%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP032^2 : 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 : n031.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 08:55:00 AM UTC 2026
% Result : Theorem 2.80s 1.99s
% Output : Refutation 2.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP032^2 : 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
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:25:03 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP032^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer BinaryTree problem prob_359__3253628_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : BinaryTree/prob_359__3253628_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.33 v9.1.0, 0.00 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 358 ( 137 unt; 57 typ; 0 def)
% 0.30/0.47 % Number of atoms : 747 ( 284 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.47 % Number of connectives : 3401 ( 90 ~; 20 |; 57 &;2911 @)
% 0.30/0.47 % ( 0 <=>; 323 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 17 ( 7 avg)
% 0.30/0.47 % Number of types : 3 ( 2 usr)
% 0.30/0.47 % Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 58 ( 55 usr; 7 con; 0-5 aty)
% 0.30/0.47 % Number of variables : 1039 ( 84 ^; 864 !; 42 ?;1039 :)
% 0.30/0.47 % ( 49 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.47 % SPC : TH1_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:19.593
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (4)
% 0.30/0.47 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree,type,
% 0.30/0.47 binary1291135688e_Tree: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Set_Oset,type,
% 0.30/0.47 set: $tType > $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_t_Int_Oint,type,
% 0.30/0.47 int: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_tf_a,type,
% 0.30/0.47 a: $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (53)
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.47 bounded_lattice:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_HOL_Otype,type,
% 0.30/0.47 type:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ominus,type,
% 0.30/0.47 minus:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.47 bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.47 ord:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.47 order:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.30/0.47 group_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Olattice,type,
% 0.30/0.47 lattice:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Ono__bot,type,
% 0.30/0.47 no_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Ono__top,type,
% 0.30/0.47 no_top:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.47 linorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.47 preorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.47 order_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Owellorder,type,
% 0.30/0.47 wellorder:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Orderings_Odense__order,type,
% 0.30/0.47 dense_order:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.30/0.47 linordered_idom:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Fields_Olinordered__field,type,
% 0.30/0.47 linordered_field:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.30/0.47 semilattice_sup:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.30/0.47 ordered_ab_group_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.30/0.47 cancel146912293up_add:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/0.47 bounde1808546759up_bot:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.30/0.47 condit1656338222tinuum:
% 0.30/0.47 !>[A: $tType] : $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT,type,
% 0.30/0.47 binary210054475elle_T:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip,type,
% 0.30/0.47 binary1746293266le_Tip:
% 0.30/0.47 !>[A: $tType] : ( binary1291135688e_Tree @ A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree,type,
% 0.30/0.47 binary536355927e_Tree:
% 0.30/0.47 !>[B: $tType,A: $tType] : ( B > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B ) > ( binary1291135688e_Tree @ A ) > B ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Opred__Tree,type,
% 0.30/0.47 binary1693644968d_Tree:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree,type,
% 0.30/0.47 binary1929596613c_Tree:
% 0.30/0.47 !>[C: $tType,A: $tType] : ( C > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C ) > ( binary1291135688e_Tree @ A ) > C ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree,type,
% 0.30/0.47 binary2130109271t_Tree:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Obinsert,type,
% 0.30/0.47 binary1830089824insert:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs,type,
% 0.30/0.47 binary64540844le_eqs:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Omemb,type,
% 0.30/0.47 binary827270440e_memb:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf,type,
% 0.30/0.47 binary1653327646_setOf:
% 0.30/0.47 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree,type,
% 0.30/0.47 binary1610619414edTree:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred,type,
% 0.30/0.47 binary231205461t_pred:
% 0.30/0.47 !>[A: $tType] : ( ( A > int ) > A > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.30/0.47 minus_minus:
% 0.30/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_HOL_OThe,type,
% 0.30/0.47 the:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.47 sup_sup:
% 0.30/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.47 bot_bot:
% 0.30/0.47 !>[A: $tType] : A ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.47 ord_less:
% 0.30/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.47 ord_less_eq:
% 0.30/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_OCollect,type,
% 0.30/0.47 collect:
% 0.30/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oinsert,type,
% 0.30/0.47 insert:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__empty,type,
% 0.30/0.47 is_empty:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.47 is_singleton:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Oremove,type,
% 0.30/0.47 remove:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.47 the_elem:
% 0.30/0.47 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member,type,
% 0.30/0.47 member:
% 0.30/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_e,type,
% 0.30/0.47 e: a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_h,type,
% 0.30/0.47 h: a > int ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_t1____,type,
% 0.30/0.47 t1: binary1291135688e_Tree @ a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_t2____,type,
% 0.30/0.47 t2: binary1291135688e_Tree @ a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_w____,type,
% 0.30/0.47 w: a ).
% 0.30/0.47
% 0.30/0.47 thf(sy_v_x____,type,
% 0.30/0.47 x: a ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (256)
% 0.30/0.47 thf(fact_0_whSet,axiom,
% 0.30/0.47 member @ a @ w @ ( binary1653327646_setOf @ a @ t1 ) ).
% 0.30/0.47
% 0.30/0.47 % whSet
% 0.30/0.47 thf(fact_1_s,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ).
% 0.30/0.47
% 0.30/0.47 % s
% 0.30/0.47 thf(fact_2_s2,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ t2 ).
% 0.30/0.47
% 0.30/0.47 % s2
% 0.30/0.47 thf(fact_3_s1,axiom,
% 0.30/0.47 binary1610619414edTree @ a @ h @ t1 ).
% 0.30/0.47
% 0.30/0.47 % s1
% 0.30/0.47 thf(fact_4_eNotLess,axiom,
% 0.30/0.47 ~ ( ord_less @ int @ ( h @ e ) @ ( h @ x ) ) ).
% 0.30/0.47
% 0.30/0.47 % eNotLess
% 0.30/0.47 thf(fact_5_xNotLess,axiom,
% 0.30/0.47 ~ ( ord_less @ int @ ( h @ x ) @ ( h @ e ) ) ).
% 0.30/0.47
% 0.30/0.47 % xNotLess
% 0.30/0.47 thf(fact_6_whEq,axiom,
% 0.30/0.47 member @ a @ w @ ( binary64540844le_eqs @ a @ h @ e ) ).
% 0.30/0.47
% 0.30/0.47 % whEq
% 0.30/0.47 thf(fact_7_xeqe,axiom,
% 0.30/0.47 ( ( h @ x )
% 0.30/0.47 = ( h @ e ) ) ).
% 0.30/0.47
% 0.30/0.47 % xeqe
% 0.30/0.47 thf(fact_8_Tree_Oinject,axiom,
% 0.30/0.47 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A,Y21: binary1291135688e_Tree @ A,Y22: A,Y23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( ( binary210054475elle_T @ A @ X21 @ X22 @ X23 )
% 0.30/0.47 = ( binary210054475elle_T @ A @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 )
% 0.30/0.47 & ( X23 = Y23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.inject
% 0.30/0.47 thf(fact_9_calculation,axiom,
% 0.30/0.47 member @ a @ x @ ( binary64540844le_eqs @ a @ h @ e ) ).
% 0.30/0.47
% 0.30/0.47 % calculation
% 0.30/0.47 thf(fact_10_minf_I11_J,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( ord @ C )
% 0.30/0.47 => ! [F: D] :
% 0.30/0.47 ? [Z: C] :
% 0.30/0.47 ! [X: C] :
% 0.30/0.47 ( ( ord_less @ C @ X @ Z )
% 0.30/0.47 => ( F = F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(11)
% 0.30/0.47 thf(fact_11_minf_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(7)
% 0.30/0.47 thf(fact_12_minf_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ( ord_less @ A @ X @ T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(5)
% 0.30/0.47 thf(fact_13_minf_I4_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ( X != T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(4)
% 0.30/0.47 thf(fact_14_minf_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ( X != T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(3)
% 0.30/0.47 thf(fact_15_minf_I2_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.47 => ( ( P @ X2 )
% 0.30/0.47 = ( P2 @ X2 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.47 => ( ( Q @ X2 )
% 0.30/0.47 = ( Q2 @ X2 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ( ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) )
% 0.30/0.47 = ( ( P2 @ X )
% 0.30/0.47 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(2)
% 0.30/0.47 thf(fact_16_minf_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.47 => ( ( P @ X2 )
% 0.30/0.47 = ( P2 @ X2 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.47 => ( ( Q @ X2 )
% 0.30/0.47 = ( Q2 @ X2 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ X @ Z )
% 0.30/0.47 => ( ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) )
% 0.30/0.47 = ( ( P2 @ X )
% 0.30/0.47 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minf(1)
% 0.30/0.47 thf(fact_17_pinf_I11_J,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( ord @ C )
