
% 0.21/0.47 thf(fact_90_document__ptr_Osize__gen_I2_J,axiom,
% 0.21/0.47 ! [Document_ptr: $tType,X: Document_ptr > nat,X2: Document_ptr] :
% 0.21/0.47 ( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ext @ Document_ptr @ X2 ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr.size_gen(2)
% 0.21/0.47 thf(fact_91_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none,axiom,
% 0.21/0.47 ! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) )] :
% 0.21/0.47 ( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
% 0.21/0.47 = ( none @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) ) )
% 0.21/0.47 = ( ~ ? [Document2: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 0.21/0.47 ( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document2 )
% 0.21/0.47 = Obj ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_none
% 0.21/0.47 thf(fact_92_list__ex1__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] :
% 0.21/0.47 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_ex1_simps(1)
% 0.21/0.47 thf(fact_93_is__document__kind__def,axiom,
% 0.21/0.47 ! [Object: $tType,Document: $tType,Node: $tType,CharacterData: $tType,Element: $tType,Shadow_root_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType] :
% 0.21/0.47 ( ( is_document_kind @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object )
% 0.21/0.47 = ( ^ [Ptr: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] :
% 0.21/0.47 ( ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object @ Ptr )
% 0.21/0.47 != ( none @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_document_kind_def
% 0.21/0.47 thf(fact_94_add__right__cancel,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel_semigroup_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.21/0.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.21/0.47 = ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_right_cancel
% 0.21/0.47 thf(fact_95_add__left__cancel,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel_semigroup_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.21/0.47 = ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_left_cancel
% 0.21/0.47 thf(fact_96_zero__eq__add__iff__both__eq__0,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( canoni770627133id_add @ A )
% 0.21/0.47 => ! [X: A,Y: A] :
% 0.21/0.47 ( ( ( zero_zero @ A )
% 0.21/0.47 = ( plus_plus @ A @ X @ Y ) )
% 0.21/0.47 = ( ( X
% 0.21/0.47 = ( zero_zero @ A ) )
% 0.21/0.47 & ( Y
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % zero_eq_add_iff_both_eq_0
% 0.21/0.47 thf(fact_97_add__eq__0__iff__both__eq__0,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( canoni770627133id_add @ A )
% 0.21/0.47 => ! [X: A,Y: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ X @ Y )
% 0.21/0.47 = ( zero_zero @ A ) )
% 0.21/0.47 = ( ( X
% 0.21/0.47 = ( zero_zero @ A ) )
% 0.21/0.47 & ( Y
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_eq_0_iff_both_eq_0
% 0.21/0.47 thf(fact_98_add__cancel__right__right,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel1352612707id_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.21/0.47 = ( B2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_cancel_right_right
% 0.21/0.47 thf(fact_99_add__cancel__right__left,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel1352612707id_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.21/0.47 = ( B2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_cancel_right_left
% 0.21/0.47 thf(fact_100_add__cancel__left__right,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel1352612707id_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.21/0.47 = A2 )
% 0.21/0.47 = ( B2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_cancel_left_right
% 0.21/0.47 thf(fact_101_add__cancel__left__left,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel1352612707id_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.21/0.47 = A2 )
% 0.21/0.47 = ( B2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_cancel_left_left
% 0.21/0.47 thf(fact_102_double__zero__sym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linord219039673up_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ( zero_zero @ A )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % double_zero_sym
% 0.21/0.47 thf(fact_103_double__zero,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linord219039673up_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.21/0.47 = ( zero_zero @ A ) )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % double_zero
% 0.21/0.47 thf(fact_104_add_Oright__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( monoid_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.right_neutral
% 0.21/0.47 thf(fact_105_add_Oleft__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( monoid_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.left_neutral
% 0.21/0.47 thf(fact_106_add__Suc__right,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( plus_plus @ nat @ M2 @ ( suc @ N ) )
% 0.21/0.47 = ( suc @ ( plus_plus @ nat @ M2 @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_Suc_right
% 0.21/0.47 thf(fact_107_Nat_Oadd__0__right,axiom,
% 0.21/0.47 ! [M2: nat] :
% 0.21/0.47 ( ( plus_plus @ nat @ M2 @ ( zero_zero @ nat ) )
% 0.21/0.47 = M2 ) ).
% 0.21/0.47
% 0.21/0.47 % Nat.add_0_right
% 0.21/0.47 thf(fact_108_add__is__0,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( ( plus_plus @ nat @ M2 @ N )
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 = ( ( M2
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 & ( N
% 0.21/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_is_0
% 0.21/0.47 thf(fact_109_gen__length__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( gen_length @ A )
% 0.21/0.47 = ( ^ [N4: nat,Xs3: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % gen_length_def
% 0.21/0.47 thf(fact_110_add__right__imp__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel_semigroup_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.21/0.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.21/0.47 => ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_right_imp_eq
% 0.21/0.47 thf(fact_111_add__left__imp__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel_semigroup_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.21/0.47 => ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_left_imp_eq
% 0.21/0.47 thf(fact_112_add_Oleft__commute,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ab_semigroup_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.left_commute
% 0.21/0.47 thf(fact_113_add_Ocommute,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ab_semigroup_add @ A )
% 0.21/0.47 => ( ( plus_plus @ A )
% 0.21/0.47 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.commute
% 0.21/0.47 thf(fact_114_add_Oright__cancel,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( group_add @ A )
% 0.21/0.47 => ! [B2: A,A2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.21/0.47 = ( plus_plus @ A @ C2 @ A2 ) )
% 0.21/0.47 = ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.right_cancel
% 0.21/0.47 thf(fact_115_add_Oleft__cancel,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( group_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ C2 ) )
% 0.21/0.47 = ( B2 = C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.left_cancel
% 0.21/0.47 thf(fact_116_add_Oassoc,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( semigroup_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.assoc
% 0.21/0.47 thf(fact_117_group__cancel_Oadd2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comm_monoid_add @ A )
% 0.21/0.47 => ! [B4: A,K2: A,B2: A,A2: A] :
% 0.21/0.47 ( ( B4
% 0.21/0.47 = ( plus_plus @ A @ K2 @ B2 ) )
% 0.21/0.47 => ( ( plus_plus @ A @ A2 @ B4 )
% 0.21/0.47 = ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % group_cancel.add2
% 0.21/0.47 thf(fact_118_group__cancel_Oadd1,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comm_monoid_add @ A )
% 0.21/0.47 => ! [A3: A,K2: A,A2: A,B2: A] :
% 0.21/0.47 ( ( A3
% 0.21/0.47 = ( plus_plus @ A @ K2 @ A2 ) )
% 0.21/0.47 => ( ( plus_plus @ A @ A3 @ B2 )
% 0.21/0.47 = ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % group_cancel.add1
% 0.21/0.47 thf(fact_119_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordere779506340up_add @ A )
% 0.21/0.47 => ! [I2: A,J2: A,K2: A,L2: A] :
% 0.21/0.47 ( ( ( I2 = J2 )
% 0.21/0.47 & ( K2 = L2 ) )
% 0.21/0.47 => ( ( plus_plus @ A @ I2 @ K2 )
% 0.21/0.47 = ( plus_plus @ A @ J2 @ L2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_mono_thms_linordered_semiring(4)
% 0.21/0.47 thf(fact_120_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ab_semigroup_add @ A )
% 0.21/0.47 => ! [A2: A,B2: A,C2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 0.21/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.21/0.47 thf(fact_121_add_Ogroup__left__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( group_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.group_left_neutral
% 0.21/0.47 thf(fact_122_add_Ocomm__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comm_monoid_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % add.comm_neutral
% 0.21/0.47 thf(fact_123_comm__monoid__add__class_Oadd__0,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( comm_monoid_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % comm_monoid_add_class.add_0
% 0.21/0.47 thf(fact_124_add__Suc,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N )
% 0.21/0.47 = ( suc @ ( plus_plus @ nat @ M2 @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_Suc
% 0.21/0.47 thf(fact_125_nat__arith_Osuc1,axiom,
% 0.21/0.47 ! [A3: nat,K2: nat,A2: nat] :
% 0.21/0.47 ( ( A3
% 0.21/0.47 = ( plus_plus @ nat @ K2 @ A2 ) )
% 0.21/0.47 => ( ( suc @ A3 )
% 0.21/0.47 = ( plus_plus @ nat @ K2 @ ( suc @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_arith.suc1
% 0.21/0.47 thf(fact_126_add__Suc__shift,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N )
% 0.21/0.47 = ( plus_plus @ nat @ M2 @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_Suc_shift
% 0.21/0.47 thf(fact_127_add__eq__self__zero,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( ( plus_plus @ nat @ M2 @ N )
% 0.21/0.47 = M2 )
% 0.21/0.47 => ( N
% 0.21/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_eq_self_zero
% 0.21/0.47 thf(fact_128_plus__nat_Oadd__0,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % plus_nat.add_0
% 0.21/0.47 thf(fact_129_one__is__add,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( ( suc @ ( zero_zero @ nat ) )
% 0.21/0.47 = ( plus_plus @ nat @ M2 @ N ) )
% 0.21/0.47 = ( ( ( M2
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) )
% 0.21/0.47 & ( N
% 0.21/0.47 = ( zero_zero @ nat ) ) )
% 0.21/0.47 | ( ( M2
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 & ( N
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % one_is_add
% 0.21/0.47 thf(fact_130_add__is__1,axiom,
% 0.21/0.47 ! [M2: nat,N: nat] :
% 0.21/0.47 ( ( ( plus_plus @ nat @ M2 @ N )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) )
% 0.21/0.47 = ( ( ( M2
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) )
% 0.21/0.47 & ( N
% 0.21/0.47 = ( zero_zero @ nat ) ) )
% 0.21/0.47 | ( ( M2
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 & ( N
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_is_1
% 0.21/0.47 thf(fact_131_gen__length__code_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,N: nat] :
% 0.21/0.47 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % gen_length_code(1)
% 0.21/0.47 thf(fact_132_Euclid__induct,axiom,
% 0.21/0.47 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 0.21/0.47 ( ! [A5: nat,B5: nat] :
% 0.21/0.47 ( ( P @ A5 @ B5 )
% 0.21/0.47 = ( P @ B5 @ A5 ) )
% 0.21/0.47 => ( ! [A5: nat] : ( P @ A5 @ ( zero_zero @ nat ) )
% 0.21/0.47 => ( ! [A5: nat,B5: nat] :
% 0.21/0.47 ( ( P @ A5 @ B5 )
% 0.21/0.47 => ( P @ A5 @ ( plus_plus @ nat @ A5 @ B5 ) ) )
% 0.21/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Euclid_induct
% 0.21/0.47 thf(fact_133_triangle__Suc,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( ( nat_triangle @ ( suc @ N ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % triangle_Suc
% 0.21/0.47 thf(fact_134_verit__sum__simplify,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel1352612707id_add @ A )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % verit_sum_simplify
% 0.21/0.47 thf(fact_135_add__0__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( semiri456707255roduct @ A )
% 0.21/0.47 => ! [B2: A,A2: A] :
% 0.21/0.47 ( ( B2
% 0.21/0.47 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % add_0_iff
% 0.21/0.47 thf(fact_136_option_Osize__gen_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X: A > nat,X2: A] :
% 0.21/0.47 ( ( size_option @ A @ X @ ( some @ A @ X2 ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.size_gen(2)
% 0.21/0.47 thf(fact_137_option_Oinject,axiom,
% 0.21/0.47 ! [A: $tType,X2: A,Y2: A] :
% 0.21/0.47 ( ( ( some @ A @ X2 )
% 0.21/0.47 = ( some @ A @ Y2 ) )
% 0.21/0.47 = ( X2 = Y2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.inject
% 0.21/0.47 thf(fact_138_not__Some__eq,axiom,
% 0.21/0.47 ! [A: $tType,X: option @ A] :
% 0.21/0.47 ( ( ! [Y5: A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( some @ A @ Y5 ) ) )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( none @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_Some_eq
% 0.21/0.47 thf(fact_139_not__None__eq,axiom,
% 0.21/0.47 ! [A: $tType,X: option @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( none @ A ) )
% 0.21/0.47 = ( ? [Y5: A] :
% 0.21/0.47 ( X
% 0.21/0.47 = ( some @ A @ Y5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_None_eq
% 0.21/0.47 thf(fact_140_triangle__0,axiom,
% 0.21/0.47 ( ( nat_triangle @ ( zero_zero @ nat ) )
% 0.21/0.47 = ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % triangle_0
% 0.21/0.47 thf(fact_141_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv,axiom,
% 0.21/0.47 ! [I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 0.21/0.47 ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 ) )
% 0.21/0.47 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_inv
% 0.21/0.47 thf(fact_142_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some,axiom,
% 0.21/0.47 ! [I: $tType,D: $tType,H: $tType,G: $tType,F: $tType,E: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 0.21/0.47 ( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
% 0.21/0.47 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) )
% 0.21/0.47 = ( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 )
% 0.21/0.47 = Obj ) ) ).
% 0.21/0.47
% 0.21/0.47 % cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_some
% 0.21/0.47 thf(fact_143_option_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X2: A] :
% 0.21/0.47 ( ( none @ A )
% 0.21/0.47 != ( some @ A @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.distinct(1)
% 0.21/0.47 thf(fact_144_option_OdiscI,axiom,
% 0.21/0.47 ! [A: $tType,Option: option @ A,X2: A] :
% 0.21/0.47 ( ( Option
% 0.21/0.47 = ( some @ A @ X2 ) )
% 0.21/0.47 => ( Option
% 0.21/0.47 != ( none @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.discI
% 0.21/0.47 thf(fact_145_option_Oexhaust,axiom,
% 0.21/0.47 ! [A: $tType,Y: option @ A] :
% 0.21/0.47 ( ( Y
% 0.21/0.47 != ( none @ A ) )
% 0.21/0.47 => ~ ! [X22: A] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( some @ A @ X22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.exhaust
% 0.21/0.47 thf(fact_146_option_Oinducts,axiom,
% 0.21/0.47 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 0.21/0.47 ( ( P @ ( none @ A ) )
% 0.21/0.47 => ( ! [X4: A] : ( P @ ( some @ A @ X4 ) )
% 0.21/0.47 => ( P @ Option ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.inducts
% 0.21/0.47 thf(fact_147_split__option__ex,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.21/0.47 ? [X5: option @ A] : ( P2 @ X5 ) )
% 0.21/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.21/0.47 ( ( P3 @ ( none @ A ) )
% 0.21/0.47 | ? [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % split_option_ex
% 0.21/0.47 thf(fact_148_split__option__all,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [P2: ( option @ A ) > $o] :
% 0.21/0.47 ! [X5: option @ A] : ( P2 @ X5 ) )
% 0.21/0.47 = ( ^ [P3: ( option @ A ) > $o] :
% 0.21/0.47 ( ( P3 @ ( none @ A ) )
% 0.21/0.47 & ! [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % split_option_all
% 0.21/0.47 thf(fact_149_combine__options__cases,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 0.21/0.47 ( ( ( X
% 0.21/0.47 = ( none @ A ) )
% 0.21/0.47 => ( P @ X @ Y ) )
% 0.21/0.47 => ( ( ( Y
% 0.21/0.47 = ( none @ B ) )
% 0.21/0.47 => ( P @ X @ Y ) )
% 0.21/0.47 => ( ! [A5: A,B5: B] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( some @ A @ A5 ) )
% 0.21/0.47 => ( ( Y
% 0.21/0.47 = ( some @ B @ B5 ) )
% 0.21/0.47 => ( P @ X @ Y ) ) )
% 0.21/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % combine_options_cases
% 0.21/0.47 thf(fact_150_option_Osize_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,X2: A] :
% 0.21/0.47 ( ( size_size @ ( option @ A ) @ ( some @ A @ X2 ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % option.size(4)
% 0.21/0.47 thf(fact_151_document__ptr__casts__commute2,axiom,
% 0.21/0.47 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ A] :
% 0.21/0.47 ( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 ) )
% 0.21/0.47 = ( some @ ( document_ptr @ A ) @ Document_ptr3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr_casts_commute2
% 0.21/0.47 thf(fact_152_document__ptr__casts__commute,axiom,
% 0.21/0.47 ! [E: $tType,A: $tType,D: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ D ) ) ) @ ( sum_sum @ ( document_ptr @ A ) @ E ) ),Document_ptr3: document_ptr @ A] :
% 0.21/0.47 ( ( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ Ptr2 )
% 0.21/0.47 = ( some @ ( document_ptr @ A ) @ Document_ptr3 ) )
% 0.21/0.47 = ( ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 )
% 0.21/0.47 = Ptr2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % document_ptr_casts_commute
% 0.21/0.47 thf(fact_153_length__splice,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_splice
% 0.21/0.47 thf(fact_154_get__document__ptr__simp,axiom,
% 0.21/0.47 ! [K: $tType,D: $tType,J: $tType,I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,A: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ),Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
% 0.21/0.47 ( ( ( Ptr2
% 0.21/0.47 = ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
% 0.21/0.47 => ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
% 0.21/0.47 = ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ H @ I @ J @ D @ K @ Obj ) ) )
% 0.21/0.47 & ( ( Ptr2
% 0.21/0.47 != ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
% 0.21/0.47 => ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
% 0.21/0.47 = ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ H2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_document_ptr_simp
% 0.21/0.47 thf(fact_155_split__Nil__iff,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( splice @ A @ Xs @ Ys )
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 = ( ( Xs
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 & ( Ys
% 0.21/0.47 = ( nil @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % split_Nil_iff
% 0.21/0.47 thf(fact_156_splice__Nil2,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 0.21/0.47 = Xs ) ).
% 0.21/0.47
% 0.21/0.47 % splice_Nil2
% 0.21/0.47 thf(fact_157_get__document__ptr__simp2,axiom,
% 0.21/0.47 ! [K: $tType,F: $tType,J: $tType,I: $tType,H: $tType,G: $tType,B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document_ptr4: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document3: rObject_ext @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ D ) @ ( sum_sum @ ( character_data_ptr @ E ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ D @ E @ A @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ) @ K ) )] :
% 0.21/0.47 ( ( Document_ptr3 != Document_ptr4 )
% 0.21/0.47 => ( ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ Document_ptr4 @ Document3 @ H2 ) )
% 0.21/0.47 = ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ H2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_document_ptr_simp2
% 0.21/0.47 thf(fact_158_get__document__ptr__simp1,axiom,
% 0.21/0.47 ! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
% 0.21/0.47 ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ E @ F @ A @ B @ C @ D @ G @ H @ I @ J @ K @ Document_ptr3 @ Document3 @ H2 ) )
% 0.21/0.47 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_document_ptr_simp1
% 0.21/0.47 thf(fact_159_splice_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Ys: list @ A] :
% 0.21/0.47 ( ( splice @ A @ ( nil @ A ) @ Ys )
% 0.21/0.47 = Ys ) ).
% 0.21/0.47
% 0.21/0.47 % splice.simps(1)
% 0.21/0.47 thf(fact_160_get__object__ptr__simp1,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Object_ptr2: object_ptr @ B,Object2: rObject_ext @ A,H2: heap @ B @ A] :
% 0.21/0.47 ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ Object2 @ H2 ) )
% 0.21/0.47 = ( some @ ( rObject_ext @ A ) @ Object2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_object_ptr_simp1
% 0.21/0.47 thf(fact_161_list_Osize_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: A,X222: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X222 ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X222 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.size(4)
% 0.21/0.47 thf(fact_162_count__list_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Y: A] :
% 0.21/0.47 ( ( count_list @ A @ ( nil @ A ) @ Y )
% 0.21/0.47 = ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % count_list.simps(1)
% 0.21/0.47 thf(fact_163_list_Oinject,axiom,
% 0.21/0.47 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.21/0.47 ( ( ( cons @ A @ X21 @ X222 )
% 0.21/0.47 = ( cons @ A @ Y21 @ Y22 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X222 = Y22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.inject
% 0.21/0.47 thf(fact_164_get__object__ptr__simp2,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,Object_ptr2: object_ptr @ A,Object_ptr3: object_ptr @ A,Object2: rObject_ext @ B,H2: heap @ A @ B] :
% 0.21/0.47 ( ( Object_ptr2 != Object_ptr3 )
% 0.21/0.47 => ( ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ ( put_O_b_j_e_c_t @ A @ B @ Object_ptr3 @ Object2 @ H2 ) )
% 0.21/0.47 = ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ H2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_object_ptr_simp2
% 0.21/0.47 thf(fact_165_splice_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.21/0.47 = ( cons @ A @ X @ ( splice @ A @ Ys @ Xs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splice.simps(2)
% 0.21/0.47 thf(fact_166_not__Cons__self2,axiom,
% 0.21/0.47 ! [A: $tType,X: A,Xs: list @ A] :
% 0.21/0.47 ( ( cons @ A @ X @ Xs )
% 0.21/0.47 != Xs ) ).
% 0.21/0.47
% 0.21/0.47 % not_Cons_self2
% 0.21/0.47 thf(fact_167_transpose_Ocases,axiom,
% 0.21/0.47 ! [A: $tType,X: list @ ( list @ A )] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( nil @ ( list @ A ) ) )
% 0.21/0.47 => ( ! [Xss: list @ ( list @ A )] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.21/0.47 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % transpose.cases
% 0.21/0.47 thf(fact_168_list_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: A,X222: list @ A] :
% 0.21/0.47 ( ( nil @ A )
% 0.21/0.47 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.distinct(1)
% 0.21/0.47 thf(fact_169_list_OdiscI,axiom,
% 0.21/0.47 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.21/0.47 ( ( List
% 0.21/0.47 = ( cons @ A @ X21 @ X222 ) )
% 0.21/0.47 => ( List
% 0.21/0.47 != ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.discI
% 0.21/0.47 thf(fact_170_list_Oexhaust,axiom,
% 0.21/0.47 ! [A: $tType,Y: list @ A] :
% 0.21/0.47 ( ( Y
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ~ ! [X212: A,X223: list @ A] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.exhaust
% 0.21/0.47 thf(fact_171_list_Oinducts,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.21/0.47 ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X12: A,X22: list @ A] :
% 0.21/0.47 ( ( P @ X22 )
% 0.21/0.47 => ( P @ ( cons @ A @ X12 @ X22 ) ) )
% 0.21/0.47 => ( P @ List ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list.inducts
% 0.21/0.47 thf(fact_172_neq__Nil__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 = ( ? [Y5: A,Ys2: list @ A] :
% 0.21/0.47 ( Xs
% 0.21/0.47 = ( cons @ A @ Y5 @ Ys2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_Nil_conv
% 0.21/0.47 thf(fact_173_list__induct2_H,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.21/0.47 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 0.21/0.47 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.21/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 0.21/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_induct2'
% 0.21/0.47 thf(fact_174_splice_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.21/0.47 ( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.21/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splice.induct
% 0.21/0.47 thf(fact_175_induct__list012,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.21/0.47 ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [X4: A,Y3: A,Zs: list @ A] :
% 0.21/0.47 ( ( P @ Zs )
% 0.21/0.47 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 0.21/0.47 => ( P @ Xs ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % induct_list012
% 0.21/0.47 thf(fact_176_min__list_Ocases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [X: list @ A] :
% 0.21/0.47 ( ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ A @ X4 @ Xs2 ) )
% 0.21/0.47 => ( X
% 0.21/0.47 = ( nil @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_list.cases
% 0.21/0.47 thf(fact_177_min__list_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.21/0.47 ( ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( ! [X213: A,X224: list @ A] :
% 0.21/0.47 ( ( Xs2
% 0.21/0.47 = ( cons @ A @ X213 @ X224 ) )
% 0.21/0.47 => ( P @ Xs2 ) )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % min_list.induct
% 0.21/0.47 thf(fact_178_shuffles_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.21/0.47 ( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
% 0.21/0.47 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.21/0.47 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.21/0.47 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % shuffles.induct
% 0.21/0.47 thf(fact_179_remdups__adj_Ocases,axiom,
% 0.21/0.47 ! [A: $tType,X: list @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ~ ! [X4: A,Y3: A,Xs2: list @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % remdups_adj.cases
% 0.21/0.47 thf(fact_180_sorted__wrt_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.21/0.47 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.21/0.47 => ( ! [P4: A > A > $o,X4: A,Ys3: list @ A] :
% 0.21/0.47 ( ( P @ P4 @ Ys3 )
% 0.21/0.47 => ( P @ P4 @ ( cons @ A @ X4 @ Ys3 ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % sorted_wrt.induct
% 0.21/0.47 thf(fact_181_remdups__adj_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.21/0.47 ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [X4: A,Y3: A,Xs2: list @ A] :
% 0.21/0.47 ( ( ( X4 = Y3 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( ( ( X4 != Y3 )
% 0.21/0.47 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % remdups_adj.induct
% 0.21/0.47 thf(fact_182_arg__min__list_Oinduct,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( linorder @ B )
% 0.21/0.47 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.21/0.47 ( ! [F2: A > B,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [F2: A > B,X4: A,Y3: A,Zs: list @ A] :
% 0.21/0.47 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs ) )
% 0.21/0.47 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.21/0.47 => ( ! [A5: A > B] : ( P @ A5 @ ( nil @ A ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % arg_min_list.induct
% 0.21/0.47 thf(fact_183_successively_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.21/0.47 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.21/0.47 => ( ! [P4: A > A > $o,X4: A] : ( P @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [P4: A > A > $o,X4: A,Y3: A,Xs2: list @ A] :
% 0.21/0.47 ( ( P @ P4 @ ( cons @ A @ Y3 @ Xs2 ) )
% 0.21/0.47 => ( P @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % successively.induct
% 0.21/0.47 thf(fact_184_list__nonempty__induct,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( ( Xs2
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ( ( P @ Xs2 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 0.21/0.47 => ( P @ Xs ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_nonempty_induct
% 0.21/0.47 thf(fact_185_map__tailrec__rev_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.21/0.47 ( ! [F2: A > B,X_12: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_12 )
% 0.21/0.47 => ( ! [F2: A > B,A5: A,As: list @ A,Bs: list @ B] :
% 0.21/0.47 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A5 ) @ Bs ) )
% 0.21/0.47 => ( P @ F2 @ ( cons @ A @ A5 @ As ) @ Bs ) )
% 0.21/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % map_tailrec_rev.induct
% 0.21/0.47 thf(fact_186_strict__sorted_Ocases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X: list @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ~ ! [X4: A,Ys3: list @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( cons @ A @ X4 @ Ys3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strict_sorted.cases
% 0.21/0.47 thf(fact_187_strict__sorted_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.21/0.47 ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A,Ys3: list @ A] :
% 0.21/0.47 ( ( P @ Ys3 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Ys3 ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strict_sorted.induct
% 0.21/0.47 thf(fact_188_length__Suc__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,N: nat] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( suc @ N ) )
% 0.21/0.47 = ( ? [Y5: A,Ys2: list @ A] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( cons @ A @ Y5 @ Ys2 ) )
% 0.21/0.47 & ( ( size_size @ ( list @ A ) @ Ys2 )
% 0.21/0.47 = N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_Suc_conv
% 0.21/0.47 thf(fact_189_Suc__length__conv,axiom,
% 0.21/0.47 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.21/0.47 ( ( ( suc @ N )
% 0.21/0.47 = ( size_size @ ( list @ A ) @ Xs ) )
% 0.21/0.47 = ( ? [Y5: A,Ys2: list @ A] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( cons @ A @ Y5 @ Ys2 ) )
% 0.21/0.47 & ( ( size_size @ ( list @ A ) @ Ys2 )
% 0.21/0.47 = N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_length_conv
% 0.21/0.47 thf(fact_190_list__induct4,axiom,
% 0.21/0.47 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,Ws: list @ D,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > ( list @ D ) > $o] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 0.21/0.47 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ C ) @ Zs2 )
% 0.21/0.47 = ( size_size @ ( list @ D ) @ Ws ) )
% 0.21/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) @ ( nil @ D ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C,W: D,Ws2: list @ D] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys3 )
% 0.21/0.47 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ C ) @ Zs )
% 0.21/0.47 = ( size_size @ ( list @ D ) @ Ws2 ) )
% 0.21/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) @ ( cons @ D @ W @ Ws2 ) ) ) ) ) )
% 0.21/0.47 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_induct4
% 0.21/0.47 thf(fact_191_list__induct3,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 0.21/0.47 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.21/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 0.21/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys3 )
% 0.21/0.47 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.21/0.47 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) ) ) ) )
% 0.21/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_induct3
% 0.21/0.47 thf(fact_192_list__induct2,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.21/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 0.21/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.21/0.47 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 0.21/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_induct2
% 0.21/0.47 thf(fact_193_splice_Oelims,axiom,
% 0.21/0.47 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.21/0.47 ( ( ( splice @ A @ X @ Xa )
% 0.21/0.47 = Y )
% 0.21/0.47 => ( ( ( X
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 => ( Y != Xa ) )
% 0.21/0.47 => ~ ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( cons @ A @ X4 @ Xs2 ) )
% 0.21/0.47 => ( Y
% 0.21/0.47 != ( cons @ A @ X4 @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splice.elims
% 0.21/0.47 thf(fact_194_gen__length__code_I2_J,axiom,
% 0.21/0.47 ! [B: $tType,N: nat,X: B,Xs: list @ B] :
% 0.21/0.47 ( ( gen_length @ B @ N @ ( cons @ B @ X @ Xs ) )
% 0.21/0.47 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 0.21/0.47
% 0.21/0.47 % gen_length_code(2)
% 0.21/0.47 thf(fact_195_get__object__ptr__simp,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,Ptr2: object_ptr @ B,Object_ptr2: object_ptr @ B,Obj: rObject_ext @ A,H2: heap @ B @ A] :
% 0.21/0.47 ( ( ( Ptr2 = Object_ptr2 )
% 0.21/0.47 => ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
% 0.21/0.47 = ( some @ ( rObject_ext @ A ) @ Obj ) ) )
% 0.21/0.47 & ( ( Ptr2 != Object_ptr2 )
% 0.21/0.47 => ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
% 0.21/0.47 = ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ H2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % get_object_ptr_simp
% 0.21/0.47 thf(fact_196_length__Cons,axiom,
% 0.21/0.47 ! [A: $tType,X: A,Xs: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X @ Xs ) )
% 0.21/0.47 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_Cons
% 0.21/0.47 thf(fact_197_map__M_Oinduct,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,Result: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ X6] :
% 0.21/0.47 ( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ F2 @ ( nil @ X6 ) )
% 0.21/0.47 => ( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: X6,Xs2: list @ X6] :
% 0.21/0.47 ( ! [Xa2: Result] : ( P @ F2 @ Xs2 )
% 0.21/0.47 => ( P @ F2 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % map_M.induct
% 0.21/0.47 thf(fact_198_prog_Osize__neq,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,Result: $tType,X: heap_Error_prog @ Heap @ E @ Result] :
% 0.21/0.47 ( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ X )
% 0.21/0.47 != ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % prog.size_neq
% 0.21/0.47 thf(fact_199_forall__M_Oinduct,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,Result: $tType,Y6: $tType,P: ( Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ Y6 ) > $o,A0: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ Y6] :
% 0.21/0.47 ( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ P4 @ ( nil @ Y6 ) )
% 0.21/0.47 => ( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: Y6,Xs2: list @ Y6] :
% 0.21/0.47 ( ! [Xa2: Result] : ( P @ P4 @ Xs2 )
% 0.21/0.47 => ( P @ P4 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % forall_M.induct
% 0.21/0.47 thf(fact_200_filter__M_Oinduct,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ $o ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ $o ),A1: list @ X6] :
% 0.21/0.47 ( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o )] : ( P @ P4 @ ( nil @ X6 ) )
% 0.21/0.47 => ( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o ),X4: X6,Xs2: list @ X6] :
% 0.21/0.47 ( ! [Xa2: $o] : ( P @ P4 @ Xs2 )
% 0.21/0.47 => ( P @ P4 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % filter_M.induct
% 0.21/0.47 thf(fact_201_fold__M_Oinduct,axiom,
% 0.21/0.47 ! [Result: $tType,E: $tType,Heap: $tType,Y6: $tType,P: ( Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > Result > ( list @ Y6 ) > $o,A0: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: Result,A22: list @ Y6] :
% 0.21/0.47 ( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result] : ( P @ F2 @ D2 @ ( nil @ Y6 ) )
% 0.21/0.47 => ( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result,X4: Y6,Xs2: list @ Y6] :
% 0.21/0.47 ( ! [Xa2: Result] : ( P @ F2 @ Xa2 @ Xs2 )
% 0.21/0.47 => ( P @ F2 @ D2 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
% 0.21/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % fold_M.induct
% 0.21/0.47 thf(fact_202_n__lists__Nil,axiom,
% 0.21/0.47 ! [A: $tType,N: nat] :
% 0.21/0.47 ( ( ( N
% 0.21/0.47 = ( zero_zero @ nat ) )
% 0.21/0.47 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.21/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.21/0.47 & ( ( N
% 0.21/0.47 != ( zero_zero @ nat ) )
% 0.21/0.47 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.21/0.47 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % n_lists_Nil
% 0.21/0.47 thf(fact_203_n__lists_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.21/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % n_lists.simps(1)
% 0.21/0.47 thf(fact_204_product__lists_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.21/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % product_lists.simps(1)
% 0.21/0.47 thf(fact_205_subseqs_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( subseqs @ A @ ( nil @ A ) )
% 0.21/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subseqs.simps(1)
% 0.21/0.47 thf(fact_206_insert__Nil,axiom,
% 0.21/0.47 ! [A: $tType,X: A] :
% 0.21/0.47 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.21/0.47 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_Nil
% 0.21/0.47 thf(fact_207_nths__singleton,axiom,
% 0.21/0.47 ! [A: $tType,A3: set @ nat,X: A] :
% 0.21/0.47 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A3 )
% 0.21/0.47 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
% 0.21/0.47 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.21/0.47 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A3 )
% 0.21/0.47 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
% 0.21/0.47 = ( nil @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nths_singleton
% 0.21/0.47 thf(fact_208_nths__nil,axiom,
% 0.21/0.47 ! [A: $tType,A3: set @ nat] :
% 0.21/0.47 ( ( nths @ A @ ( nil @ A ) @ A3 )
% 0.21/0.47 = ( nil @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % nths_nil
% 0.21/0.47 thf(fact_209_nths__empty,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( nths @ A @ Xs @ ( bot_bot @ ( set @ nat ) ) )
% 0.21/0.47 = ( nil @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % nths_empty
% 0.21/0.47 thf(fact_210_prog_Osize_I2_J,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,Result: $tType,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
% 0.21/0.47 ( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prog.size(2)
% 0.21/0.47 thf(fact_211_get_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 0.21/0.47 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
% 0.21/0.47 ( ( get_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Element @ CharacterData @ Node @ Document @ Object )
% 0.21/0.47 = ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),H3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] : ( bind @ ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) @ ( get_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ H3 ) @ ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
% 0.21/0.47 thf(fact_212_bind__runit,axiom,
% 0.21/0.47 ! [A: $tType,X: option @ A] :
% 0.21/0.47 ( ( bind @ A @ A @ X @ ( some @ A ) )
% 0.21/0.47 = X ) ).
% 0.21/0.47
% 0.21/0.47 % bind_runit
% 0.21/0.47 thf(fact_213_bind__split__asm,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
% 0.21/0.47 ( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
% 0.21/0.47 = ( ~ ( ( ( M2
% 0.21/0.47 = ( none @ B ) )
% 0.21/0.47 & ~ ( P @ ( none @ A ) ) )
% 0.21/0.47 | ? [X3: B] :
% 0.21/0.47 ( ( M2
% 0.21/0.47 = ( some @ B @ X3 ) )
% 0.21/0.47 & ~ ( P @ ( F3 @ X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_split_asm
% 0.21/0.47 thf(fact_214_bind__split,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
% 0.21/0.47 ( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
% 0.21/0.47 = ( ( ( M2
% 0.21/0.47 = ( none @ B ) )
% 0.21/0.47 => ( P @ ( none @ A ) ) )
% 0.21/0.47 & ! [V3: B] :
% 0.21/0.47 ( ( M2
% 0.21/0.47 = ( some @ B @ V3 ) )
% 0.21/0.47 => ( P @ ( F3 @ V3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_split
% 0.21/0.47 thf(fact_215_Option_Obind__cong,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B ),G2: A > ( option @ B )] :
% 0.21/0.47 ( ( X = Y )
% 0.21/0.47 => ( ! [A5: A] :
% 0.21/0.47 ( ( Y
% 0.21/0.47 = ( some @ A @ A5 ) )
% 0.21/0.47 => ( ( F3 @ A5 )
% 0.21/0.47 = ( G2 @ A5 ) ) )
% 0.21/0.47 => ( ( bind @ A @ B @ X @ F3 )
% 0.21/0.47 = ( bind @ A @ B @ Y @ G2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Option.bind_cong
% 0.21/0.47 thf(fact_216_bind_Obind__lunit,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X: A,F3: A > ( option @ B )] :
% 0.21/0.47 ( ( bind @ A @ B @ ( some @ A @ X ) @ F3 )
% 0.21/0.47 = ( F3 @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind.bind_lunit
% 0.21/0.47 thf(fact_217_bind__eq__Some__conv,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,F3: option @ B,G2: B > ( option @ A ),X: A] :
% 0.21/0.47 ( ( ( bind @ B @ A @ F3 @ G2 )
% 0.21/0.47 = ( some @ A @ X ) )
% 0.21/0.47 = ( ? [Y5: B] :
% 0.21/0.47 ( ( F3
% 0.21/0.47 = ( some @ B @ Y5 ) )
% 0.21/0.47 & ( ( G2 @ Y5 )
% 0.21/0.47 = ( some @ A @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_eq_Some_conv
% 0.21/0.47 thf(fact_218_bind_Obind__lzero,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,F3: A > ( option @ B )] :
% 0.21/0.47 ( ( bind @ A @ B @ ( none @ A ) @ F3 )
% 0.21/0.47 = ( none @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind.bind_lzero
% 0.21/0.47 thf(fact_219_bind__option__cong__code,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B )] :
% 0.21/0.47 ( ( X = Y )
% 0.21/0.47 => ( ( bind @ A @ B @ X @ F3 )
% 0.21/0.47 = ( bind @ A @ B @ Y @ F3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bind_option_cong_code
% 0.21/0.47 thf(fact_220_prog_Osize__gen,axiom,
% 0.21/0.47 ! [Heap: $tType,E: $tType,Result: $tType,Xc: Heap > nat,Xb: E > nat,Xa: Result > nat,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
% 0.21/0.47 ( ( heap_Error_size_prog @ Heap @ E @ Result @ Xc @ Xb @ Xa @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
% 0.21/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prog.size_gen
% 0.21/0.47 thf(fact_221_set__encode__empty,axiom,
% 0.21/0.47 ( ( nat_set_encode @ ( bot_bot @ ( set @ nat ) ) )
% 0.21/0.47 = ( zero_zero @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_encode_empty
% 0.21/0.47 thf(fact_222_set__decode__zero,axiom,
% 0.21/0.47 ( ( nat_set_decode @ ( zero_zero @ nat ) )
% 0.21/0.47 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_decode_zero
% 0.21/0.47 thf(fact_223_length__append__singleton,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,X: A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.21/0.47 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_append_singleton
% 0.21/0.47 thf(fact_224_same__append__eq,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = ( append @ A @ Xs @ Zs2 ) )
% 0.21/0.47 = ( Ys = Zs2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % same_append_eq
% 0.21/0.47 thf(fact_225_append__same__eq,axiom,
% 0.21/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Ys @ Xs )
% 0.21/0.47 = ( append @ A @ Zs2 @ Xs ) )
% 0.21/0.47 = ( Ys = Zs2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_same_eq
% 0.21/0.47 thf(fact_226_append__assoc,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.21/0.47 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 0.21/0.47 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_assoc
% 0.21/0.47 thf(fact_227_append_Oassoc,axiom,
% 0.21/0.47 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 0.21/0.47 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 0.21/0.47 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append.assoc
% 0.21/0.47 thf(fact_228_append__Nil2,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.21/0.47 = Xs ) ).
% 0.21/0.47
% 0.21/0.47 % append_Nil2
% 0.21/0.47 thf(fact_229_append__self__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = Xs )
% 0.21/0.47 = ( Ys
% 0.21/0.47 = ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv
% 0.21/0.47 thf(fact_230_self__append__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 = ( append @ A @ Xs @ Ys ) )
% 0.21/0.47 = ( Ys
% 0.21/0.47 = ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv
% 0.21/0.47 thf(fact_231_append__self__conv2,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = Ys )
% 0.21/0.47 = ( Xs
% 0.21/0.47 = ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_self_conv2
% 0.21/0.47 thf(fact_232_self__append__conv2,axiom,
% 0.21/0.47 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.21/0.47 ( ( Ys
% 0.21/0.47 = ( append @ A @ Xs @ Ys ) )
% 0.21/0.47 = ( Xs
% 0.21/0.47 = ( nil @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % self_append_conv2
% 0.21/0.47 thf(fact_233_Nil__is__append__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( nil @ A )
% 0.21/0.47 = ( append @ A @ Xs @ Ys ) )
% 0.21/0.47 = ( ( Xs
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 & ( Ys
% 0.21/0.47 = ( nil @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nil_is_append_conv
% 0.21/0.47 thf(fact_234_append__is__Nil__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 = ( ( Xs
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 & ( Ys
% 0.21/0.47 = ( nil @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_is_Nil_conv
% 0.21/0.47 thf(fact_235_append_Oright__neutral,axiom,
% 0.21/0.47 ! [A: $tType,A2: list @ A] :
% 0.21/0.47 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % append.right_neutral
% 0.21/0.47 thf(fact_236_append__eq__append__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Us: list @ A,Vs: list @ A] :
% 0.21/0.47 ( ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.21/0.47 | ( ( size_size @ ( list @ A ) @ Us )
% 0.21/0.47 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 0.21/0.47 => ( ( ( append @ A @ Xs @ Us )
% 0.21/0.47 = ( append @ A @ Ys @ Vs ) )
% 0.21/0.47 = ( ( Xs = Ys )
% 0.21/0.47 & ( Us = Vs ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_eq_append_conv
% 0.21/0.47 thf(fact_237_set__decode__inverse,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % set_decode_inverse
% 0.21/0.47 thf(fact_238_append1__eq__conv,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.21/0.47 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.21/0.47 = ( ( Xs = Ys )
% 0.21/0.47 & ( X = Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append1_eq_conv
% 0.21/0.47 thf(fact_239_length__append,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) )
% 0.21/0.47 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_append
% 0.21/0.47 thf(fact_240_append__eq__append__conv2,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = ( append @ A @ Zs2 @ Ts ) )
% 0.21/0.47 = ( ? [Us2: list @ A] :
% 0.21/0.47 ( ( ( Xs
% 0.21/0.47 = ( append @ A @ Zs2 @ Us2 ) )
% 0.21/0.47 & ( ( append @ A @ Us2 @ Ys )
% 0.21/0.47 = Ts ) )
% 0.21/0.47 | ( ( ( append @ A @ Xs @ Us2 )
% 0.21/0.47 = Zs2 )
% 0.21/0.47 & ( Ys
% 0.21/0.47 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_eq_append_conv2
% 0.21/0.47 thf(fact_241_append__eq__appendI,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Xs @ Xs1 )
% 0.21/0.47 = Zs2 )
% 0.21/0.47 => ( ( Ys
% 0.21/0.47 = ( append @ A @ Xs1 @ Us ) )
% 0.21/0.47 => ( ( append @ A @ Xs @ Ys )
% 0.21/0.47 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_eq_appendI
% 0.21/0.47 thf(fact_242_rev__induct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.21/0.47 ( ( P @ ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( ( P @ Xs2 )
% 0.21/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 0.21/0.47 => ( P @ Xs ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rev_induct
% 0.21/0.47 thf(fact_243_rev__exhaust,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ~ ! [Ys3: list @ A,Y3: A] :
% 0.21/0.47 ( Xs
% 0.21/0.47 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rev_exhaust
% 0.21/0.47 thf(fact_244_Cons__eq__append__conv,axiom,
% 0.21/0.47 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.21/0.47 ( ( ( cons @ A @ X @ Xs )
% 0.21/0.47 = ( append @ A @ Ys @ Zs2 ) )
% 0.21/0.47 = ( ( ( Ys
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 & ( ( cons @ A @ X @ Xs )
% 0.21/0.47 = Zs2 ) )
% 0.21/0.47 | ? [Ys4: list @ A] :
% 0.21/0.47 ( ( ( cons @ A @ X @ Ys4 )
% 0.21/0.47 = Ys )
% 0.21/0.47 & ( Xs
% 0.21/0.47 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Cons_eq_append_conv
% 0.21/0.47 thf(fact_245_append__eq__Cons__conv,axiom,
% 0.21/0.47 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 0.21/0.47 ( ( ( append @ A @ Ys @ Zs2 )
% 0.21/0.47 = ( cons @ A @ X @ Xs ) )
% 0.21/0.47 = ( ( ( Ys
% 0.21/0.47 = ( nil @ A ) )
% 0.21/0.47 & ( Zs2
% 0.21/0.47 = ( cons @ A @ X @ Xs ) ) )
% 0.21/0.47 | ? [Ys4: list @ A] :
% 0.21/0.47 ( ( Ys
% 0.21/0.47 = ( cons @ A @ X @ Ys4 ) )
% 0.21/0.47 & ( ( append @ A @ Ys4 @ Zs2 )
% 0.21/0.47 = Xs ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_eq_Cons_conv
% 0.21/0.47 thf(fact_246_rev__nonempty__induct,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.21/0.47 ( ( Xs
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.21/0.47 => ( ! [X4: A,Xs2: list @ A] :
% 0.21/0.47 ( ( Xs2
% 0.21/0.47 != ( nil @ A ) )
% 0.21/0.47 => ( ( P @ Xs2 )
% 0.21/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 0.21/0.47 => ( P @ Xs ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % rev_nonempty_induct
% 0.21/0.47 thf(fact_247_eq__Nil__appendI,axiom,
% 0.21/0.47 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( Xs = Ys )
% 0.21/0.47 => ( Xs
% 0.21/0.47 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_Nil_appendI
% 0.21/0.47 thf(fact_248_append__Nil,axiom,
% 0.21/0.47 ! [A: $tType,Ys: list @ A] :
% 0.21/0.47 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.21/0.47 = Ys ) ).
% 0.21/0.47
% 0.21/0.47 % append_Nil
% 0.21/0.47 thf(fact_249_append_Oleft__neutral,axiom,
% 0.21/0.47 ! [A: $tType,A2: list @ A] :
% 0.21/0.47 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % append.left_neutral
% 0.21/0.47 thf(fact_250_append__Cons,axiom,
% 0.21/0.47 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.21/0.47 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % append_Cons
% 0.21/0.47
% 0.21/0.47 % Type constructors (53)
% 0.21/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] :
% 0.21/0.47 ( ( ord @ A7 )
% 0.21/0.47 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] :
% 0.21/0.47 ( ( bot @ A7 )
% 0.21/0.47 => ( bot @ ( A6 > A7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.21/0.47 semiri456707255roduct @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.21/0.47 canoni770627133id_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.21/0.47 ordere779506340up_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.21/0.47 cancel1352612707id_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.21/0.47 cancel_semigroup_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.21/0.47 ab_semigroup_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.21/0.47 comm_monoid_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.21/0.47 semigroup_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.21/0.47 linorder @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.21/0.47 monoid_add @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.21/0.47 ord @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Obot_2,axiom,
% 0.21/0.47 bot @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.21/0.47 zero @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.21/0.47 size @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.21/0.47 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Obot_4,axiom,
% 0.21/0.47 ! [A6: $tType] : ( bot @ ( set @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 0.21/0.47 linorder @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.21/0.47 ord @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Obot_7,axiom,
% 0.21/0.47 bot @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_FSet_Ofset___Orderings_Oord_8,axiom,
% 0.21/0.47 ! [A6: $tType] : ( ord @ ( fset @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_FSet_Ofset___Orderings_Obot_9,axiom,
% 0.21/0.47 ! [A6: $tType] : ( bot @ ( fset @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_FSet_Ofset___Nat_Osize_10,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( fset @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_List_Olist___Nat_Osize_11,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( list @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_String_Ochar___Nat_Osize_12,axiom,
% 0.21/0.47 size @ char ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Sum__Type_Osum___Orderings_Olinorder_13,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] :
% 0.21/0.47 ( ( ( linorder @ A6 )
% 0.21/0.47 & ( linorder @ A7 ) )
% 0.21/0.47 => ( linorder @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Sum__Type_Osum___Orderings_Oord_14,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] :
% 0.21/0.47 ( ( ( linorder @ A6 )
% 0.21/0.47 & ( linorder @ A7 ) )
% 0.21/0.47 => ( ord @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Sum__Type_Osum___Nat_Osize_15,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Option_Ooption___Nat_Osize_16,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( option @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ObjectClass_Oheap___Nat_Osize_17,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType] : ( size @ ( heap @ A6 @ A7 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_18,axiom,
% 0.21/0.47 linorder @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oord_19,axiom,
% 0.21/0.47 ord @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Product__Type_Ounit___Orderings_Obot_20,axiom,
% 0.21/0.47 bot @ product_unit ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_NodePointer_Onode__ptr___Orderings_Olinorder_21,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( node_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_NodePointer_Onode__ptr___Orderings_Oord_22,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( node_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_NodePointer_Onode__ptr___Nat_Osize_23,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( node_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Heap__Error__Monad_Oprog___Nat_Osize_24,axiom,
% 0.21/0.47 ! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( heap_Error_prog @ A6 @ A7 @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Olinorder_25,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( object_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Oord_26,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( object_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ObjectPointer_Oobject__ptr___Nat_Osize_27,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( object_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Olinorder_28,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( element_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Oord_29,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( element_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ElementPointer_Oelement__ptr___Nat_Osize_30,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( element_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Olinorder_31,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( document_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Oord_32,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( document_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_DocumentPointer_Odocument__ptr___Nat_Osize_33,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( document_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Olinorder_34,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( shadow_root_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Oord_35,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( shadow_root_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Nat_Osize_36,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( shadow_root_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Olinorder_37,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( linorder @ ( character_data_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Oord_38,axiom,
% 0.21/0.47 ! [A6: $tType] :
% 0.21/0.47 ( ( linorder @ A6 )
% 0.21/0.47 => ( ord @ ( character_data_ptr @ A6 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Nat_Osize_39,axiom,
% 0.21/0.47 ! [A6: $tType] : ( size @ ( character_data_ptr @ A6 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Conjectures (4)
% 0.21/0.47 thf(conj_0,hypothesis,
% 0.21/0.47 ( ( document_ptrs @ a @ b @ c @ d @ e @ f @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ h2 )
% 0.21/0.47 = ( bot_bot @ ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(conj_1,hypothesis,
% 0.21/0.47 ( h3
% 0.21/0.47 = ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ a @ b @ c @ f @ ( document_Ref @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ ( suc @ ( zero_zero @ nat ) ) ) ) @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) @ h2 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(conj_2,hypothesis,
% 0.21/0.47 type_wf @ a @ b @ c @ d @ e @ f @ g @ h @ i @ j @ k @ l @ h2 ).
% 0.21/0.47
% 0.21/0.47 thf(conj_3,conjecture,
% 0.21/0.47 is_document_kind @ c @ a @ b @ d @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 2.97/1.58 ---- Embedded in THF ---
% 2.97/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.97/1.58 %%% Generated on Tue Feb 24 08:28:55 EST 2026
% 2.97/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.97/1.58 %%% Logic specification used:
% 2.97/1.58 %%% thf(spec, logic, $$dhol).
% 2.97/1.58
% 2.97/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rDZlZRFXfP/DTF2DTF16337.p
% 2.97/1.58 thf(ty_t_CharacterDataClass_ORCharacterData_ORCharacterData__ext, type, rCharacterData_ext: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_ShadowRootClass_ORShadowRoot_ORShadowRoot__ext, type, rShadowRoot_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.97/1.58 thf(ty_t_CharacterDataPointer_Ocharacter__data__ptr, type, character_data_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_DocumentClass_ORDocument_ORDocument__ext, type, rDocument_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.97/1.58 thf(ty_t_ElementClass_ORElement_ORElement__ext, type, rElement_ext: ($tType > ($tType > ($tType > ($tType > ($tType > $tType)))))).
% 2.97/1.58 thf(ty_t_ShadowRootPointer_Oshadow__root__ptr, type, shadow_root_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_ObjectClass_ORObject_ORObject__ext, type, rObject_ext: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_DocumentPointer_Odocument__ptr, type, document_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_NodeClass_ORNode_ORNode__ext, type, rNode_ext: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_ElementPointer_Oelement__ptr, type, element_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_ObjectPointer_Oobject__ptr, type, object_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_Heap__Error__Monad_Oprog, type, heap_Error_prog: ($tType > ($tType > ($tType > $tType)))).
% 2.97/1.58 thf(ty_t_NodePointer_Onode__ptr, type, node_ptr: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.97/1.58 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.97/1.58 thf(ty_t_ObjectClass_Oheap, type, heap: ($tType > ($tType > $tType))).
% 2.97/1.58 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.97/1.58 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_String_Ochar, type, char: $tType).
% 2.97/1.58 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_FSet_Ofset, type, fset: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.97/1.58 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.97/1.58 thf(ty_tf_l, type, l: $tType).
% 2.97/1.58 thf(ty_tf_k, type, k: $tType).
% 2.97/1.58 thf(ty_tf_j, type, j: $tType).
% 2.97/1.58 thf(ty_tf_i, type, i: $tType).
% 2.97/1.58 thf(ty_tf_h, type, h: $tType).
% 2.97/1.58 thf(ty_tf_g, type, g: $tType).
% 2.97/1.58 thf(ty_tf_f, type, f: $tType).
% 2.97/1.58 thf(ty_tf_e, type, e: $tType).
% 2.97/1.58 thf(ty_tf_d, type, d: $tType).
% 2.97/1.58 thf(ty_tf_c, type, c: $tType).
% 2.97/1.58 thf(ty_tf_b, type, b: $tType).
% 2.97/1.58 thf(ty_tf_a, type, a: $tType).
% 2.97/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: ($o))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_ORDocument__ext, type, rDocument_ext2: (!> [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType]: ((product_unit > ((list @ char) > ((option @ (element_ptr @ Element_ptr)) > ((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) > (Z > ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes, type, disconnected_nodes: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes__update, type, discon1635973971update: (!> [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType]: ((((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr))))) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odoctype, type, doctype: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (list @ char))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odoctype__update, type, doctype_update: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: ((((list @ char) > (list @ char)) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odocument__element, type, document_element: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (option @ (element_ptr @ Element_ptr)))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Odocument__element__update, type, docume446011358update: (!> [Element_ptr:$tType,Node_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: ((((option @ (element_ptr @ Element_ptr)) > (option @ (element_ptr @ Element_ptr))) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Omore, type, more: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > Z)))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Omore__update, type, more_update: (!> [Z:$tType,Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType]: (((Z > Z) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Onothing, type, nothing: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > product_unit)))).
% 2.97/1.58 thf(sy_c_DocumentClass_ORDocument_Onothing__update, type, nothing_update: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Z:$tType]: (((product_unit > product_unit) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t, type, cast_D42511940_e_c_t: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Document:$tType,Shadow_root_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Object:$tType]: (((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) > (rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t, type, cast_O1159777348_e_n_t: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Shadow_root_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Document:$tType,Object:$tType]: (((rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) > (option @ (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document)))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_Odocument__ptrs, type, document_ptrs: (!> [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Shadow_root_ptr:$tType,Document_ptr:$tType,Object_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Document:$tType,Object:$tType]: ((((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) > (fset @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_Oget_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t, type, get_D_o_c_u_m_e_n_t: (!> [Shadow_root_ptr:$tType,Document_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Object_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Document:$tType,Object:$tType]: (((document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)) > (((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) > (option @ (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))))))))).
% 2.97/1.58 thf(sy_c_DocumentClass_Ois__document__kind, type, is_document_kind: (!> [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Shadow_root_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Document:$tType,Object:$tType]: (((rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) > $o)))).
% 2.97/1.58 thf(sy_c_DocumentClass_Oput_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t, type, put_D_o_c_u_m_e_n_t: (!> [Shadow_root_ptr:$tType,Document_ptr:$tType,Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Document:$tType,Object_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Object:$tType]: (((document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)) > ((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) > (((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) > ((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))))))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r, type, cast_d1427782271_p_t_r: (!> [Document_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Object_ptr:$tType]: (((document_ptr @ Document_ptr) > (object_ptr @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ Document_ptr)) @ Object_ptr))))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r, type, cast_o823910367_p_t_r: (!> [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Document_ptr:$tType,Object_ptr:$tType]: (((object_ptr @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ Document_ptr)) @ Object_ptr))) > (option @ (document_ptr @ Document_ptr)))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Odocument__ptr_OExt, type, document_Ext: (!> [Document_ptr:$tType]: ((Document_ptr > (document_ptr @ Document_ptr))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Odocument__ptr_ORef, type, document_Ref: (!> [Document_ptr:$tType]: ((nat > (document_ptr @ Document_ptr))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Odocument__ptr_Osize__document__ptr, type, docume1907984069nt_ptr: (!> [Document_ptr:$tType]: (((Document_ptr > nat) > ((document_ptr @ Document_ptr) > nat))))).
% 2.97/1.58 thf(sy_c_DocumentPointer_Ois__document__ptr_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r, type, is_doc697300620_p_t_r: (!> [Document_ptr:$tType]: (((document_ptr @ Document_ptr) > $o)))).
% 2.97/1.58 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.97/1.58 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.97/1.58 thf(sy_c_Heap__Error__Monad_Oprog_OProg, type, heap_Error_Prog: (!> [Heap:$tType,E:$tType,Result:$tType]: (((Heap > ((sum_sum @ E) @ ((product_prod @ Result) @ Heap))) > (((heap_Error_prog @ Heap) @ E) @ Result))))).
% 2.97/1.58 thf(sy_c_Heap__Error__Monad_Oprog_Osize__prog, type, heap_Error_size_prog: (!> [Heap:$tType,E:$tType,Result:$tType]: (((Heap > nat) > ((E > nat) > ((Result > nat) > ((((heap_Error_prog @ Heap) @ E) @ Result) > nat))))))).
% 2.97/1.58 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Ocount__list, type, count_list: (!> [A:$tType]: (((list @ A) > (A > nat))))).
% 2.97/1.58 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 2.97/1.58 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.97/1.58 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.97/1.58 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 2.97/1.58 thf(sy_c_List_Onths, type, nths: (!> [A:$tType]: (((list @ A) > ((set @ nat) > (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.97/1.58 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.97/1.58 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.97/1.58 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.97/1.58 thf(sy_c_Nat__Bijection_Oset__decode, type, nat_set_decode: (nat > (set @ nat))).
% 2.97/1.58 thf(sy_c_Nat__Bijection_Oset__encode, type, nat_set_encode: ((set @ nat) > nat)).
% 2.97/1.58 thf(sy_c_Nat__Bijection_Otriangle, type, nat_triangle: (nat > nat)).
% 2.97/1.58 thf(sy_c_ObjectClass_ORObject_ORObject__ext, type, rObject_ext2: (!> [Z:$tType]: ((product_unit > (Z > (rObject_ext @ Z)))))).
% 2.97/1.58 thf(sy_c_ObjectClass_ORObject_Oextend, type, extend: (!> [Z:$tType]: (((rObject_ext @ product_unit) > (Z > (rObject_ext @ Z)))))).
% 2.97/1.58 thf(sy_c_ObjectClass_ORObject_Omore, type, more2: (!> [Z:$tType]: (((rObject_ext @ Z) > Z)))).
% 2.97/1.58 thf(sy_c_ObjectClass_ORObject_Onothing, type, nothing2: (!> [Z:$tType]: (((rObject_ext @ Z) > product_unit)))).
% 2.97/1.58 thf(sy_c_ObjectClass_Oget_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t, type, get_O_b_j_e_c_t: (!> [Object_ptr:$tType,Object:$tType]: (((object_ptr @ Object_ptr) > (((heap @ Object_ptr) @ Object) > (option @ (rObject_ext @ Object))))))).
% 2.97/1.58 thf(sy_c_ObjectClass_Oput_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t, type, put_O_b_j_e_c_t: (!> [Object_ptr:$tType,Object:$tType]: (((object_ptr @ Object_ptr) > ((rObject_ext @ Object) > (((heap @ Object_ptr) @ Object) > ((heap @ Object_ptr) @ Object))))))).
% 2.97/1.58 thf(sy_c_Option_Obind, type, bind: (!> [A:$tType,B:$tType]: (((option @ A) > ((A > (option @ B)) > (option @ B)))))).
% 2.97/1.58 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.97/1.58 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.97/1.58 thf(sy_c_Option_Ooption_Osize__option, type, size_option: (!> [A:$tType]: (((A > nat) > ((option @ A) > nat))))).
% 2.97/1.58 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.97/1.58 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 2.97/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.97/1.58 thf(sy_c_ShadowRootClass_Otype__wf, type, type_wf: (!> [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,G:$tType,H:$tType,I:$tType,J:$tType,K:$tType,L:$tType]: ((((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ A)) @ ((sum_sum @ (character_data_ptr @ B)) @ C)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ D)) @ E))) @ F))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ C) @ A) @ B) @ D) @ (option @ G))) @ ((sum_sum @ (rCharacterData_ext @ (option @ H))) @ I)))) @ ((sum_sum @ ((((rDocument_ext @ C) @ A) @ B) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ C) @ A) @ B) @ (option @ J))) @ K)))) @ L))) > $o)))).
% 2.97/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.97/1.58 thf(sy_v_h, type, h2: ((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ a)) @ ((sum_sum @ (character_data_ptr @ b)) @ c)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ d)) @ e))) @ f))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ c) @ a) @ b) @ d) @ (option @ g))) @ ((sum_sum @ (rCharacterData_ext @ (option @ h))) @ i)))) @ ((sum_sum @ ((((rDocument_ext @ c) @ a) @ b) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))) @ l)))).
% 2.97/1.58 thf(sy_v_h_H, type, h3: ((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ a)) @ ((sum_sum @ (character_data_ptr @ b)) @ c)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ d)) @ e))) @ f))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ c) @ a) @ b) @ d) @ (option @ g))) @ ((sum_sum @ (rCharacterData_ext @ (option @ h))) @ i)))) @ ((sum_sum @ ((((rDocument_ext @ c) @ a) @ b) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))) @ l)))).
% 2.97/1.58 thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject, axiom, (! [I:$tType,G:$tType,F:$tType,E:$tType,D:$tType,H:$tType,C:$tType,B:$tType,A:$tType,X:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ H))),Y:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ H)))]: (((((((((((((cast_D42511940_e_c_t @ A) @ B) @ C) @ H) @ D) @ E) @ F) @ G) @ I) @ X) = ((((((((((cast_D42511940_e_c_t @ A) @ B) @ C) @ H) @ D) @ E) @ F) @ G) @ I) @ Y)) = (X = Y))))).
% 2.97/1.58 thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject, axiom, (! [E:$tType,C:$tType,B:$tType,A:$tType,D:$tType,X:(document_ptr @ D),Y:(document_ptr @ D)]: (((((((((cast_d1427782271_p_t_r @ D) @ A) @ B) @ C) @ E) @ X) = ((((((cast_d1427782271_p_t_r @ D) @ A) @ B) @ C) @ E) @ Y)) = (X = Y))))).
% 2.97/1.58 thf(fact_2_document__ptr_Oinject_I1_J, axiom, (! [Document_ptr:$tType,X1:nat,Y1:nat]: (((((document_Ref @ Document_ptr) @ X1) = ((document_Ref @ Document_ptr) @ Y1)) = (X1 = Y1))))).
% 2.97/1.58 thf(fact_3_RDocument_Oext__inject, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z,Nothinga2:product_unit,Doctype2:(list @ char),Document_element2:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes2:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More2:Z]: ((((((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More) = (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga2) @ Doctype2) @ Document_element2) @ Disconnected_nodes2) @ More2)) = ((Nothinga = Nothinga2) & ((Doctype = Doctype2) & ((Document_element = Document_element2) & ((Disconnected_nodes = Disconnected_nodes2) & (More = More2))))))))).
% 2.97/1.58 thf(fact_4_RObject_Oext__inject, axiom, (! [Z:$tType,Nothing:product_unit,More:Z,Nothing2:product_unit,More2:Z]: ((((((rObject_ext2 @ Z) @ Nothing) @ More) = (((rObject_ext2 @ Z) @ Nothing2) @ More2)) = ((Nothing = Nothing2) & (More = More2)))))).
% 2.97/1.58 thf(fact_5_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 2.97/1.58 thf(fact_6_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.97/1.58 thf(fact_7_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X3:D]: ((bot_bot @ C)))))))).
% 2.97/1.58 thf(fact_8_RDocument_Ocases__scheme, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))]: ((~ ((! [Nothing3:product_unit,Nothinga3:product_unit,Doctype3:(list @ char),Document_element3:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes3:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More3:Z]: ((R != (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing3) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga3) @ Doctype3) @ Document_element3) @ Disconnected_nodes3) @ More3)))))))))).
% 2.97/1.58 thf(fact_9_RDocument_Oinduct__scheme, axiom, (! [Z:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType,P:((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) > $o),R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))]: (((! [Nothing3:product_unit,Nothinga3:product_unit,Doctype3:(list @ char),Document_element3:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes3:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More3:Z]: ((P @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing3) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga3) @ Doctype3) @ Document_element3) @ Disconnected_nodes3) @ More3))))) => (P @ R))))).
% 2.97/1.58 thf(fact_10_RDocument_Oinduct, axiom, (! [Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType,P:((rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ product_unit)) > $o),R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ product_unit))]: (((! [Nothing3:product_unit,Nothinga3:product_unit,Doctype3:(list @ char),Document_element3:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes3:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr))))]: ((P @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ product_unit)) @ Nothing3) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ product_unit) @ Nothinga3) @ Doctype3) @ Document_element3) @ Disconnected_nodes3) @ product_Unity))))) => (P @ R))))).