% 0.30/0.47 => ! [F: D] :
% 0.30/0.47 ? [Z: C] :
% 0.30/0.47 ! [X: C] :
% 0.30/0.47 ( ( ord_less @ C @ Z @ X )
% 0.30/0.47 => ( F = F ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(11)
% 0.30/0.47 thf(fact_18_res,axiom,
% 0.30/0.47 ( ( binary1830089824insert @ a @ h @ e @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) )
% 0.30/0.47 = ( binary210054475elle_T @ a @ t1 @ e @ t2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % res
% 0.30/0.47 thf(fact_19_sortLemmaR,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 => ( binary1610619414edTree @ A @ H @ T2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortLemmaR
% 0.30/0.47 thf(fact_20_sortLemmaL,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 => ( binary1610619414edTree @ A @ H @ T1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortLemmaL
% 0.30/0.47 thf(fact_21_sortedTree_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 = ( ( binary1610619414edTree @ A @ H @ T1 )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T1 ) )
% 0.30/0.47 => ( ord_less @ int @ ( H @ X4 ) @ ( H @ X3 ) ) )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T2 ) )
% 0.30/0.47 => ( ord_less @ int @ ( H @ X3 ) @ ( H @ X4 ) ) )
% 0.30/0.47 & ( binary1610619414edTree @ A @ H @ T2 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortedTree.simps(2)
% 0.30/0.47 thf(fact_22_pinf_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.47 => ( ( P @ X2 )
% 0.30/0.47 = ( P2 @ X2 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.47 => ( ( Q @ X2 )
% 0.30/0.47 = ( Q2 @ X2 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ( ( ( P @ X )
% 0.30/0.47 & ( Q @ X ) )
% 0.30/0.47 = ( ( P2 @ X )
% 0.30/0.47 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(1)
% 0.30/0.47 thf(fact_23_pinf_I2_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.47 ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.47 => ( ( P @ X2 )
% 0.30/0.47 = ( P2 @ X2 ) ) )
% 0.30/0.47 => ( ? [Z2: A] :
% 0.30/0.47 ! [X2: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.47 => ( ( Q @ X2 )
% 0.30/0.47 = ( Q2 @ X2 ) ) )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ( ( ( P @ X )
% 0.30/0.47 | ( Q @ X ) )
% 0.30/0.47 = ( ( P2 @ X )
% 0.30/0.47 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(2)
% 0.30/0.47 thf(fact_24_pinf_I3_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ( X != T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(3)
% 0.30/0.47 thf(fact_25_pinf_I4_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ( X != T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(4)
% 0.30/0.47 thf(fact_26_pinf_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(5)
% 0.30/0.47 thf(fact_27_pinf_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [T: A] :
% 0.30/0.47 ? [Z: A] :
% 0.30/0.47 ! [X: A] :
% 0.30/0.47 ( ( ord_less @ A @ Z @ X )
% 0.30/0.47 => ( ord_less @ A @ T @ X ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % pinf(7)
% 0.30/0.47 thf(fact_28_sorted__distinct__pred__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary231205461t_pred @ A )
% 0.30/0.47 = ( ^ [H2: A > int,A2: A,B2: A,T3: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( ( binary1610619414edTree @ A @ H2 @ T3 )
% 0.30/0.47 & ( member @ A @ A2 @ ( binary1653327646_setOf @ A @ T3 ) )
% 0.30/0.47 & ( member @ A @ B2 @ ( binary1653327646_setOf @ A @ T3 ) )
% 0.30/0.47 & ( ( H2 @ A2 )
% 0.30/0.47 = ( H2 @ B2 ) ) )
% 0.30/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sorted_distinct_pred_def
% 0.30/0.47 thf(fact_29_memb__spec,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,T: binary1291135688e_Tree @ A,X3: A] :
% 0.30/0.47 ( ( binary1610619414edTree @ A @ H @ T )
% 0.30/0.47 => ( ( binary827270440e_memb @ A @ H @ X3 @ T )
% 0.30/0.47 = ( member @ A @ X3 @ ( binary1653327646_setOf @ A @ T ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % memb_spec
% 0.30/0.47 thf(fact_30_binsert_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,E: A,X3: A,T1: binary1291135688e_Tree @ A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( ( ord_less @ int @ ( H @ E ) @ ( H @ X3 ) )
% 0.30/0.47 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 = ( binary210054475elle_T @ A @ ( binary1830089824insert @ A @ H @ E @ T1 ) @ X3 @ T2 ) ) )
% 0.30/0.47 & ( ~ ( ord_less @ int @ ( H @ E ) @ ( H @ X3 ) )
% 0.30/0.47 => ( ( ( ord_less @ int @ ( H @ X3 ) @ ( H @ E ) )
% 0.30/0.47 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 = ( binary210054475elle_T @ A @ T1 @ X3 @ ( binary1830089824insert @ A @ H @ E @ T2 ) ) ) )
% 0.30/0.47 & ( ~ ( ord_less @ int @ ( H @ X3 ) @ ( H @ E ) )
% 0.30/0.47 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 = ( binary210054475elle_T @ A @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % binsert.simps(2)
% 0.30/0.47 thf(fact_31_ex__gt__or__lt,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( condit1656338222tinuum @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ? [B3: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.30/0.47 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_gt_or_lt
% 0.30/0.47 thf(fact_32_linorder__neqE__linordered__idom,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_idom @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( X3 != Y )
% 0.30/0.47 => ( ~ ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_neqE_linordered_idom
% 0.30/0.47 thf(fact_33_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ( A3 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_implies_not_eq
% 0.30/0.47 thf(fact_34_linordered__field__no__ub,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_field @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % linordered_field_no_ub
% 0.30/0.47 thf(fact_35_linordered__field__no__lb,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linordered_field @ A )
% 0.30/0.47 => ! [X: A] :
% 0.30/0.47 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.30/0.47
% 0.30/0.47 % linordered_field_no_lb
% 0.30/0.47 thf(fact_36_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( A3 != B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_implies_not_eq
% 0.30/0.47 thf(fact_37_dependent__wellorder__choice,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ! [P: ( A > B ) > A > B > $o] :
% 0.30/0.47 ( ! [R: B,F2: A > B,G: A > B,X2: A] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y3 @ X2 )
% 0.30/0.47 => ( ( F2 @ Y3 )
% 0.30/0.47 = ( G @ Y3 ) ) )
% 0.30/0.47 => ( ( P @ F2 @ X2 @ R )
% 0.30/0.47 = ( P @ G @ X2 @ R ) ) )
% 0.30/0.47 => ( ! [X2: A,F2: A > B] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y3 @ X2 )
% 0.30/0.47 => ( P @ F2 @ Y3 @ ( F2 @ Y3 ) ) )
% 0.30/0.47 => ? [X_12: B] : ( P @ F2 @ X2 @ X_12 ) )
% 0.30/0.47 => ? [F2: A > B] :
% 0.30/0.47 ! [X: A] : ( P @ F2 @ X @ ( F2 @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dependent_wellorder_choice
% 0.30/0.47 thf(fact_38_sorted__distinct,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,A3: A,B4: A,T: binary1291135688e_Tree @ A] : ( binary231205461t_pred @ A @ H @ A3 @ B4 @ T ) ).
% 0.30/0.47
% 0.30/0.47 % sorted_distinct
% 0.30/0.47 thf(fact_39_ord__eq__less__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A3: A,F3: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 = ( F3 @ B4 ) )
% 0.30/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X2: B,Y2: B] :
% 0.30/0.47 ( ( ord_less @ B @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less @ A @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A3 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_subst
% 0.30/0.47 thf(fact_40_ord__less__eq__subst,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( ord @ B )
% 0.30/0.47 & ( ord @ A ) )
% 0.30/0.47 => ! [A3: A,B4: A,F3: A > B,C2: B] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ( F3 @ B4 )
% 0.30/0.47 = C2 )
% 0.30/0.47 => ( ! [X2: A,Y2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less @ B @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 0.30/0.47 => ( ord_less @ B @ ( F3 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_subst
% 0.30/0.47 thf(fact_41_order__less__subst1,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType] :
% 0.30/0.47 ( ( ( order @ B )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A3: A,F3: B > A,B4: B,C2: B] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ ( F3 @ B4 ) )
% 0.30/0.47 => ( ( ord_less @ B @ B4 @ C2 )
% 0.30/0.47 => ( ! [X2: B,Y2: B] :
% 0.30/0.47 ( ( ord_less @ B @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less @ A @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 0.30/0.47 => ( ord_less @ A @ A3 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst1
% 0.30/0.47 thf(fact_42_order__less__subst2,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType] :
% 0.30/0.47 ( ( ( order @ C )
% 0.30/0.47 & ( order @ A ) )
% 0.30/0.47 => ! [A3: A,B4: A,F3: A > C,C2: C] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ord_less @ C @ ( F3 @ B4 ) @ C2 )
% 0.30/0.47 => ( ! [X2: A,Y2: A] :
% 0.30/0.47 ( ( ord_less @ A @ X2 @ Y2 )
% 0.30/0.47 => ( ord_less @ C @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 0.30/0.47 => ( ord_less @ C @ ( F3 @ A3 ) @ C2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order_less_subst2
% 0.30/0.47 thf(fact_43_lt__ex,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_bot @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ? [Y2: A] : ( ord_less @ A @ Y2 @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % lt_ex
% 0.30/0.47 thf(fact_44_gt__ex,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( no_top @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.30/0.47
% 0.30/0.47 % gt_ex
% 0.30/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.47 = ( P @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % mem_Collect_eq
% 0.30/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( collect @ A
% 0.30/0.47 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_mem_eq
% 0.30/0.47 thf(fact_47_Collect__cong,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ( P @ X2 )
% 0.30/0.47 = ( Q @ X2 ) )
% 0.30/0.47 => ( ( collect @ A @ P )
% 0.30/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_cong
% 0.30/0.47 thf(fact_48_ext,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ( F3 @ X2 )
% 0.30/0.47 = ( G2 @ X2 ) )
% 0.30/0.47 => ( F3 = G2 ) ) ).