% 2.97/1.58 thf(fact_11_RDocument_Ocases, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ product_unit))]: ((~ ((! [Nothing3:product_unit,Nothinga3:product_unit,Doctype3:(list @ char),Document_element3:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes3:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr))))]: ((R != (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ product_unit)) @ Nothing3) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ product_unit) @ Nothinga3) @ Doctype3) @ Document_element3) @ Disconnected_nodes3) @ product_Unity)))))))))).
% 2.97/1.58 thf(fact_12_bot__nat__def, axiom, ((bot_bot @ nat) = (zero_zero @ nat))).
% 2.97/1.58 thf(fact_13_RObject_Oinduct, axiom, (! [P:((rObject_ext @ product_unit) > $o),R:(rObject_ext @ product_unit)]: (((! [Nothing3:product_unit]: ((P @ (((rObject_ext2 @ product_unit) @ Nothing3) @ product_Unity)))) => (P @ R))))).
% 2.97/1.58 thf(fact_14_RObject_Ocases, axiom, (! [R:(rObject_ext @ product_unit)]: ((~ ((! [Nothing3:product_unit]: ((R != (((rObject_ext2 @ product_unit) @ Nothing3) @ product_Unity))))))))).
% 2.97/1.58 thf(fact_15_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_16_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X3:A]: ((bot_bot @ B)))))))).
% 2.97/1.58 thf(fact_17_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.97/1.58 thf(fact_18_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.97/1.58 thf(fact_19_RObject_Oinduct__scheme, axiom, (! [Z:$tType,P:((rObject_ext @ Z) > $o),R:(rObject_ext @ Z)]: (((! [Nothing3:product_unit,More3:Z]: ((P @ (((rObject_ext2 @ Z) @ Nothing3) @ More3)))) => (P @ R))))).
% 2.97/1.58 thf(fact_20_RObject_Ocases__scheme, axiom, (! [Z:$tType,R:(rObject_ext @ Z)]: ((~ ((! [Nothing3:product_unit,More3:Z]: ((R != (((rObject_ext2 @ Z) @ Nothing3) @ More3))))))))).
% 2.97/1.58 thf(fact_21_RDocument_Oext__induct, axiom, (! [Z:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType,P:(((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) > $o),R:((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)]: (((! [Nothinga3:product_unit,Doctype3:(list @ char),Document_element3:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes3:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More3:Z]: ((P @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga3) @ Doctype3) @ Document_element3) @ Disconnected_nodes3) @ More3)))) => (P @ R))))).
% 2.97/1.58 thf(fact_22_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M:nat]: ((N = (suc @ M)))))))).
% 2.97/1.58 thf(fact_23_old_Onat_Oinducts, axiom, (! [P:(nat > $o),Nat:nat]: (((P @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P @ Nat3) => (P @ (suc @ Nat3))))) => (P @ Nat)))))).
% 2.97/1.58 thf(fact_24_old_Onat_Oexhaust, axiom, (! [Y:nat]: (((Y != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y != (suc @ Nat3)))))))))).
% 2.97/1.58 thf(fact_25_Zero__not__Suc, axiom, (! [M2:nat]: (((zero_zero @ nat) != (suc @ M2))))).
% 2.97/1.58 thf(fact_26_Zero__neq__Suc, axiom, (! [M2:nat]: (((zero_zero @ nat) != (suc @ M2))))).
% 2.97/1.58 thf(fact_27_Suc__neq__Zero, axiom, (! [M2:nat]: (((suc @ M2) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_28_zero__induct, axiom, (! [P:(nat > $o),K2:nat]: (((P @ K2) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (zero_zero @ nat))))))).
% 2.97/1.58 thf(fact_29_diff__induct, axiom, (! [P:(nat > (nat > $o)),M2:nat,N:nat]: (((! [X4:nat]: (((P @ X4) @ (zero_zero @ nat)))) => ((! [Y3:nat]: (((P @ (zero_zero @ nat)) @ (suc @ Y3)))) => ((! [X4:nat,Y3:nat]: ((((P @ X4) @ Y3) => ((P @ (suc @ X4)) @ (suc @ Y3))))) => ((P @ M2) @ N))))))).
% 2.97/1.58 thf(fact_30_nat__induct, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((P @ N2) => (P @ (suc @ N2))))) => (P @ N)))))).
% 2.97/1.58 thf(fact_31_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_32_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.97/1.58 thf(fact_33_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_34_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 2.97/1.58 thf(fact_35_document__ptr_Osize__gen_I1_J, axiom, (! [Document_ptr:$tType,X:(Document_ptr > nat),X1:nat]: (((((docume1907984069nt_ptr @ Document_ptr) @ X) @ ((document_Ref @ Document_ptr) @ X1)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_36_document__ptr_Osize_I3_J, axiom, (! [Document_ptr:$tType,X1:nat]: ((((size_size @ (document_ptr @ Document_ptr)) @ ((document_Ref @ Document_ptr) @ X1)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_37_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def, axiom, (! [Node_ptr:$tType,Element_ptr:$tType,Character_data_ptr:$tType,Document:$tType,Object_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Object:$tType,Document_ptr:$tType,Shadow_root_ptr:$tType]: (((((((((((((put_D_o_c_u_m_e_n_t @ Shadow_root_ptr) @ Document_ptr) @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Document) @ Object_ptr) @ Element) @ CharacterData) @ Node) @ Object) = (^ [Document_ptr2:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)),Document2:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document)))]: (((((put_O_b_j_e_c_t @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) @ ((((((cast_d1427782271_p_t_r @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)) @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Object_ptr) @ Document_ptr2)) @ ((((((((((cast_D42511940_e_c_t @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Document) @ Shadow_root_ptr) @ Element) @ CharacterData) @ Node) @ Object) @ Document2)))))))).
% 2.97/1.58 thf(fact_38_exists__least__lemma, axiom, (! [P:(nat > $o)]: (((~ ((P @ (zero_zero @ nat)))) => ((? [X_1:nat]: ((P @ X_1))) => (? [N2:nat]: (((~ ((P @ N2))) & (P @ (suc @ N2)))))))))).
% 2.97/1.58 thf(fact_39_dependent__nat__choice, axiom, (! [A:$tType,P:(nat > (A > $o)),Q:(nat > (A > (A > $o)))]: (((? [X_1:A]: (((P @ (zero_zero @ nat)) @ X_1))) => ((! [X4:A,N2:nat]: ((((P @ N2) @ X4) => (? [Y4:A]: ((((P @ (suc @ N2)) @ Y4) & (((Q @ N2) @ X4) @ Y4))))))) => (? [F2:(nat > A)]: ((! [N3:nat]: ((((P @ N3) @ (F2 @ N3)) & (((Q @ N3) @ (F2 @ N3)) @ (F2 @ (suc @ N3))))))))))))).
% 2.97/1.58 thf(fact_40_list__decode_Ocases, axiom, (! [X:nat]: (((X != (zero_zero @ nat)) => (~ ((! [N2:nat]: ((X != (suc @ N2)))))))))).
% 2.97/1.58 thf(fact_41_object__empty, axiom, (! [A:$tType,X:(rObject_ext @ A)]: (((((rObject_ext2 @ A) @ product_Unity) @ ((more2 @ A) @ X)) = X)))).
% 2.97/1.58 thf(fact_42_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.97/1.58 thf(fact_43_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.97/1.58 thf(fact_44_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.97/1.58 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G2:(A > B)]: (((! [X4:A]: (((F3 @ X4) = (G2 @ X4)))) => (F3 = G2))))).
% 2.97/1.58 thf(fact_46_RDocument_Oupdate__convs_I1_J, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,Nothing2:(product_unit > product_unit),Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: ((((((((nothing_update @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ Nothing2) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ (Nothing2 @ Nothinga)) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More)))))).
% 2.97/1.58 thf(fact_47_RDocument_Oupdate__convs_I2_J, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,Doctype2:((list @ char) > (list @ char)),Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: ((((((((doctype_update @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ Doctype2) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ (Doctype2 @ Doctype)) @ Document_element) @ Disconnected_nodes) @ More)))))).
% 2.97/1.58 thf(fact_48_RDocument_Oupdate__convs_I3_J, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,Document_element2:((option @ (element_ptr @ Element_ptr)) > (option @ (element_ptr @ Element_ptr))),Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: ((((((((docume446011358update @ Element_ptr) @ Node_ptr) @ Character_data_ptr) @ Z) @ Document_element2) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ (Document_element2 @ Document_element)) @ Disconnected_nodes) @ More)))))).
% 2.97/1.58 thf(fact_49_RDocument_Oupdate__convs_I4_J, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,Disconnected_nodes2:((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr))))),Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: ((((((((discon1635973971update @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Disconnected_nodes2) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ (Disconnected_nodes2 @ Disconnected_nodes)) @ More)))))).
% 2.97/1.58 thf(fact_50_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X:A,Y:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y)) => (X != Y)))))))).
% 2.97/1.58 thf(fact_51_RObject_Oselect__convs_I2_J, axiom, (! [Z:$tType,Nothing:product_unit,More:Z]: ((((more2 @ Z) @ (((rObject_ext2 @ Z) @ Nothing) @ More)) = More)))).
% 2.97/1.58 thf(fact_52_document__ptr_Osize__neq, axiom, (! [Document_ptr:$tType,X:(document_ptr @ Document_ptr)]: ((((size_size @ (document_ptr @ Document_ptr)) @ X) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_53_object__more__extend__id, axiom, (! [A:$tType,X:(rObject_ext @ product_unit),Y:A]: ((((more2 @ A) @ (((extend @ A) @ X) @ Y)) = Y)))).
% 2.97/1.58 thf(fact_54_RDocument_Oupdate__convs_I5_J, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Z:$tType,More2:(Z > Z),Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: ((((((((more_update @ Z) @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ More2) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ (More2 @ More))))))).
% 2.97/1.58 thf(fact_55_is__document__ptr__ref, axiom, (! [A:$tType,N:nat]: (((is_doc697300620_p_t_r @ A) @ ((document_Ref @ A) @ N))))).
% 2.97/1.58 thf(fact_56_RDocument_Oselect__convs_I5_J, axiom, (! [Node_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Z:$tType,Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: (((((((more @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = More)))).
% 2.97/1.58 thf(fact_57_RDocument_Oselect__convs_I4_J, axiom, (! [Z:$tType,Node_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: (((((((disconnected_nodes @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = Disconnected_nodes)))).
% 2.97/1.58 thf(fact_58_RDocument_Oselect__convs_I3_J, axiom, (! [Z:$tType,Node_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: (((((((document_element @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = Document_element)))).
% 2.97/1.58 thf(fact_59_RDocument_Oselect__convs_I2_J, axiom, (! [Z:$tType,Node_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: (((((((doctype @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = Doctype)))).
% 2.97/1.58 thf(fact_60_RDocument_Oselect__convs_I1_J, axiom, (! [Z:$tType,Node_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Nothing:product_unit,Nothinga:product_unit,Doctype:(list @ char),Document_element:(option @ (element_ptr @ Element_ptr)),Disconnected_nodes:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))),More:Z]: (((((((nothing @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ Nothing) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ Nothinga) @ Doctype) @ Document_element) @ Disconnected_nodes) @ More))) = Nothinga)))).
% 2.97/1.58 thf(fact_61_RDocument_Ounfold__congs_I6_J, axiom, (! [A:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A)),V:A,F3:(A > A),F4:(A > A)]: (((R = R2) => (((((((more @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A) @ R2) = V) => ((! [V2:A]: (((V2 = V) => ((F3 @ V2) = (F4 @ V2))))) => (((((((more_update @ A) @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ F3) @ R) = ((((((more_update @ A) @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_62_RDocument_Ofold__congs_I6_J, axiom, (! [A:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A)),V:A,F3:(A > A),F4:(A > A)]: (((R = R2) => (((((((more @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ A) @ R2) = V) => ((! [V2:A]: (((V = V2) => ((F3 @ V2) = (F4 @ V2))))) => (((((((more_update @ A) @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ F3) @ R) = ((((((more_update @ A) @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_63_heap_Osize__neq, axiom, (! [Object_ptr:$tType,Object:$tType,X:((heap @ Object_ptr) @ Object)]: ((((size_size @ ((heap @ Object_ptr) @ Object)) @ X) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_64_RDocument_Ounfold__congs_I3_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(list @ char),F3:((list @ char) > (list @ char)),F4:((list @ char) > (list @ char))]: (((R = R2) => (((((((doctype @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(list @ char)]: (((V2 = V) => ((F3 @ V2) = (F4 @ V2))))) => (((((((doctype_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((doctype_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_65_RDocument_Ounfold__congs_I4_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(option @ (element_ptr @ Element_ptr2)),F3:((option @ (element_ptr @ Element_ptr2)) > (option @ (element_ptr @ Element_ptr2))),F4:((option @ (element_ptr @ Element_ptr2)) > (option @ (element_ptr @ Element_ptr2)))]: (((R = R2) => (((((((document_element @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(option @ (element_ptr @ Element_ptr2))]: (((V2 = V) => ((F3 @ V2) = (F4 @ V2))))) => (((((((docume446011358update @ Element_ptr2) @ Node_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((docume446011358update @ Element_ptr2) @ Node_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_66_RDocument_Ounfold__congs_I5_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))),F3:((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2))))),F4:((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))))]: (((R = R2) => (((((((disconnected_nodes @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2))))]: (((V2 = V) => ((F3 @ V2) = (F4 @ V2))))) => (((((((discon1635973971update @ Element_ptr2) @ Character_data_ptr2) @ Node_ptr2) @ Z2) @ F3) @ R) = ((((((discon1635973971update @ Element_ptr2) @ Character_data_ptr2) @ Node_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_67_RDocument_Ofold__congs_I3_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(list @ char),F3:((list @ char) > (list @ char)),F4:((list @ char) > (list @ char))]: (((R = R2) => (((((((doctype @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(list @ char)]: (((V = V2) => ((F3 @ V2) = (F4 @ V2))))) => (((((((doctype_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((doctype_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_68_RDocument_Ofold__congs_I4_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(option @ (element_ptr @ Element_ptr2)),F3:((option @ (element_ptr @ Element_ptr2)) > (option @ (element_ptr @ Element_ptr2))),F4:((option @ (element_ptr @ Element_ptr2)) > (option @ (element_ptr @ Element_ptr2)))]: (((R = R2) => (((((((document_element @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(option @ (element_ptr @ Element_ptr2))]: (((V = V2) => ((F3 @ V2) = (F4 @ V2))))) => (((((((docume446011358update @ Element_ptr2) @ Node_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((docume446011358update @ Element_ptr2) @ Node_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_69_RDocument_Ofold__congs_I5_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))),F3:((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2))))),F4:((list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))) > (list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2)))))]: (((R = R2) => (((((((disconnected_nodes @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:(list @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr2)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr2)) @ Node_ptr2))))]: (((V = V2) => ((F3 @ V2) = (F4 @ V2))))) => (((((((discon1635973971update @ Element_ptr2) @ Character_data_ptr2) @ Node_ptr2) @ Z2) @ F3) @ R) = ((((((discon1635973971update @ Element_ptr2) @ Character_data_ptr2) @ Node_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_70_RDocument_Ounfold__congs_I2_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:product_unit,F3:(product_unit > product_unit),F4:(product_unit > product_unit)]: (((R = R2) => (((((((nothing @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:product_unit]: (((V2 = V) => ((F3 @ V2) = (F4 @ V2))))) => (((((((nothing_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((nothing_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_71_RDocument_Ofold__congs_I2_J, axiom, (! [Z2:$tType,Character_data_ptr2:$tType,Element_ptr2:$tType,Node_ptr2:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2)),V:product_unit,F3:(product_unit > product_unit),F4:(product_unit > product_unit)]: (((R = R2) => (((((((nothing @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ R2) = V) => ((! [V2:product_unit]: (((V = V2) => ((F3 @ V2) = (F4 @ V2))))) => (((((((nothing_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F3) @ R) = ((((((nothing_update @ Node_ptr2) @ Element_ptr2) @ Character_data_ptr2) @ Z2) @ F4) @ R2)))))))).
% 2.97/1.58 thf(fact_72_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 2.97/1.58 thf(fact_73_RDocument_Osurjective, axiom, (! [Z:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))]: ((R = (((rObject_ext2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ ((nothing2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ R)) @ (((((((((rDocument_ext2 @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Z) @ (((((nothing @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R)) @ (((((doctype @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R)) @ (((((document_element @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R)) @ (((((disconnected_nodes @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R)) @ (((((more @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R))))))).
% 2.97/1.58 thf(fact_74_RDocument_Oequality, axiom, (! [Z:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType,R:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)),R2:(rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z))]: (((((nothing2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ R) = ((nothing2 @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z)) @ R2)) => (((((((nothing @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R) = (((((nothing @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R2)) => (((((((doctype @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R) = (((((doctype @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R2)) => (((((((document_element @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R) = (((((document_element @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R2)) => (((((((disconnected_nodes @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R) = (((((disconnected_nodes @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R2)) => (((((((more @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R) = (((((more @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Z) @ R2)) => (R = R2)))))))))).
% 2.97/1.58 thf(fact_75_option_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (option @ A)) @ (none @ A)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_76_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_77_document__ptr_Osize_I4_J, axiom, (! [Document_ptr:$tType,X2:Document_ptr]: ((((size_size @ (document_ptr @ Document_ptr)) @ ((document_Ext @ Document_ptr) @ X2)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_78_RObject_Osurjective, axiom, (! [Z:$tType,R:(rObject_ext @ Z)]: ((R = (((rObject_ext2 @ Z) @ ((nothing2 @ Z) @ R)) @ ((more2 @ Z) @ R)))))).
% 2.97/1.58 thf(fact_79_document__ptr_Oinject_I2_J, axiom, (! [Document_ptr:$tType,X2:Document_ptr,Y2:Document_ptr]: (((((document_Ext @ Document_ptr) @ X2) = ((document_Ext @ Document_ptr) @ Y2)) = (X2 = Y2))))).
% 2.97/1.58 thf(fact_80_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys)) => (Xs != Ys))))).
% 2.97/1.58 thf(fact_81_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N)))))).
% 2.97/1.58 thf(fact_82_document__ptr_Odistinct_I1_J, axiom, (! [Document_ptr:$tType,X1:nat,X2:Document_ptr]: ((((document_Ref @ Document_ptr) @ X1) != ((document_Ext @ Document_ptr) @ X2))))).
% 2.97/1.58 thf(fact_83_document__ptr_Oinduct, axiom, (! [Document_ptr:$tType,P:((document_ptr @ Document_ptr) > $o),Document_ptr3:(document_ptr @ Document_ptr)]: (((! [X4:nat]: ((P @ ((document_Ref @ Document_ptr) @ X4)))) => ((! [X4:Document_ptr]: ((P @ ((document_Ext @ Document_ptr) @ X4)))) => (P @ Document_ptr3)))))).
% 2.97/1.58 thf(fact_84_document__ptr_Oexhaust, axiom, (! [Document_ptr:$tType,Y:(document_ptr @ Document_ptr)]: (((! [X12:nat]: ((Y != ((document_Ref @ Document_ptr) @ X12)))) => (~ ((! [X22:Document_ptr]: ((Y != ((document_Ext @ Document_ptr) @ X22)))))))))).
% 2.97/1.58 thf(fact_85_RObject_Oselect__convs_I1_J, axiom, (! [Z:$tType,Nothing:product_unit,More:Z]: ((((nothing2 @ Z) @ (((rObject_ext2 @ Z) @ Nothing) @ More)) = Nothing)))).
% 2.97/1.58 thf(fact_86_RObject_Oequality, axiom, (! [Z:$tType,R:(rObject_ext @ Z),R2:(rObject_ext @ Z)]: (((((nothing2 @ Z) @ R) = ((nothing2 @ Z) @ R2)) => ((((more2 @ Z) @ R) = ((more2 @ Z) @ R2)) => (R = R2)))))).
% 2.97/1.58 thf(fact_87_option_Osize__neq, axiom, (! [A:$tType,X:(option @ A)]: ((((size_size @ (option @ A)) @ X) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_88_option_Osize__gen_I1_J, axiom, (! [A:$tType,X:(A > nat)]: (((((size_option @ A) @ X) @ (none @ A)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_89_length__code, axiom, (! [A:$tType]: (((size_size @ (list @ A)) = ((gen_length @ A) @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_90_document__ptr_Osize__gen_I2_J, axiom, (! [Document_ptr:$tType,X:(Document_ptr > nat),X2:Document_ptr]: (((((docume1907984069nt_ptr @ Document_ptr) @ X) @ ((document_Ext @ Document_ptr) @ X2)) = (((plus_plus @ nat) @ (X @ X2)) @ (suc @ (zero_zero @ nat))))))).
% 2.97/1.58 thf(fact_91_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none, axiom, (! [E:$tType,F:$tType,G:$tType,H:$tType,I:$tType,D:$tType,C:$tType,B:$tType,A:$tType,Obj:(rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ F))) @ ((sum_sum @ (rCharacterData_ext @ (option @ G))) @ H)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ I)))]: (((((((((((((cast_O1159777348_e_n_t @ A) @ B) @ C) @ E) @ F) @ G) @ H) @ D) @ I) @ Obj) = (none @ (rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))))) = (~ ((? [Document2:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))]: ((((((((((((cast_D42511940_e_c_t @ A) @ B) @ C) @ D) @ E) @ F) @ G) @ H) @ I) @ Document2) = Obj))))))))).
% 2.97/1.58 thf(fact_92_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.97/1.58 thf(fact_93_is__document__kind__def, axiom, (! [Object:$tType,Document:$tType,Node:$tType,CharacterData:$tType,Element:$tType,Shadow_root_ptr:$tType,Character_data_ptr:$tType,Element_ptr:$tType,Node_ptr:$tType]: (((((((((((is_document_kind @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ Element) @ CharacterData) @ Node) @ Document) @ Object) = (^ [Ptr:(rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object)))]: ((((((((((((cast_O1159777348_e_n_t @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ Element) @ CharacterData) @ Node) @ Document) @ Object) @ Ptr) != (none @ (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))))))))))).
% 2.97/1.58 thf(fact_94_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.97/1.58 thf(fact_95_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.97/1.58 thf(fact_96_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X) @ Y)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.97/1.58 thf(fact_97_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.97/1.58 thf(fact_98_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_99_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_100_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_101_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_102_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_103_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_104_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.97/1.58 thf(fact_105_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.97/1.58 thf(fact_106_add__Suc__right, axiom, (! [M2:nat,N:nat]: (((((plus_plus @ nat) @ M2) @ (suc @ N)) = (suc @ (((plus_plus @ nat) @ M2) @ N)))))).
% 2.97/1.58 thf(fact_107_Nat_Oadd__0__right, axiom, (! [M2:nat]: (((((plus_plus @ nat) @ M2) @ (zero_zero @ nat)) = M2)))).
% 2.97/1.58 thf(fact_108_add__is__0, axiom, (! [M2:nat,N:nat]: ((((((plus_plus @ nat) @ M2) @ N) = (zero_zero @ nat)) = ((M2 = (zero_zero @ nat)) & (N = (zero_zero @ nat))))))).
% 2.97/1.58 thf(fact_109_gen__length__def, axiom, (! [A:$tType]: (((gen_length @ A) = (^ [N4:nat,Xs3:(list @ A)]: ((((plus_plus @ nat) @ N4) @ ((size_size @ (list @ A)) @ Xs3)))))))).
% 2.97/1.58 thf(fact_110_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) => (B2 = C2)))))))).
% 2.97/1.58 thf(fact_111_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) => (B2 = C2)))))))).
% 2.97/1.58 thf(fact_112_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.97/1.58 thf(fact_113_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A4:A,B3:A]: ((((plus_plus @ A) @ B3) @ A4)))))))).
% 2.97/1.58 thf(fact_114_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C2) @ A2)) = (B2 = C2)))))))).
% 2.97/1.58 thf(fact_115_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C2)) = (B2 = C2)))))))).
% 2.97/1.58 thf(fact_116_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.97/1.58 thf(fact_117_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B4:A,K2:A,B2:A,A2:A]: (((B4 = (((plus_plus @ A) @ K2) @ B2)) => ((((plus_plus @ A) @ A2) @ B4) = (((plus_plus @ A) @ K2) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.97/1.58 thf(fact_118_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A3:A,K2:A,A2:A,B2:A]: (((A3 = (((plus_plus @ A) @ K2) @ A2)) => ((((plus_plus @ A) @ A3) @ B2) = (((plus_plus @ A) @ K2) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 2.97/1.58 thf(fact_119_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I2:A,J2:A,K2:A,L2:A]: ((((I2 = J2) & (K2 = L2)) => ((((plus_plus @ A) @ I2) @ K2) = (((plus_plus @ A) @ J2) @ L2))))))))).
% 2.97/1.58 thf(fact_120_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.97/1.58 thf(fact_121_add_Ogroup__left__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.97/1.58 thf(fact_122_add_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.97/1.58 thf(fact_123_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.97/1.58 thf(fact_124_add__Suc, axiom, (! [M2:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M2)) @ N) = (suc @ (((plus_plus @ nat) @ M2) @ N)))))).
% 2.97/1.58 thf(fact_125_nat__arith_Osuc1, axiom, (! [A3:nat,K2:nat,A2:nat]: (((A3 = (((plus_plus @ nat) @ K2) @ A2)) => ((suc @ A3) = (((plus_plus @ nat) @ K2) @ (suc @ A2))))))).
% 2.97/1.58 thf(fact_126_add__Suc__shift, axiom, (! [M2:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M2)) @ N) = (((plus_plus @ nat) @ M2) @ (suc @ N)))))).
% 2.97/1.58 thf(fact_127_add__eq__self__zero, axiom, (! [M2:nat,N:nat]: ((((((plus_plus @ nat) @ M2) @ N) = M2) => (N = (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_128_plus__nat_Oadd__0, axiom, (! [N:nat]: (((((plus_plus @ nat) @ (zero_zero @ nat)) @ N) = N)))).
% 2.97/1.58 thf(fact_129_one__is__add, axiom, (! [M2:nat,N:nat]: ((((suc @ (zero_zero @ nat)) = (((plus_plus @ nat) @ M2) @ N)) = (((M2 = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M2 = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.97/1.58 thf(fact_130_add__is__1, axiom, (! [M2:nat,N:nat]: ((((((plus_plus @ nat) @ M2) @ N) = (suc @ (zero_zero @ nat))) = (((M2 = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M2 = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.97/1.58 thf(fact_131_gen__length__code_I1_J, axiom, (! [A:$tType,N:nat]: (((((gen_length @ A) @ N) @ (nil @ A)) = N)))).
% 2.97/1.58 thf(fact_132_Euclid__induct, axiom, (! [P:(nat > (nat > $o)),A2:nat,B2:nat]: (((! [A5:nat,B5:nat]: ((((P @ A5) @ B5) = ((P @ B5) @ A5)))) => ((! [A5:nat]: (((P @ A5) @ (zero_zero @ nat)))) => ((! [A5:nat,B5:nat]: ((((P @ A5) @ B5) => ((P @ A5) @ (((plus_plus @ nat) @ A5) @ B5))))) => ((P @ A2) @ B2))))))).
% 2.97/1.58 thf(fact_133_triangle__Suc, axiom, (! [N:nat]: (((nat_triangle @ (suc @ N)) = (((plus_plus @ nat) @ (nat_triangle @ N)) @ (suc @ N)))))).
% 2.97/1.58 thf(fact_134_verit__sum__simplify, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.97/1.58 thf(fact_135_add__0__iff, axiom, (! [A:$tType]: (((semiri456707255roduct @ A) => (! [B2:A,A2:A]: (((B2 = (((plus_plus @ A) @ B2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.97/1.58 thf(fact_136_option_Osize__gen_I2_J, axiom, (! [A:$tType,X:(A > nat),X2:A]: (((((size_option @ A) @ X) @ ((some @ A) @ X2)) = (((plus_plus @ nat) @ (X @ X2)) @ (suc @ (zero_zero @ nat))))))).
% 2.97/1.58 thf(fact_137_option_Oinject, axiom, (! [A:$tType,X2:A,Y2:A]: (((((some @ A) @ X2) = ((some @ A) @ Y2)) = (X2 = Y2))))).
% 2.97/1.58 thf(fact_138_not__Some__eq, axiom, (! [A:$tType,X:(option @ A)]: (((! [Y5:A]: ((X != ((some @ A) @ Y5)))) = (X = (none @ A)))))).
% 2.97/1.58 thf(fact_139_not__None__eq, axiom, (! [A:$tType,X:(option @ A)]: (((X != (none @ A)) = (? [Y5:A]: ((X = ((some @ A) @ Y5)))))))).
% 2.97/1.58 thf(fact_140_triangle__0, axiom, ((nat_triangle @ (zero_zero @ nat)) = (zero_zero @ nat))).
% 2.97/1.58 thf(fact_141_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv, axiom, (! [I:$tType,H:$tType,G:$tType,F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,Document3:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))]: ((((((((((((cast_O1159777348_e_n_t @ A) @ B) @ C) @ E) @ F) @ G) @ H) @ D) @ I) @ ((((((((((cast_D42511940_e_c_t @ A) @ B) @ C) @ D) @ E) @ F) @ G) @ H) @ I) @ Document3)) = ((some @ (rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))) @ Document3))))).
% 2.97/1.58 thf(fact_142_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some, axiom, (! [I:$tType,D:$tType,H:$tType,G:$tType,F:$tType,E:$tType,C:$tType,B:$tType,A:$tType,Obj:(rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ F))) @ ((sum_sum @ (rCharacterData_ext @ (option @ G))) @ H)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ I))),Document3:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))]: (((((((((((((cast_O1159777348_e_n_t @ A) @ B) @ C) @ E) @ F) @ G) @ H) @ D) @ I) @ Obj) = ((some @ (rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))) @ Document3)) = (((((((((((cast_D42511940_e_c_t @ A) @ B) @ C) @ D) @ E) @ F) @ G) @ H) @ I) @ Document3) = Obj))))).
% 2.97/1.58 thf(fact_143_option_Odistinct_I1_J, axiom, (! [A:$tType,X2:A]: (((none @ A) != ((some @ A) @ X2))))).
% 2.97/1.58 thf(fact_144_option_OdiscI, axiom, (! [A:$tType,Option:(option @ A),X2:A]: (((Option = ((some @ A) @ X2)) => (Option != (none @ A)))))).
% 2.97/1.58 thf(fact_145_option_Oexhaust, axiom, (! [A:$tType,Y:(option @ A)]: (((Y != (none @ A)) => (~ ((! [X22:A]: ((Y != ((some @ A) @ X22)))))))))).
% 2.97/1.58 thf(fact_146_option_Oinducts, axiom, (! [A:$tType,P:((option @ A) > $o),Option:(option @ A)]: (((P @ (none @ A)) => ((! [X4:A]: ((P @ ((some @ A) @ X4)))) => (P @ Option)))))).
% 2.97/1.58 thf(fact_147_split__option__ex, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((? [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) | (? [X3:A]: ((P3 @ ((some @ A) @ X3))))))))))).
% 2.97/1.58 thf(fact_148_split__option__all, axiom, (! [A:$tType]: (((^ [P2:((option @ A) > $o)]: ((! [X5:(option @ A)]: ((P2 @ X5))))) = (^ [P3:((option @ A) > $o)]: (((P3 @ (none @ A)) & (! [X3:A]: ((P3 @ ((some @ A) @ X3))))))))))).
% 2.97/1.58 thf(fact_149_combine__options__cases, axiom, (! [A:$tType,B:$tType,X:(option @ A),P:((option @ A) > ((option @ B) > $o)),Y:(option @ B)]: ((((X = (none @ A)) => ((P @ X) @ Y)) => (((Y = (none @ B)) => ((P @ X) @ Y)) => ((! [A5:A,B5:B]: (((X = ((some @ A) @ A5)) => ((Y = ((some @ B) @ B5)) => ((P @ X) @ Y))))) => ((P @ X) @ Y))))))).
% 2.97/1.58 thf(fact_150_option_Osize_I4_J, axiom, (! [A:$tType,X2:A]: ((((size_size @ (option @ A)) @ ((some @ A) @ X2)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_151_document__ptr__casts__commute2, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,Document_ptr3:(document_ptr @ A)]: ((((((((cast_o823910367_p_t_r @ B) @ C) @ D) @ A) @ E) @ ((((((cast_d1427782271_p_t_r @ A) @ B) @ C) @ D) @ E) @ Document_ptr3)) = ((some @ (document_ptr @ A)) @ Document_ptr3))))).
% 2.97/1.58 thf(fact_152_document__ptr__casts__commute, axiom, (! [E:$tType,A:$tType,D:$tType,C:$tType,B:$tType,Ptr2:(object_ptr @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ D)))) @ ((sum_sum @ (document_ptr @ A)) @ E))),Document_ptr3:(document_ptr @ A)]: (((((((((cast_o823910367_p_t_r @ B) @ C) @ D) @ A) @ E) @ Ptr2) = ((some @ (document_ptr @ A)) @ Document_ptr3)) = (((((((cast_d1427782271_p_t_r @ A) @ B) @ C) @ D) @ E) @ Document_ptr3) = Ptr2))))).
% 2.97/1.58 thf(fact_153_length__splice, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((size_size @ (list @ A)) @ (((splice @ A) @ Xs) @ Ys)) = (((plus_plus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ ((size_size @ (list @ A)) @ Ys)))))).
% 2.97/1.58 thf(fact_154_get__document__ptr__simp, axiom, (! [K:$tType,D:$tType,J:$tType,I:$tType,H:$tType,G:$tType,F:$tType,E:$tType,A:$tType,C:$tType,B:$tType,Ptr2:(object_ptr @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ A)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F))) @ G))),Document_ptr3:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F)),Obj:(rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ K))),H2:((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ A)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F))) @ G))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ K)))]: ((((Ptr2 = ((((((cast_d1427782271_p_t_r @ ((sum_sum @ (shadow_root_ptr @ E)) @ F)) @ B) @ C) @ A) @ G) @ Document_ptr3)) => ((((((((((((((get_D_o_c_u_m_e_n_t @ E) @ F) @ B) @ C) @ A) @ G) @ H) @ I) @ J) @ D) @ K) @ Document_ptr3) @ (((((put_O_b_j_e_c_t @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ A)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F))) @ G))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ K))) @ Ptr2) @ Obj) @ H2)) = ((((((((((cast_O1159777348_e_n_t @ A) @ B) @ C) @ E) @ H) @ I) @ J) @ D) @ K) @ Obj))) & ((Ptr2 != ((((((cast_d1427782271_p_t_r @ ((sum_sum @ (shadow_root_ptr @ E)) @ F)) @ B) @ C) @ A) @ G) @ Document_ptr3)) => ((((((((((((((get_D_o_c_u_m_e_n_t @ E) @ F) @ B) @ C) @ A) @ G) @ H) @ I) @ J) @ D) @ K) @ Document_ptr3) @ (((((put_O_b_j_e_c_t @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ A)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F))) @ G))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ K))) @ Ptr2) @ Obj) @ H2)) = (((((((((((((get_D_o_c_u_m_e_n_t @ E) @ F) @ B) @ C) @ A) @ G) @ H) @ I) @ J) @ D) @ K) @ Document_ptr3) @ H2))))))).
% 2.97/1.58 thf(fact_155_split__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((splice @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.97/1.58 thf(fact_156_splice__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((splice @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.97/1.58 thf(fact_157_get__document__ptr__simp2, axiom, (! [K:$tType,F:$tType,J:$tType,I:$tType,H:$tType,G:$tType,B:$tType,A:$tType,C:$tType,E:$tType,D:$tType,Document_ptr3:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ A)) @ B)),Document_ptr4:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ A)) @ B)),Document3:(rObject_ext @ ((((rDocument_ext @ C) @ D) @ E) @ (option @ F))),H2:((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ D)) @ ((sum_sum @ (character_data_ptr @ E)) @ C)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ A)) @ B))) @ G))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ C) @ D) @ E) @ A) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ C) @ D) @ E) @ (option @ F))) @ K)))]: (((Document_ptr3 != Document_ptr4) => ((((((((((((((get_D_o_c_u_m_e_n_t @ A) @ B) @ D) @ E) @ C) @ G) @ H) @ I) @ J) @ F) @ K) @ Document_ptr3) @ ((((((((((((((put_D_o_c_u_m_e_n_t @ A) @ B) @ C) @ D) @ E) @ F) @ G) @ H) @ I) @ J) @ K) @ Document_ptr4) @ Document3) @ H2)) = (((((((((((((get_D_o_c_u_m_e_n_t @ A) @ B) @ D) @ E) @ C) @ G) @ H) @ I) @ J) @ F) @ K) @ Document_ptr3) @ H2)))))).
% 2.97/1.58 thf(fact_158_get__document__ptr__simp1, axiom, (! [E:$tType,F:$tType,G:$tType,H:$tType,I:$tType,J:$tType,K:$tType,D:$tType,C:$tType,B:$tType,A:$tType,Document_ptr3:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F)),Document3:(rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))),H2:((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ B)) @ ((sum_sum @ (character_data_ptr @ C)) @ A)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ E)) @ F))) @ G))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ A) @ B) @ C) @ E) @ (option @ H))) @ ((sum_sum @ (rCharacterData_ext @ (option @ I))) @ J)))) @ ((sum_sum @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D))) @ K)))]: (((((((((((((((get_D_o_c_u_m_e_n_t @ E) @ F) @ B) @ C) @ A) @ G) @ H) @ I) @ J) @ D) @ K) @ Document_ptr3) @ ((((((((((((((put_D_o_c_u_m_e_n_t @ E) @ F) @ A) @ B) @ C) @ D) @ G) @ H) @ I) @ J) @ K) @ Document_ptr3) @ Document3) @ H2)) = ((some @ (rObject_ext @ ((((rDocument_ext @ A) @ B) @ C) @ (option @ D)))) @ Document3))))).
% 2.97/1.58 thf(fact_159_splice_Osimps_I1_J, axiom, (! [A:$tType,Ys:(list @ A)]: (((((splice @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.97/1.58 thf(fact_160_get__object__ptr__simp1, axiom, (! [B:$tType,A:$tType,Object_ptr2:(object_ptr @ B),Object2:(rObject_ext @ A),H2:((heap @ B) @ A)]: ((((((get_O_b_j_e_c_t @ B) @ A) @ Object_ptr2) @ (((((put_O_b_j_e_c_t @ B) @ A) @ Object_ptr2) @ Object2) @ H2)) = ((some @ (rObject_ext @ A)) @ Object2))))).
% 2.97/1.58 thf(fact_161_list_Osize_I4_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((size_size @ (list @ A)) @ (((cons @ A) @ X21) @ X222)) = (((plus_plus @ nat) @ ((size_size @ (list @ A)) @ X222)) @ (suc @ (zero_zero @ nat))))))).
% 2.97/1.58 thf(fact_162_count__list_Osimps_I1_J, axiom, (! [A:$tType,Y:A]: (((((count_list @ A) @ (nil @ A)) @ Y) = (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_163_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.97/1.58 thf(fact_164_get__object__ptr__simp2, axiom, (! [B:$tType,A:$tType,Object_ptr2:(object_ptr @ A),Object_ptr3:(object_ptr @ A),Object2:(rObject_ext @ B),H2:((heap @ A) @ B)]: (((Object_ptr2 != Object_ptr3) => (((((get_O_b_j_e_c_t @ A) @ B) @ Object_ptr2) @ (((((put_O_b_j_e_c_t @ A) @ B) @ Object_ptr3) @ Object2) @ H2)) = ((((get_O_b_j_e_c_t @ A) @ B) @ Object_ptr2) @ H2)))))).
% 2.97/1.58 thf(fact_165_splice_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((splice @ A) @ Ys) @ Xs)))))).
% 2.97/1.58 thf(fact_166_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.97/1.58 thf(fact_167_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X4:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X4) @ Xs2)) @ Xss))))))))))).
% 2.97/1.58 thf(fact_168_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 2.97/1.58 thf(fact_169_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 2.97/1.58 thf(fact_170_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 2.97/1.58 thf(fact_171_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X22:(list @ A)]: (((P @ X22) => (P @ (((cons @ A) @ X12) @ X22))))) => (P @ List)))))).
% 2.97/1.58 thf(fact_172_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y5:A,Ys2:(list @ A)]: ((Xs = (((cons @ A) @ Y5) @ Ys2)))))))).
% 2.97/1.58 thf(fact_173_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X4) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys3)))) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3))))) => ((P @ Xs) @ Ys)))))))).
% 2.97/1.58 thf(fact_174_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_12:(list @ A)]: (((P @ (nil @ A)) @ X_12))) => ((! [X4:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.97/1.58 thf(fact_175_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y3:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y3) @ Zs)) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Zs))))))) => (P @ Xs))))))).
% 2.97/1.58 thf(fact_176_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.97/1.58 thf(fact_177_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X4:A,Xs2:(list @ A)]: (((! [X213:A,X224:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X224)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X4) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.97/1.58 thf(fact_178_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_12:(list @ A)]: (((P @ (nil @ A)) @ X_12))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y3) @ Ys3)) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.97/1.58 thf(fact_179_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X4:A]: ((X != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.97/1.58 thf(fact_180_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X4:A,Ys3:(list @ A)]: ((((P @ P4) @ Ys3) => ((P @ P4) @ (((cons @ A) @ X4) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.97/1.58 thf(fact_181_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y3:A,Xs2:(list @ A)]: ((((X4 = Y3) => (P @ (((cons @ A) @ X4) @ Xs2))) => (((X4 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.97/1.58 thf(fact_182_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X4:A]: (((P @ F2) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [F2:(A > B),X4:A,Y3:A,Zs:(list @ A)]: ((((P @ F2) @ (((cons @ A) @ Y3) @ Zs)) => ((P @ F2) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Zs)))))) => ((! [A5:(A > B)]: (((P @ A5) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.97/1.58 thf(fact_183_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X4:A]: (((P @ P4) @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X4:A,Y3:A,Xs2:(list @ A)]: ((((P @ P4) @ (((cons @ A) @ Y3) @ Xs2)) => ((P @ P4) @ (((cons @ A) @ X4) @ (((cons @ A) @ Y3) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.97/1.58 thf(fact_184_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X4) @ Xs2)))))) => (P @ Xs))))))).
% 2.97/1.58 thf(fact_185_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X_12:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X_12))) => ((! [F2:(A > B),A5:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A5)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A5) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.97/1.58 thf(fact_186_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X4:A,Ys3:(list @ A)]: ((X != (((cons @ A) @ X4) @ Ys3))))))))))))).
% 2.97/1.58 thf(fact_187_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X4) @ Ys3))))) => (P @ A0))))))))).
% 2.97/1.58 thf(fact_188_length__Suc__conv, axiom, (! [A:$tType,Xs:(list @ A),N:nat]: (((((size_size @ (list @ A)) @ Xs) = (suc @ N)) = (? [Y5:A,Ys2:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys2)) & (((size_size @ (list @ A)) @ Ys2) = N)))))))).
% 2.97/1.58 thf(fact_189_Suc__length__conv, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: ((((suc @ N) = ((size_size @ (list @ A)) @ Xs)) = (? [Y5:A,Ys2:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys2)) & (((size_size @ (list @ A)) @ Ys2) = N)))))))).
% 2.97/1.58 thf(fact_190_list__induct4, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,Xs:(list @ A),Ys:(list @ B),Zs2:(list @ C),Ws:(list @ D),P:((list @ A) > ((list @ B) > ((list @ C) > ((list @ D) > $o))))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => ((((size_size @ (list @ B)) @ Ys) = ((size_size @ (list @ C)) @ Zs2)) => ((((size_size @ (list @ C)) @ Zs2) = ((size_size @ (list @ D)) @ Ws)) => (((((P @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) @ (nil @ D)) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B),Z3:C,Zs:(list @ C),W:D,Ws2:(list @ D)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys3)) => ((((size_size @ (list @ B)) @ Ys3) = ((size_size @ (list @ C)) @ Zs)) => ((((size_size @ (list @ C)) @ Zs) = ((size_size @ (list @ D)) @ Ws2)) => (((((P @ Xs2) @ Ys3) @ Zs) @ Ws2) => ((((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3)) @ (((cons @ C) @ Z3) @ Zs)) @ (((cons @ D) @ W) @ Ws2)))))))) => ((((P @ Xs) @ Ys) @ Zs2) @ Ws))))))))).
% 2.97/1.58 thf(fact_191_list__induct3, axiom, (! [B:$tType,A:$tType,C:$tType,Xs:(list @ A),Ys:(list @ B),Zs2:(list @ C),P:((list @ A) > ((list @ B) > ((list @ C) > $o)))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => ((((size_size @ (list @ B)) @ Ys) = ((size_size @ (list @ C)) @ Zs2)) => ((((P @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B),Z3:C,Zs:(list @ C)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys3)) => ((((size_size @ (list @ B)) @ Ys3) = ((size_size @ (list @ C)) @ Zs)) => ((((P @ Xs2) @ Ys3) @ Zs) => (((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3)) @ (((cons @ C) @ Z3) @ Zs))))))) => (((P @ Xs) @ Ys) @ Zs2)))))))).
% 2.97/1.58 thf(fact_192_list__induct2, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys3)) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3)))))) => ((P @ Xs) @ Ys))))))).
% 2.97/1.58 thf(fact_193_splice_Oelims, axiom, (! [A:$tType,X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((splice @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != Xa)) => (~ ((! [X4:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X4) @ Xs2)) => (Y != (((cons @ A) @ X4) @ (((splice @ A) @ Xa) @ Xs2))))))))))))).
% 2.97/1.58 thf(fact_194_gen__length__code_I2_J, axiom, (! [B:$tType,N:nat,X:B,Xs:(list @ B)]: (((((gen_length @ B) @ N) @ (((cons @ B) @ X) @ Xs)) = (((gen_length @ B) @ (suc @ N)) @ Xs))))).
% 2.97/1.58 thf(fact_195_get__object__ptr__simp, axiom, (! [A:$tType,B:$tType,Ptr2:(object_ptr @ B),Object_ptr2:(object_ptr @ B),Obj:(rObject_ext @ A),H2:((heap @ B) @ A)]: ((((Ptr2 = Object_ptr2) => (((((get_O_b_j_e_c_t @ B) @ A) @ Object_ptr2) @ (((((put_O_b_j_e_c_t @ B) @ A) @ Ptr2) @ Obj) @ H2)) = ((some @ (rObject_ext @ A)) @ Obj))) & ((Ptr2 != Object_ptr2) => (((((get_O_b_j_e_c_t @ B) @ A) @ Object_ptr2) @ (((((put_O_b_j_e_c_t @ B) @ A) @ Ptr2) @ Obj) @ H2)) = ((((get_O_b_j_e_c_t @ B) @ A) @ Object_ptr2) @ H2))))))).
% 2.97/1.58 thf(fact_196_length__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((size_size @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) = (suc @ ((size_size @ (list @ A)) @ Xs)))))).
% 2.97/1.58 thf(fact_197_map__M_Oinduct, axiom, (! [Heap:$tType,E:$tType,Result:$tType,X6:$tType,P:((X6 > (((heap_Error_prog @ Heap) @ E) @ Result)) > ((list @ X6) > $o)),A0:(X6 > (((heap_Error_prog @ Heap) @ E) @ Result)),A1:(list @ X6)]: (((! [F2:(X6 > (((heap_Error_prog @ Heap) @ E) @ Result))]: (((P @ F2) @ (nil @ X6)))) => ((! [F2:(X6 > (((heap_Error_prog @ Heap) @ E) @ Result)),X4:X6,Xs2:(list @ X6)]: (((! [Xa2:Result]: (((P @ F2) @ Xs2))) => ((P @ F2) @ (((cons @ X6) @ X4) @ Xs2))))) => ((P @ A0) @ A1)))))).
% 2.97/1.58 thf(fact_198_prog_Osize__neq, axiom, (! [Heap:$tType,E:$tType,Result:$tType,X:(((heap_Error_prog @ Heap) @ E) @ Result)]: ((((size_size @ (((heap_Error_prog @ Heap) @ E) @ Result)) @ X) != (zero_zero @ nat))))).
% 2.97/1.58 thf(fact_199_forall__M_Oinduct, axiom, (! [Heap:$tType,E:$tType,Result:$tType,Y6:$tType,P:((Y6 > (((heap_Error_prog @ Heap) @ E) @ Result)) > ((list @ Y6) > $o)),A0:(Y6 > (((heap_Error_prog @ Heap) @ E) @ Result)),A1:(list @ Y6)]: (((! [P4:(Y6 > (((heap_Error_prog @ Heap) @ E) @ Result))]: (((P @ P4) @ (nil @ Y6)))) => ((! [P4:(Y6 > (((heap_Error_prog @ Heap) @ E) @ Result)),X4:Y6,Xs2:(list @ Y6)]: (((! [Xa2:Result]: (((P @ P4) @ Xs2))) => ((P @ P4) @ (((cons @ Y6) @ X4) @ Xs2))))) => ((P @ A0) @ A1)))))).
% 2.97/1.58 thf(fact_200_filter__M_Oinduct, axiom, (! [Heap:$tType,E:$tType,X6:$tType,P:((X6 > (((heap_Error_prog @ Heap) @ E) @ $o)) > ((list @ X6) > $o)),A0:(X6 > (((heap_Error_prog @ Heap) @ E) @ $o)),A1:(list @ X6)]: (((! [P4:(X6 > (((heap_Error_prog @ Heap) @ E) @ $o))]: (((P @ P4) @ (nil @ X6)))) => ((! [P4:(X6 > (((heap_Error_prog @ Heap) @ E) @ $o)),X4:X6,Xs2:(list @ X6)]: (((! [Xa2:$o]: (((P @ P4) @ Xs2))) => ((P @ P4) @ (((cons @ X6) @ X4) @ Xs2))))) => ((P @ A0) @ A1)))))).
% 2.97/1.58 thf(fact_201_fold__M_Oinduct, axiom, (! [Result:$tType,E:$tType,Heap:$tType,Y6:$tType,P:((Result > (Y6 > (((heap_Error_prog @ Heap) @ E) @ Result))) > (Result > ((list @ Y6) > $o))),A0:(Result > (Y6 > (((heap_Error_prog @ Heap) @ E) @ Result))),A1:Result,A22:(list @ Y6)]: (((! [F2:(Result > (Y6 > (((heap_Error_prog @ Heap) @ E) @ Result))),D2:Result]: ((((P @ F2) @ D2) @ (nil @ Y6)))) => ((! [F2:(Result > (Y6 > (((heap_Error_prog @ Heap) @ E) @ Result))),D2:Result,X4:Y6,Xs2:(list @ Y6)]: (((! [Xa2:Result]: ((((P @ F2) @ Xa2) @ Xs2))) => (((P @ F2) @ D2) @ (((cons @ Y6) @ X4) @ Xs2))))) => (((P @ A0) @ A1) @ A22)))))).
% 2.97/1.58 thf(fact_202_n__lists__Nil, axiom, (! [A:$tType,N:nat]: ((((N = (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N != (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 2.97/1.58 thf(fact_203_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.97/1.58 thf(fact_204_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.97/1.58 thf(fact_205_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.97/1.58 thf(fact_206_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.97/1.58 thf(fact_207_nths__singleton, axiom, (! [A:$tType,A3:(set @ nat),X:A]: ((((((member @ nat) @ (zero_zero @ nat)) @ A3) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A3) = (((cons @ A) @ X) @ (nil @ A)))) & ((~ ((((member @ nat) @ (zero_zero @ nat)) @ A3))) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A3) = (nil @ A))))))).
% 2.97/1.58 thf(fact_208_nths__nil, axiom, (! [A:$tType,A3:(set @ nat)]: (((((nths @ A) @ (nil @ A)) @ A3) = (nil @ A))))).
% 2.97/1.58 thf(fact_209_nths__empty, axiom, (! [A:$tType,Xs:(list @ A)]: (((((nths @ A) @ Xs) @ (bot_bot @ (set @ nat))) = (nil @ A))))).
% 2.97/1.58 thf(fact_210_prog_Osize_I2_J, axiom, (! [Heap:$tType,E:$tType,Result:$tType,X:(Heap > ((sum_sum @ E) @ ((product_prod @ Result) @ Heap)))]: ((((size_size @ (((heap_Error_prog @ Heap) @ E) @ Result)) @ ((((heap_Error_Prog @ Heap) @ E) @ Result) @ X)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_211_get_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def, axiom, (! [Element_ptr:$tType,Character_data_ptr:$tType,Node_ptr:$tType,Object_ptr:$tType,Element:$tType,CharacterData:$tType,Node:$tType,Document:$tType,Object:$tType,Document_ptr:$tType,Shadow_root_ptr:$tType]: (((((((((((((get_D_o_c_u_m_e_n_t @ Shadow_root_ptr) @ Document_ptr) @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Object_ptr) @ Element) @ CharacterData) @ Node) @ Document) @ Object) = (^ [Document_ptr2:(document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)),H3:((heap @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object)))]: (((((bind @ (rObject_ext @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object)))) @ (rObject_ext @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document)))) @ ((((get_O_b_j_e_c_t @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ Element_ptr)) @ ((sum_sum @ (character_data_ptr @ Character_data_ptr)) @ Node_ptr)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr))) @ Object_ptr))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ (option @ Element))) @ ((sum_sum @ (rCharacterData_ext @ (option @ CharacterData))) @ Node)))) @ ((sum_sum @ ((((rDocument_ext @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ (option @ Document))) @ Object))) @ ((((((cast_d1427782271_p_t_r @ ((sum_sum @ (shadow_root_ptr @ Shadow_root_ptr)) @ Document_ptr)) @ Element_ptr) @ Character_data_ptr) @ Node_ptr) @ Object_ptr) @ Document_ptr2)) @ H3)) @ (((((((((cast_O1159777348_e_n_t @ Node_ptr) @ Element_ptr) @ Character_data_ptr) @ Shadow_root_ptr) @ Element) @ CharacterData) @ Node) @ Document) @ Object)))))))).
% 2.97/1.58 thf(fact_212_bind__runit, axiom, (! [A:$tType,X:(option @ A)]: ((((((bind @ A) @ A) @ X) @ (some @ A)) = X)))).
% 2.97/1.58 thf(fact_213_bind__split__asm, axiom, (! [A:$tType,B:$tType,P:((option @ A) > $o),M2:(option @ B),F3:(B > (option @ A))]: (((P @ ((((bind @ B) @ A) @ M2) @ F3)) = (~ ((((M2 = (none @ B)) & (~ ((P @ (none @ A))))) | (? [X3:B]: (((M2 = ((some @ B) @ X3)) & (~ ((P @ (F3 @ X3)))))))))))))).
% 2.97/1.58 thf(fact_214_bind__split, axiom, (! [A:$tType,B:$tType,P:((option @ A) > $o),M2:(option @ B),F3:(B > (option @ A))]: (((P @ ((((bind @ B) @ A) @ M2) @ F3)) = (((M2 = (none @ B)) => (P @ (none @ A))) & (! [V3:B]: (((M2 = ((some @ B) @ V3)) => (P @ (F3 @ V3)))))))))).
% 2.97/1.58 thf(fact_215_Option_Obind__cong, axiom, (! [B:$tType,A:$tType,X:(option @ A),Y:(option @ A),F3:(A > (option @ B)),G2:(A > (option @ B))]: (((X = Y) => ((! [A5:A]: (((Y = ((some @ A) @ A5)) => ((F3 @ A5) = (G2 @ A5))))) => (((((bind @ A) @ B) @ X) @ F3) = ((((bind @ A) @ B) @ Y) @ G2))))))).
% 2.97/1.58 thf(fact_216_bind_Obind__lunit, axiom, (! [B:$tType,A:$tType,X:A,F3:(A > (option @ B))]: ((((((bind @ A) @ B) @ ((some @ A) @ X)) @ F3) = (F3 @ X))))).
% 2.97/1.58 thf(fact_217_bind__eq__Some__conv, axiom, (! [A:$tType,B:$tType,F3:(option @ B),G2:(B > (option @ A)),X:A]: (((((((bind @ B) @ A) @ F3) @ G2) = ((some @ A) @ X)) = (? [Y5:B]: (((F3 = ((some @ B) @ Y5)) & ((G2 @ Y5) = ((some @ A) @ X))))))))).
% 2.97/1.58 thf(fact_218_bind_Obind__lzero, axiom, (! [A:$tType,B:$tType,F3:(A > (option @ B))]: ((((((bind @ A) @ B) @ (none @ A)) @ F3) = (none @ B))))).
% 2.97/1.58 thf(fact_219_bind__option__cong__code, axiom, (! [B:$tType,A:$tType,X:(option @ A),Y:(option @ A),F3:(A > (option @ B))]: (((X = Y) => (((((bind @ A) @ B) @ X) @ F3) = ((((bind @ A) @ B) @ Y) @ F3)))))).
% 2.97/1.58 thf(fact_220_prog_Osize__gen, axiom, (! [Heap:$tType,E:$tType,Result:$tType,Xc:(Heap > nat),Xb:(E > nat),Xa:(Result > nat),X:(Heap > ((sum_sum @ E) @ ((product_prod @ Result) @ Heap)))]: (((((((((heap_Error_size_prog @ Heap) @ E) @ Result) @ Xc) @ Xb) @ Xa) @ ((((heap_Error_Prog @ Heap) @ E) @ Result) @ X)) = (suc @ (zero_zero @ nat)))))).
% 2.97/1.58 thf(fact_221_set__encode__empty, axiom, ((nat_set_encode @ (bot_bot @ (set @ nat))) = (zero_zero @ nat))).
% 2.97/1.58 thf(fact_222_set__decode__zero, axiom, ((nat_set_decode @ (zero_zero @ nat)) = (bot_bot @ (set @ nat)))).
% 2.97/1.58 thf(fact_223_length__append__singleton, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((size_size @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = (suc @ ((size_size @ (list @ A)) @ Xs)))))).
% 2.97/1.58 thf(fact_224_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs2)) = (Ys = Zs2))))).
% 2.97/1.58 thf(fact_225_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys = Zs2))))).
% 2.97/1.58 thf(fact_226_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs2)))))).
% 2.97/1.58 thf(fact_227_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B2:(list @ A),C2:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B2)) @ C2) = (((append @ A) @ A2) @ (((append @ A) @ B2) @ C2)))))).
% 2.97/1.58 thf(fact_228_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.97/1.58 thf(fact_229_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.97/1.58 thf(fact_230_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.97/1.58 thf(fact_231_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.97/1.58 thf(fact_232_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.97/1.58 thf(fact_233_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.97/1.58 thf(fact_234_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.97/1.58 thf(fact_235_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.97/1.58 thf(fact_236_append__eq__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Us:(list @ A),Vs:(list @ A)]: ((((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) | (((size_size @ (list @ A)) @ Us) = ((size_size @ (list @ A)) @ Vs))) => (((((append @ A) @ Xs) @ Us) = (((append @ A) @ Ys) @ Vs)) = ((Xs = Ys) & (Us = Vs))))))).
% 2.97/1.58 thf(fact_237_set__decode__inverse, axiom, (! [N:nat]: (((nat_set_encode @ (nat_set_decode @ N)) = N)))).
% 2.97/1.58 thf(fact_238_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.97/1.58 thf(fact_239_length__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((size_size @ (list @ A)) @ (((append @ A) @ Xs) @ Ys)) = (((plus_plus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ ((size_size @ (list @ A)) @ Ys)))))).
% 2.97/1.58 thf(fact_240_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us2)) & ((((append @ A) @ Us2) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us2) = Zs2) & (Ys = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.97/1.58 thf(fact_241_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Us))))))).
% 2.97/1.58 thf(fact_242_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X4:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.97/1.58 thf(fact_243_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y3:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y3) @ (nil @ A)))))))))))).
% 2.97/1.58 thf(fact_244_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs2)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs2)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X) @ Ys4) = Ys) & (Xs = (((append @ A) @ Ys4) @ Zs2)))))))))).
% 2.97/1.58 thf(fact_245_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs2:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs2) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs2 = (((cons @ A) @ X) @ Xs))) | (? [Ys4:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs2) = Xs))))))))).
% 2.97/1.58 thf(fact_246_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.97/1.58 thf(fact_247_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.97/1.58 thf(fact_248_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.97/1.58 thf(fact_249_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.97/1.58 thf(fact_250_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.97/1.58 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.97/1.58 thf(tcon_fun___Orderings_Obot, axiom, (! [A6:$tType,A7:$tType]: (((bot @ A7) => (bot @ (A6 > A7)))))).
% 2.97/1.58 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, (semiri456707255roduct @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, (semigroup_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, (monoid_add @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Orderings_Oord_1, axiom, (ord @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Orderings_Obot_2, axiom, (bot @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.97/1.58 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.97/1.58 thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.97/1.58 thf(tcon_Set_Oset___Orderings_Obot_4, axiom, (! [A6:$tType]: ((bot @ (set @ A6))))).
% 2.97/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_5, axiom, (linorder @ $o)).
% 2.97/1.58 thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, (ord @ $o)).
% 2.97/1.58 thf(tcon_HOL_Obool___Orderings_Obot_7, axiom, (bot @ $o)).
% 2.97/1.58 thf(tcon_FSet_Ofset___Orderings_Oord_8, axiom, (! [A6:$tType]: ((ord @ (fset @ A6))))).
% 2.97/1.58 thf(tcon_FSet_Ofset___Orderings_Obot_9, axiom, (! [A6:$tType]: ((bot @ (fset @ A6))))).
% 2.97/1.58 thf(tcon_FSet_Ofset___Nat_Osize_10, axiom, (! [A6:$tType]: ((size @ (fset @ A6))))).
% 2.97/1.58 thf(tcon_List_Olist___Nat_Osize_11, axiom, (! [A6:$tType]: ((size @ (list @ A6))))).
% 2.97/1.58 thf(tcon_String_Ochar___Nat_Osize_12, axiom, (size @ char)).
% 2.97/1.58 thf(tcon_Sum__Type_Osum___Orderings_Olinorder_13, axiom, (! [A6:$tType,A7:$tType]: ((((linorder @ A6) & (linorder @ A7)) => (linorder @ ((sum_sum @ A6) @ A7)))))).
% 2.97/1.58 thf(tcon_Sum__Type_Osum___Orderings_Oord_14, axiom, (! [A6:$tType,A7:$tType]: ((((linorder @ A6) & (linorder @ A7)) => (ord @ ((sum_sum @ A6) @ A7)))))).
% 2.97/1.58 thf(tcon_Sum__Type_Osum___Nat_Osize_15, axiom, (! [A6:$tType,A7:$tType]: ((size @ ((sum_sum @ A6) @ A7))))).
% 2.97/1.58 thf(tcon_Option_Ooption___Nat_Osize_16, axiom, (! [A6:$tType]: ((size @ (option @ A6))))).
% 2.97/1.58 thf(tcon_ObjectClass_Oheap___Nat_Osize_17, axiom, (! [A6:$tType,A7:$tType]: ((size @ ((heap @ A6) @ A7))))).
% 2.97/1.58 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_18, axiom, (linorder @ product_unit)).
% 2.97/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oord_19, axiom, (ord @ product_unit)).
% 2.97/1.58 thf(tcon_Product__Type_Ounit___Orderings_Obot_20, axiom, (bot @ product_unit)).
% 2.97/1.58 thf(tcon_NodePointer_Onode__ptr___Orderings_Olinorder_21, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (node_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_NodePointer_Onode__ptr___Orderings_Oord_22, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (node_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_NodePointer_Onode__ptr___Nat_Osize_23, axiom, (! [A6:$tType]: ((size @ (node_ptr @ A6))))).
% 2.97/1.58 thf(tcon_Heap__Error__Monad_Oprog___Nat_Osize_24, axiom, (! [A6:$tType,A7:$tType,A8:$tType]: ((size @ (((heap_Error_prog @ A6) @ A7) @ A8))))).
% 2.97/1.58 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Olinorder_25, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (object_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Oord_26, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (object_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ObjectPointer_Oobject__ptr___Nat_Osize_27, axiom, (! [A6:$tType]: ((size @ (object_ptr @ A6))))).
% 2.97/1.58 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Olinorder_28, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (element_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Oord_29, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (element_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ElementPointer_Oelement__ptr___Nat_Osize_30, axiom, (! [A6:$tType]: ((size @ (element_ptr @ A6))))).
% 2.97/1.58 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Olinorder_31, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (document_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Oord_32, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (document_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_DocumentPointer_Odocument__ptr___Nat_Osize_33, axiom, (! [A6:$tType]: ((size @ (document_ptr @ A6))))).
% 2.97/1.58 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Olinorder_34, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (shadow_root_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Oord_35, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (shadow_root_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Nat_Osize_36, axiom, (! [A6:$tType]: ((size @ (shadow_root_ptr @ A6))))).
% 2.97/1.58 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Olinorder_37, axiom, (! [A6:$tType]: (((linorder @ A6) => (linorder @ (character_data_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Oord_38, axiom, (! [A6:$tType]: (((linorder @ A6) => (ord @ (character_data_ptr @ A6)))))).
% 2.97/1.58 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Nat_Osize_39, axiom, (! [A6:$tType]: ((size @ (character_data_ptr @ A6))))).
% 2.97/1.58 thf(conj_0, hypothesis, (((((((((((((document_ptrs @ a) @ b) @ c) @ d) @ e) @ f) @ g) @ h) @ i) @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)) @ l) @ h2) = (bot_bot @ (fset @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ d)) @ e)))))).