% 0.30/0.47
% 0.30/0.47 % ext
% 0.30/0.47 thf(fact_49_neqE,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( X3 != Y )
% 0.30/0.47 => ( ~ ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neqE
% 0.30/0.47 thf(fact_50_neq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( X3 != Y )
% 0.30/0.47 = ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % neq_iff
% 0.30/0.47 thf(fact_51_order_Oasym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.asym
% 0.30/0.47 thf(fact_52_dense,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( dense_order @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ? [Z: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.47 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dense
% 0.30/0.47 thf(fact_53_less__imp__neq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( X3 != Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_neq
% 0.30/0.47 thf(fact_54_less__asym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym
% 0.30/0.47 thf(fact_55_less__asym_H,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_asym'
% 0.30/0.47 thf(fact_56_less__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A,Z3: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( ( ord_less @ A @ Y @ Z3 )
% 0.30/0.47 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_trans
% 0.30/0.47 thf(fact_57_less__linear,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 | ( X3 = Y )
% 0.30/0.47 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_linear
% 0.30/0.47 thf(fact_58_less__irrefl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_irrefl
% 0.30/0.47 thf(fact_59_ord__eq__less__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( A3 = B4 )
% 0.30/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_eq_less_trans
% 0.30/0.47 thf(fact_60_ord__less__eq__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( ord @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( B4 = C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord_less_eq_trans
% 0.30/0.47 thf(fact_61_dual__order_Oasym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ~ ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.asym
% 0.30/0.47 thf(fact_62_less__imp__not__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( X3 != Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq
% 0.30/0.47 thf(fact_63_less__not__sym,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_not_sym
% 0.30/0.47 thf(fact_64_less__induct,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ! [P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ( ( ord_less @ A @ Y3 @ X2 )
% 0.30/0.47 => ( P @ Y3 ) )
% 0.30/0.47 => ( P @ X2 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_induct
% 0.30/0.47 thf(fact_65_antisym__conv3,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [Y: A,X3: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ Y @ X3 )
% 0.30/0.47 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.30/0.47 = ( X3 = Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % antisym_conv3
% 0.30/0.47 thf(fact_66_less__imp__not__eq2,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( Y != X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_eq2
% 0.30/0.47 thf(fact_67_less__imp__triv,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A,P: $o] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( ( ord_less @ A @ Y @ X3 )
% 0.30/0.47 => P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_triv
% 0.30/0.47 thf(fact_68_linorder__cases,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ( ( X3 != Y )
% 0.30/0.47 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_cases
% 0.30/0.47 thf(fact_69_dual__order_Oirrefl,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.irrefl
% 0.30/0.47 thf(fact_70_order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.47 => ( ( ord_less @ A @ B4 @ C2 )
% 0.30/0.47 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % order.strict_trans
% 0.30/0.47 thf(fact_71_less__imp__not__less,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( preorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.30/0.47 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % less_imp_not_less
% 0.30/0.47 thf(fact_72_exists__least__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( wellorder @ A )
% 0.30/0.47 => ( ( ^ [P3: A > $o] :
% 0.30/0.47 ? [X5: A] : ( P3 @ X5 ) )
% 0.30/0.47 = ( ^ [P4: A > $o] :
% 0.30/0.47 ? [N: A] :
% 0.30/0.47 ( ( P4 @ N )
% 0.30/0.47 & ! [M: A] :
% 0.30/0.47 ( ( ord_less @ A @ M @ N )
% 0.30/0.47 => ~ ( P4 @ M ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % exists_least_iff
% 0.30/0.47 thf(fact_73_linorder__less__wlog,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [P: A > A > $o,A3: A,B4: A] :
% 0.30/0.47 ( ! [A5: A,B3: A] :
% 0.30/0.47 ( ( ord_less @ A @ A5 @ B3 )
% 0.30/0.47 => ( P @ A5 @ B3 ) )
% 0.30/0.47 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 0.30/0.47 => ( ! [A5: A,B3: A] :
% 0.30/0.47 ( ( P @ B3 @ A5 )
% 0.30/0.47 => ( P @ A5 @ B3 ) )
% 0.30/0.47 => ( P @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % linorder_less_wlog
% 0.30/0.47 thf(fact_74_dual__order_Ostrict__trans,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [B4: A,A3: A,C2: A] :
% 0.30/0.47 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.47 => ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.47 => ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % dual_order.strict_trans
% 0.30/0.47 thf(fact_75_not__less__iff__gr__or__eq,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( linorder @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.30/0.47 = ( ( ord_less @ A @ Y @ X3 )
% 0.30/0.47 | ( X3 = Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_less_iff_gr_or_eq
% 0.30/0.47 thf(fact_76_binsert_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int,E: A] :
% 0.30/0.47 ( ( binary1830089824insert @ A @ H @ E @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = ( binary210054475elle_T @ A @ ( binary1746293266le_Tip @ A ) @ E @ ( binary1746293266le_Tip @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % binsert.simps(1)
% 0.30/0.47 thf(fact_77_verit__comp__simplify1_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % verit_comp_simplify1(1)
% 0.30/0.47 thf(fact_78_measure__induct,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ B )
% 0.30/0.47 => ! [F3: A > B,P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ( ( ord_less @ B @ ( F3 @ Y3 ) @ ( F3 @ X2 ) )
% 0.30/0.47 => ( P @ Y3 ) )
% 0.30/0.47 => ( P @ X2 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % measure_induct
% 0.30/0.47 thf(fact_79_measure__induct__rule,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( wellorder @ B )
% 0.30/0.47 => ! [F3: A > B,P: A > $o,A3: A] :
% 0.30/0.47 ( ! [X2: A] :
% 0.30/0.47 ( ! [Y3: A] :
% 0.30/0.47 ( ( ord_less @ B @ ( F3 @ Y3 ) @ ( F3 @ X2 ) )
% 0.30/0.47 => ( P @ Y3 ) )
% 0.30/0.47 => ( P @ X2 ) )
% 0.30/0.47 => ( P @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % measure_induct_rule
% 0.30/0.47 thf(fact_80_c2,axiom,
% 0.30/0.47 ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t2 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t2 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % c2
% 0.30/0.47 thf(fact_81_Tree_Osimps_I5_J,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.47 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(5)
% 0.30/0.47 thf(fact_82_c1,axiom,
% 0.30/0.47 ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t1 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t1 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % c1
% 0.30/0.47 thf(fact_83_Tree_Osimps_I7_J,axiom,
% 0.30/0.47 ! [C: $tType,A: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.47 = ( F22 @ X21 @ X22 @ X23 @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X21 ) @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(7)
% 0.30/0.47 thf(fact_84_Tree_Opred__inject_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o,A3: binary1291135688e_Tree @ A,Aa: A,Ab: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1693644968d_Tree @ A @ P @ ( binary210054475elle_T @ A @ A3 @ Aa @ Ab ) )
% 0.30/0.47 = ( ( binary1693644968d_Tree @ A @ P @ A3 )
% 0.30/0.47 & ( P @ Aa )
% 0.30/0.47 & ( binary1693644968d_Tree @ A @ P @ Ab ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.pred_inject(2)
% 0.30/0.47 thf(fact_85_bot__apply,axiom,
% 0.30/0.47 ! [C: $tType,D: $tType] :
% 0.30/0.47 ( ( bot @ C )
% 0.30/0.47 => ( ( bot_bot @ ( D > C ) )
% 0.30/0.47 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_apply
% 0.30/0.47 thf(fact_86_bot__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( bot @ B )
% 0.30/0.47 => ( ( bot_bot @ ( A > B ) )
% 0.30/0.47 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_fun_def
% 0.30/0.47 thf(fact_87_Tree_Osimps_I6_J,axiom,
% 0.30/0.47 ! [A: $tType,C: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C] :
% 0.30/0.47 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = F1 ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(6)
% 0.30/0.47 thf(fact_88_Tree_Osimps_I4_J,axiom,
% 0.30/0.47 ! [A: $tType,B: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B] :
% 0.30/0.47 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = F1 ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.simps(4)
% 0.30/0.47 thf(fact_89_Tree_Opred__inject_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] : ( binary1693644968d_Tree @ A @ P @ ( binary1746293266le_Tip @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.pred_inject(1)
% 0.30/0.47 thf(fact_90_setOf_Osimps_I2_J,axiom,
% 0.30/0.47 ! [A: $tType,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1653327646_setOf @ A @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary1653327646_setOf @ A @ T1 ) @ ( binary1653327646_setOf @ A @ T2 ) ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % setOf.simps(2)
% 0.30/0.47 thf(fact_91_setOf_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( binary1653327646_setOf @ A @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % setOf.simps(1)
% 0.30/0.47 thf(fact_92_bot_Onot__eq__extremum,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( A3
% 0.30/0.47 != ( bot_bot @ A ) )
% 0.30/0.47 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot.not_eq_extremum
% 0.30/0.47 thf(fact_93_bot_Oextremum__strict,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( order_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot.extremum_strict
% 0.30/0.47 thf(fact_94_Tree_Odistinct_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( binary1746293266le_Tip @ A )
% 0.30/0.47 != ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.distinct(1)
% 0.30/0.47 thf(fact_95_Tree_Oinduct,axiom,
% 0.30/0.47 ! [A: $tType,P: ( binary1291135688e_Tree @ A ) > $o,Tree: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( P @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 => ( ! [X1: binary1291135688e_Tree @ A,X24: A,X32: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( P @ X1 )
% 0.30/0.47 => ( ( P @ X32 )
% 0.30/0.47 => ( P @ ( binary210054475elle_T @ A @ X1 @ X24 @ X32 ) ) ) )
% 0.30/0.47 => ( P @ Tree ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.induct
% 0.30/0.47 thf(fact_96_Tree_Oexhaust,axiom,
% 0.30/0.47 ! [A: $tType,Y: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( ( Y
% 0.30/0.47 != ( binary1746293266le_Tip @ A ) )
% 0.30/0.47 => ~ ! [X212: binary1291135688e_Tree @ A,X222: A,X232: binary1291135688e_Tree @ A] :
% 0.30/0.47 ( Y
% 0.30/0.47 != ( binary210054475elle_T @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Tree.exhaust
% 0.30/0.47 thf(fact_97_sortedTree_Osimps_I1_J,axiom,
% 0.30/0.47 ! [A: $tType,H: A > int] : ( binary1610619414edTree @ A @ H @ ( binary1746293266le_Tip @ A ) ) ).
% 0.30/0.47
% 0.30/0.47 % sortedTree.simps(1)
% 0.30/0.47 thf(fact_98_insert__Diff__single,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 = ( insert @ A @ A3 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_Diff_single
% 0.30/0.47 thf(fact_99_Un__Diff__cancel,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_Diff_cancel
% 0.30/0.47 thf(fact_100_Un__Diff__cancel2,axiom,
% 0.30/0.47 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) @ A4 )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_Diff_cancel2
% 0.30/0.47 thf(fact_101_Diff__insert0,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.47 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B5 ) )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_insert0
% 0.30/0.47 thf(fact_102_insert__Diff1,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ X3 @ B5 )
% 0.30/0.47 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_Diff1
% 0.30/0.47 thf(fact_103_Un__insert__left,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B5 ) @ C3 )
% 0.30/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_left
% 0.30/0.47 thf(fact_104_empty__Collect__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ P ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ~ ( P @ X4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_Collect_eq
% 0.30/0.47 thf(fact_105_Collect__empty__eq,axiom,
% 0.30/0.47 ! [A: $tType,P: A > $o] :
% 0.30/0.47 ( ( ( collect @ A @ P )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ~ ( P @ X4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Collect_empty_eq
% 0.30/0.47 thf(fact_106_all__not__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( ! [X4: A] :
% 0.30/0.47 ~ ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % all_not_in_conv
% 0.30/0.47 thf(fact_107_empty__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A] :
% 0.30/0.47 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_iff
% 0.30/0.47 thf(fact_108_insert__absorb2,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 0.30/0.47 = ( insert @ A @ X3 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb2