% 2.97/1.58 thf(conj_1, hypothesis, (h3 = (((((put_O_b_j_e_c_t @ ((sum_sum @ (node_ptr @ ((sum_sum @ (element_ptr @ a)) @ ((sum_sum @ (character_data_ptr @ b)) @ c)))) @ ((sum_sum @ (document_ptr @ ((sum_sum @ (shadow_root_ptr @ d)) @ e))) @ f))) @ ((sum_sum @ (rNode_ext @ ((sum_sum @ (((((rElement_ext @ c) @ a) @ b) @ d) @ (option @ g))) @ ((sum_sum @ (rCharacterData_ext @ (option @ h))) @ i)))) @ ((sum_sum @ ((((rDocument_ext @ c) @ a) @ b) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))) @ l))) @ ((((((cast_d1427782271_p_t_r @ ((sum_sum @ (shadow_root_ptr @ d)) @ e)) @ a) @ b) @ c) @ f) @ ((document_Ref @ ((sum_sum @ (shadow_root_ptr @ d)) @ e)) @ (suc @ (zero_zero @ nat))))) @ ((((((((((cast_D42511940_e_c_t @ c) @ a) @ b) @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)) @ d) @ g) @ h) @ i) @ l) @ (((rObject_ext2 @ ((((rDocument_ext @ c) @ a) @ b) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))) @ product_Unity) @ (((((((((rDocument_ext2 @ a) @ b) @ c) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k))) @ product_Unity) @ (nil @ char)) @ (none @ (element_ptr @ a))) @ (nil @ (node_ptr @ ((sum_sum @ (element_ptr @ a)) @ ((sum_sum @ (character_data_ptr @ b)) @ c))))) @ (none @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))))) @ h2))).
% 2.97/1.58 thf(conj_2, hypothesis, (((((((((((((type_wf @ a) @ b) @ c) @ d) @ e) @ f) @ g) @ h) @ i) @ j) @ k) @ l) @ h2)).
% 2.97/1.58 thf(conj_3, conjecture, ((((((((((is_document_kind @ c) @ a) @ b) @ d) @ g) @ h) @ i) @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)) @ l) @ ((((((((((cast_D42511940_e_c_t @ c) @ a) @ b) @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)) @ d) @ g) @ h) @ i) @ l) @ (((rObject_ext2 @ ((((rDocument_ext @ c) @ a) @ b) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k)))) @ product_Unity) @ (((((((((rDocument_ext2 @ a) @ b) @ c) @ (option @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k))) @ product_Unity) @ (nil @ char)) @ (none @ (element_ptr @ a))) @ (nil @ (node_ptr @ ((sum_sum @ (element_ptr @ a)) @ ((sum_sum @ (character_data_ptr @ b)) @ c))))) @ (none @ ((sum_sum @ ((((rShadowRoot_ext @ c) @ a) @ b) @ (option @ j))) @ k))))))).
% 2.97/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.rDZlZRFXfP/DTF2DTF16337.p
% 2.97/1.58 ------------------------
% 3.26/1.64 ---- Cleaned THF ---
% 3.26/1.64 thf(ty_t_CharacterDataClass_ORCharacterData_ORCharacterData__ext,type,
% 3.26/1.64 rCharacterData_ext: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ShadowRootClass_ORShadowRoot_ORShadowRoot__ext,type,
% 3.26/1.64 rShadowRoot_ext: $tType > $tType > $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_CharacterDataPointer_Ocharacter__data__ptr,type,
% 3.26/1.64 character_data_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_DocumentClass_ORDocument_ORDocument__ext,type,
% 3.26/1.64 rDocument_ext: $tType > $tType > $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ElementClass_ORElement_ORElement__ext,type,
% 3.26/1.64 rElement_ext: $tType > $tType > $tType > $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ShadowRootPointer_Oshadow__root__ptr,type,
% 3.26/1.64 shadow_root_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ObjectClass_ORObject_ORObject__ext,type,
% 3.26/1.64 rObject_ext: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_DocumentPointer_Odocument__ptr,type,
% 3.26/1.64 document_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_NodeClass_ORNode_ORNode__ext,type,
% 3.26/1.64 rNode_ext: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ElementPointer_Oelement__ptr,type,
% 3.26/1.64 element_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ObjectPointer_Oobject__ptr,type,
% 3.26/1.64 object_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Heap__Error__Monad_Oprog,type,
% 3.26/1.64 heap_Error_prog: $tType > $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_NodePointer_Onode__ptr,type,
% 3.26/1.64 node_ptr: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Product__Type_Ounit,type,
% 3.26/1.64 product_unit: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Product__Type_Oprod,type,
% 3.26/1.64 product_prod: $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_ObjectClass_Oheap,type,
% 3.26/1.64 heap: $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Sum__Type_Osum,type,
% 3.26/1.64 sum_sum: $tType > $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Option_Ooption,type,
% 3.26/1.64 option: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_String_Ochar,type,
% 3.26/1.64 char: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_List_Olist,type,
% 3.26/1.64 list: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_FSet_Ofset,type,
% 3.26/1.64 fset: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Set_Oset,type,
% 3.26/1.64 set: $tType > $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_t_Nat_Onat,type,
% 3.26/1.64 nat: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_l,type,
% 3.26/1.64 l: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_k,type,
% 3.26/1.64 k: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_j,type,
% 3.26/1.64 j: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_i,type,
% 3.26/1.64 i: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_h,type,
% 3.26/1.64 h: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_g,type,
% 3.26/1.64 g: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_f,type,
% 3.26/1.64 f: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_e,type,
% 3.26/1.64 e: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_d,type,
% 3.26/1.64 d: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_c,type,
% 3.26/1.64 c: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_b,type,
% 3.26/1.64 b: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(ty_tf_a,type,
% 3.26/1.64 a: $tType ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_HOL_Otype,type,
% 3.26/1.64 type:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Nat_Osize,type,
% 3.26/1.64 size:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ozero,type,
% 3.26/1.64 zero:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Orderings_Obot,type,
% 3.26/1.64 bot:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Orderings_Oord,type,
% 3.26/1.64 ord:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ogroup__add,type,
% 3.26/1.64 group_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Omonoid__add,type,
% 3.26/1.64 monoid_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Orderings_Olinorder,type,
% 3.26/1.64 linorder:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Osemigroup__add,type,
% 3.26/1.64 semigroup_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 3.26/1.64 comm_monoid_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 3.26/1.64 ab_semigroup_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 3.26/1.64 cancel_semigroup_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 3.26/1.64 cancel1352612707id_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 3.26/1.64 linord219039673up_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 3.26/1.64 ordere779506340up_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 3.26/1.64 canoni770627133id_add:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 3.26/1.64 semiri456707255roduct:
% 3.26/1.64 !>[A: $tType] : $o ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_ORDocument__ext,type,
% 3.26/1.64 rDocument_ext2:
% 3.26/1.64 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( product_unit > ( list @ char ) > ( option @ ( element_ptr @ Element_ptr ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > Z > ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes,type,
% 3.26/1.64 disconnected_nodes:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes__update,type,
% 3.26/1.64 discon1635973971update:
% 3.26/1.64 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( ( ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odoctype,type,
% 3.26/1.64 doctype:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ char ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odoctype__update,type,
% 3.26/1.64 doctype_update:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( list @ char ) > ( list @ char ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odocument__element,type,
% 3.26/1.64 document_element:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Odocument__element__update,type,
% 3.26/1.64 docume446011358update:
% 3.26/1.64 !>[Element_ptr: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Omore,type,
% 3.26/1.64 more:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > Z ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Omore__update,type,
% 3.26/1.64 more_update:
% 3.26/1.64 !>[Z: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType] : ( ( Z > Z ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Onothing,type,
% 3.26/1.64 nothing:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > product_unit ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_ORDocument_Onothing__update,type,
% 3.26/1.64 nothing_update:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( product_unit > product_unit ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 3.26/1.64 cast_D42511940_e_c_t:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Ocast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 3.26/1.64 cast_O1159777348_e_n_t:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Odocument__ptrs,type,
% 3.26/1.64 document_ptrs:
% 3.26/1.64 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Shadow_root_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Oget_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 3.26/1.64 get_D_o_c_u_m_e_n_t:
% 3.26/1.64 !>[Shadow_root_ptr: $tType,Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Ois__document__kind,type,
% 3.26/1.64 is_document_kind:
% 3.26/1.64 !>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > $o ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentClass_Oput_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t,type,
% 3.26/1.64 put_D_o_c_u_m_e_n_t:
% 3.26/1.64 !>[Shadow_root_ptr: $tType,Document_ptr: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 3.26/1.64 cast_d1427782271_p_t_r:
% 3.26/1.64 !>[Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Ocast_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 3.26/1.64 cast_o823910367_p_t_r:
% 3.26/1.64 !>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType] : ( ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) > ( option @ ( document_ptr @ Document_ptr ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Odocument__ptr_OExt,type,
% 3.26/1.64 document_Ext:
% 3.26/1.64 !>[Document_ptr: $tType] : ( Document_ptr > ( document_ptr @ Document_ptr ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Odocument__ptr_ORef,type,
% 3.26/1.64 document_Ref:
% 3.26/1.64 !>[Document_ptr: $tType] : ( nat > ( document_ptr @ Document_ptr ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Odocument__ptr_Osize__document__ptr,type,
% 3.26/1.64 docume1907984069nt_ptr:
% 3.26/1.64 !>[Document_ptr: $tType] : ( ( Document_ptr > nat ) > ( document_ptr @ Document_ptr ) > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_DocumentPointer_Ois__document__ptr_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
% 3.26/1.64 is_doc697300620_p_t_r:
% 3.26/1.64 !>[Document_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > $o ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 3.26/1.64 plus_plus:
% 3.26/1.64 !>[A: $tType] : ( A > A > A ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.26/1.64 zero_zero:
% 3.26/1.64 !>[A: $tType] : A ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Heap__Error__Monad_Oprog_OProg,type,
% 3.26/1.64 heap_Error_Prog:
% 3.26/1.64 !>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) ) ) > ( heap_Error_prog @ Heap @ E @ Result ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Heap__Error__Monad_Oprog_Osize__prog,type,
% 3.26/1.64 heap_Error_size_prog:
% 3.26/1.64 !>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > nat ) > ( E > nat ) > ( Result > nat ) > ( heap_Error_prog @ Heap @ E @ Result ) > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Oappend,type,
% 3.26/1.64 append:
% 3.26/1.64 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Ocount__list,type,
% 3.26/1.64 count_list:
% 3.26/1.64 !>[A: $tType] : ( ( list @ A ) > A > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Ogen__length,type,
% 3.26/1.64 gen_length:
% 3.26/1.64 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Oinsert,type,
% 3.26/1.64 insert:
% 3.26/1.64 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Olist_OCons,type,
% 3.26/1.64 cons:
% 3.26/1.64 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Olist_ONil,type,
% 3.26/1.64 nil:
% 3.26/1.64 !>[A: $tType] : ( list @ A ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Olist__ex1,type,
% 3.26/1.64 list_ex1:
% 3.26/1.64 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_On__lists,type,
% 3.26/1.64 n_lists:
% 3.26/1.64 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Onths,type,
% 3.26/1.64 nths:
% 3.26/1.64 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Oproduct__lists,type,
% 3.26/1.64 product_lists:
% 3.26/1.64 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Osplice,type,
% 3.26/1.64 splice:
% 3.26/1.64 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_List_Osubseqs,type,
% 3.26/1.64 subseqs:
% 3.26/1.64 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Nat_OSuc,type,
% 3.26/1.64 suc: nat > nat ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Nat_Osize__class_Osize,type,
% 3.26/1.64 size_size:
% 3.26/1.64 !>[A: $tType] : ( A > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 3.26/1.64 nat_set_decode: nat > ( set @ nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 3.26/1.64 nat_set_encode: ( set @ nat ) > nat ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Nat__Bijection_Otriangle,type,
% 3.26/1.64 nat_triangle: nat > nat ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_ORObject_ORObject__ext,type,
% 3.26/1.64 rObject_ext2:
% 3.26/1.64 !>[Z: $tType] : ( product_unit > Z > ( rObject_ext @ Z ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_ORObject_Oextend,type,
% 3.26/1.64 extend:
% 3.26/1.64 !>[Z: $tType] : ( ( rObject_ext @ product_unit ) > Z > ( rObject_ext @ Z ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_ORObject_Omore,type,
% 3.26/1.64 more2:
% 3.26/1.64 !>[Z: $tType] : ( ( rObject_ext @ Z ) > Z ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_ORObject_Onothing,type,
% 3.26/1.64 nothing2:
% 3.26/1.64 !>[Z: $tType] : ( ( rObject_ext @ Z ) > product_unit ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_Oget_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 3.26/1.64 get_O_b_j_e_c_t:
% 3.26/1.64 !>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( heap @ Object_ptr @ Object ) > ( option @ ( rObject_ext @ Object ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ObjectClass_Oput_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
% 3.26/1.64 put_O_b_j_e_c_t:
% 3.26/1.64 !>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( rObject_ext @ Object ) > ( heap @ Object_ptr @ Object ) > ( heap @ Object_ptr @ Object ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Option_Obind,type,
% 3.26/1.64 bind:
% 3.26/1.64 !>[A: $tType,B: $tType] : ( ( option @ A ) > ( A > ( option @ B ) ) > ( option @ B ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Option_Ooption_ONone,type,
% 3.26/1.64 none:
% 3.26/1.64 !>[A: $tType] : ( option @ A ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Option_Ooption_OSome,type,
% 3.26/1.64 some:
% 3.26/1.64 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Option_Ooption_Osize__option,type,
% 3.26/1.64 size_option:
% 3.26/1.64 !>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.26/1.64 bot_bot:
% 3.26/1.64 !>[A: $tType] : A ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Product__Type_OUnity,type,
% 3.26/1.64 product_Unity: product_unit ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_Set_OCollect,type,
% 3.26/1.64 collect:
% 3.26/1.64 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_ShadowRootClass_Otype__wf,type,
% 3.26/1.64 type_wf:
% 3.26/1.64 !>[A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,L: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ A ) @ ( sum_sum @ ( character_data_ptr @ B ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ D ) @ E ) ) @ F ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ A @ B @ D @ ( option @ G ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ H ) ) @ I ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ A @ B @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ C @ A @ B @ ( option @ J ) ) @ K ) ) ) @ L ) ) ) > $o ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_c_member,type,
% 3.26/1.64 member:
% 3.26/1.64 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_v_h,type,
% 3.26/1.64 h2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(sy_v_h_H,type,
% 3.26/1.64 h3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject,axiom,
% 3.26/1.64 ! [I: $tType,G: $tType,F: $tType,E: $tType,D: $tType,H: $tType,C: $tType,B: $tType,A: $tType,X: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) ),Y: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) )] :
% 3.26/1.64 ( ( ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ X )
% 3.26/1.64 = ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ Y ) )
% 3.26/1.64 = ( X = Y ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject,axiom,
% 3.26/1.64 ! [E: $tType,C: $tType,B: $tType,A: $tType,D: $tType,X: document_ptr @ D,Y: document_ptr @ D] :
% 3.26/1.64 ( ( ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ X )
% 3.26/1.64 = ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ Y ) )
% 3.26/1.64 = ( X = Y ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_2_document__ptr_Oinject_I1_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X1: nat,Y1: nat] :
% 3.26/1.64 ( ( ( document_Ref @ Document_ptr @ X1 )
% 3.26/1.64 = ( document_Ref @ Document_ptr @ Y1 ) )
% 3.26/1.64 = ( X1 = Y1 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_3_RDocument_Oext__inject,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z,Nothinga2: product_unit,Doctype2: list @ char,Document_element2: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More2: Z] :
% 3.26/1.64 ( ( ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
% 3.26/1.64 = ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga2 @ Doctype2 @ Document_element2 @ Disconnected_nodes2 @ More2 ) )
% 3.26/1.64 = ( ( Nothinga = Nothinga2 )
% 3.26/1.64 & ( Doctype = Doctype2 )
% 3.26/1.64 & ( Document_element = Document_element2 )
% 3.26/1.64 & ( Disconnected_nodes = Disconnected_nodes2 )
% 3.26/1.64 & ( More = More2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_4_RObject_Oext__inject,axiom,
% 3.26/1.64 ! [Z: $tType,Nothing: product_unit,More: Z,Nothing2: product_unit,More2: Z] :
% 3.26/1.64 ( ( ( rObject_ext2 @ Z @ Nothing @ More )
% 3.26/1.64 = ( rObject_ext2 @ Z @ Nothing2 @ More2 ) )
% 3.26/1.64 = ( ( Nothing = Nothing2 )
% 3.26/1.64 & ( More = More2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_5_nat_Oinject,axiom,
% 3.26/1.64 ! [X2: nat,Y2: nat] :
% 3.26/1.64 ( ( ( suc @ X2 )
% 3.26/1.64 = ( suc @ Y2 ) )
% 3.26/1.64 = ( X2 = Y2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_6_old_Onat_Oinject,axiom,
% 3.26/1.64 ! [Nat: nat,Nat2: nat] :
% 3.26/1.64 ( ( ( suc @ Nat )
% 3.26/1.64 = ( suc @ Nat2 ) )
% 3.26/1.64 = ( Nat = Nat2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_7_bot__apply,axiom,
% 3.26/1.64 ! [C: $tType,D: $tType] :
% 3.26/1.64 ( ( bot @ C )
% 3.26/1.64 => ( ( bot_bot @ ( D > C ) )
% 3.26/1.64 = ( ^ [X3: D] : ( bot_bot @ C ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_8_RDocument_Ocases__scheme,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 3.26/1.64 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] :
% 3.26/1.64 ( R
% 3.26/1.64 != ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_9_RDocument_Oinduct__scheme,axiom,
% 3.26/1.64 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 3.26/1.64 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
% 3.26/1.64 => ( P @ R ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_10_RDocument_Oinduct,axiom,
% 3.26/1.64 ! [Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
% 3.26/1.64 ( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) )
% 3.26/1.64 => ( P @ R ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_11_RDocument_Ocases,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
% 3.26/1.64 ~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] :
% 3.26/1.64 ( R
% 3.26/1.64 != ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_12_bot__nat__def,axiom,
% 3.26/1.64 ( ( bot_bot @ nat )
% 3.26/1.64 = ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_13_RObject_Oinduct,axiom,
% 3.26/1.64 ! [P: ( rObject_ext @ product_unit ) > $o,R: rObject_ext @ product_unit] :
% 3.26/1.64 ( ! [Nothing3: product_unit] : ( P @ ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) )
% 3.26/1.64 => ( P @ R ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_14_RObject_Ocases,axiom,
% 3.26/1.64 ! [R: rObject_ext @ product_unit] :
% 3.26/1.64 ~ ! [Nothing3: product_unit] :
% 3.26/1.64 ( R
% 3.26/1.64 != ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_15_zero__reorient,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( zero @ A )
% 3.26/1.64 => ! [X: A] :
% 3.26/1.64 ( ( ( zero_zero @ A )
% 3.26/1.64 = X )
% 3.26/1.64 = ( X
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_16_bot__fun__def,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType] :
% 3.26/1.64 ( ( bot @ B )
% 3.26/1.64 => ( ( bot_bot @ ( A > B ) )
% 3.26/1.64 = ( ^ [X3: A] : ( bot_bot @ B ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_17_n__not__Suc__n,axiom,
% 3.26/1.64 ! [N: nat] :
% 3.26/1.64 ( N
% 3.26/1.64 != ( suc @ N ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_18_Suc__inject,axiom,
% 3.26/1.64 ! [X: nat,Y: nat] :
% 3.26/1.64 ( ( ( suc @ X )
% 3.26/1.64 = ( suc @ Y ) )
% 3.26/1.64 => ( X = Y ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_19_RObject_Oinduct__scheme,axiom,
% 3.26/1.64 ! [Z: $tType,P: ( rObject_ext @ Z ) > $o,R: rObject_ext @ Z] :
% 3.26/1.64 ( ! [Nothing3: product_unit,More3: Z] : ( P @ ( rObject_ext2 @ Z @ Nothing3 @ More3 ) )
% 3.26/1.64 => ( P @ R ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_20_RObject_Ocases__scheme,axiom,
% 3.26/1.64 ! [Z: $tType,R: rObject_ext @ Z] :
% 3.26/1.64 ~ ! [Nothing3: product_unit,More3: Z] :
% 3.26/1.64 ( R
% 3.26/1.64 != ( rObject_ext2 @ Z @ Nothing3 @ More3 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_21_RDocument_Oext__induct,axiom,
% 3.26/1.64 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) > $o,R: rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z] :
% 3.26/1.64 ( ! [Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
% 3.26/1.64 => ( P @ R ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_22_not0__implies__Suc,axiom,
% 3.26/1.64 ! [N: nat] :
% 3.26/1.64 ( ( N
% 3.26/1.64 != ( zero_zero @ nat ) )
% 3.26/1.64 => ? [M: nat] :
% 3.26/1.64 ( N
% 3.26/1.64 = ( suc @ M ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_23_old_Onat_Oinducts,axiom,
% 3.26/1.64 ! [P: nat > $o,Nat: nat] :
% 3.26/1.64 ( ( P @ ( zero_zero @ nat ) )
% 3.26/1.64 => ( ! [Nat3: nat] :
% 3.26/1.64 ( ( P @ Nat3 )
% 3.26/1.64 => ( P @ ( suc @ Nat3 ) ) )
% 3.26/1.64 => ( P @ Nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_24_old_Onat_Oexhaust,axiom,
% 3.26/1.64 ! [Y: nat] :
% 3.26/1.64 ( ( Y
% 3.26/1.64 != ( zero_zero @ nat ) )
% 3.26/1.64 => ~ ! [Nat3: nat] :
% 3.26/1.64 ( Y
% 3.26/1.64 != ( suc @ Nat3 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_25_Zero__not__Suc,axiom,
% 3.26/1.64 ! [M2: nat] :
% 3.26/1.64 ( ( zero_zero @ nat )
% 3.26/1.64 != ( suc @ M2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_26_Zero__neq__Suc,axiom,
% 3.26/1.64 ! [M2: nat] :
% 3.26/1.64 ( ( zero_zero @ nat )
% 3.26/1.64 != ( suc @ M2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_27_Suc__neq__Zero,axiom,
% 3.26/1.64 ! [M2: nat] :
% 3.26/1.64 ( ( suc @ M2 )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_28_zero__induct,axiom,
% 3.26/1.64 ! [P: nat > $o,K2: nat] :
% 3.26/1.64 ( ( P @ K2 )
% 3.26/1.64 => ( ! [N2: nat] :
% 3.26/1.64 ( ( P @ ( suc @ N2 ) )
% 3.26/1.64 => ( P @ N2 ) )
% 3.26/1.64 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_29_diff__induct,axiom,
% 3.26/1.64 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 3.26/1.64 ( ! [X4: nat] : ( P @ X4 @ ( zero_zero @ nat ) )
% 3.26/1.64 => ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
% 3.26/1.64 => ( ! [X4: nat,Y3: nat] :
% 3.26/1.64 ( ( P @ X4 @ Y3 )
% 3.26/1.64 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 3.26/1.64 => ( P @ M2 @ N ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_30_nat__induct,axiom,
% 3.26/1.64 ! [P: nat > $o,N: nat] :
% 3.26/1.64 ( ( P @ ( zero_zero @ nat ) )
% 3.26/1.64 => ( ! [N2: nat] :
% 3.26/1.64 ( ( P @ N2 )
% 3.26/1.64 => ( P @ ( suc @ N2 ) ) )
% 3.26/1.64 => ( P @ N ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_31_nat_OdiscI,axiom,
% 3.26/1.64 ! [Nat: nat,X2: nat] :
% 3.26/1.64 ( ( Nat
% 3.26/1.64 = ( suc @ X2 ) )
% 3.26/1.64 => ( Nat
% 3.26/1.64 != ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_32_old_Onat_Odistinct_I1_J,axiom,
% 3.26/1.64 ! [Nat2: nat] :
% 3.26/1.64 ( ( zero_zero @ nat )
% 3.26/1.64 != ( suc @ Nat2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_33_old_Onat_Odistinct_I2_J,axiom,
% 3.26/1.64 ! [Nat4: nat] :
% 3.26/1.64 ( ( suc @ Nat4 )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_34_nat_Odistinct_I1_J,axiom,
% 3.26/1.64 ! [X2: nat] :
% 3.26/1.64 ( ( zero_zero @ nat )
% 3.26/1.64 != ( suc @ X2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_35_document__ptr_Osize__gen_I1_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X: Document_ptr > nat,X1: nat] :
% 3.26/1.64 ( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ref @ Document_ptr @ X1 ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_36_document__ptr_Osize_I3_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X1: nat] :
% 3.26/1.64 ( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ref @ Document_ptr @ X1 ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_37_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 3.26/1.64 ! [Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
% 3.26/1.64 ( ( put_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Object_ptr @ Element @ CharacterData @ Node @ Object )
% 3.26/1.64 = ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),Document2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) )] : ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ ( cast_D42511940_e_c_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Object @ Document2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_38_exists__least__lemma,axiom,
% 3.26/1.64 ! [P: nat > $o] :
% 3.26/1.64 ( ~ ( P @ ( zero_zero @ nat ) )
% 3.26/1.64 => ( ? [X_1: nat] : ( P @ X_1 )
% 3.26/1.64 => ? [N2: nat] :
% 3.26/1.64 ( ~ ( P @ N2 )
% 3.26/1.64 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_39_dependent__nat__choice,axiom,
% 3.26/1.64 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 3.26/1.64 ( ? [X_1: A] : ( P @ ( zero_zero @ nat ) @ X_1 )
% 3.26/1.64 => ( ! [X4: A,N2: nat] :
% 3.26/1.64 ( ( P @ N2 @ X4 )
% 3.26/1.64 => ? [Y4: A] :
% 3.26/1.64 ( ( P @ ( suc @ N2 ) @ Y4 )
% 3.26/1.64 & ( Q @ N2 @ X4 @ Y4 ) ) )
% 3.26/1.64 => ? [F2: nat > A] :
% 3.26/1.64 ! [N3: nat] :
% 3.26/1.64 ( ( P @ N3 @ ( F2 @ N3 ) )
% 3.26/1.64 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_40_list__decode_Ocases,axiom,
% 3.26/1.64 ! [X: nat] :
% 3.26/1.64 ( ( X
% 3.26/1.64 != ( zero_zero @ nat ) )
% 3.26/1.64 => ~ ! [N2: nat] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( suc @ N2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_41_object__empty,axiom,
% 3.26/1.64 ! [A: $tType,X: rObject_ext @ A] :
% 3.26/1.64 ( ( rObject_ext2 @ A @ product_Unity @ ( more2 @ A @ X ) )
% 3.26/1.64 = X ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_42_mem__Collect__eq,axiom,
% 3.26/1.64 ! [A: $tType,A2: A,P: A > $o] :
% 3.26/1.64 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.26/1.64 = ( P @ A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_43_Collect__mem__eq,axiom,
% 3.26/1.64 ! [A: $tType,A3: set @ A] :
% 3.26/1.64 ( ( collect @ A
% 3.26/1.64 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 3.26/1.64 = A3 ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_44_Collect__cong,axiom,
% 3.26/1.64 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.26/1.64 ( ! [X4: A] :
% 3.26/1.64 ( ( P @ X4 )
% 3.26/1.64 = ( Q @ X4 ) )
% 3.26/1.64 => ( ( collect @ A @ P )
% 3.26/1.64 = ( collect @ A @ Q ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_45_ext,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 3.26/1.64 ( ! [X4: A] :
% 3.26/1.64 ( ( F3 @ X4 )
% 3.26/1.64 = ( G2 @ X4 ) )
% 3.26/1.64 => ( F3 = G2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_46_RDocument_Oupdate__convs_I1_J,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( nothing_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Nothing2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_47_RDocument_Oupdate__convs_I2_J,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Doctype2: ( list @ char ) > ( list @ char ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( doctype_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Doctype2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_48_RDocument_Oupdate__convs_I3_J,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Document_element2: ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( docume446011358update @ Element_ptr @ Node_ptr @ Character_data_ptr @ Z @ Document_element2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_49_RDocument_Oupdate__convs_I4_J,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Disconnected_nodes2: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( discon1635973971update @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Disconnected_nodes2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_50_size__neq__size__imp__neq,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( size @ A )
% 3.26/1.64 => ! [X: A,Y: A] :
% 3.26/1.64 ( ( ( size_size @ A @ X )
% 3.26/1.64 != ( size_size @ A @ Y ) )
% 3.26/1.64 => ( X != Y ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_51_RObject_Oselect__convs_I2_J,axiom,
% 3.26/1.64 ! [Z: $tType,Nothing: product_unit,More: Z] :
% 3.26/1.64 ( ( more2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
% 3.26/1.64 = More ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_52_document__ptr_Osize__neq,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X: document_ptr @ Document_ptr] :
% 3.26/1.64 ( ( size_size @ ( document_ptr @ Document_ptr ) @ X )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_53_object__more__extend__id,axiom,
% 3.26/1.64 ! [A: $tType,X: rObject_ext @ product_unit,Y: A] :
% 3.26/1.64 ( ( more2 @ A @ ( extend @ A @ X @ Y ) )
% 3.26/1.64 = Y ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_54_RDocument_Oupdate__convs_I5_J,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,More2: Z > Z,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( more_update @ Z @ Node_ptr @ Element_ptr @ Character_data_ptr @ More2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_55_is__document__ptr__ref,axiom,
% 3.26/1.64 ! [A: $tType,N: nat] : ( is_doc697300620_p_t_r @ A @ ( document_Ref @ A @ N ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_56_RDocument_Oselect__convs_I5_J,axiom,
% 3.26/1.64 ! [Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Z: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = More ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_57_RDocument_Oselect__convs_I4_J,axiom,
% 3.26/1.64 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = Disconnected_nodes ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_58_RDocument_Oselect__convs_I3_J,axiom,
% 3.26/1.64 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = Document_element ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_59_RDocument_Oselect__convs_I2_J,axiom,
% 3.26/1.64 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = Doctype ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_60_RDocument_Oselect__convs_I1_J,axiom,
% 3.26/1.64 ! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
% 3.26/1.64 ( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
% 3.26/1.64 = Nothinga ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_61_RDocument_Ounfold__congs_I6_J,axiom,
% 3.26/1.64 ! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: A] :
% 3.26/1.64 ( ( V2 = V )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
% 3.26/1.64 = ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_62_RDocument_Ofold__congs_I6_J,axiom,
% 3.26/1.64 ! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: A] :
% 3.26/1.64 ( ( V = V2 )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
% 3.26/1.64 = ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_63_heap_Osize__neq,axiom,
% 3.26/1.64 ! [Object_ptr: $tType,Object: $tType,X: heap @ Object_ptr @ Object] :
% 3.26/1.64 ( ( size_size @ ( heap @ Object_ptr @ Object ) @ X )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_64_RDocument_Ounfold__congs_I3_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: list @ char] :
% 3.26/1.64 ( ( V2 = V )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_65_RDocument_Ounfold__congs_I4_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
% 3.26/1.64 ( ( V2 = V )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_66_RDocument_Ounfold__congs_I5_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
% 3.26/1.64 ( ( V2 = V )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_67_RDocument_Ofold__congs_I3_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: list @ char] :
% 3.26/1.64 ( ( V = V2 )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_68_RDocument_Ofold__congs_I4_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
% 3.26/1.64 ( ( V = V2 )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_69_RDocument_Ofold__congs_I5_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
% 3.26/1.64 ( ( V = V2 )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_70_RDocument_Ounfold__congs_I2_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: product_unit] :
% 3.26/1.64 ( ( V2 = V )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_71_RDocument_Ofold__congs_I2_J,axiom,
% 3.26/1.64 ! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
% 3.26/1.64 ( ( R = R2 )
% 3.26/1.64 => ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
% 3.26/1.64 = V )
% 3.26/1.64 => ( ! [V2: product_unit] :
% 3.26/1.64 ( ( V = V2 )
% 3.26/1.64 => ( ( F3 @ V2 )
% 3.26/1.64 = ( F4 @ V2 ) ) )
% 3.26/1.64 => ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
% 3.26/1.64 = ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_72_length__0__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 = ( Xs
% 3.26/1.64 = ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_73_RDocument_Osurjective,axiom,
% 3.26/1.64 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 3.26/1.64 ( R
% 3.26/1.64 = ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R ) @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_74_RDocument_Oequality,axiom,
% 3.26/1.64 ! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
% 3.26/1.64 ( ( ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R )
% 3.26/1.64 = ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R2 ) )
% 3.26/1.64 => ( ( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 3.26/1.64 = ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 3.26/1.64 => ( ( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 3.26/1.64 = ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 3.26/1.64 => ( ( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 3.26/1.64 = ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 3.26/1.64 => ( ( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 3.26/1.64 = ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 3.26/1.64 => ( ( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