% 0.30/0.47 thf(fact_109_insert__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/0.47 = ( ( A3 = B4 )
% 0.30/0.47 | ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_iff
% 0.30/0.47 thf(fact_110_insertCI,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 0.30/0.47 ( ( ~ ( member @ A @ A3 @ B5 )
% 0.30/0.47 => ( A3 = B4 ) )
% 0.30/0.47 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertCI
% 0.30/0.47 thf(fact_111_Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 | ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_iff
% 0.30/0.47 thf(fact_112_UnCI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( ~ ( member @ A @ C2 @ B5 )
% 0.30/0.47 => ( member @ A @ C2 @ A4 ) )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnCI
% 0.30/0.47 thf(fact_113_Diff__idemp,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) @ B5 )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_idemp
% 0.30/0.47 thf(fact_114_Diff__iff,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 & ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_iff
% 0.30/0.47 thf(fact_115_DiffI,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( ~ ( member @ A @ C2 @ B5 )
% 0.30/0.47 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % DiffI
% 0.30/0.47 thf(fact_116_singletonI,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonI
% 0.30/0.47 thf(fact_117_Un__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty
% 0.30/0.47 thf(fact_118_Diff__cancel,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_cancel
% 0.30/0.47 thf(fact_119_empty__Diff,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % empty_Diff
% 0.30/0.47 thf(fact_120_Diff__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_empty
% 0.30/0.47 thf(fact_121_Un__insert__right,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 0.30/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_insert_right
% 0.30/0.47 thf(fact_122_bot__set__def,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_set_def
% 0.30/0.47 thf(fact_123_not__psubset__empty,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % not_psubset_empty
% 0.30/0.47 thf(fact_124_ex__in__conv,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 0.30/0.47 = ( A4
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ex_in_conv
% 0.30/0.47 thf(fact_125_equals0I,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ! [Y2: A] :
% 0.30/0.47 ~ ( member @ A @ Y2 @ A4 )
% 0.30/0.47 => ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0I
% 0.30/0.47 thf(fact_126_equals0D,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % equals0D
% 0.30/0.47 thf(fact_127_emptyE,axiom,
% 0.30/0.47 ! [A: $tType,A3: A] :
% 0.30/0.47 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % emptyE
% 0.30/0.47 thf(fact_128_mk__disjoint__insert,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ? [B6: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ A3 @ B6 ) )
% 0.30/0.47 & ~ ( member @ A @ A3 @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % mk_disjoint_insert
% 0.30/0.47 thf(fact_129_insert__commute,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A4 ) )
% 0.30/0.47 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_commute
% 0.30/0.47 thf(fact_130_insert__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A,B4: A,B5: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ( ~ ( member @ A @ B4 @ B5 )
% 0.30/0.47 => ( ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 = ( insert @ A @ B4 @ B5 ) )
% 0.30/0.47 = ( ( ( A3 = B4 )
% 0.30/0.47 => ( A4 = B5 ) )
% 0.30/0.47 & ( ( A3 != B4 )
% 0.30/0.47 => ? [C4: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ B4 @ C4 ) )
% 0.30/0.47 & ~ ( member @ A @ B4 @ C4 )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ A3 @ C4 ) )
% 0.30/0.47 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_eq_iff
% 0.30/0.47 thf(fact_131_insert__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 = A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_absorb
% 0.30/0.47 thf(fact_132_insert__ident,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.47 => ( ~ ( member @ A @ X3 @ B5 )
% 0.30/0.47 => ( ( ( insert @ A @ X3 @ A4 )
% 0.30/0.47 = ( insert @ A @ X3 @ B5 ) )
% 0.30/0.47 = ( A4 = B5 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_ident
% 0.30/0.47 thf(fact_133_Set_Oset__insert,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ X3 @ A4 )
% 0.30/0.47 => ~ ! [B6: set @ A] :
% 0.30/0.47 ( ( A4
% 0.30/0.47 = ( insert @ A @ X3 @ B6 ) )
% 0.30/0.47 => ( member @ A @ X3 @ B6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Set.set_insert
% 0.30/0.47 thf(fact_134_insertI2,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 0.30/0.47 ( ( member @ A @ A3 @ B5 )
% 0.30/0.47 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI2
% 0.30/0.47 thf(fact_135_insertI1,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B5: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertI1
% 0.30/0.47 thf(fact_136_insertE,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 0.30/0.47 => ( ( A3 != B4 )
% 0.30/0.47 => ( member @ A @ A3 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insertE
% 0.30/0.47 thf(fact_137_Un__left__commute,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_commute
% 0.30/0.47 thf(fact_138_Un__left__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_left_absorb
% 0.30/0.47 thf(fact_139_Un__commute,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.47 = ( ^ [A6: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A6 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_commute
% 0.30/0.47 thf(fact_140_Un__absorb,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_absorb
% 0.30/0.47 thf(fact_141_Un__assoc,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_assoc
% 0.30/0.47 thf(fact_142_ball__Un,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ( P @ X4 ) ) )
% 0.30/0.47 = ( ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A4 )
% 0.30/0.47 => ( P @ X4 ) )
% 0.30/0.47 & ! [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ B5 )
% 0.30/0.47 => ( P @ X4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ball_Un
% 0.30/0.47 thf(fact_143_bex__Un,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.30/0.47 ( ( ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 & ( P @ X4 ) ) )
% 0.30/0.47 = ( ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ A4 )
% 0.30/0.47 & ( P @ X4 ) )
% 0.30/0.47 | ? [X4: A] :
% 0.30/0.47 ( ( member @ A @ X4 @ B5 )
% 0.30/0.47 & ( P @ X4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bex_Un
% 0.30/0.47 thf(fact_144_UnI2,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ B5 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI2
% 0.30/0.47 thf(fact_145_UnI1,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnI1
% 0.30/0.47 thf(fact_146_UnE,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ( ~ ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % UnE
% 0.30/0.47 thf(fact_147_psubset__imp__ex__mem,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 => ? [B3: A] : ( member @ A @ B3 @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_imp_ex_mem
% 0.30/0.47 thf(fact_148_DiffD2,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ~ ( member @ A @ C2 @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % DiffD2
% 0.30/0.47 thf(fact_149_DiffD1,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ( member @ A @ C2 @ A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % DiffD1
% 0.30/0.47 thf(fact_150_DiffE,axiom,
% 0.30/0.47 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 => ~ ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % DiffE
% 0.30/0.47 thf(fact_151_singleton__inject,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A] :
% 0.30/0.47 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( A3 = B4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_inject
% 0.30/0.47 thf(fact_152_insert__not__empty,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( insert @ A @ A3 @ A4 )
% 0.30/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_not_empty
% 0.30/0.47 thf(fact_153_doubleton__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,B4: A,C2: A,D2: A] :
% 0.30/0.47 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 = ( ( ( A3 = C2 )
% 0.30/0.47 & ( B4 = D2 ) )
% 0.30/0.47 | ( ( A3 = D2 )
% 0.30/0.47 & ( B4 = C2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % doubleton_eq_iff
% 0.30/0.47 thf(fact_154_singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,B4: A,A3: A] :
% 0.30/0.47 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( B4 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_iff
% 0.30/0.47 thf(fact_155_singletonD,axiom,
% 0.30/0.47 ! [A: $tType,B4: A,A3: A] :
% 0.30/0.47 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 => ( B4 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % singletonD
% 0.30/0.47 thf(fact_156_Un__empty__right,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = A4 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_right
% 0.30/0.47 thf(fact_157_Un__empty__left,axiom,
% 0.30/0.47 ! [A: $tType,B5: set @ A] :
% 0.30/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B5 )
% 0.30/0.47 = B5 ) ).
% 0.30/0.47
% 0.30/0.47 % Un_empty_left
% 0.30/0.47 thf(fact_158_insert__Diff__if,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,B5: set @ A,A4: set @ A] :
% 0.30/0.47 ( ( ( member @ A @ X3 @ B5 )
% 0.30/0.47 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) )
% 0.30/0.47 & ( ~ ( member @ A @ X3 @ B5 )
% 0.30/0.47 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 0.30/0.47 = ( insert @ A @ X3 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_Diff_if
% 0.30/0.47 thf(fact_159_Un__Diff,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_Diff
% 0.30/0.47 thf(fact_160_singleton__Un__iff,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 0.30/0.47 ( ( ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.47 = ( ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % singleton_Un_iff
% 0.30/0.47 thf(fact_161_Un__singleton__iff,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,X3: A] :
% 0.30/0.47 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = ( ( ( A4
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 | ( ( A4
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 & ( B5
% 0.30/0.47 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Un_singleton_iff
% 0.30/0.47 thf(fact_162_insert__is__Un,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( insert @ A )
% 0.30/0.47 = ( ^ [A2: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_is_Un
% 0.30/0.47 thf(fact_163_Diff__insert__absorb,axiom,
% 0.30/0.47 ! [A: $tType,X3: A,A4: set @ A] :
% 0.30/0.47 ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.47 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.47 = A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_insert_absorb
% 0.30/0.47 thf(fact_164_Diff__insert2,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B5 ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_insert2
% 0.30/0.47 thf(fact_165_insert__Diff,axiom,
% 0.30/0.47 ! [A: $tType,A3: A,A4: set @ A] :
% 0.30/0.47 ( ( member @ A @ A3 @ A4 )
% 0.30/0.47 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.47 = A4 ) ) ).
% 0.30/0.47
% 0.30/0.47 % insert_Diff
% 0.30/0.47 thf(fact_166_Diff__insert,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 0.30/0.47 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 0.30/0.47 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % Diff_insert
% 0.30/0.47 thf(fact_167_sup__bot_Oright__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.right_neutral
% 0.30/0.47 thf(fact_168_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ A3 @ B4 ) )
% 0.30/0.47 = ( ( A3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B4
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.neutr_eq_iff
% 0.30/0.47 thf(fact_169_sup__bot_Oleft__neutral,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.left_neutral
% 0.30/0.47 thf(fact_170_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ A3 @ B4 )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( A3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( B4
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot.eq_neutr_iff
% 0.30/0.47 thf(fact_171_sup__eq__bot__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ( sup_sup @ A @ X3 @ Y )
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 = ( ( X3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_eq_bot_iff
% 0.30/0.47 thf(fact_172_minus__apply,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( minus @ B )
% 0.30/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.30/0.47 = ( ^ [A6: A > B,B7: A > B,X4: A] : ( minus_minus @ B @ ( A6 @ X4 ) @ ( B7 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % minus_apply
% 0.30/0.47 thf(fact_173_sup__apply,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ B )
% 0.30/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.47 = ( ^ [F4: A > B,G3: A > B,X4: A] : ( sup_sup @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_apply
% 0.30/0.47 thf(fact_174_sup_Oidem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A3 @ A3 )
% 0.30/0.47 = A3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.idem
% 0.30/0.47 thf(fact_175_sup__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X3 @ X3 )
% 0.30/0.47 = X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_idem
% 0.30/0.47 thf(fact_176_sup_Oleft__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B4 ) )
% 0.30/0.47 = ( sup_sup @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.left_idem
% 0.30/0.47 thf(fact_177_sup__left__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y ) )
% 0.30/0.47 = ( sup_sup @ A @ X3 @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_left_idem
% 0.30/0.47 thf(fact_178_sup_Oright__idem,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.47 => ! [A3: A,B4: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B4 ) @ B4 )
% 0.30/0.47 = ( sup_sup @ A @ A3 @ B4 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup.right_idem
% 0.30/0.47 thf(fact_179_sup__bot__left,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 0.30/0.47 = X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_left
% 0.30/0.47 thf(fact_180_sup__bot__right,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 0.30/0.47 = X3 ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_bot_right
% 0.30/0.47 thf(fact_181_bot__eq__sup__iff,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( bounde1808546759up_bot @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( ( bot_bot @ A )
% 0.30/0.47 = ( sup_sup @ A @ X3 @ Y ) )
% 0.30/0.47 = ( ( X3
% 0.30/0.47 = ( bot_bot @ A ) )
% 0.30/0.47 & ( Y
% 0.30/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % bot_eq_sup_iff
% 0.30/0.47 thf(fact_182_psubsetD,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 => ( ( member @ A @ C2 @ A4 )
% 0.30/0.47 => ( member @ A @ C2 @ B5 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubsetD
% 0.30/0.47 thf(fact_183_psubset__trans,axiom,
% 0.30/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 0.30/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.47 => ( ( ord_less @ ( set @ A ) @ B5 @ C3 )
% 0.30/0.47 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % psubset_trans
% 0.30/0.47 thf(fact_184_fun__diff__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( minus @ B )
% 0.30/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.30/0.47 = ( ^ [A6: A > B,B7: A > B,X4: A] : ( minus_minus @ B @ ( A6 @ X4 ) @ ( B7 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % fun_diff_def
% 0.30/0.47 thf(fact_185_inf__sup__aci_I8_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X3: A,Y: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y ) )
% 0.30/0.47 = ( sup_sup @ A @ X3 @ Y ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(8)
% 0.30/0.47 thf(fact_186_inf__sup__aci_I7_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X3: A,Y: A,Z3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) )
% 0.30/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X3 @ Z3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(7)
% 0.30/0.47 thf(fact_187_inf__sup__aci_I6_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ! [X3: A,Y: A,Z3: A] :
% 0.30/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y ) @ Z3 )
% 0.30/0.47 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(6)
% 0.30/0.47 thf(fact_188_inf__sup__aci_I5_J,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( lattice @ A )
% 0.30/0.47 => ( ( sup_sup @ A )
% 0.30/0.47 = ( ^ [X4: A,Y4: A] : ( sup_sup @ A @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % inf_sup_aci(5)
% 0.30/0.47 thf(fact_189_sup__fun__def,axiom,
% 0.30/0.47 ! [B: $tType,A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ B )
% 0.30/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.47 = ( ^ [F4: A > B,G3: A > B,X4: A] : ( sup_sup @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sup_fun_def
% 0.30/0.47 thf(fact_190_boolean__algebra__cancel_Osup1,axiom,
% 0.30/0.47 ! [A: $tType] :
% 0.30/0.47 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [A4: A,K: A,A3: A,B4: A] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 = ( sup_sup @ A @ K @ A3 ) )
% 0.30/0.48 => ( ( sup_sup @ A @ A4 @ B4 )
% 0.30/0.48 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % boolean_algebra_cancel.sup1
% 0.30/0.48 thf(fact_191_boolean__algebra__cancel_Osup2,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [B5: A,K: A,B4: A,A3: A] :
% 0.30/0.48 ( ( B5
% 0.30/0.48 = ( sup_sup @ A @ K @ B4 ) )
% 0.30/0.48 => ( ( sup_sup @ A @ A3 @ B5 )
% 0.30/0.48 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % boolean_algebra_cancel.sup2
% 0.30/0.48 thf(fact_192_sup_Oassoc,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B4 ) @ C2 )
% 0.30/0.48 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.assoc
% 0.30/0.48 thf(fact_193_sup__assoc,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [X3: A,Y: A,Z3: A] :
% 0.30/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y ) @ Z3 )
% 0.30/0.48 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup_assoc
% 0.30/0.48 thf(fact_194_sup_Ocommute,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ( ( sup_sup @ A )
% 0.30/0.48 = ( ^ [A2: A,B2: A] : ( sup_sup @ A @ B2 @ A2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.commute
% 0.30/0.48 thf(fact_195_sup__commute,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ( ( sup_sup @ A )
% 0.30/0.48 = ( ^ [X4: A,Y4: A] : ( sup_sup @ A @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup_commute
% 0.30/0.48 thf(fact_196_sup_Oleft__commute,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [B4: A,A3: A,C2: A] :
% 0.30/0.48 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A3 @ C2 ) )
% 0.30/0.48 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.left_commute
% 0.30/0.48 thf(fact_197_sup__left__commute,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [X3: A,Y: A,Z3: A] :
% 0.30/0.48 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) )
% 0.30/0.48 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X3 @ Z3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup_left_commute
% 0.30/0.48 thf(fact_198_less__supI1,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [X3: A,A3: A,B4: A] :
% 0.30/0.48 ( ( ord_less @ A @ X3 @ A3 )
% 0.30/0.48 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % less_supI1
% 0.30/0.48 thf(fact_199_less__supI2,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [X3: A,B4: A,A3: A] :
% 0.30/0.48 ( ( ord_less @ A @ X3 @ B4 )
% 0.30/0.48 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % less_supI2
% 0.30/0.48 thf(fact_200_sup_Ostrict__boundedE,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [B4: A,C2: A,A3: A] :
% 0.30/0.48 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A3 )
% 0.30/0.48 => ~ ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.48 => ~ ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.strict_boundedE
% 0.30/0.48 thf(fact_201_sup_Ostrict__order__iff,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ( ( ord_less @ A )
% 0.30/0.48 = ( ^ [B2: A,A2: A] :
% 0.30/0.48 ( ( A2
% 0.30/0.48 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/0.48 & ( A2 != B2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.strict_order_iff
% 0.30/0.48 thf(fact_202_sup_Ostrict__coboundedI1,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [C2: A,A3: A,B4: A] :
% 0.30/0.48 ( ( ord_less @ A @ C2 @ A3 )
% 0.30/0.48 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.strict_coboundedI1
% 0.30/0.48 thf(fact_203_sup_Ostrict__coboundedI2,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A )
% 0.30/0.48 => ! [C2: A,B4: A,A3: A] :
% 0.30/0.48 ( ( ord_less @ A @ C2 @ B4 )
% 0.30/0.48 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup.strict_coboundedI2
% 0.30/0.48 thf(fact_204_h2,axiom,
% 0.30/0.48 ( ( binary1610619414edTree @ a @ h @ t2 )
% 0.30/0.48 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t2 ) )
% 0.30/0.48 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t2 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % h2
% 0.30/0.48 thf(fact_205_h1,axiom,
% 0.30/0.48 ( ( binary1610619414edTree @ a @ h @ t1 )
% 0.30/0.48 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t1 ) )
% 0.30/0.48 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t1 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % h1
% 0.30/0.48 thf(fact_206__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,axiom,
% 0.30/0.48 ( ( binary1610619414edTree @ a @ h @ ( binary1746293266le_Tip @ a ) )
% 0.30/0.48 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ ( binary1746293266le_Tip @ a ) ) )
% 0.30/0.48 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ ( binary1746293266le_Tip @ a ) ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % \<open>sortedTree h Tip \<longrightarrow> setOf (binsert h e Tip) = setOf Tip - eqs h e \<union> {e}\<close>
% 0.30/0.48 thf(fact_207_singleton__conv,axiom,
% 0.30/0.48 ! [A: $tType,A3: A] :
% 0.30/0.48 ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] : ( X4 = A3 ) )
% 0.30/0.48 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % singleton_conv
% 0.30/0.48 thf(fact_208_singleton__conv2,axiom,
% 0.30/0.48 ! [A: $tType,A3: A] :
% 0.30/0.48 ( ( collect @ A
% 0.30/0.48 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.30/0.48 @ A3 ) )
% 0.30/0.48 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % singleton_conv2
% 0.30/0.48 thf(fact_209_Un__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.48 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( member @ A @ X4 @ A6 )
% 0.30/0.48 | ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Un_def
% 0.30/0.48 thf(fact_210_empty__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.48 = ( collect @ A
% 0.30/0.48 @ ^ [X4: A] : $false ) ) ).
% 0.30/0.48
% 0.30/0.48 % empty_def
% 0.30/0.48 thf(fact_211_insert__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( insert @ A )
% 0.30/0.48 = ( ^ [A2: A] :
% 0.30/0.48 ( sup_sup @ ( set @ A )
% 0.30/0.48 @ ( collect @ A
% 0.30/0.48 @ ^ [X4: A] : ( X4 = A2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % insert_def
% 0.30/0.48 thf(fact_212_sup__set__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.48 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ( sup_sup @ ( A > $o )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup_set_def
% 0.30/0.48 thf(fact_213_Collect__conv__if,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.48 ( ( ( P @ A3 )
% 0.30/0.48 => ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( X4 = A3 )
% 0.30/0.48 & ( P @ X4 ) ) )
% 0.30/0.48 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.48 & ( ~ ( P @ A3 )
% 0.30/0.48 => ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( X4 = A3 )
% 0.30/0.48 & ( P @ X4 ) ) )
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_conv_if
% 0.30/0.48 thf(fact_214_Collect__disj__eq,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.48 ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( P @ X4 )
% 0.30/0.48 | ( Q @ X4 ) ) )
% 0.30/0.48 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_disj_eq
% 0.30/0.48 thf(fact_215_Collect__conv__if2,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,A3: A] :
% 0.30/0.48 ( ( ( P @ A3 )
% 0.30/0.48 => ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( A3 = X4 )
% 0.30/0.48 & ( P @ X4 ) ) )
% 0.30/0.48 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.48 & ( ~ ( P @ A3 )
% 0.30/0.48 => ( ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( A3 = X4 )
% 0.30/0.48 & ( P @ X4 ) ) )
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_conv_if2
% 0.30/0.48 thf(fact_216_less__set__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ord_less @ ( set @ A ) )
% 0.30/0.48 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.30/0.48 ( ord_less @ ( A > $o )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % less_set_def
% 0.30/0.48 thf(fact_217_Tree_Ocase__distrib,axiom,
% 0.30/0.48 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,Tree: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ( H @ ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ Tree ) )
% 0.30/0.48 = ( binary536355927e_Tree @ C @ A @ ( H @ F1 )
% 0.30/0.48 @ ^ [X12: binary1291135688e_Tree @ A,X25: A,X33: binary1291135688e_Tree @ A] : ( H @ ( F22 @ X12 @ X25 @ X33 ) )
% 0.30/0.48 @ Tree ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.case_distrib
% 0.30/0.48 thf(fact_218_Tree_Opred__True,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( binary1693644968d_Tree @ A
% 0.30/0.48 @ ^ [Uu: A] : $true )
% 0.30/0.48 = ( ^ [Uu: binary1291135688e_Tree @ A] : $true ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.pred_True
% 0.30/0.48 thf(fact_219_eqs__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( binary64540844le_eqs @ A )
% 0.30/0.48 = ( ^ [H2: A > int,X4: A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ^ [Y4: A] :
% 0.30/0.48 ( ( H2 @ Y4 )
% 0.30/0.48 = ( H2 @ X4 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % eqs_def
% 0.30/0.48 thf(fact_220_insert__Collect,axiom,
% 0.30/0.48 ! [A: $tType,A3: A,P: A > $o] :
% 0.30/0.48 ( ( insert @ A @ A3 @ ( collect @ A @ P ) )
% 0.30/0.48 = ( collect @ A
% 0.30/0.48 @ ^ [U: A] :
% 0.30/0.48 ( ( U != A3 )
% 0.30/0.48 => ( P @ U ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % insert_Collect
% 0.30/0.48 thf(fact_221_minus__set__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( minus_minus @ ( set @ A ) )
% 0.30/0.48 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ( minus_minus @ ( A > $o )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % minus_set_def
% 0.30/0.48 thf(fact_222_insert__compr,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( insert @ A )
% 0.30/0.48 = ( ^ [A2: A,B7: set @ A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( X4 = A2 )
% 0.30/0.48 | ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % insert_compr
% 0.30/0.48 thf(fact_223_set__diff__eq,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( minus_minus @ ( set @ A ) )
% 0.30/0.48 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.30/0.48 ( collect @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( ( member @ A @ X4 @ A6 )
% 0.30/0.48 & ~ ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % set_diff_eq
% 0.30/0.48 thf(fact_224_the__elem__eq,axiom,
% 0.30/0.48 ! [A: $tType,X3: A] :
% 0.30/0.48 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.48 = X3 ) ).