% 3.26/1.64 = ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
% 3.26/1.64 => ( R = R2 ) ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_75_option_Osize_I3_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( size_size @ ( option @ A ) @ ( none @ A ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_76_list_Osize_I3_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 3.26/1.64 = ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_77_document__ptr_Osize_I4_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X2: Document_ptr] :
% 3.26/1.64 ( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ext @ Document_ptr @ X2 ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_78_RObject_Osurjective,axiom,
% 3.26/1.64 ! [Z: $tType,R: rObject_ext @ Z] :
% 3.26/1.64 ( R
% 3.26/1.64 = ( rObject_ext2 @ Z @ ( nothing2 @ Z @ R ) @ ( more2 @ Z @ R ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_79_document__ptr_Oinject_I2_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X2: Document_ptr,Y2: Document_ptr] :
% 3.26/1.64 ( ( ( document_Ext @ Document_ptr @ X2 )
% 3.26/1.64 = ( document_Ext @ Document_ptr @ Y2 ) )
% 3.26/1.64 = ( X2 = Y2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_80_neq__if__length__neq,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 != ( size_size @ ( list @ A ) @ Ys ) )
% 3.26/1.64 => ( Xs != Ys ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_81_Ex__list__of__length,axiom,
% 3.26/1.64 ! [A: $tType,N: nat] :
% 3.26/1.64 ? [Xs2: list @ A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.26/1.64 = N ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_82_document__ptr_Odistinct_I1_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X1: nat,X2: Document_ptr] :
% 3.26/1.64 ( ( document_Ref @ Document_ptr @ X1 )
% 3.26/1.64 != ( document_Ext @ Document_ptr @ X2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_83_document__ptr_Oinduct,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,P: ( document_ptr @ Document_ptr ) > $o,Document_ptr3: document_ptr @ Document_ptr] :
% 3.26/1.64 ( ! [X4: nat] : ( P @ ( document_Ref @ Document_ptr @ X4 ) )
% 3.26/1.64 => ( ! [X4: Document_ptr] : ( P @ ( document_Ext @ Document_ptr @ X4 ) )
% 3.26/1.64 => ( P @ Document_ptr3 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_84_document__ptr_Oexhaust,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,Y: document_ptr @ Document_ptr] :
% 3.26/1.64 ( ! [X12: nat] :
% 3.26/1.64 ( Y
% 3.26/1.64 != ( document_Ref @ Document_ptr @ X12 ) )
% 3.26/1.64 => ~ ! [X22: Document_ptr] :
% 3.26/1.64 ( Y
% 3.26/1.64 != ( document_Ext @ Document_ptr @ X22 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_85_RObject_Oselect__convs_I1_J,axiom,
% 3.26/1.64 ! [Z: $tType,Nothing: product_unit,More: Z] :
% 3.26/1.64 ( ( nothing2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
% 3.26/1.64 = Nothing ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_86_RObject_Oequality,axiom,
% 3.26/1.64 ! [Z: $tType,R: rObject_ext @ Z,R2: rObject_ext @ Z] :
% 3.26/1.64 ( ( ( nothing2 @ Z @ R )
% 3.26/1.64 = ( nothing2 @ Z @ R2 ) )
% 3.26/1.64 => ( ( ( more2 @ Z @ R )
% 3.26/1.64 = ( more2 @ Z @ R2 ) )
% 3.26/1.64 => ( R = R2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_87_option_Osize__neq,axiom,
% 3.26/1.64 ! [A: $tType,X: option @ A] :
% 3.26/1.64 ( ( size_size @ ( option @ A ) @ X )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_88_option_Osize__gen_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,X: A > nat] :
% 3.26/1.64 ( ( size_option @ A @ X @ ( none @ A ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_89_length__code,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) )
% 3.26/1.64 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_90_document__ptr_Osize__gen_I2_J,axiom,
% 3.26/1.64 ! [Document_ptr: $tType,X: Document_ptr > nat,X2: Document_ptr] :
% 3.26/1.64 ( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ext @ Document_ptr @ X2 ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_91_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none,axiom,
% 3.26/1.64 ! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) )] :
% 3.26/1.64 ( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
% 3.26/1.64 = ( none @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) ) )
% 3.26/1.64 = ( ~ ? [Document2: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 3.26/1.64 ( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document2 )
% 3.26/1.64 = Obj ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_92_list__ex1__simps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,P: A > $o] :
% 3.26/1.64 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_93_is__document__kind__def,axiom,
% 3.26/1.64 ! [Object: $tType,Document: $tType,Node: $tType,CharacterData: $tType,Element: $tType,Shadow_root_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType] :
% 3.26/1.64 ( ( is_document_kind @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object )
% 3.26/1.64 = ( ^ [Ptr: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] :
% 3.26/1.64 ( ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object @ Ptr )
% 3.26/1.64 != ( none @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_94_add__right__cancel,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel_semigroup_add @ A )
% 3.26/1.64 => ! [B2: A,A2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ B2 @ A2 )
% 3.26/1.64 = ( plus_plus @ A @ C2 @ A2 ) )
% 3.26/1.64 = ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_95_add__left__cancel,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel_semigroup_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ A2 @ B2 )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ C2 ) )
% 3.26/1.64 = ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_96_zero__eq__add__iff__both__eq__0,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( canoni770627133id_add @ A )
% 3.26/1.64 => ! [X: A,Y: A] :
% 3.26/1.64 ( ( ( zero_zero @ A )
% 3.26/1.64 = ( plus_plus @ A @ X @ Y ) )
% 3.26/1.64 = ( ( X
% 3.26/1.64 = ( zero_zero @ A ) )
% 3.26/1.64 & ( Y
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_97_add__eq__0__iff__both__eq__0,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( canoni770627133id_add @ A )
% 3.26/1.64 => ! [X: A,Y: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ X @ Y )
% 3.26/1.64 = ( zero_zero @ A ) )
% 3.26/1.64 = ( ( X
% 3.26/1.64 = ( zero_zero @ A ) )
% 3.26/1.64 & ( Y
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_98_add__cancel__right__right,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel1352612707id_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A] :
% 3.26/1.64 ( ( A2
% 3.26/1.64 = ( plus_plus @ A @ A2 @ B2 ) )
% 3.26/1.64 = ( B2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_99_add__cancel__right__left,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel1352612707id_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A] :
% 3.26/1.64 ( ( A2
% 3.26/1.64 = ( plus_plus @ A @ B2 @ A2 ) )
% 3.26/1.64 = ( B2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_100_add__cancel__left__right,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel1352612707id_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ A2 @ B2 )
% 3.26/1.64 = A2 )
% 3.26/1.64 = ( B2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_101_add__cancel__left__left,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel1352612707id_add @ A )
% 3.26/1.64 => ! [B2: A,A2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ B2 @ A2 )
% 3.26/1.64 = A2 )
% 3.26/1.64 = ( B2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_102_double__zero__sym,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( linord219039673up_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( ( zero_zero @ A )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ A2 ) )
% 3.26/1.64 = ( A2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_103_double__zero,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( linord219039673up_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ A2 @ A2 )
% 3.26/1.64 = ( zero_zero @ A ) )
% 3.26/1.64 = ( A2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_104_add_Oright__neutral,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( monoid_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_105_add_Oleft__neutral,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( monoid_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_106_add__Suc__right,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( plus_plus @ nat @ M2 @ ( suc @ N ) )
% 3.26/1.64 = ( suc @ ( plus_plus @ nat @ M2 @ N ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_107_Nat_Oadd__0__right,axiom,
% 3.26/1.64 ! [M2: nat] :
% 3.26/1.64 ( ( plus_plus @ nat @ M2 @ ( zero_zero @ nat ) )
% 3.26/1.64 = M2 ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_108_add__is__0,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( ( plus_plus @ nat @ M2 @ N )
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 = ( ( M2
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 & ( N
% 3.26/1.64 = ( zero_zero @ nat ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_109_gen__length__def,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( gen_length @ A )
% 3.26/1.64 = ( ^ [N4: nat,Xs3: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs3 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_110_add__right__imp__eq,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel_semigroup_add @ A )
% 3.26/1.64 => ! [B2: A,A2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ B2 @ A2 )
% 3.26/1.64 = ( plus_plus @ A @ C2 @ A2 ) )
% 3.26/1.64 => ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_111_add__left__imp__eq,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel_semigroup_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ A2 @ B2 )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ C2 ) )
% 3.26/1.64 => ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_112_add_Oleft__commute,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ab_semigroup_add @ A )
% 3.26/1.64 => ! [B2: A,A2: A,C2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_113_add_Ocommute,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ab_semigroup_add @ A )
% 3.26/1.64 => ( ( plus_plus @ A )
% 3.26/1.64 = ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_114_add_Oright__cancel,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( group_add @ A )
% 3.26/1.64 => ! [B2: A,A2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ B2 @ A2 )
% 3.26/1.64 = ( plus_plus @ A @ C2 @ A2 ) )
% 3.26/1.64 = ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_115_add_Oleft__cancel,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( group_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A,C2: A] :
% 3.26/1.64 ( ( ( plus_plus @ A @ A2 @ B2 )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ C2 ) )
% 3.26/1.64 = ( B2 = C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_116_add_Oassoc,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( semigroup_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A,C2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_117_group__cancel_Oadd2,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( comm_monoid_add @ A )
% 3.26/1.64 => ! [B4: A,K2: A,B2: A,A2: A] :
% 3.26/1.64 ( ( B4
% 3.26/1.64 = ( plus_plus @ A @ K2 @ B2 ) )
% 3.26/1.64 => ( ( plus_plus @ A @ A2 @ B4 )
% 3.26/1.64 = ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_118_group__cancel_Oadd1,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( comm_monoid_add @ A )
% 3.26/1.64 => ! [A3: A,K2: A,A2: A,B2: A] :
% 3.26/1.64 ( ( A3
% 3.26/1.64 = ( plus_plus @ A @ K2 @ A2 ) )
% 3.26/1.64 => ( ( plus_plus @ A @ A3 @ B2 )
% 3.26/1.64 = ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_119_add__mono__thms__linordered__semiring_I4_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ordere779506340up_add @ A )
% 3.26/1.64 => ! [I2: A,J2: A,K2: A,L2: A] :
% 3.26/1.64 ( ( ( I2 = J2 )
% 3.26/1.64 & ( K2 = L2 ) )
% 3.26/1.64 => ( ( plus_plus @ A @ I2 @ K2 )
% 3.26/1.64 = ( plus_plus @ A @ J2 @ L2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_120_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ab_semigroup_add @ A )
% 3.26/1.64 => ! [A2: A,B2: A,C2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
% 3.26/1.64 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_121_add_Ogroup__left__neutral,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( group_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_122_add_Ocomm__neutral,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( comm_monoid_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_123_comm__monoid__add__class_Oadd__0,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( comm_monoid_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_124_add__Suc,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N )
% 3.26/1.64 = ( suc @ ( plus_plus @ nat @ M2 @ N ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_125_nat__arith_Osuc1,axiom,
% 3.26/1.64 ! [A3: nat,K2: nat,A2: nat] :
% 3.26/1.64 ( ( A3
% 3.26/1.64 = ( plus_plus @ nat @ K2 @ A2 ) )
% 3.26/1.64 => ( ( suc @ A3 )
% 3.26/1.64 = ( plus_plus @ nat @ K2 @ ( suc @ A2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_126_add__Suc__shift,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N )
% 3.26/1.64 = ( plus_plus @ nat @ M2 @ ( suc @ N ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_127_add__eq__self__zero,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( ( plus_plus @ nat @ M2 @ N )
% 3.26/1.64 = M2 )
% 3.26/1.64 => ( N
% 3.26/1.64 = ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_128_plus__nat_Oadd__0,axiom,
% 3.26/1.64 ! [N: nat] :
% 3.26/1.64 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 3.26/1.64 = N ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_129_one__is__add,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( ( suc @ ( zero_zero @ nat ) )
% 3.26/1.64 = ( plus_plus @ nat @ M2 @ N ) )
% 3.26/1.64 = ( ( ( M2
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) )
% 3.26/1.64 & ( N
% 3.26/1.64 = ( zero_zero @ nat ) ) )
% 3.26/1.64 | ( ( M2
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 & ( N
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_130_add__is__1,axiom,
% 3.26/1.64 ! [M2: nat,N: nat] :
% 3.26/1.64 ( ( ( plus_plus @ nat @ M2 @ N )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) )
% 3.26/1.64 = ( ( ( M2
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) )
% 3.26/1.64 & ( N
% 3.26/1.64 = ( zero_zero @ nat ) ) )
% 3.26/1.64 | ( ( M2
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 & ( N
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_131_gen__length__code_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,N: nat] :
% 3.26/1.64 ( ( gen_length @ A @ N @ ( nil @ A ) )
% 3.26/1.64 = N ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_132_Euclid__induct,axiom,
% 3.26/1.64 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 3.26/1.64 ( ! [A5: nat,B5: nat] :
% 3.26/1.64 ( ( P @ A5 @ B5 )
% 3.26/1.64 = ( P @ B5 @ A5 ) )
% 3.26/1.64 => ( ! [A5: nat] : ( P @ A5 @ ( zero_zero @ nat ) )
% 3.26/1.64 => ( ! [A5: nat,B5: nat] :
% 3.26/1.64 ( ( P @ A5 @ B5 )
% 3.26/1.64 => ( P @ A5 @ ( plus_plus @ nat @ A5 @ B5 ) ) )
% 3.26/1.64 => ( P @ A2 @ B2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_133_triangle__Suc,axiom,
% 3.26/1.64 ! [N: nat] :
% 3.26/1.64 ( ( nat_triangle @ ( suc @ N ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_134_verit__sum__simplify,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( cancel1352612707id_add @ A )
% 3.26/1.64 => ! [A2: A] :
% 3.26/1.64 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 3.26/1.64 = A2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_135_add__0__iff,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( semiri456707255roduct @ A )
% 3.26/1.64 => ! [B2: A,A2: A] :
% 3.26/1.64 ( ( B2
% 3.26/1.64 = ( plus_plus @ A @ B2 @ A2 ) )
% 3.26/1.64 = ( A2
% 3.26/1.64 = ( zero_zero @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_136_option_Osize__gen_I2_J,axiom,
% 3.26/1.64 ! [A: $tType,X: A > nat,X2: A] :
% 3.26/1.64 ( ( size_option @ A @ X @ ( some @ A @ X2 ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_137_option_Oinject,axiom,
% 3.26/1.64 ! [A: $tType,X2: A,Y2: A] :
% 3.26/1.64 ( ( ( some @ A @ X2 )
% 3.26/1.64 = ( some @ A @ Y2 ) )
% 3.26/1.64 = ( X2 = Y2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_138_not__Some__eq,axiom,
% 3.26/1.64 ! [A: $tType,X: option @ A] :
% 3.26/1.64 ( ( ! [Y5: A] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( some @ A @ Y5 ) ) )
% 3.26/1.64 = ( X
% 3.26/1.64 = ( none @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_139_not__None__eq,axiom,
% 3.26/1.64 ! [A: $tType,X: option @ A] :
% 3.26/1.64 ( ( X
% 3.26/1.64 != ( none @ A ) )
% 3.26/1.64 = ( ? [Y5: A] :
% 3.26/1.64 ( X
% 3.26/1.64 = ( some @ A @ Y5 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_140_triangle__0,axiom,
% 3.26/1.64 ( ( nat_triangle @ ( zero_zero @ nat ) )
% 3.26/1.64 = ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_141_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv,axiom,
% 3.26/1.64 ! [I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 3.26/1.64 ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 ) )
% 3.26/1.64 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_142_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some,axiom,
% 3.26/1.64 ! [I: $tType,D: $tType,H: $tType,G: $tType,F: $tType,E: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
% 3.26/1.64 ( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
% 3.26/1.64 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) )
% 3.26/1.64 = ( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 )
% 3.26/1.64 = Obj ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_143_option_Odistinct_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,X2: A] :
% 3.26/1.64 ( ( none @ A )
% 3.26/1.64 != ( some @ A @ X2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_144_option_OdiscI,axiom,
% 3.26/1.64 ! [A: $tType,Option: option @ A,X2: A] :
% 3.26/1.64 ( ( Option
% 3.26/1.64 = ( some @ A @ X2 ) )
% 3.26/1.64 => ( Option
% 3.26/1.64 != ( none @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_145_option_Oexhaust,axiom,
% 3.26/1.64 ! [A: $tType,Y: option @ A] :
% 3.26/1.64 ( ( Y
% 3.26/1.64 != ( none @ A ) )
% 3.26/1.64 => ~ ! [X22: A] :
% 3.26/1.64 ( Y
% 3.26/1.64 != ( some @ A @ X22 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_146_option_Oinducts,axiom,
% 3.26/1.64 ! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
% 3.26/1.64 ( ( P @ ( none @ A ) )
% 3.26/1.64 => ( ! [X4: A] : ( P @ ( some @ A @ X4 ) )
% 3.26/1.64 => ( P @ Option ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_147_split__option__ex,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.26/1.64 ? [X5: option @ A] : ( P2 @ X5 ) )
% 3.26/1.64 = ( ^ [P3: ( option @ A ) > $o] :
% 3.26/1.64 ( ( P3 @ ( none @ A ) )
% 3.26/1.64 | ? [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_148_split__option__all,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ^ [P2: ( option @ A ) > $o] :
% 3.26/1.64 ! [X5: option @ A] : ( P2 @ X5 ) )
% 3.26/1.64 = ( ^ [P3: ( option @ A ) > $o] :
% 3.26/1.64 ( ( P3 @ ( none @ A ) )
% 3.26/1.64 & ! [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_149_combine__options__cases,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
% 3.26/1.64 ( ( ( X
% 3.26/1.64 = ( none @ A ) )
% 3.26/1.64 => ( P @ X @ Y ) )
% 3.26/1.64 => ( ( ( Y
% 3.26/1.64 = ( none @ B ) )
% 3.26/1.64 => ( P @ X @ Y ) )
% 3.26/1.64 => ( ! [A5: A,B5: B] :
% 3.26/1.64 ( ( X
% 3.26/1.64 = ( some @ A @ A5 ) )
% 3.26/1.64 => ( ( Y
% 3.26/1.64 = ( some @ B @ B5 ) )
% 3.26/1.64 => ( P @ X @ Y ) ) )
% 3.26/1.64 => ( P @ X @ Y ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_150_option_Osize_I4_J,axiom,
% 3.26/1.64 ! [A: $tType,X2: A] :
% 3.26/1.64 ( ( size_size @ ( option @ A ) @ ( some @ A @ X2 ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_151_document__ptr__casts__commute2,axiom,
% 3.26/1.64 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ A] :
% 3.26/1.64 ( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 ) )
% 3.26/1.64 = ( some @ ( document_ptr @ A ) @ Document_ptr3 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_152_document__ptr__casts__commute,axiom,
% 3.26/1.64 ! [E: $tType,A: $tType,D: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ D ) ) ) @ ( sum_sum @ ( document_ptr @ A ) @ E ) ),Document_ptr3: document_ptr @ A] :
% 3.26/1.64 ( ( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ Ptr2 )
% 3.26/1.64 = ( some @ ( document_ptr @ A ) @ Document_ptr3 ) )
% 3.26/1.64 = ( ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 )
% 3.26/1.64 = Ptr2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_153_length__splice,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_154_get__document__ptr__simp,axiom,
% 3.26/1.64 ! [K: $tType,D: $tType,J: $tType,I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,A: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ),Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
% 3.26/1.64 ( ( ( Ptr2
% 3.26/1.64 = ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
% 3.26/1.64 => ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
% 3.26/1.64 = ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ H @ I @ J @ D @ K @ Obj ) ) )
% 3.26/1.64 & ( ( Ptr2
% 3.26/1.64 != ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
% 3.26/1.64 => ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
% 3.26/1.64 = ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ H2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_155_split__Nil__iff,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( splice @ A @ Xs @ Ys )
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 = ( ( Xs
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 & ( Ys
% 3.26/1.64 = ( nil @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_156_splice__Nil2,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 3.26/1.64 = Xs ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_157_get__document__ptr__simp2,axiom,
% 3.26/1.64 ! [K: $tType,F: $tType,J: $tType,I: $tType,H: $tType,G: $tType,B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document_ptr4: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document3: rObject_ext @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ D ) @ ( sum_sum @ ( character_data_ptr @ E ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ D @ E @ A @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ) @ K ) )] :
% 3.26/1.64 ( ( Document_ptr3 != Document_ptr4 )
% 3.26/1.64 => ( ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ Document_ptr4 @ Document3 @ H2 ) )
% 3.26/1.64 = ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ H2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_158_get__document__ptr__simp1,axiom,
% 3.26/1.64 ! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
% 3.26/1.64 ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ E @ F @ A @ B @ C @ D @ G @ H @ I @ J @ K @ Document_ptr3 @ Document3 @ H2 ) )
% 3.26/1.64 = ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_159_splice_Osimps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,Ys: list @ A] :
% 3.26/1.64 ( ( splice @ A @ ( nil @ A ) @ Ys )
% 3.26/1.64 = Ys ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_160_get__object__ptr__simp1,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,Object_ptr2: object_ptr @ B,Object2: rObject_ext @ A,H2: heap @ B @ A] :
% 3.26/1.64 ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ Object2 @ H2 ) )
% 3.26/1.64 = ( some @ ( rObject_ext @ A ) @ Object2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_161_list_Osize_I4_J,axiom,
% 3.26/1.64 ! [A: $tType,X21: A,X222: list @ A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X222 ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X222 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_162_count__list_Osimps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,Y: A] :
% 3.26/1.64 ( ( count_list @ A @ ( nil @ A ) @ Y )
% 3.26/1.64 = ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_163_list_Oinject,axiom,
% 3.26/1.64 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 3.26/1.64 ( ( ( cons @ A @ X21 @ X222 )
% 3.26/1.64 = ( cons @ A @ Y21 @ Y22 ) )
% 3.26/1.64 = ( ( X21 = Y21 )
% 3.26/1.64 & ( X222 = Y22 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_164_get__object__ptr__simp2,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,Object_ptr2: object_ptr @ A,Object_ptr3: object_ptr @ A,Object2: rObject_ext @ B,H2: heap @ A @ B] :
% 3.26/1.64 ( ( Object_ptr2 != Object_ptr3 )
% 3.26/1.64 => ( ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ ( put_O_b_j_e_c_t @ A @ B @ Object_ptr3 @ Object2 @ H2 ) )
% 3.26/1.64 = ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ H2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_165_splice_Osimps_I2_J,axiom,
% 3.26/1.64 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 3.26/1.64 = ( cons @ A @ X @ ( splice @ A @ Ys @ Xs ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_166_not__Cons__self2,axiom,
% 3.26/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 3.26/1.64 ( ( cons @ A @ X @ Xs )
% 3.26/1.64 != Xs ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_167_transpose_Ocases,axiom,
% 3.26/1.64 ! [A: $tType,X: list @ ( list @ A )] :
% 3.26/1.64 ( ( X
% 3.26/1.64 != ( nil @ ( list @ A ) ) )
% 3.26/1.64 => ( ! [Xss: list @ ( list @ A )] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 3.26/1.64 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_168_list_Odistinct_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,X21: A,X222: list @ A] :
% 3.26/1.64 ( ( nil @ A )
% 3.26/1.64 != ( cons @ A @ X21 @ X222 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_169_list_OdiscI,axiom,
% 3.26/1.64 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 3.26/1.64 ( ( List
% 3.26/1.64 = ( cons @ A @ X21 @ X222 ) )
% 3.26/1.64 => ( List
% 3.26/1.64 != ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_170_list_Oexhaust,axiom,
% 3.26/1.64 ! [A: $tType,Y: list @ A] :
% 3.26/1.64 ( ( Y
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ~ ! [X212: A,X223: list @ A] :
% 3.26/1.64 ( Y
% 3.26/1.64 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_171_list_Oinducts,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 3.26/1.64 ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X12: A,X22: list @ A] :
% 3.26/1.64 ( ( P @ X22 )
% 3.26/1.64 => ( P @ ( cons @ A @ X12 @ X22 ) ) )
% 3.26/1.64 => ( P @ List ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_172_neq__Nil__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 = ( ? [Y5: A,Ys2: list @ A] :
% 3.26/1.64 ( Xs
% 3.26/1.64 = ( cons @ A @ Y5 @ Ys2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_173_list__induct2_H,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 3.26/1.64 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 3.26/1.64 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 3.26/1.64 ( ( P @ Xs2 @ Ys3 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 3.26/1.64 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_174_splice_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.26/1.64 ( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 3.26/1.64 ( ( P @ Ys3 @ Xs2 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_175_induct__list012,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 3.26/1.64 ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [X4: A,Y3: A,Zs: list @ A] :
% 3.26/1.64 ( ( P @ Zs )
% 3.26/1.64 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 3.26/1.64 => ( P @ Xs ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_176_min__list_Ocases,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ord @ A )
% 3.26/1.64 => ! [X: list @ A] :
% 3.26/1.64 ( ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ A @ X4 @ Xs2 ) )
% 3.26/1.64 => ( X
% 3.26/1.64 = ( nil @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_177_min__list_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( ord @ A )
% 3.26/1.64 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.26/1.64 ( ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( ! [X213: A,X224: list @ A] :
% 3.26/1.64 ( ( Xs2
% 3.26/1.64 = ( cons @ A @ X213 @ X224 ) )
% 3.26/1.64 => ( P @ Xs2 ) )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( P @ A0 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_178_shuffles_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.26/1.64 ( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
% 3.26/1.64 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 3.26/1.64 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 3.26/1.64 => ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_179_remdups__adj_Ocases,axiom,
% 3.26/1.64 ! [A: $tType,X: list @ A] :
% 3.26/1.64 ( ( X
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ~ ! [X4: A,Y3: A,Xs2: list @ A] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_180_sorted__wrt_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.26/1.64 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 3.26/1.64 => ( ! [P4: A > A > $o,X4: A,Ys3: list @ A] :
% 3.26/1.64 ( ( P @ P4 @ Ys3 )
% 3.26/1.64 => ( P @ P4 @ ( cons @ A @ X4 @ Ys3 ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_181_remdups__adj_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 3.26/1.64 ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [X4: A,Y3: A,Xs2: list @ A] :
% 3.26/1.64 ( ( ( X4 = Y3 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( ( ( X4 != Y3 )
% 3.26/1.64 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 3.26/1.64 => ( P @ A0 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_182_arg__min__list_Oinduct,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType] :
% 3.26/1.64 ( ( linorder @ B )
% 3.26/1.64 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 3.26/1.64 ( ! [F2: A > B,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [F2: A > B,X4: A,Y3: A,Zs: list @ A] :
% 3.26/1.64 ( ( P @ F2 @ ( cons @ A @ Y3 @ Zs ) )
% 3.26/1.64 => ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 3.26/1.64 => ( ! [A5: A > B] : ( P @ A5 @ ( nil @ A ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_183_successively_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.26/1.64 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 3.26/1.64 => ( ! [P4: A > A > $o,X4: A] : ( P @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [P4: A > A > $o,X4: A,Y3: A,Xs2: list @ A] :
% 3.26/1.64 ( ( P @ P4 @ ( cons @ A @ Y3 @ Xs2 ) )
% 3.26/1.64 => ( P @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_184_list__nonempty__induct,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( ( Xs2
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ( ( P @ Xs2 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 3.26/1.64 => ( P @ Xs ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_185_map__tailrec__rev_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 3.26/1.64 ( ! [F2: A > B,X_12: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_12 )
% 3.26/1.64 => ( ! [F2: A > B,A5: A,As: list @ A,Bs: list @ B] :
% 3.26/1.64 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A5 ) @ Bs ) )
% 3.26/1.64 => ( P @ F2 @ ( cons @ A @ A5 @ As ) @ Bs ) )
% 3.26/1.64 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_186_strict__sorted_Ocases,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( linorder @ A )
% 3.26/1.64 => ! [X: list @ A] :
% 3.26/1.64 ( ( X
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ~ ! [X4: A,Ys3: list @ A] :
% 3.26/1.64 ( X
% 3.26/1.64 != ( cons @ A @ X4 @ Ys3 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_187_strict__sorted_Oinduct,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( linorder @ A )
% 3.26/1.64 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.26/1.64 ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A,Ys3: list @ A] :
% 3.26/1.64 ( ( P @ Ys3 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Ys3 ) ) )
% 3.26/1.64 => ( P @ A0 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_188_length__Suc__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,N: nat] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( suc @ N ) )
% 3.26/1.64 = ( ? [Y5: A,Ys2: list @ A] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 = ( cons @ A @ Y5 @ Ys2 ) )
% 3.26/1.64 & ( ( size_size @ ( list @ A ) @ Ys2 )
% 3.26/1.64 = N ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_189_Suc__length__conv,axiom,
% 3.26/1.64 ! [A: $tType,N: nat,Xs: list @ A] :
% 3.26/1.64 ( ( ( suc @ N )
% 3.26/1.64 = ( size_size @ ( list @ A ) @ Xs ) )
% 3.26/1.64 = ( ? [Y5: A,Ys2: list @ A] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 = ( cons @ A @ Y5 @ Ys2 ) )
% 3.26/1.64 & ( ( size_size @ ( list @ A ) @ Ys2 )
% 3.26/1.64 = N ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_190_list__induct4,axiom,
% 3.26/1.64 ! [C: $tType,A: $tType,B: $tType,D: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,Ws: list @ D,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > ( list @ D ) > $o] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 3.26/1.64 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ C ) @ Zs2 )
% 3.26/1.64 = ( size_size @ ( list @ D ) @ Ws ) )
% 3.26/1.64 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) @ ( nil @ D ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C,W: D,Ws2: list @ D] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ B ) @ Ys3 )
% 3.26/1.64 = ( size_size @ ( list @ C ) @ Zs ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ C ) @ Zs )
% 3.26/1.64 = ( size_size @ ( list @ D ) @ Ws2 ) )
% 3.26/1.64 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) @ ( cons @ D @ W @ Ws2 ) ) ) ) ) )
% 3.26/1.64 => ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_191_list__induct3,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 3.26/1.64 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 3.26/1.64 => ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 3.26/1.64 => ( ( ( size_size @ ( list @ B ) @ Ys3 )
% 3.26/1.64 = ( size_size @ ( list @ C ) @ Zs ) )
% 3.26/1.64 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) ) ) ) )
% 3.26/1.64 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_192_list__induct2,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys ) )
% 3.26/1.64 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 3.26/1.64 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 3.26/1.64 = ( size_size @ ( list @ B ) @ Ys3 ) )
% 3.26/1.64 => ( ( P @ Xs2 @ Ys3 )
% 3.26/1.64 => ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
% 3.26/1.64 => ( P @ Xs @ Ys ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_193_splice_Oelims,axiom,
% 3.26/1.64 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 3.26/1.64 ( ( ( splice @ A @ X @ Xa )
% 3.26/1.64 = Y )
% 3.26/1.64 => ( ( ( X
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 => ( Y != Xa ) )
% 3.26/1.64 => ~ ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( ( X
% 3.26/1.64 = ( cons @ A @ X4 @ Xs2 ) )
% 3.26/1.64 => ( Y
% 3.26/1.64 != ( cons @ A @ X4 @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_194_gen__length__code_I2_J,axiom,
% 3.26/1.64 ! [B: $tType,N: nat,X: B,Xs: list @ B] :
% 3.26/1.64 ( ( gen_length @ B @ N @ ( cons @ B @ X @ Xs ) )
% 3.26/1.64 = ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_195_get__object__ptr__simp,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,Ptr2: object_ptr @ B,Object_ptr2: object_ptr @ B,Obj: rObject_ext @ A,H2: heap @ B @ A] :
% 3.26/1.64 ( ( ( Ptr2 = Object_ptr2 )
% 3.26/1.64 => ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
% 3.26/1.64 = ( some @ ( rObject_ext @ A ) @ Obj ) ) )
% 3.26/1.64 & ( ( Ptr2 != Object_ptr2 )
% 3.26/1.64 => ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
% 3.26/1.64 = ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ H2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_196_length__Cons,axiom,
% 3.26/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X @ Xs ) )
% 3.26/1.64 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_197_map__M_Oinduct,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,Result: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ X6] :