% 0.30/0.48
% 0.30/0.48 % the_elem_eq
% 0.30/0.48 thf(fact_225_bot__empty__eq,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.48 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bot_empty_eq
% 0.30/0.48 thf(fact_226_sup1CI,axiom,
% 0.30/0.48 ! [A: $tType,B5: A > $o,X3: A,A4: A > $o] :
% 0.30/0.48 ( ( ~ ( B5 @ X3 )
% 0.30/0.48 => ( A4 @ X3 ) )
% 0.30/0.48 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup1CI
% 0.30/0.48 thf(fact_227_sup1E,axiom,
% 0.30/0.48 ! [A: $tType,A4: A > $o,B5: A > $o,X3: A] :
% 0.30/0.48 ( ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 )
% 0.30/0.48 => ( ~ ( A4 @ X3 )
% 0.30/0.48 => ( B5 @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup1E
% 0.30/0.48 thf(fact_228_sup1I1,axiom,
% 0.30/0.48 ! [A: $tType,A4: A > $o,X3: A,B5: A > $o] :
% 0.30/0.48 ( ( A4 @ X3 )
% 0.30/0.48 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup1I1
% 0.30/0.48 thf(fact_229_sup1I2,axiom,
% 0.30/0.48 ! [A: $tType,B5: A > $o,X3: A,A4: A > $o] :
% 0.30/0.48 ( ( B5 @ X3 )
% 0.30/0.48 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup1I2
% 0.30/0.48 thf(fact_230_sup__Un__eq,axiom,
% 0.30/0.48 ! [A: $tType,R2: set @ A,S: set @ A] :
% 0.30/0.48 ( ( sup_sup @ ( A > $o )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ R2 )
% 0.30/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 0.30/0.48 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R2 @ S ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sup_Un_eq
% 0.30/0.48 thf(fact_231_Collect__empty__eq__bot,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o] :
% 0.30/0.48 ( ( ( collect @ A @ P )
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 = ( P
% 0.30/0.48 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_empty_eq_bot
% 0.30/0.48 thf(fact_232_is__singleton__the__elem,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( is_singleton @ A )
% 0.30/0.48 = ( ^ [A6: set @ A] :
% 0.30/0.48 ( A6
% 0.30/0.48 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % is_singleton_the_elem
% 0.30/0.48 thf(fact_233_is__singletonI,axiom,
% 0.30/0.48 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % is_singletonI
% 0.30/0.48 thf(fact_234_is__singletonI_H,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] :
% 0.30/0.48 ( ( A4
% 0.30/0.48 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.48 => ( ! [X2: A,Y2: A] :
% 0.30/0.48 ( ( member @ A @ X2 @ A4 )
% 0.30/0.48 => ( ( member @ A @ Y2 @ A4 )
% 0.30/0.48 => ( X2 = Y2 ) ) )
% 0.30/0.48 => ( is_singleton @ A @ A4 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % is_singletonI'
% 0.30/0.48 thf(fact_235_is__singleton__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( is_singleton @ A )
% 0.30/0.48 = ( ^ [A6: set @ A] :
% 0.30/0.48 ? [X4: A] :
% 0.30/0.48 ( A6
% 0.30/0.48 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % is_singleton_def
% 0.30/0.48 thf(fact_236_is__singletonE,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A] :
% 0.30/0.48 ( ( is_singleton @ A @ A4 )
% 0.30/0.48 => ~ ! [X2: A] :
% 0.30/0.48 ( A4
% 0.30/0.48 != ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % is_singletonE
% 0.30/0.48 thf(fact_237_diff__strict__right__mono,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ordered_ab_group_add @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A] :
% 0.30/0.48 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.48 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_strict_right_mono
% 0.30/0.48 thf(fact_238_diff__strict__left__mono,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ordered_ab_group_add @ A )
% 0.30/0.48 => ! [B4: A,A3: A,C2: A] :
% 0.30/0.48 ( ( ord_less @ A @ B4 @ A3 )
% 0.30/0.48 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A3 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_strict_left_mono
% 0.30/0.48 thf(fact_239_diff__eq__diff__eq,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( group_add @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A,D2: A] :
% 0.30/0.48 ( ( ( minus_minus @ A @ A3 @ B4 )
% 0.30/0.48 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.30/0.48 => ( ( A3 = B4 )
% 0.30/0.48 = ( C2 = D2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_eq_diff_eq
% 0.30/0.48 thf(fact_240_diff__right__commute,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( cancel146912293up_add @ A )
% 0.30/0.48 => ! [A3: A,C2: A,B4: A] :
% 0.30/0.48 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C2 ) @ B4 )
% 0.30/0.48 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B4 ) @ C2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_right_commute
% 0.30/0.48 thf(fact_241_diff__strict__mono,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ordered_ab_group_add @ A )
% 0.30/0.48 => ! [A3: A,B4: A,D2: A,C2: A] :
% 0.30/0.48 ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.48 => ( ( ord_less @ A @ D2 @ C2 )
% 0.30/0.48 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ D2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_strict_mono
% 0.30/0.48 thf(fact_242_diff__eq__diff__less,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( ordered_ab_group_add @ A )
% 0.30/0.48 => ! [A3: A,B4: A,C2: A,D2: A] :
% 0.30/0.48 ( ( ( minus_minus @ A @ A3 @ B4 )
% 0.30/0.48 = ( minus_minus @ A @ C2 @ D2 ) )
% 0.30/0.48 => ( ( ord_less @ A @ A3 @ B4 )
% 0.30/0.48 = ( ord_less @ A @ C2 @ D2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % diff_eq_diff_less
% 0.30/0.48 thf(fact_243_remove__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( remove @ A )
% 0.30/0.48 = ( ^ [X4: A,A6: set @ A] : ( minus_minus @ ( set @ A ) @ A6 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % remove_def
% 0.30/0.48 thf(fact_244_Tree_Osimps_I15_J,axiom,
% 0.30/0.48 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 0.30/0.48 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary2130109271t_Tree @ A @ X21 ) @ ( insert @ A @ X22 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( binary2130109271t_Tree @ A @ X23 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.simps(15)
% 0.30/0.48 thf(fact_245_member__remove,axiom,
% 0.30/0.48 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 0.30/0.48 ( ( member @ A @ X3 @ ( remove @ A @ Y @ A4 ) )
% 0.30/0.48 = ( ( member @ A @ X3 @ A4 )
% 0.30/0.48 & ( X3 != Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % member_remove
% 0.30/0.48 thf(fact_246_Tree_Osimps_I14_J,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( binary2130109271t_Tree @ A @ ( binary1746293266le_Tip @ A ) )
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.simps(14)
% 0.30/0.48 thf(fact_247_Tree_Oset__intros_I3_J,axiom,
% 0.30/0.48 ! [A: $tType,Ya: A,X23: binary1291135688e_Tree @ A,X21: binary1291135688e_Tree @ A,X22: A] :
% 0.30/0.48 ( ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ X23 ) )
% 0.30/0.48 => ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.set_intros(3)
% 0.30/0.48 thf(fact_248_Tree_Oset__intros_I2_J,axiom,
% 0.30/0.48 ! [A: $tType,X22: A,X21: binary1291135688e_Tree @ A,X23: binary1291135688e_Tree @ A] : ( member @ A @ X22 @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.set_intros(2)
% 0.30/0.48 thf(fact_249_Tree_Oset__intros_I1_J,axiom,
% 0.30/0.48 ! [A: $tType,Y: A,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ X21 ) )
% 0.30/0.48 => ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.set_intros(1)
% 0.30/0.48 thf(fact_250_Tree_Oset__cases,axiom,
% 0.30/0.48 ! [A: $tType,E: A,A3: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ( member @ A @ E @ ( binary2130109271t_Tree @ A @ A3 ) )
% 0.30/0.48 => ( ! [Z1: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ? [Z22: A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( A3
% 0.30/0.48 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 0.30/0.48 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z1 ) ) )
% 0.30/0.48 => ( ! [Z1: binary1291135688e_Tree @ A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( A3
% 0.30/0.48 != ( binary210054475elle_T @ A @ Z1 @ E @ Z32 ) )
% 0.30/0.48 => ~ ! [Z1: binary1291135688e_Tree @ A,Z22: A,Z32: binary1291135688e_Tree @ A] :
% 0.30/0.48 ( ( A3
% 0.30/0.48 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 0.30/0.48 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z32 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.set_cases
% 0.30/0.48 thf(fact_251_Tree_Opred__cong,axiom,
% 0.30/0.48 ! [A: $tType,X3: binary1291135688e_Tree @ A,Ya: binary1291135688e_Tree @ A,P: A > $o,Pa: A > $o] :
% 0.30/0.48 ( ( X3 = Ya )
% 0.30/0.48 => ( ! [Z: A] :
% 0.30/0.48 ( ( member @ A @ Z @ ( binary2130109271t_Tree @ A @ Ya ) )
% 0.30/0.48 => ( ( P @ Z )
% 0.30/0.48 = ( Pa @ Z ) ) )
% 0.30/0.48 => ( ( binary1693644968d_Tree @ A @ P @ X3 )
% 0.30/0.48 = ( binary1693644968d_Tree @ A @ Pa @ Ya ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.pred_cong
% 0.30/0.48 thf(fact_252_Tree_Opred__mono__strong,axiom,
% 0.30/0.48 ! [A: $tType,P: A > $o,X3: binary1291135688e_Tree @ A,Pa: A > $o] :
% 0.30/0.48 ( ( binary1693644968d_Tree @ A @ P @ X3 )
% 0.30/0.48 => ( ! [Z: A] :
% 0.30/0.48 ( ( member @ A @ Z @ ( binary2130109271t_Tree @ A @ X3 ) )
% 0.30/0.48 => ( ( P @ Z )
% 0.30/0.48 => ( Pa @ Z ) ) )
% 0.30/0.48 => ( binary1693644968d_Tree @ A @ Pa @ X3 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Tree.pred_mono_strong
% 0.30/0.48 thf(fact_253_Set_Ois__empty__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( is_empty @ A )
% 0.30/0.48 = ( ^ [A6: set @ A] :
% 0.30/0.48 ( A6
% 0.30/0.48 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Set.is_empty_def
% 0.30/0.48 thf(fact_254_the__elem__def,axiom,
% 0.30/0.48 ! [A: $tType] :
% 0.30/0.48 ( ( the_elem @ A )
% 0.30/0.48 = ( ^ [X6: set @ A] :
% 0.30/0.48 ( the @ A
% 0.30/0.48 @ ^ [X4: A] :
% 0.30/0.48 ( X6
% 0.30/0.48 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % the_elem_def
% 0.30/0.48 thf(fact_255_psubset__insert__iff,axiom,
% 0.30/0.48 ! [A: $tType,A4: set @ A,X3: A,B5: set @ A] :
% 0.30/0.48 ( ( ord_less @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B5 ) )
% 0.30/0.48 = ( ( ( member @ A @ X3 @ B5 )
% 0.30/0.48 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) )
% 0.30/0.48 & ( ~ ( member @ A @ X3 @ B5 )
% 0.30/0.48 => ( ( ( member @ A @ X3 @ A4 )
% 0.30/0.48 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B5 ) )
% 0.30/0.48 & ( ~ ( member @ A @ X3 @ A4 )
% 0.30/0.48 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % psubset_insert_iff
% 0.30/0.48
% 0.30/0.48 % Type constructors (44)
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.48 bounded_lattice @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bounded_lattice @ A8 )
% 0.30/0.48 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bounded_lattice @ A8 )
% 0.30/0.48 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( semilattice_sup @ A8 )
% 0.30/0.48 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( order_bot @ A8 )
% 0.30/0.48 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( preorder @ A8 )
% 0.30/0.48 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( lattice @ A8 )
% 0.30/0.48 => ( lattice @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( order @ A8 )
% 0.30/0.48 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( ord @ A8 )
% 0.30/0.48 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( bot @ A8 )
% 0.30/0.48 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_fun___Groups_Ominus,axiom,
% 0.30/0.48 ! [A7: $tType,A8: $tType] :
% 0.30/0.48 ( ( minus @ A8 )
% 0.30/0.48 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.30/0.48 cancel146912293up_add @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 0.30/0.48 ordered_ab_group_add @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3,axiom,
% 0.30/0.48 semilattice_sup @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.30/0.48 linordered_idom @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Opreorder_4,axiom,
% 0.30/0.48 preorder @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 0.30/0.48 linorder @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 0.30/0.48 no_top @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 0.30/0.48 no_bot @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Lattices_Olattice_5,axiom,
% 0.30/0.48 lattice @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 0.30/0.48 group_add @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Oorder_6,axiom,
% 0.30/0.48 order @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Orderings_Oord_7,axiom,
% 0.30/0.48 ord @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Int_Oint___Groups_Ominus_8,axiom,
% 0.30/0.48 minus @ int ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 0.30/0.48 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 0.30/0.48 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 0.30/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 0.30/0.48 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 0.30/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Oord_15,axiom,
% 0.30/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Orderings_Obot_16,axiom,
% 0.30/0.48 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_Set_Oset___Groups_Ominus_17,axiom,
% 0.30/0.48 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_18,axiom,
% 0.30/0.48 bounde1808546759up_bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19,axiom,
% 0.30/0.48 semilattice_sup @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oorder__bot_20,axiom,
% 0.30/0.48 order_bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 0.30/0.48 preorder @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder_22,axiom,
% 0.30/0.48 linorder @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Lattices_Olattice_23,axiom,
% 0.30/0.48 lattice @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_24,axiom,
% 0.30/0.48 order @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Oord_25,axiom,
% 0.30/0.48 ord @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Orderings_Obot_26,axiom,
% 0.30/0.48 bot @ $o ).