% 3.26/1.64 ( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ F2 @ ( nil @ X6 ) )
% 3.26/1.64 => ( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: X6,Xs2: list @ X6] :
% 3.26/1.64 ( ! [Xa2: Result] : ( P @ F2 @ Xs2 )
% 3.26/1.64 => ( P @ F2 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_198_prog_Osize__neq,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,Result: $tType,X: heap_Error_prog @ Heap @ E @ Result] :
% 3.26/1.64 ( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ X )
% 3.26/1.64 != ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_199_forall__M_Oinduct,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,Result: $tType,Y6: $tType,P: ( Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ Y6 ) > $o,A0: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ Y6] :
% 3.26/1.64 ( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ P4 @ ( nil @ Y6 ) )
% 3.26/1.64 => ( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: Y6,Xs2: list @ Y6] :
% 3.26/1.64 ( ! [Xa2: Result] : ( P @ P4 @ Xs2 )
% 3.26/1.64 => ( P @ P4 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_200_filter__M_Oinduct,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ $o ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ $o ),A1: list @ X6] :
% 3.26/1.64 ( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o )] : ( P @ P4 @ ( nil @ X6 ) )
% 3.26/1.64 => ( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o ),X4: X6,Xs2: list @ X6] :
% 3.26/1.64 ( ! [Xa2: $o] : ( P @ P4 @ Xs2 )
% 3.26/1.64 => ( P @ P4 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_201_fold__M_Oinduct,axiom,
% 3.26/1.64 ! [Result: $tType,E: $tType,Heap: $tType,Y6: $tType,P: ( Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > Result > ( list @ Y6 ) > $o,A0: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: Result,A22: list @ Y6] :
% 3.26/1.64 ( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result] : ( P @ F2 @ D2 @ ( nil @ Y6 ) )
% 3.26/1.64 => ( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result,X4: Y6,Xs2: list @ Y6] :
% 3.26/1.64 ( ! [Xa2: Result] : ( P @ F2 @ Xa2 @ Xs2 )
% 3.26/1.64 => ( P @ F2 @ D2 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
% 3.26/1.64 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_202_n__lists__Nil,axiom,
% 3.26/1.64 ! [A: $tType,N: nat] :
% 3.26/1.64 ( ( ( N
% 3.26/1.64 = ( zero_zero @ nat ) )
% 3.26/1.64 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 3.26/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 3.26/1.64 & ( ( N
% 3.26/1.64 != ( zero_zero @ nat ) )
% 3.26/1.64 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 3.26/1.64 = ( nil @ ( list @ A ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_203_n__lists_Osimps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 3.26/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_204_product__lists_Osimps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 3.26/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_205_subseqs_Osimps_I1_J,axiom,
% 3.26/1.64 ! [A: $tType] :
% 3.26/1.64 ( ( subseqs @ A @ ( nil @ A ) )
% 3.26/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_206_insert__Nil,axiom,
% 3.26/1.64 ! [A: $tType,X: A] :
% 3.26/1.64 ( ( insert @ A @ X @ ( nil @ A ) )
% 3.26/1.64 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_207_nths__singleton,axiom,
% 3.26/1.64 ! [A: $tType,A3: set @ nat,X: A] :
% 3.26/1.64 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A3 )
% 3.26/1.64 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
% 3.26/1.64 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 3.26/1.64 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A3 )
% 3.26/1.64 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
% 3.26/1.64 = ( nil @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_208_nths__nil,axiom,
% 3.26/1.64 ! [A: $tType,A3: set @ nat] :
% 3.26/1.64 ( ( nths @ A @ ( nil @ A ) @ A3 )
% 3.26/1.64 = ( nil @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_209_nths__empty,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( nths @ A @ Xs @ ( bot_bot @ ( set @ nat ) ) )
% 3.26/1.64 = ( nil @ A ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_210_prog_Osize_I2_J,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,Result: $tType,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
% 3.26/1.64 ( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_211_get_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
% 3.26/1.64 ! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
% 3.26/1.64 ( ( get_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Element @ CharacterData @ Node @ Document @ Object )
% 3.26/1.64 = ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),H3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] : ( bind @ ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) @ ( get_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ H3 ) @ ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_212_bind__runit,axiom,
% 3.26/1.64 ! [A: $tType,X: option @ A] :
% 3.26/1.64 ( ( bind @ A @ A @ X @ ( some @ A ) )
% 3.26/1.64 = X ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_213_bind__split__asm,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
% 3.26/1.64 ( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
% 3.26/1.64 = ( ~ ( ( ( M2
% 3.26/1.64 = ( none @ B ) )
% 3.26/1.64 & ~ ( P @ ( none @ A ) ) )
% 3.26/1.64 | ? [X3: B] :
% 3.26/1.64 ( ( M2
% 3.26/1.64 = ( some @ B @ X3 ) )
% 3.26/1.64 & ~ ( P @ ( F3 @ X3 ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_214_bind__split,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
% 3.26/1.64 ( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
% 3.26/1.64 = ( ( ( M2
% 3.26/1.64 = ( none @ B ) )
% 3.26/1.64 => ( P @ ( none @ A ) ) )
% 3.26/1.64 & ! [V3: B] :
% 3.26/1.64 ( ( M2
% 3.26/1.64 = ( some @ B @ V3 ) )
% 3.26/1.64 => ( P @ ( F3 @ V3 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_215_Option_Obind__cong,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B ),G2: A > ( option @ B )] :
% 3.26/1.64 ( ( X = Y )
% 3.26/1.64 => ( ! [A5: A] :
% 3.26/1.64 ( ( Y
% 3.26/1.64 = ( some @ A @ A5 ) )
% 3.26/1.64 => ( ( F3 @ A5 )
% 3.26/1.64 = ( G2 @ A5 ) ) )
% 3.26/1.64 => ( ( bind @ A @ B @ X @ F3 )
% 3.26/1.64 = ( bind @ A @ B @ Y @ G2 ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_216_bind_Obind__lunit,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,X: A,F3: A > ( option @ B )] :
% 3.26/1.64 ( ( bind @ A @ B @ ( some @ A @ X ) @ F3 )
% 3.26/1.64 = ( F3 @ X ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_217_bind__eq__Some__conv,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,F3: option @ B,G2: B > ( option @ A ),X: A] :
% 3.26/1.64 ( ( ( bind @ B @ A @ F3 @ G2 )
% 3.26/1.64 = ( some @ A @ X ) )
% 3.26/1.64 = ( ? [Y5: B] :
% 3.26/1.64 ( ( F3
% 3.26/1.64 = ( some @ B @ Y5 ) )
% 3.26/1.64 & ( ( G2 @ Y5 )
% 3.26/1.64 = ( some @ A @ X ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_218_bind_Obind__lzero,axiom,
% 3.26/1.64 ! [A: $tType,B: $tType,F3: A > ( option @ B )] :
% 3.26/1.64 ( ( bind @ A @ B @ ( none @ A ) @ F3 )
% 3.26/1.64 = ( none @ B ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_219_bind__option__cong__code,axiom,
% 3.26/1.64 ! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B )] :
% 3.26/1.64 ( ( X = Y )
% 3.26/1.64 => ( ( bind @ A @ B @ X @ F3 )
% 3.26/1.64 = ( bind @ A @ B @ Y @ F3 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_220_prog_Osize__gen,axiom,
% 3.26/1.64 ! [Heap: $tType,E: $tType,Result: $tType,Xc: Heap > nat,Xb: E > nat,Xa: Result > nat,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
% 3.26/1.64 ( ( heap_Error_size_prog @ Heap @ E @ Result @ Xc @ Xb @ Xa @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
% 3.26/1.64 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_221_set__encode__empty,axiom,
% 3.26/1.64 ( ( nat_set_encode @ ( bot_bot @ ( set @ nat ) ) )
% 3.26/1.64 = ( zero_zero @ nat ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_222_set__decode__zero,axiom,
% 3.26/1.64 ( ( nat_set_decode @ ( zero_zero @ nat ) )
% 3.26/1.64 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_223_length__append__singleton,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 3.26/1.64 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_224_same__append__eq,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = ( append @ A @ Xs @ Zs2 ) )
% 3.26/1.64 = ( Ys = Zs2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_225_append__same__eq,axiom,
% 3.26/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Ys @ Xs )
% 3.26/1.64 = ( append @ A @ Zs2 @ Xs ) )
% 3.26/1.64 = ( Ys = Zs2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_226_append__assoc,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 3.26/1.64 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 3.26/1.64 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_227_append_Oassoc,axiom,
% 3.26/1.64 ! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
% 3.26/1.64 ( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
% 3.26/1.64 = ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_228_append__Nil2,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( append @ A @ Xs @ ( nil @ A ) )
% 3.26/1.64 = Xs ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_229_append__self__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = Xs )
% 3.26/1.64 = ( Ys
% 3.26/1.64 = ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_230_self__append__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 = ( append @ A @ Xs @ Ys ) )
% 3.26/1.64 = ( Ys
% 3.26/1.64 = ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_231_append__self__conv2,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = Ys )
% 3.26/1.64 = ( Xs
% 3.26/1.64 = ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_232_self__append__conv2,axiom,
% 3.26/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 3.26/1.64 ( ( Ys
% 3.26/1.64 = ( append @ A @ Xs @ Ys ) )
% 3.26/1.64 = ( Xs
% 3.26/1.64 = ( nil @ A ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_233_Nil__is__append__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( nil @ A )
% 3.26/1.64 = ( append @ A @ Xs @ Ys ) )
% 3.26/1.64 = ( ( Xs
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 & ( Ys
% 3.26/1.64 = ( nil @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_234_append__is__Nil__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 = ( ( Xs
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 & ( Ys
% 3.26/1.64 = ( nil @ A ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_235_append_Oright__neutral,axiom,
% 3.26/1.64 ! [A: $tType,A2: list @ A] :
% 3.26/1.64 ( ( append @ A @ A2 @ ( nil @ A ) )
% 3.26/1.64 = A2 ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_236_append__eq__append__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Us: list @ A,Vs: list @ A] :
% 3.26/1.64 ( ( ( ( size_size @ ( list @ A ) @ Xs )
% 3.26/1.64 = ( size_size @ ( list @ A ) @ Ys ) )
% 3.26/1.64 | ( ( size_size @ ( list @ A ) @ Us )
% 3.26/1.64 = ( size_size @ ( list @ A ) @ Vs ) ) )
% 3.26/1.64 => ( ( ( append @ A @ Xs @ Us )
% 3.26/1.64 = ( append @ A @ Ys @ Vs ) )
% 3.26/1.64 = ( ( Xs = Ys )
% 3.26/1.64 & ( Us = Vs ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_237_set__decode__inverse,axiom,
% 3.26/1.64 ! [N: nat] :
% 3.26/1.64 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 3.26/1.64 = N ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_238_append1__eq__conv,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.26/1.64 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 3.26/1.64 = ( ( Xs = Ys )
% 3.26/1.64 & ( X = Y ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_239_length__append,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) )
% 3.26/1.64 = ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_240_append__eq__append__conv2,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = ( append @ A @ Zs2 @ Ts ) )
% 3.26/1.64 = ( ? [Us2: list @ A] :
% 3.26/1.64 ( ( ( Xs
% 3.26/1.64 = ( append @ A @ Zs2 @ Us2 ) )
% 3.26/1.64 & ( ( append @ A @ Us2 @ Ys )
% 3.26/1.64 = Ts ) )
% 3.26/1.64 | ( ( ( append @ A @ Xs @ Us2 )
% 3.26/1.64 = Zs2 )
% 3.26/1.64 & ( Ys
% 3.26/1.64 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_241_append__eq__appendI,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Xs @ Xs1 )
% 3.26/1.64 = Zs2 )
% 3.26/1.64 => ( ( Ys
% 3.26/1.64 = ( append @ A @ Xs1 @ Us ) )
% 3.26/1.64 => ( ( append @ A @ Xs @ Ys )
% 3.26/1.64 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_242_rev__induct,axiom,
% 3.26/1.64 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 3.26/1.64 ( ( P @ ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( ( P @ Xs2 )
% 3.26/1.64 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 3.26/1.64 => ( P @ Xs ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_243_rev__exhaust,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ~ ! [Ys3: list @ A,Y3: A] :
% 3.26/1.64 ( Xs
% 3.26/1.64 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_244_Cons__eq__append__conv,axiom,
% 3.26/1.64 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 3.26/1.64 ( ( ( cons @ A @ X @ Xs )
% 3.26/1.64 = ( append @ A @ Ys @ Zs2 ) )
% 3.26/1.64 = ( ( ( Ys
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 & ( ( cons @ A @ X @ Xs )
% 3.26/1.64 = Zs2 ) )
% 3.26/1.64 | ? [Ys4: list @ A] :
% 3.26/1.64 ( ( ( cons @ A @ X @ Ys4 )
% 3.26/1.64 = Ys )
% 3.26/1.64 & ( Xs
% 3.26/1.64 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_245_append__eq__Cons__conv,axiom,
% 3.26/1.64 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 3.26/1.64 ( ( ( append @ A @ Ys @ Zs2 )
% 3.26/1.64 = ( cons @ A @ X @ Xs ) )
% 3.26/1.64 = ( ( ( Ys
% 3.26/1.64 = ( nil @ A ) )
% 3.26/1.64 & ( Zs2
% 3.26/1.64 = ( cons @ A @ X @ Xs ) ) )
% 3.26/1.64 | ? [Ys4: list @ A] :
% 3.26/1.64 ( ( Ys
% 3.26/1.64 = ( cons @ A @ X @ Ys4 ) )
% 3.26/1.64 & ( ( append @ A @ Ys4 @ Zs2 )
% 3.26/1.64 = Xs ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_246_rev__nonempty__induct,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 3.26/1.64 ( ( Xs
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 3.26/1.64 => ( ! [X4: A,Xs2: list @ A] :
% 3.26/1.64 ( ( Xs2
% 3.26/1.64 != ( nil @ A ) )
% 3.26/1.64 => ( ( P @ Xs2 )
% 3.26/1.64 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 3.26/1.64 => ( P @ Xs ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_247_eq__Nil__appendI,axiom,
% 3.26/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( Xs = Ys )
% 3.26/1.64 => ( Xs
% 3.26/1.64 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_248_append__Nil,axiom,
% 3.26/1.64 ! [A: $tType,Ys: list @ A] :
% 3.26/1.64 ( ( append @ A @ ( nil @ A ) @ Ys )
% 3.26/1.64 = Ys ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_249_append_Oleft__neutral,axiom,
% 3.26/1.64 ! [A: $tType,A2: list @ A] :
% 3.26/1.64 ( ( append @ A @ ( nil @ A ) @ A2 )
% 3.26/1.64 = A2 ) ).
% 3.26/1.64
% 3.26/1.64 thf(fact_250_append__Cons,axiom,
% 3.26/1.64 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 3.26/1.64 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 3.26/1.64 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_fun___Orderings_Oord,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] :
% 3.26/1.64 ( ( ord @ A7 )
% 3.26/1.64 => ( ord @ ( A6 > A7 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_fun___Orderings_Obot,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] :
% 3.26/1.64 ( ( bot @ A7 )
% 3.26/1.64 => ( bot @ ( A6 > A7 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 3.26/1.64 semiri456707255roduct @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 3.26/1.64 canoni770627133id_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 3.26/1.64 ordere779506340up_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 3.26/1.64 cancel1352612707id_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 3.26/1.64 cancel_semigroup_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 3.26/1.64 ab_semigroup_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 3.26/1.64 comm_monoid_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 3.26/1.64 semigroup_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.26/1.64 linorder @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 3.26/1.64 monoid_add @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 3.26/1.64 ord @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Orderings_Obot_2,axiom,
% 3.26/1.64 bot @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 3.26/1.64 zero @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 3.26/1.64 size @ nat ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 3.26/1.64 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Set_Oset___Orderings_Obot_4,axiom,
% 3.26/1.64 ! [A6: $tType] : ( bot @ ( set @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 3.26/1.64 linorder @ $o ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 3.26/1.64 ord @ $o ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_HOL_Obool___Orderings_Obot_7,axiom,
% 3.26/1.64 bot @ $o ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_FSet_Ofset___Orderings_Oord_8,axiom,
% 3.26/1.64 ! [A6: $tType] : ( ord @ ( fset @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_FSet_Ofset___Orderings_Obot_9,axiom,
% 3.26/1.64 ! [A6: $tType] : ( bot @ ( fset @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_FSet_Ofset___Nat_Osize_10,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( fset @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_List_Olist___Nat_Osize_11,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( list @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_String_Ochar___Nat_Osize_12,axiom,
% 3.26/1.64 size @ char ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Sum__Type_Osum___Orderings_Olinorder_13,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] :
% 3.26/1.64 ( ( ( linorder @ A6 )
% 3.26/1.64 & ( linorder @ A7 ) )
% 3.26/1.64 => ( linorder @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Sum__Type_Osum___Orderings_Oord_14,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] :
% 3.26/1.64 ( ( ( linorder @ A6 )
% 3.26/1.64 & ( linorder @ A7 ) )
% 3.26/1.64 => ( ord @ ( sum_sum @ A6 @ A7 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Sum__Type_Osum___Nat_Osize_15,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Option_Ooption___Nat_Osize_16,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( option @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ObjectClass_Oheap___Nat_Osize_17,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType] : ( size @ ( heap @ A6 @ A7 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_18,axiom,
% 3.26/1.64 linorder @ product_unit ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Product__Type_Ounit___Orderings_Oord_19,axiom,
% 3.26/1.64 ord @ product_unit ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Product__Type_Ounit___Orderings_Obot_20,axiom,
% 3.26/1.64 bot @ product_unit ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_NodePointer_Onode__ptr___Orderings_Olinorder_21,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( node_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_NodePointer_Onode__ptr___Orderings_Oord_22,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( node_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_NodePointer_Onode__ptr___Nat_Osize_23,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( node_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_Heap__Error__Monad_Oprog___Nat_Osize_24,axiom,
% 3.26/1.64 ! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( heap_Error_prog @ A6 @ A7 @ A8 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Olinorder_25,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( object_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Oord_26,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( object_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ObjectPointer_Oobject__ptr___Nat_Osize_27,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( object_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Olinorder_28,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( element_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ElementPointer_Oelement__ptr___Orderings_Oord_29,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( element_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ElementPointer_Oelement__ptr___Nat_Osize_30,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( element_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Olinorder_31,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( document_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Oord_32,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( document_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_DocumentPointer_Odocument__ptr___Nat_Osize_33,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( document_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Olinorder_34,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( shadow_root_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Oord_35,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( shadow_root_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Nat_Osize_36,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( shadow_root_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Olinorder_37,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( linorder @ ( character_data_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Oord_38,axiom,
% 3.26/1.64 ! [A6: $tType] :
% 3.26/1.64 ( ( linorder @ A6 )
% 3.26/1.64 => ( ord @ ( character_data_ptr @ A6 ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Nat_Osize_39,axiom,
% 3.26/1.64 ! [A6: $tType] : ( size @ ( character_data_ptr @ A6 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(conj_0,hypothesis,
% 3.26/1.64 ( ( document_ptrs @ a @ b @ c @ d @ e @ f @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ h2 )
% 3.26/1.64 = ( bot_bot @ ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) ) ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(conj_1,hypothesis,
% 3.26/1.64 ( h3
% 3.26/1.64 = ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ a @ b @ c @ f @ ( document_Ref @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ ( suc @ ( zero_zero @ nat ) ) ) ) @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) @ h2 ) ) ).
% 3.26/1.64
% 3.26/1.64 thf(conj_2,hypothesis,
% 3.26/1.64 type_wf @ a @ b @ c @ d @ e @ f @ g @ h @ i @ j @ k @ l @ h2 ).
% 3.26/1.64
% 3.26/1.64 thf(conj_3,conjecture,
% 3.26/1.64 is_document_kind @ c @ a @ b @ d @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) ).
% 3.26/1.64 ------------------------
% 3.26/1.67 % (16529)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/183Mi)
% 3.26/1.67 % (16531)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/27Mi)
% 3.26/1.67 % (16533)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/2Mi)
% 3.26/1.67 % (16533)Instruction limit reached!
% 3.26/1.67 % (16533)------------------------------
% 3.26/1.67 % (16533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.67 % (16533)Termination reason: Unknown
% 3.26/1.67 % (16533)Termination phase: shuffling
% 3.26/1.67
% 3.26/1.67 % (16533)Memory used [KB]: 1407
% 3.26/1.67 % (16533)Time elapsed: 0.002 s
% 3.26/1.67 % (16533)Instructions burned: 3 (million)
% 3.26/1.67 % (16533)------------------------------
% 3.26/1.67 % (16533)------------------------------
% 3.26/1.67 % (16534)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/275Mi)
% 3.26/1.67 % (16535)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/18Mi)
% 3.26/1.67 % (16530)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/4Mi)
% 3.26/1.67 % (16530)Instruction limit reached!
% 3.26/1.67 % (16530)------------------------------
% 3.26/1.67 % (16530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.67 % (16530)Termination reason: Unknown
% 3.26/1.67 % (16530)Termination phase: shuffling
% 3.26/1.67
% 3.26/1.67 % (16530)Memory used [KB]: 1535
% 3.26/1.67 % (16530)Time elapsed: 0.003 s
% 3.26/1.67 % (16530)Instructions burned: 4 (million)
% 3.26/1.67 % (16530)------------------------------
% 3.26/1.67 % (16530)------------------------------
% 3.26/1.67 % (16532)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/2Mi)
% 3.26/1.67 % (16532)Instruction limit reached!
% 3.26/1.67 % (16532)------------------------------
% 3.26/1.67 % (16532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.67 % (16532)Termination reason: Unknown
% 3.26/1.67 % (16532)Termination phase: shuffling
% 3.26/1.67
% 3.26/1.67 % (16532)Memory used [KB]: 1407
% 3.26/1.67 % (16532)Time elapsed: 0.002 s
% 3.26/1.67 % (16532)Instructions burned: 2 (million)
% 3.26/1.67 % (16532)------------------------------
% 3.26/1.67 % (16532)------------------------------
% 3.26/1.68 % (16531)Instruction limit reached!
% 3.26/1.68 % (16531)------------------------------
% 3.26/1.68 % (16531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.68 % (16531)Termination reason: Unknown
% 3.26/1.68 % (16531)Termination phase: Property scanning
% 3.26/1.68
% 3.26/1.68 % (16531)Memory used [KB]: 1918
% 3.26/1.68 % (16531)Time elapsed: 0.011 s
% 3.26/1.68 % (16531)Instructions burned: 29 (million)
% 3.26/1.68 % (16531)------------------------------
% 3.26/1.68 % (16531)------------------------------
% 3.26/1.68 % (16536)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/3Mi)
% 3.26/1.68 % (16535)Instruction limit reached!
% 3.26/1.68 % (16535)------------------------------
% 3.26/1.68 % (16535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.68 % (16535)Termination reason: Unknown
% 3.26/1.68 % (16535)Termination phase: Property scanning
% 3.26/1.68
% 3.26/1.68 % (16535)Memory used [KB]: 1791
% 3.26/1.68 % (16535)Time elapsed: 0.008 s
% 3.26/1.68 % (16535)Instructions burned: 21 (million)
% 3.26/1.68 % (16535)------------------------------
% 3.26/1.68 % (16535)------------------------------
% 3.26/1.68 % (16536)Instruction limit reached!
% 3.26/1.68 % (16536)------------------------------
% 3.26/1.68 % (16536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.68 % (16536)Termination reason: Unknown
% 3.26/1.68 % (16536)Termination phase: shuffling
% 3.26/1.68
% 3.26/1.68 % (16536)Memory used [KB]: 1535
% 3.26/1.68 % (16536)Time elapsed: 0.002 s
% 3.26/1.68 % (16536)Instructions burned: 3 (million)
% 3.26/1.68 % (16536)------------------------------
% 3.26/1.68 % (16536)------------------------------
% 3.26/1.68 % (16540)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/37Mi)
% 3.26/1.68 % (16542)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/15Mi)
% 3.26/1.69 % (16544)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/3Mi)
% 3.26/1.69 % (16544)Instruction limit reached!
% 3.26/1.69 % (16544)------------------------------
% 3.26/1.69 % (16544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.69 % (16544)Termination reason: Unknown
% 3.26/1.69 % (16544)Termination phase: shuffling
% 3.26/1.69
% 3.26/1.69 % (16544)Memory used [KB]: 1407
% 3.26/1.69 % (16544)Time elapsed: 0.002 s
% 3.26/1.69 % (16544)Instructions burned: 3 (million)
% 3.26/1.69 % (16544)------------------------------
% 3.26/1.69 % (16544)------------------------------
% 3.26/1.69 % (16545)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/1041Mi)
% 3.26/1.69 % (16546)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/7Mi)
% 3.26/1.69 % (16542)Instruction limit reached!
% 3.26/1.69 % (16542)------------------------------
% 3.26/1.69 % (16542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.69 % (16542)Termination reason: Unknown
% 3.26/1.69 % (16542)Termination phase: Property scanning
% 3.26/1.69
% 3.26/1.69 % (16542)Memory used [KB]: 1791
% 3.26/1.69 % (16542)Time elapsed: 0.007 s
% 3.26/1.69 % (16542)Instructions burned: 17 (million)
% 3.26/1.69 % (16542)------------------------------
% 3.26/1.69 % (16542)------------------------------
% 3.26/1.69 % (16546)Instruction limit reached!
% 3.26/1.69 % (16546)------------------------------
% 3.26/1.69 % (16546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.69 % (16546)Termination reason: Unknown
% 3.26/1.69 % (16546)Termination phase: shuffling
% 3.26/1.69
% 3.26/1.69 % (16546)Memory used [KB]: 1663
% 3.26/1.69 % (16546)Time elapsed: 0.004 s
% 3.26/1.69 % (16546)Instructions burned: 9 (million)
% 3.26/1.69 % (16546)------------------------------
% 3.26/1.69 % (16546)------------------------------
% 3.26/1.69 % (16540)Instruction limit reached!
% 3.26/1.69 % (16540)------------------------------
% 3.26/1.69 % (16540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.69 % (16540)Termination reason: Unknown
% 3.26/1.69 % (16540)Termination phase: shuffling
% 3.26/1.69 % (16534)Refutation not found, incomplete strategy
% 3.26/1.69 % (16534)------------------------------
% 3.26/1.69 % (16534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.26/1.69
% 3.26/1.69 % (16540)Memory used [KB]: 2302
% 3.26/1.69 % (16540)Time elapsed: 0.012 s
% 3.26/1.69 % (16540)Instructions burned: 40 (million)
% 3.26/1.69 % (16540)------------------------------
% 3.26/1.69 % (16540)------------------------------
% 3.26/1.69 % (16534)Termination reason: Refutation not found, incomplete strategy
% 3.26/1.69
% 3.26/1.69
% 3.26/1.69 % (16534)Memory used [KB]: 6908
% 3.26/1.69 % (16534)Time elapsed: 0.026 s
% 3.26/1.69 % (16534)Instructions burned: 73 (million)
% 3.26/1.69 % (16534)------------------------------
% 3.26/1.69 % (16534)------------------------------
% 3.26/1.70 % (16547)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/16Mi)
% 3.32/1.70 % (16548)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/3Mi)
% 3.32/1.70 % (16549)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/3Mi)
% 3.32/1.70 % (16548)Instruction limit reached!
% 3.32/1.70 % (16548)------------------------------
% 3.32/1.70 % (16548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.70 % (16548)Termination reason: Unknown
% 3.32/1.70 % (16548)Termination phase: shuffling
% 3.32/1.70
% 3.32/1.70 % (16548)Memory used [KB]: 1407
% 3.32/1.70 % (16548)Time elapsed: 0.002 s
% 3.32/1.70 % (16548)Instructions burned: 3 (million)
% 3.32/1.70 % (16548)------------------------------
% 3.32/1.70 % (16548)------------------------------
% 3.32/1.70 % (16549)Instruction limit reached!
% 3.32/1.70 % (16549)------------------------------
% 3.32/1.70 % (16549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.70 % (16549)Termination reason: Unknown
% 3.32/1.70 % (16549)Termination phase: shuffling
% 3.32/1.70
% 3.32/1.70 % (16549)Memory used [KB]: 1535
% 3.32/1.70 % (16549)Time elapsed: 0.002 s
% 3.32/1.70 % (16549)Instructions burned: 4 (million)
% 3.32/1.70 % (16549)------------------------------
% 3.32/1.70 % (16549)------------------------------
% 3.32/1.70 % (16547)Instruction limit reached!
% 3.32/1.70 % (16547)------------------------------
% 3.32/1.70 % (16547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.70 % (16547)Termination reason: Unknown
% 3.32/1.70 % (16547)Termination phase: shuffling
% 3.32/1.70
% 3.32/1.70 % (16547)Memory used [KB]: 1791
% 3.32/1.70 % (16547)Time elapsed: 0.006 s
% 3.32/1.70 % (16547)Instructions burned: 16 (million)
% 3.32/1.70 % (16547)------------------------------
% 3.32/1.70 % (16547)------------------------------
% 3.32/1.70 % (16550)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/7Mi)
% 3.32/1.70 % (16551)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/3Mi)
% 3.32/1.70 % (16551)Instruction limit reached!
% 3.32/1.70 % (16551)------------------------------
% 3.32/1.70 % (16551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.70 % (16551)Termination reason: Unknown
% 3.32/1.70 % (16551)Termination phase: shuffling
% 3.32/1.70
% 3.32/1.70 % (16551)Memory used [KB]: 1535
% 3.32/1.70 % (16551)Time elapsed: 0.002 s
% 3.32/1.70 % (16551)Instructions burned: 4 (million)
% 3.32/1.70 % (16551)------------------------------
% 3.32/1.70 % (16551)------------------------------
% 3.32/1.70 % (16550)Instruction limit reached!
% 3.32/1.70 % (16550)------------------------------
% 3.32/1.70 % (16550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.70 % (16550)Termination reason: Unknown
% 3.32/1.70 % (16550)Termination phase: shuffling
% 3.32/1.70
% 3.32/1.70 % (16550)Memory used [KB]: 1535
% 3.32/1.70 % (16550)Time elapsed: 0.003 s
% 3.32/1.70 % (16550)Instructions burned: 7 (million)
% 3.32/1.70 % (16550)------------------------------
% 3.32/1.70 % (16550)------------------------------
% 3.32/1.71 % (16552)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/4Mi)
% 3.32/1.71 % (16553)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/18Mi)
% 3.32/1.71 % (16552)Instruction limit reached!
% 3.32/1.71 % (16552)------------------------------
% 3.32/1.71 % (16552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.71 % (16552)Termination reason: Unknown
% 3.32/1.71 % (16552)Termination phase: shuffling
% 3.32/1.71
% 3.32/1.71 % (16552)Memory used [KB]: 1535
% 3.32/1.71 % (16554)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/710Mi)
% 3.32/1.71 % (16552)Time elapsed: 0.002 s
% 3.32/1.71 % (16552)Instructions burned: 4 (million)
% 3.32/1.71 % (16552)------------------------------
% 3.32/1.71 % (16552)------------------------------
% 3.32/1.71 % (16555)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/6Mi)
% 3.32/1.71 % (16556)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/902Mi)
% 3.32/1.71 % (16555)Instruction limit reached!
% 3.32/1.71 % (16555)------------------------------
% 3.32/1.71 % (16555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.71 % (16555)Termination reason: Unknown
% 3.32/1.71 % (16555)Termination phase: shuffling
% 3.32/1.71
% 3.32/1.71 % (16555)Memory used [KB]: 1535
% 3.32/1.71 % (16555)Time elapsed: 0.003 s
% 3.32/1.71 % (16555)Instructions burned: 7 (million)
% 3.32/1.71 % (16555)------------------------------
% 3.32/1.71 % (16555)------------------------------
% 3.32/1.72 % (16553)Instruction limit reached!
% 3.32/1.72 % (16553)------------------------------
% 3.32/1.72 % (16553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.72 % (16553)Termination reason: Unknown
% 3.32/1.72 % (16553)Termination phase: Property scanning
% 3.32/1.72
% 3.32/1.72 % (16553)Memory used [KB]: 1918
% 3.32/1.72 % (16553)Time elapsed: 0.007 s
% 3.32/1.72 % (16553)Instructions burned: 19 (million)
% 3.32/1.72 % (16553)------------------------------
% 3.32/1.72 % (16553)------------------------------
% 3.32/1.72 % (16557)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/21Mi)
% 3.32/1.72 % (16529)Instruction limit reached!
% 3.32/1.72 % (16529)------------------------------
% 3.32/1.72 % (16529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.72 % (16529)Termination reason: Unknown
% 3.32/1.72 % (16529)Termination phase: Saturation
% 3.32/1.72
% 3.32/1.72 % (16529)Memory used [KB]: 7547
% 3.32/1.72 % (16529)Time elapsed: 0.055 s
% 3.32/1.72 % (16529)Instructions burned: 183 (million)
% 3.32/1.72 % (16529)------------------------------
% 3.32/1.72 % (16529)------------------------------
% 3.32/1.72 % (16558)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/5Mi)
% 3.32/1.72 % (16559)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/6Mi)
% 3.32/1.73 % (16558)Instruction limit reached!
% 3.32/1.73 % (16558)------------------------------
% 3.32/1.73 % (16558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.73 % (16558)Termination reason: Unknown
% 3.32/1.73 % (16558)Termination phase: shuffling
% 3.32/1.73
% 3.32/1.73 % (16558)Memory used [KB]: 1663
% 3.32/1.73 % (16558)Time elapsed: 0.003 s
% 3.32/1.73 % (16558)Instructions burned: 7 (million)
% 3.32/1.73 % (16558)------------------------------
% 3.32/1.73 % (16558)------------------------------
% 3.32/1.73 % (16557)Instruction limit reached!
% 3.32/1.73 % (16557)------------------------------
% 3.32/1.73 % (16557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.73 % (16557)Termination reason: Unknown
% 3.32/1.73 % (16557)Termination phase: shuffling
% 3.32/1.73
% 3.32/1.73 % (16557)Memory used [KB]: 1918
% 3.32/1.73 % (16557)Time elapsed: 0.008 s
% 3.32/1.73 % (16557)Instructions burned: 22 (million)
% 3.32/1.73 % (16557)------------------------------
% 3.32/1.73 % (16557)------------------------------
% 3.32/1.73 % (16559)Instruction limit reached!