% 0.30/0.48
% 0.30/0.48 thf(tcon_HOL_Obool___Groups_Ominus_27,axiom,
% 0.30/0.48 minus @ $o ).
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 ord_less @ int @ ( h @ w ) @ ( h @ x ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.55/1.66 ---- Embedded in THF ---
% 2.55/1.66 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.55/1.66 %%% Generated on Tue Feb 24 08:25:04 EST 2026
% 2.55/1.66 %%% using '$$dhol' embedding, version 1.3.0.
% 2.55/1.66 %%% Logic specification used:
% 2.55/1.66 %%% thf(spec, logic, $$dhol).
% 2.55/1.66
% 2.55/1.66 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2DTF13441.p
% 2.55/1.66 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree, type, binary1291135688e_Tree: ($tType > $tType)).
% 2.55/1.66 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.55/1.66 thf(ty_t_Int_Oint, type, int: $tType).
% 2.55/1.66 thf(ty_tf_a, type, a: $tType).
% 2.55/1.66 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT, type, binary210054475elle_T: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (binary1291135688e_Tree @ A))))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip, type, binary1746293266le_Tip: (!> [A:$tType]: ((binary1291135688e_Tree @ A)))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree, type, binary536355927e_Tree: (!> [B:$tType,A:$tType]: ((B > (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))) > ((binary1291135688e_Tree @ A) > B)))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Opred__Tree, type, binary1693644968d_Tree: (!> [A:$tType]: (((A > $o) > ((binary1291135688e_Tree @ A) > $o))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree, type, binary1929596613c_Tree: (!> [C:$tType,A:$tType]: ((C > (((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C))))) > ((binary1291135688e_Tree @ A) > C)))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree, type, binary2130109271t_Tree: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (set @ A))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Obinsert, type, binary1830089824insert: (!> [A:$tType]: (((A > int) > (A > ((binary1291135688e_Tree @ A) > (binary1291135688e_Tree @ A))))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs, type, binary64540844le_eqs: (!> [A:$tType]: (((A > int) > (A > (set @ A)))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Omemb, type, binary827270440e_memb: (!> [A:$tType]: (((A > int) > (A > ((binary1291135688e_Tree @ A) > $o)))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf, type, binary1653327646_setOf: (!> [A:$tType]: (((binary1291135688e_Tree @ A) > (set @ A))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree, type, binary1610619414edTree: (!> [A:$tType]: (((A > int) > ((binary1291135688e_Tree @ A) > $o))))).
% 2.55/1.66 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred, type, binary231205461t_pred: (!> [A:$tType]: (((A > int) > (A > (A > ((binary1291135688e_Tree @ A) > $o))))))).
% 2.55/1.66 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.55/1.66 thf(sy_c_HOL_OThe, type, the: (!> [A:$tType]: (((A > $o) > A)))).
% 2.55/1.66 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.55/1.66 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.55/1.66 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.55/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.55/1.66 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.55/1.66 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.55/1.66 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.55/1.66 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.55/1.66 thf(sy_c_Set_Oremove, type, remove: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.55/1.66 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.55/1.66 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.55/1.66 thf(sy_v_e, type, e: a).
% 2.55/1.66 thf(sy_v_h, type, h: (a > int)).
% 2.55/1.66 thf(sy_v_t1____, type, t1: (binary1291135688e_Tree @ a)).
% 2.55/1.66 thf(sy_v_t2____, type, t2: (binary1291135688e_Tree @ a)).
% 2.55/1.66 thf(sy_v_w____, type, w: a).
% 2.55/1.66 thf(sy_v_x____, type, x: a).
% 2.55/1.66 thf(fact_0_whSet, axiom, (((member @ a) @ w) @ ((binary1653327646_setOf @ a) @ t1))).
% 2.55/1.66 thf(fact_1_s, axiom, (((binary1610619414edTree @ a) @ h) @ ((((binary210054475elle_T @ a) @ t1) @ x) @ t2))).
% 2.55/1.66 thf(fact_2_s2, axiom, (((binary1610619414edTree @ a) @ h) @ t2)).
% 2.55/1.66 thf(fact_3_s1, axiom, (((binary1610619414edTree @ a) @ h) @ t1)).
% 2.55/1.66 thf(fact_4_eNotLess, axiom, (~ ((((ord_less @ int) @ (h @ e)) @ (h @ x))))).
% 2.55/1.66 thf(fact_5_xNotLess, axiom, (~ ((((ord_less @ int) @ (h @ x)) @ (h @ e))))).
% 2.55/1.67 thf(fact_6_whEq, axiom, (((member @ a) @ w) @ (((binary64540844le_eqs @ a) @ h) @ e))).
% 2.55/1.67 thf(fact_7_xeqe, axiom, ((h @ x) = (h @ e))).
% 2.55/1.67 thf(fact_8_Tree_Oinject, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A),Y21:(binary1291135688e_Tree @ A),Y22:A,Y23:(binary1291135688e_Tree @ A)]: (((((((binary210054475elle_T @ A) @ X21) @ X22) @ X23) = ((((binary210054475elle_T @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.55/1.67 thf(fact_9_calculation, axiom, (((member @ a) @ x) @ (((binary64540844le_eqs @ a) @ h) @ e))).
% 2.55/1.67 thf(fact_10_minf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ X) @ Z) => (F = F)))))))))))).
% 2.55/1.67 thf(fact_11_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (~ ((((ord_less @ A) @ T) @ X)))))))))))))).
% 2.55/1.67 thf(fact_12_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((ord_less @ A) @ X) @ T)))))))))))).
% 2.55/1.67 thf(fact_13_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 2.55/1.67 thf(fact_14_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (X != T)))))))))))).
% 2.55/1.67 thf(fact_15_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 2.55/1.67 thf(fact_16_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ X) @ Z) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 2.55/1.67 thf(fact_17_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X:C]: (((((ord_less @ C) @ Z) @ X) => (F = F)))))))))))).
% 2.55/1.67 thf(fact_18_res, axiom, (((((binary1830089824insert @ a) @ h) @ e) @ ((((binary210054475elle_T @ a) @ t1) @ x) @ t2)) = ((((binary210054475elle_T @ a) @ t1) @ e) @ t2))).
% 2.55/1.67 thf(fact_19_sortLemmaR, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X3:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) => (((binary1610619414edTree @ A) @ H) @ T2))))).
% 2.55/1.67 thf(fact_20_sortLemmaL, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X3:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) => (((binary1610619414edTree @ A) @ H) @ T1))))).
% 2.55/1.67 thf(fact_21_sortedTree_Osimps_I2_J, axiom, (! [A:$tType,H:(A > int),T1:(binary1291135688e_Tree @ A),X3:A,T2:(binary1291135688e_Tree @ A)]: (((((binary1610619414edTree @ A) @ H) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) = ((((binary1610619414edTree @ A) @ H) @ T1) & ((! [X4:A]: (((((member @ A) @ X4) @ ((binary1653327646_setOf @ A) @ T1)) => (((ord_less @ int) @ (H @ X4)) @ (H @ X3))))) & ((! [X4:A]: (((((member @ A) @ X4) @ ((binary1653327646_setOf @ A) @ T2)) => (((ord_less @ int) @ (H @ X3)) @ (H @ X4))))) & (((binary1610619414edTree @ A) @ H) @ T2)))))))).
% 2.55/1.67 thf(fact_22_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) & (Q @ X)) = ((P2 @ X) & (Q2 @ X)))))))))))))))).
% 2.55/1.67 thf(fact_23_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((P @ X) | (Q @ X)) = ((P2 @ X) | (Q2 @ X)))))))))))))))).
% 2.55/1.67 thf(fact_24_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 2.55/1.67 thf(fact_25_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (X != T)))))))))))).
% 2.55/1.67 thf(fact_26_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (~ ((((ord_less @ A) @ X) @ T)))))))))))))).
% 2.55/1.67 thf(fact_27_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X:A]: (((((ord_less @ A) @ Z) @ X) => (((ord_less @ A) @ T) @ X)))))))))))).