% 3.32/1.73 % (16559)------------------------------
% 3.32/1.73 % (16559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.73 % (16559)Termination reason: Unknown
% 3.32/1.73 % (16559)Termination phase: shuffling
% 3.32/1.73
% 3.32/1.73 % (16559)Memory used [KB]: 1663
% 3.32/1.73 % (16559)Time elapsed: 0.003 s
% 3.32/1.73 % (16559)Instructions burned: 7 (million)
% 3.32/1.73 % (16559)------------------------------
% 3.32/1.73 % (16559)------------------------------
% 3.32/1.73 % (16560)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/377Mi)
% 3.32/1.74 % (16562)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/779Mi)
% 3.32/1.74 % (16563)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/19Mi)
% 3.32/1.74 % (16554)First to succeed.
% 3.32/1.74 % (16564)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16337 for (2999ds/879Mi)
% 3.32/1.74 % (16554)Refutation found. Thanks to Tanya!
% 3.32/1.74 % SZS status Theorem for DTF2THF_16337
% 3.32/1.74 % SZS output start Proof for DTF2THF_16337
% 3.32/1.74 thf(type_def_5, type, product_unit: $tType).
% 3.32/1.74 thf(type_def_6, type, char: $tType).
% 3.32/1.74 thf(type_def_7, type, list: ($tType) > $tType).
% 3.32/1.74 thf(type_def_8, type, element_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_9, type, option: ($tType) > $tType).
% 3.32/1.74 thf(type_def_10, type, character_data_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_11, type, sum_sum: ($tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_12, type, node_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_13, type, rDocument_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_15, type, rObject_ext: ($tType) > $tType).
% 3.32/1.74 thf(type_def_16, type, rElement_ext: ($tType * $tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_17, type, rCharacterData_ext: ($tType) > $tType).
% 3.32/1.74 thf(type_def_18, type, rNode_ext: ($tType) > $tType).
% 3.32/1.74 thf(type_def_19, type, shadow_root_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_20, type, document_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_21, type, heap: ($tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_22, type, fset: ($tType) > $tType).
% 3.32/1.74 thf(type_def_23, type, object_ptr: ($tType) > $tType).
% 3.32/1.74 thf(type_def_24, type, nat: $tType).
% 3.32/1.74 thf(type_def_25, type, product_prod: ($tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_26, type, heap_Error_prog: ($tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_27, type, set: ($tType) > $tType).
% 3.32/1.74 thf(type_def_28, type, rShadowRoot_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(type_def_29, type, a: $tType).
% 3.32/1.74 thf(type_def_30, type, b: $tType).
% 3.32/1.74 thf(type_def_31, type, c: $tType).
% 3.32/1.74 thf(type_def_32, type, d: $tType).
% 3.32/1.74 thf(type_def_33, type, e: $tType).
% 3.32/1.74 thf(type_def_34, type, f: $tType).
% 3.32/1.74 thf(type_def_35, type, g: $tType).
% 3.32/1.74 thf(type_def_36, type, h: $tType).
% 3.32/1.74 thf(type_def_37, type, i: $tType).
% 3.32/1.74 thf(type_def_38, type, j: $tType).
% 3.32/1.74 thf(type_def_39, type, k: $tType).
% 3.32/1.74 thf(type_def_40, type, l: $tType).
% 3.32/1.74 thf(func_def_0, type, rCharacterData_ext: ($tType) > $tType).
% 3.32/1.74 thf(func_def_1, type, rShadowRoot_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_2, type, character_data_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_3, type, rDocument_ext: ($tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_4, type, rElement_ext: ($tType * $tType * $tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_5, type, shadow_root_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_6, type, rObject_ext: ($tType) > $tType).
% 3.32/1.74 thf(func_def_7, type, document_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_8, type, rNode_ext: ($tType) > $tType).
% 3.32/1.74 thf(func_def_9, type, element_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_10, type, object_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_11, type, heap_Error_prog: ($tType * $tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_12, type, node_ptr: ($tType) > $tType).
% 3.32/1.74 thf(func_def_13, type, product_unit: $tType).
% 3.32/1.74 thf(func_def_14, type, product_prod: ($tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_15, type, heap: ($tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_16, type, sum_sum: ($tType * $tType) > $tType).
% 3.32/1.74 thf(func_def_17, type, option: ($tType) > $tType).
% 3.32/1.74 thf(func_def_18, type, char: $tType).
% 3.32/1.74 thf(func_def_19, type, list: ($tType) > $tType).
% 3.32/1.74 thf(func_def_20, type, fset: ($tType) > $tType).
% 3.32/1.74 thf(func_def_21, type, set: ($tType) > $tType).
% 3.32/1.74 thf(func_def_22, type, nat: $tType).
% 3.32/1.74 thf(func_def_23, type, l: $tType).
% 3.32/1.74 thf(func_def_24, type, k: $tType).
% 3.32/1.74 thf(func_def_25, type, j: $tType).
% 3.32/1.74 thf(func_def_26, type, i: $tType).
% 3.32/1.74 thf(func_def_27, type, h: $tType).
% 3.32/1.74 thf(func_def_28, type, g: $tType).
% 3.32/1.74 thf(func_def_29, type, f: $tType).
% 3.32/1.74 thf(func_def_30, type, e: $tType).
% 3.32/1.74 thf(func_def_31, type, d: $tType).
% 3.32/1.74 thf(func_def_32, type, c: $tType).
% 3.32/1.74 thf(func_def_33, type, b: $tType).
% 3.32/1.74 thf(func_def_34, type, a: $tType).
% 3.32/1.74 thf(func_def_35, type, type: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_36, type, size: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_37, type, zero: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_38, type, bot: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_39, type, ord: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_40, type, group_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_41, type, monoid_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_42, type, linorder: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_43, type, semigroup_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_44, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_45, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_46, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_47, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_48, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_49, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_50, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_51, type, semiri456707255roduct: !>[X0: $tType]:($o)).
% 3.32/1.74 thf(func_def_52, type, rDocument_ext2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_unit > list @ char > option @ element_ptr @ X0 > list @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2 > X3 > rDocument_ext @ X2 @ X0 @ X1 @ X3)).
% 3.32/1.74 thf(func_def_53, type, disconnected_nodes: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > list @ node_ptr @ sum_sum @ element_ptr @ X1 @ sum_sum @ character_data_ptr @ X2 @ X0)).
% 3.32/1.74 thf(func_def_54, type, discon1635973971update: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2 > list @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2) > rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3)).
% 3.32/1.74 thf(func_def_55, type, doctype: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > list @ char)).
% 3.32/1.74 thf(func_def_56, type, doctype_update: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((list @ char > list @ char) > rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3)).
% 3.32/1.74 thf(func_def_57, type, document_element: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > option @ element_ptr @ X1)).
% 3.32/1.74 thf(func_def_58, type, docume446011358update: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((option @ element_ptr @ X0 > option @ element_ptr @ X0) > rObject_ext @ rDocument_ext @ X1 @ X0 @ X2 @ X3 > rObject_ext @ rDocument_ext @ X1 @ X0 @ X2 @ X3)).
% 3.32/1.74 thf(func_def_59, type, more: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > X3)).
% 3.32/1.74 thf(func_def_60, type, more_update: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X0) > rObject_ext @ rDocument_ext @ X1 @ X2 @ X3 @ X0 > rObject_ext @ rDocument_ext @ X1 @ X2 @ X3 @ X0)).
% 3.32/1.74 thf(func_def_61, type, nothing: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > product_unit)).
% 3.32/1.74 thf(func_def_62, type, nothing_update: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_unit > product_unit) > rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3 > rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ X3)).
% 3.32/1.74 thf(func_def_63, type, cast_D42511940_e_c_t: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType]:(rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ option @ X3 > rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X0 @ X1 @ X2 @ X4 @ option @ X5 @ sum_sum @ rCharacterData_ext @ option @ X6 @ X7 @ sum_sum @ rDocument_ext @ X0 @ X1 @ X2 @ option @ X3 @ X8)).
% 3.32/1.74 thf(func_def_64, type, cast_O1159777348_e_n_t: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType]:(rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X0 @ X1 @ X2 @ X3 @ option @ X4 @ sum_sum @ rCharacterData_ext @ option @ X5 @ X6 @ sum_sum @ rDocument_ext @ X0 @ X1 @ X2 @ option @ X7 @ X8 > option @ rObject_ext @ rDocument_ext @ X0 @ X1 @ X2 @ option @ X7)).
% 3.32/1.74 thf(func_def_65, type, document_ptrs: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType, X9: $tType, X10: $tType]:(heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2 @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ X3 @ X4 @ X5 @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X2 @ X0 @ X1 @ X3 @ option @ X6 @ sum_sum @ rCharacterData_ext @ option @ X7 @ X8 @ sum_sum @ rDocument_ext @ X2 @ X0 @ X1 @ option @ X9 @ X10 > fset @ document_ptr @ sum_sum @ shadow_root_ptr @ X3 @ X4)).
% 3.32/1.74 thf(func_def_66, type, get_D_o_c_u_m_e_n_t: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType, X9: $tType, X10: $tType]:(document_ptr @ sum_sum @ shadow_root_ptr @ X0 @ X1 > heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X2 @ sum_sum @ character_data_ptr @ X3 @ X4 @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ X0 @ X1 @ X5 @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X4 @ X2 @ X3 @ X0 @ option @ X6 @ sum_sum @ rCharacterData_ext @ option @ X7 @ X8 @ sum_sum @ rDocument_ext @ X4 @ X2 @ X3 @ option @ X9 @ X10 > option @ rObject_ext @ rDocument_ext @ X4 @ X2 @ X3 @ option @ X9)).
% 3.32/1.74 thf(func_def_67, type, is_document_kind: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType]:(rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X0 @ X1 @ X2 @ X3 @ option @ X4 @ sum_sum @ rCharacterData_ext @ option @ X5 @ X6 @ sum_sum @ rDocument_ext @ X0 @ X1 @ X2 @ option @ X7 @ X8 > $o)).
% 3.32/1.74 thf(func_def_68, type, put_D_o_c_u_m_e_n_t: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType, X9: $tType, X10: $tType]:(document_ptr @ sum_sum @ shadow_root_ptr @ X0 @ X1 > rObject_ext @ rDocument_ext @ X2 @ X3 @ X4 @ option @ X5 > heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X3 @ sum_sum @ character_data_ptr @ X4 @ X2 @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ X0 @ X1 @ X6 @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X2 @ X3 @ X4 @ X0 @ option @ X7 @ sum_sum @ rCharacterData_ext @ option @ X8 @ X9 @ sum_sum @ rDocument_ext @ X2 @ X3 @ X4 @ option @ X5 @ X10 > heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X3 @ sum_sum @ character_data_ptr @ X4 @ X2 @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ X0 @ X1 @ X6 @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X2 @ X3 @ X4 @ X0 @ option @ X7 @ sum_sum @ rCharacterData_ext @ option @ X8 @ X9 @ sum_sum @ rDocument_ext @ X2 @ X3 @ X4 @ option @ X5 @ X10)).
% 3.32/1.74 thf(func_def_69, type, cast_d1427782271_p_t_r: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(document_ptr @ X0 > object_ptr @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X1 @ sum_sum @ character_data_ptr @ X2 @ X3 @ sum_sum @ document_ptr @ X0 @ X4)).
% 3.32/1.74 thf(func_def_70, type, cast_o823910367_p_t_r: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(object_ptr @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2 @ sum_sum @ document_ptr @ X3 @ X4 > option @ document_ptr @ X3)).
% 3.32/1.74 thf(func_def_71, type, document_Ext: !>[X0: $tType]:(X0 > document_ptr @ X0)).
% 3.32/1.74 thf(func_def_72, type, document_Ref: !>[X0: $tType]:(nat > document_ptr @ X0)).
% 3.32/1.74 thf(func_def_73, type, docume1907984069nt_ptr: !>[X0: $tType]:((X0 > nat) > document_ptr @ X0 > nat)).
% 3.32/1.74 thf(func_def_74, type, is_doc697300620_p_t_r: !>[X0: $tType]:(document_ptr @ X0 > $o)).
% 3.32/1.74 thf(func_def_75, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.32/1.74 thf(func_def_76, type, zero_zero: !>[X0: $tType]:(X0)).
% 3.32/1.74 thf(func_def_77, type, heap_Error_Prog: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > sum_sum @ X1 @ product_prod @ X2 @ X0) > heap_Error_prog @ X0 @ X1 @ X2)).
% 3.32/1.74 thf(func_def_78, type, heap_Error_size_prog: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > nat) > (X1 > nat) > (X2 > nat) > heap_Error_prog @ X0 @ X1 @ X2 > nat)).
% 3.32/1.74 thf(func_def_79, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 3.32/1.74 thf(func_def_80, type, count_list: !>[X0: $tType]:(list @ X0 > X0 > nat)).
% 3.32/1.74 thf(func_def_81, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 3.32/1.74 thf(func_def_82, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 3.32/1.74 thf(func_def_83, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 3.32/1.74 thf(func_def_84, type, nil: !>[X0: $tType]:(list @ X0)).
% 3.32/1.74 thf(func_def_85, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 3.32/1.74 thf(func_def_86, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 3.32/1.74 thf(func_def_87, type, nths: !>[X0: $tType]:(list @ X0 > set @ nat > list @ X0)).
% 3.32/1.74 thf(func_def_88, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 3.32/1.74 thf(func_def_89, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 3.32/1.74 thf(func_def_90, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 3.32/1.74 thf(func_def_91, type, suc: nat > nat).
% 3.32/1.74 thf(func_def_92, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 3.32/1.74 thf(func_def_93, type, nat_set_decode: nat > set @ nat).
% 3.32/1.74 thf(func_def_94, type, nat_set_encode: set @ nat > nat).
% 3.32/1.74 thf(func_def_95, type, nat_triangle: nat > nat).
% 3.32/1.74 thf(func_def_96, type, rObject_ext2: !>[X0: $tType]:(product_unit > X0 > rObject_ext @ X0)).
% 3.32/1.74 thf(func_def_97, type, extend: !>[X0: $tType]:(rObject_ext @ product_unit > X0 > rObject_ext @ X0)).
% 3.32/1.74 thf(func_def_98, type, more2: !>[X0: $tType]:(rObject_ext @ X0 > X0)).
% 3.32/1.74 thf(func_def_99, type, nothing2: !>[X0: $tType]:(rObject_ext @ X0 > product_unit)).
% 3.32/1.74 thf(func_def_100, type, get_O_b_j_e_c_t: !>[X0: $tType, X1: $tType]:(object_ptr @ X0 > heap @ X0 @ X1 > option @ rObject_ext @ X1)).
% 3.32/1.74 thf(func_def_101, type, put_O_b_j_e_c_t: !>[X0: $tType, X1: $tType]:(object_ptr @ X0 > rObject_ext @ X1 > heap @ X0 @ X1 > heap @ X0 @ X1)).
% 3.32/1.74 thf(func_def_102, type, bind: !>[X0: $tType, X1: $tType]:(option @ X0 > (X0 > option @ X1) > option @ X1)).
% 3.32/1.74 thf(func_def_103, type, none: !>[X0: $tType]:(option @ X0)).
% 3.32/1.74 thf(func_def_104, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 3.32/1.74 thf(func_def_105, type, size_option: !>[X0: $tType]:((X0 > nat) > option @ X0 > nat)).
% 3.32/1.74 thf(func_def_106, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.32/1.74 thf(func_def_107, type, product_Unity: product_unit).
% 3.32/1.74 thf(func_def_108, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.32/1.74 thf(func_def_109, type, type_wf: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType, X9: $tType, X10: $tType, X11: $tType]:(heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2 @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ X3 @ X4 @ X5 @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X2 @ X0 @ X1 @ X3 @ option @ X6 @ sum_sum @ rCharacterData_ext @ option @ X7 @ X8 @ sum_sum @ rDocument_ext @ X2 @ X0 @ X1 @ option @ sum_sum @ rShadowRoot_ext @ X2 @ X0 @ X1 @ option @ X9 @ X10 @ X11 > $o)).
% 3.32/1.74 thf(func_def_110, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.32/1.74 thf(func_def_111, type, h2: heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ d @ e @ f @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ c @ a @ b @ d @ option @ g @ sum_sum @ rCharacterData_ext @ option @ h @ i @ sum_sum @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l).
% 3.32/1.74 thf(func_def_112, type, h3: heap @ sum_sum @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ sum_sum @ document_ptr @ sum_sum @ shadow_root_ptr @ d @ e @ f @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ c @ a @ b @ d @ option @ g @ sum_sum @ rCharacterData_ext @ option @ h @ i @ sum_sum @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l).
% 3.32/1.74 thf(func_def_125, type, sP0: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o)).
% 3.32/1.74 thf(func_def_126, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > product_unit)).
% 3.32/1.74 thf(func_def_127, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > product_unit)).
% 3.32/1.74 thf(func_def_128, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > list @ char)).
% 3.32/1.74 thf(func_def_129, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > option @ element_ptr @ X0)).
% 3.32/1.74 thf(func_def_130, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > list @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2)).
% 3.32/1.74 thf(func_def_131, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ X3 > X3)).
% 3.32/1.74 thf(func_def_132, type, sK7: nat > nat).
% 3.32/1.74 thf(func_def_133, type, sK8: (rObject_ext @ product_unit > $o) > product_unit).
% 3.32/1.74 thf(func_def_134, type, sK9: !>[X0: $tType]:(option @ X0 > X0)).
% 3.32/1.74 thf(func_def_135, type, sK10: !>[X0: $tType]:(document_ptr @ X0 > X0)).
% 3.32/1.74 thf(func_def_136, type, sK11: !>[X0: $tType]:(document_ptr @ X0 > nat)).
% 3.32/1.74 thf(func_def_137, type, sK12: (nat > $o) > nat).
% 3.32/1.74 thf(func_def_138, type, sK13: !>[X0: $tType]:((rObject_ext @ X0 > $o) > product_unit)).
% 3.32/1.74 thf(func_def_139, type, sK14: !>[X0: $tType]:((rObject_ext @ X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_140, type, sK15: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1)).
% 3.32/1.74 thf(func_def_141, type, sK16: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0)).
% 3.32/1.74 thf(func_def_142, type, sK17: !>[X0: $tType]:((option @ X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_143, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ product_unit > product_unit)).
% 3.32/1.74 thf(func_def_144, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ product_unit > product_unit)).
% 3.32/1.74 thf(func_def_145, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ product_unit > list @ char)).
% 3.32/1.74 thf(func_def_146, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ product_unit > option @ element_ptr @ X0)).
% 3.32/1.74 thf(func_def_147, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:(rObject_ext @ rDocument_ext @ X2 @ X0 @ X1 @ product_unit > list @ node_ptr @ sum_sum @ element_ptr @ X0 @ sum_sum @ character_data_ptr @ X1 @ X2)).
% 3.32/1.74 thf(func_def_148, type, sK23: !>[X0: $tType]:(option @ X0 > X0)).
% 3.32/1.74 thf(func_def_149, type, sK24: rObject_ext @ product_unit > product_unit).
% 3.32/1.74 thf(func_def_150, type, sK25: !>[X0: $tType]:(rObject_ext @ X0 > product_unit)).
% 3.32/1.74 thf(func_def_151, type, sK26: !>[X0: $tType]:(rObject_ext @ X0 > X0)).
% 3.32/1.74 thf(func_def_152, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > product_unit)).
% 3.32/1.74 thf(func_def_153, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > product_unit)).
% 3.32/1.74 thf(func_def_154, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > list @ char)).
% 3.32/1.74 thf(func_def_155, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > option @ element_ptr @ X2)).
% 3.32/1.74 thf(func_def_156, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > list @ node_ptr @ sum_sum @ element_ptr @ X2 @ sum_sum @ character_data_ptr @ X1 @ X3)).
% 3.32/1.74 thf(func_def_157, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rObject_ext @ rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_158, type, sK33: (nat > $o) > nat).
% 3.32/1.74 thf(func_def_159, type, sK34: !>[X0: $tType]:(option @ X0 > X0)).
% 3.32/1.74 thf(func_def_160, type, sK35: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_161, type, sK36: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 3.32/1.74 thf(func_def_162, type, sK37: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 3.32/1.74 thf(func_def_163, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:((rObject_ext @ rDocument_ext @ X2 @ X1 @ X0 @ product_unit > $o) > product_unit)).
% 3.32/1.74 thf(func_def_164, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:((rObject_ext @ rDocument_ext @ X2 @ X1 @ X0 @ product_unit > $o) > product_unit)).
% 3.32/1.74 thf(func_def_165, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((rObject_ext @ rDocument_ext @ X2 @ X1 @ X0 @ product_unit > $o) > list @ char)).
% 3.32/1.74 thf(func_def_166, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((rObject_ext @ rDocument_ext @ X2 @ X1 @ X0 @ product_unit > $o) > option @ element_ptr @ X1)).
% 3.32/1.74 thf(func_def_167, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((rObject_ext @ rDocument_ext @ X2 @ X1 @ X0 @ product_unit > $o) > list @ node_ptr @ sum_sum @ element_ptr @ X1 @ sum_sum @ character_data_ptr @ X0 @ X2)).
% 3.32/1.74 thf(func_def_168, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.32/1.74 thf(func_def_169, type, sK44: !>[X0: $tType]:((document_ptr @ X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_170, type, sK45: !>[X0: $tType]:((document_ptr @ X0 > $o) > nat)).
% 3.32/1.74 thf(func_def_171, type, sK46: (nat > $o) > nat).
% 3.32/1.74 thf(func_def_172, type, sK47: (nat > $o) > nat).
% 3.32/1.74 thf(func_def_173, type, sK48: nat > nat).
% 3.32/1.74 thf(func_def_174, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > product_unit)).
% 3.32/1.74 thf(func_def_175, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > list @ char)).
% 3.32/1.74 thf(func_def_176, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > option @ element_ptr @ X2)).
% 3.32/1.74 thf(func_def_177, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > list @ node_ptr @ sum_sum @ element_ptr @ X2 @ sum_sum @ character_data_ptr @ X1 @ X3)).
% 3.32/1.74 thf(func_def_178, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((rDocument_ext @ X3 @ X2 @ X1 @ X0 > $o) > X0)).
% 3.32/1.74 thf(func_def_179, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType, X7: $tType, X8: $tType]:(rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4 > rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5)).
% 3.32/1.74 thf(func_def_180, type, sK55: nat > nat).
% 3.32/1.74 thf(func_def_181, type, sK56: (nat > nat > $o) > nat).
% 3.32/1.74 thf(func_def_182, type, sK57: (nat > nat > $o) > nat).
% 3.32/1.74 thf(func_def_183, type, sK58: (nat > nat > $o) > nat).
% 3.32/1.74 thf(func_def_184, type, sK59: (nat > nat > $o) > nat).
% 3.32/1.74 thf(f1010,plain,(
% 3.32/1.74 $false),
% 3.32/1.74 inference(subsumption_resolution,[status(thm)],[f1006,f1000])).
% 3.32/1.74 thf(f1000,plain,(
% 3.32/1.74 ( ! [X5 : $tType,X4 : $tType,X7 : $tType,X6 : $tType,X8 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X11 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 != (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ (cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X11)))) )),
% 3.32/1.74 inference(equality_resolution,[status(thm)],[f957])).
% 3.32/1.74 thf(f957,plain,(
% 3.32/1.74 ( ! [X5 : $tType,X4 : $tType,X7 : $tType,X6 : $tType,X8 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X11 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X11) != X9) | (none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 != (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9))) )),
% 3.32/1.74 inference(cnf_transformation,[status(thm)],[f828])).
% 3.32/1.74 thf(f828,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)) | ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ (sK54 @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9)) = X9)) & (! [X11 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X11) != X9) | (none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 != (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9))))),
% 3.32/1.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f826,f827])).
% 3.32/1.74 thf(f827,plain,(
% 3.32/1.74 ! [X8 : $tType,X7 : $tType,X6 : $tType,X5 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (? [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) = X9) => ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ (sK54 @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9)) = X9))),
% 3.32/1.74 introduced(definition,[],[choice_axiom])).
% 3.32/1.74 thf(f826,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)) | ? [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) = X9)) & (! [X11 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X11) != X9) | (none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 != (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9))))),
% 3.32/1.74 inference(rectify,[status(thm)],[f825])).
% 3.32/1.74 thf(f825,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)) | ? [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) = X9)) & (! [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) != X9) | (none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 != (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9))))),
% 3.32/1.74 inference(nnf_transformation,[status(thm)],[f744])).
% 3.32/1.74 thf(f744,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : ((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)) <=> ! [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) != X9))),
% 3.32/1.74 inference(ennf_transformation,[status(thm)],[f580])).
% 3.32/1.74 thf(f580,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : ((none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)) <=> ~? [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) = X9))),
% 3.32/1.74 inference(fool_elimination,[status(thm)],[f579])).
% 3.32/1.74 thf(f579,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType,X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X0 @ option @ X1 @ sum_sum @ rCharacterData_ext @ option @ X2 @ X3 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 @ X4] : (~? [X10 : rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5] : ((cast_D42511940_e_c_t @ X8 @ X7 @ X6 @ X5 @ X0 @ X1 @ X2 @ X3 @ X4 @ X10) = X9) = (none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X5 = (cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X0 @ X1 @ X2 @ X3 @ X5 @ X4 @ X9)))),
% 3.32/1.74 inference(rectify,[status(thm)],[f92])).
% 3.32/1.74 thf(f92,axiom,(
% 3.32/1.74 ! [X14 : $tType,X19 : $tType,X20 : $tType,X21 : $tType,X22 : $tType,X18 : $tType,X17 : $tType,X16 : $tType,X0 : $tType,X89 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X0 @ X16 @ X17 @ X14 @ option @ X19 @ sum_sum @ rCharacterData_ext @ option @ X20 @ X21 @ sum_sum @ rDocument_ext @ X0 @ X16 @ X17 @ option @ X18 @ X22] : (~? [X65 : rObject_ext @ rDocument_ext @ X0 @ X16 @ X17 @ option @ X18] : ((cast_D42511940_e_c_t @ X0 @ X16 @ X17 @ X18 @ X14 @ X19 @ X20 @ X21 @ X22 @ X65) = X89) = ((cast_O1159777348_e_n_t @ X0 @ X16 @ X17 @ X14 @ X19 @ X20 @ X21 @ X18 @ X22 @ X89) = none @ rObject_ext @ rDocument_ext @ X0 @ X16 @ X17 @ option @ X18))),
% 3.32/1.74 file('/export/starexec/sandbox/tmp/tmp.rDZlZRFXfP/DTF2THF_16337.p',fact_91_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none)).
% 3.32/1.74 thf(f1006,plain,(
% 3.32/1.74 ((cast_O1159777348_e_n_t @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) = none @ rObject_ext @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)),
% 3.32/1.74 inference(equality_proxy_clausification,[status(thm)],[f1005])).
% 3.32/1.74 thf(f1005,plain,(
% 3.32/1.74 (((cast_O1159777348_e_n_t @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) = none @ rObject_ext @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k) = $true)),
% 3.32/1.74 inference(not_proxy_clausification,[status(thm)],[f1004])).
% 3.32/1.74 thf(f1004,plain,(
% 3.32/1.74 ((~ ((cast_O1159777348_e_n_t @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) = none @ rObject_ext @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)) != $true)),
% 3.32/1.74 inference(beta_eta_normalization,[status(thm)],[f970])).
% 3.32/1.74 thf(f970,plain,(
% 3.32/1.74 (((^[Y0 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ c @ a @ b @ d @ option @ g @ sum_sum @ rCharacterData_ext @ option @ h @ i @ sum_sum @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l]: (~ ((cast_O1159777348_e_n_t @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ Y0) = none @ rObject_ext @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k))) @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) != $true)),
% 3.32/1.74 inference(definition_unfolding,[status(thm)],[f902,f938])).
% 3.32/1.74 thf(f938,plain,(
% 3.32/1.74 ( ! [X5 : $tType,X4 : $tType,X7 : $tType,X6 : $tType,X8 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (((^[Y0 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X5 @ option @ X4 @ sum_sum @ rCharacterData_ext @ option @ X3 @ X2 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1 @ X0]: (~ ((cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ Y0) = none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1))) = is_document_kind @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0)) )),
% 3.32/1.74 inference(cnf_transformation,[status(thm)],[f612])).
% 3.32/1.74 thf(f612,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType] : ((^[Y0 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X5 @ option @ X4 @ sum_sum @ rCharacterData_ext @ option @ X3 @ X2 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1 @ X0]: (~ ((cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ Y0) = none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1))) = is_document_kind @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0)),
% 3.32/1.74 inference(fool_elimination,[status(thm)],[f611])).
% 3.32/1.74 thf(f611,plain,(
% 3.32/1.74 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : $tType,X8 : $tType] : ((^[X9 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X8 @ X7 @ X6 @ X5 @ option @ X4 @ sum_sum @ rCharacterData_ext @ option @ X3 @ X2 @ sum_sum @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1 @ X0] : (((cast_O1159777348_e_n_t @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0 @ X9) != none @ rObject_ext @ rDocument_ext @ X8 @ X7 @ X6 @ option @ X1))) = is_document_kind @ X8 @ X7 @ X6 @ X5 @ X4 @ X3 @ X2 @ X1 @ X0)),
% 3.32/1.74 inference(rectify,[status(thm)],[f94])).
% 3.32/1.74 thf(f94,axiom,(
% 3.32/1.74 ! [X10 : $tType,X5 : $tType,X9 : $tType,X8 : $tType,X7 : $tType,X6 : $tType,X2 : $tType,X1 : $tType,X3 : $tType] : ((^[X90 : rObject_ext @ sum_sum @ rNode_ext @ sum_sum @ rElement_ext @ X3 @ X1 @ X2 @ X6 @ option @ X7 @ sum_sum @ rCharacterData_ext @ option @ X8 @ X9 @ sum_sum @ rDocument_ext @ X3 @ X1 @ X2 @ option @ X5 @ X10] : (((cast_O1159777348_e_n_t @ X3 @ X1 @ X2 @ X6 @ X7 @ X8 @ X9 @ X5 @ X10 @ X90) != none @ rObject_ext @ rDocument_ext @ X3 @ X1 @ X2 @ option @ X5))) = is_document_kind @ X3 @ X1 @ X2 @ X6 @ X7 @ X8 @ X9 @ X5 @ X10)),
% 3.32/1.74 file('/export/starexec/sandbox/tmp/tmp.rDZlZRFXfP/DTF2THF_16337.p',fact_93_is__document__kind__def)).
% 3.32/1.74 thf(f902,plain,(
% 3.32/1.74 ((is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) != $true)),
% 3.32/1.74 inference(cnf_transformation,[status(thm)],[f661])).
% 3.32/1.74 thf(f661,plain,(
% 3.32/1.74 ((is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) != $true)),
% 3.32/1.74 inference(flattening,[status(thm)],[f392])).
% 3.32/1.74 thf(f392,plain,(
% 3.32/1.74 ~((is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k)))) = $true)),
% 3.32/1.74 inference(fool_elimination,[status(thm)],[f391])).
% 3.32/1.74 thf(f391,plain,(
% 3.32/1.74 ~(is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k))))),
% 3.32/1.74 inference(rectify,[status(thm)],[f309])).
% 3.32/1.74 thf(f309,negated_conjecture,(
% 3.32/1.74 ~(is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k))))),
% 3.32/1.74 inference(negated_conjecture,[status(cth)],[f308])).
% 3.32/1.74 thf(f308,conjecture,(
% 3.32/1.74 (is_document_kind @ c @ a @ b @ d @ g @ h @ i @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ l @ (cast_D42511940_e_c_t @ c @ a @ b @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ d @ g @ h @ i @ l @ (rObject_ext2 @ rDocument_ext @ c @ a @ b @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ (rDocument_ext2 @ a @ b @ c @ option @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k @ product_Unity @ nil @ char @ none @ element_ptr @ a @ nil @ node_ptr @ sum_sum @ element_ptr @ a @ sum_sum @ character_data_ptr @ b @ c @ none @ sum_sum @ rShadowRoot_ext @ c @ a @ b @ option @ j @ k))))),
% 3.32/1.74 file('/export/starexec/sandbox/tmp/tmp.rDZlZRFXfP/DTF2THF_16337.p',conj_3)).
% 3.32/1.74 % SZS output end Proof for DTF2THF_16337
% 3.32/1.74 % (16554)------------------------------
% 3.32/1.74 % (16554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.74 % (16554)Termination reason: Refutation
% 3.32/1.74
% 3.32/1.74 % (16554)Memory used [KB]: 6780
% 3.32/1.74 % (16554)Time elapsed: 0.028 s
% 3.32/1.74 % (16554)Instructions burned: 73 (million)
% 3.32/1.74 % (16554)------------------------------
% 3.32/1.74 % (16554)------------------------------
% 3.32/1.74 % (16528)Success in time 0.082 s
%------------------------------------------------------------------------------