% 2.55/1.67 thf(fact_28_sorted__distinct__pred__def, axiom, (! [A:$tType]: (((binary231205461t_pred @ A) = (^ [H2:(A > int),A2:A,B2:A,T3:(binary1291135688e_Tree @ A)]: ((((((binary1610619414edTree @ A) @ H2) @ T3) & ((((member @ A) @ A2) @ ((binary1653327646_setOf @ A) @ T3)) & ((((member @ A) @ B2) @ ((binary1653327646_setOf @ A) @ T3)) & ((H2 @ A2) = (H2 @ B2))))) => (A2 = B2)))))))).
% 2.55/1.67 thf(fact_29_memb__spec, axiom, (! [A:$tType,H:(A > int),T:(binary1291135688e_Tree @ A),X3:A]: (((((binary1610619414edTree @ A) @ H) @ T) => (((((binary827270440e_memb @ A) @ H) @ X3) @ T) = (((member @ A) @ X3) @ ((binary1653327646_setOf @ A) @ T))))))).
% 2.55/1.67 thf(fact_30_binsert_Osimps_I2_J, axiom, (! [A:$tType,H:(A > int),E:A,X3:A,T1:(binary1291135688e_Tree @ A),T2:(binary1291135688e_Tree @ A)]: ((((((ord_less @ int) @ (H @ E)) @ (H @ X3)) => (((((binary1830089824insert @ A) @ H) @ E) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) = ((((binary210054475elle_T @ A) @ ((((binary1830089824insert @ A) @ H) @ E) @ T1)) @ X3) @ T2))) & ((~ ((((ord_less @ int) @ (H @ E)) @ (H @ X3)))) => (((((ord_less @ int) @ (H @ X3)) @ (H @ E)) => (((((binary1830089824insert @ A) @ H) @ E) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) = ((((binary210054475elle_T @ A) @ T1) @ X3) @ ((((binary1830089824insert @ A) @ H) @ E) @ T2)))) & ((~ ((((ord_less @ int) @ (H @ X3)) @ (H @ E)))) => (((((binary1830089824insert @ A) @ H) @ E) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) = ((((binary210054475elle_T @ A) @ T1) @ E) @ T2))))))))).
% 2.55/1.67 thf(fact_31_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A3:A]: ((? [B3:A]: (((((ord_less @ A) @ A3) @ B3) | (((ord_less @ A) @ B3) @ A3)))))))))).
% 2.55/1.67 thf(fact_32_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X3:A,Y:A]: (((X3 != Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less @ A) @ Y) @ X3))))))))).
% 2.55/1.67 thf(fact_33_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less @ A) @ B4) @ A3) => (A3 != B4)))))))).
% 2.55/1.67 thf(fact_34_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 2.55/1.67 thf(fact_35_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 2.55/1.67 thf(fact_36_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (A3 != B4)))))))).
% 2.55/1.67 thf(fact_37_dependent__wellorder__choice, axiom, (! [B:$tType,A:$tType]: (((wellorder @ A) => (! [P:((A > B) > (A > (B > $o)))]: (((! [R:B,F2:(A > B),G:(A > B),X2:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X2) => ((F2 @ Y3) = (G @ Y3))))) => ((((P @ F2) @ X2) @ R) = (((P @ G) @ X2) @ R))))) => ((! [X2:A,F2:(A > B)]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X2) => (((P @ F2) @ Y3) @ (F2 @ Y3))))) => (? [X_12:B]: ((((P @ F2) @ X2) @ X_12)))))) => (? [F2:(A > B)]: ((! [X:A]: ((((P @ F2) @ X) @ (F2 @ X)))))))))))))).
% 2.55/1.67 thf(fact_38_sorted__distinct, axiom, (! [A:$tType,H:(A > int),A3:A,B4:A,T:(binary1291135688e_Tree @ A)]: ((((((binary231205461t_pred @ A) @ H) @ A3) @ B4) @ T)))).
% 2.55/1.67 thf(fact_39_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F3:(B > A),B4:B,C2:B]: (((A3 = (F3 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F3 @ X2)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A3) @ (F3 @ C2))))))))))).
% 2.55/1.67 thf(fact_40_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B4:A,F3:(A > B),C2:B]: (((((ord_less @ A) @ A3) @ B4) => (((F3 @ B4) = C2) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ B) @ (F3 @ X2)) @ (F3 @ Y2))))) => (((ord_less @ B) @ (F3 @ A3)) @ C2)))))))))).
% 2.55/1.67 thf(fact_41_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F3:(B > A),B4:B,C2:B]: (((((ord_less @ A) @ A3) @ (F3 @ B4)) => ((((ord_less @ B) @ B4) @ C2) => ((! [X2:B,Y2:B]: (((((ord_less @ B) @ X2) @ Y2) => (((ord_less @ A) @ (F3 @ X2)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A3) @ (F3 @ C2))))))))))).
% 2.55/1.67 thf(fact_42_order__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A3:A,B4:A,F3:(A > C),C2:C]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ C) @ (F3 @ B4)) @ C2) => ((! [X2:A,Y2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less @ C) @ (F3 @ X2)) @ (F3 @ Y2))))) => (((ord_less @ C) @ (F3 @ A3)) @ C2)))))))))).
% 2.55/1.67 thf(fact_43_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X3))))))))).
% 2.55/1.67 thf(fact_44_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 2.55/1.67 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.55/1.67 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A4)))) = A4)))).
% 2.55/1.67 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.55/1.67 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G2:(A > B)]: (((! [X2:A]: (((F3 @ X2) = (G2 @ X2)))) => (F3 = G2))))).
% 2.55/1.67 thf(fact_49_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((X3 != Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less @ A) @ Y) @ X3))))))))).
% 2.55/1.67 thf(fact_50_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((X3 != Y) = ((((ord_less @ A) @ X3) @ Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 2.55/1.67 thf(fact_51_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (~ ((((ord_less @ A) @ B4) @ A3)))))))))).
% 2.55/1.67 thf(fact_52_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X3) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 2.55/1.67 thf(fact_53_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 2.55/1.67 thf(fact_54_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 2.55/1.67 thf(fact_55_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) => (~ ((((ord_less @ A) @ B4) @ A3)))))))))).
% 2.55/1.67 thf(fact_56_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 2.55/1.67 thf(fact_57_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) | ((X3 = Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 2.55/1.67 thf(fact_58_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 2.55/1.67 thf(fact_59_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((A3 = B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.55/1.67 thf(fact_60_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => ((B4 = C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.55/1.67 thf(fact_61_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A]: (((((ord_less @ A) @ B4) @ A3) => (~ ((((ord_less @ A) @ A3) @ B4)))))))))).
% 2.55/1.67 thf(fact_62_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 2.55/1.67 thf(fact_63_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 2.55/1.67 thf(fact_64_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A3:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X2) => (P @ Y3)))) => (P @ X2)))) => (P @ A3)))))))).
% 2.55/1.67 thf(fact_65_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X3:A]: (((~ ((((ord_less @ A) @ Y) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y))) = (X3 = Y))))))))).
% 2.55/1.67 thf(fact_66_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (Y != X3)))))))).
% 2.55/1.67 thf(fact_67_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,P:$o]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ X3) => P)))))))).
% 2.55/1.67 thf(fact_68_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((X3 != Y) => (((ord_less @ A) @ Y) @ X3))))))))).
% 2.55/1.67 thf(fact_69_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.55/1.67 thf(fact_70_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ A) @ B4) @ C2) => (((ord_less @ A) @ A3) @ C2))))))))).
% 2.55/1.67 thf(fact_71_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 2.55/1.67 thf(fact_72_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X5:A]: ((P3 @ X5))))) = (^ [P4:(A > $o)]: ((? [N:A]: (((P4 @ N) & (! [M:A]: (((((ord_less @ A) @ M) @ N) => (~ ((P4 @ M)))))))))))))))).
% 2.55/1.67 thf(fact_73_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B4:A]: (((! [A5:A,B3:A]: (((((ord_less @ A) @ A5) @ B3) => ((P @ A5) @ B3)))) => ((! [A5:A]: (((P @ A5) @ A5))) => ((! [A5:A,B3:A]: ((((P @ B3) @ A5) => ((P @ A5) @ B3)))) => ((P @ A3) @ B4)))))))))).
% 2.55/1.67 thf(fact_74_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B4:A,A3:A,C2:A]: (((((ord_less @ A) @ B4) @ A3) => ((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ A3))))))))).
% 2.55/1.67 thf(fact_75_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) = ((((ord_less @ A) @ Y) @ X3) | (X3 = Y))))))))).
% 2.55/1.67 thf(fact_76_binsert_Osimps_I1_J, axiom, (! [A:$tType,H:(A > int),E:A]: ((((((binary1830089824insert @ A) @ H) @ E) @ (binary1746293266le_Tip @ A)) = ((((binary210054475elle_T @ A) @ (binary1746293266le_Tip @ A)) @ E) @ (binary1746293266le_Tip @ A)))))).
% 2.55/1.67 thf(fact_77_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 2.55/1.67 thf(fact_78_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F3:(A > B),P:(A > $o),A3:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F3 @ Y3)) @ (F3 @ X2)) => (P @ Y3)))) => (P @ X2)))) => (P @ A3)))))))).
% 2.55/1.67 thf(fact_79_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F3:(A > B),P:(A > $o),A3:A]: (((! [X2:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F3 @ Y3)) @ (F3 @ X2)) => (P @ Y3)))) => (P @ X2)))) => (P @ A3)))))))).
% 2.55/1.67 thf(fact_80_c2, axiom, (((binary1653327646_setOf @ a) @ ((((binary1830089824insert @ a) @ h) @ e) @ t2)) = (((sup_sup @ (set @ a)) @ (((minus_minus @ (set @ a)) @ ((binary1653327646_setOf @ a) @ t2)) @ (((binary64540844le_eqs @ a) @ h) @ e))) @ (((insert @ a) @ e) @ (bot_bot @ (set @ a)))))).
% 2.55/1.67 thf(fact_81_Tree_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))),X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((F22 @ X21) @ X22) @ X23))))).
% 2.55/1.67 thf(fact_82_c1, axiom, (((binary1653327646_setOf @ a) @ ((((binary1830089824insert @ a) @ h) @ e) @ t1)) = (((sup_sup @ (set @ a)) @ (((minus_minus @ (set @ a)) @ ((binary1653327646_setOf @ a) @ t1)) @ (((binary64540844le_eqs @ a) @ h) @ e))) @ (((insert @ a) @ e) @ (bot_bot @ (set @ a)))))).
% 2.55/1.67 thf(fact_83_Tree_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C))))),X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((((F22 @ X21) @ X22) @ X23) @ (((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ X21)) @ (((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ X23)))))).
% 2.55/1.67 thf(fact_84_Tree_Opred__inject_I2_J, axiom, (! [A:$tType,P:(A > $o),A3:(binary1291135688e_Tree @ A),Aa:A,Ab:(binary1291135688e_Tree @ A)]: (((((binary1693644968d_Tree @ A) @ P) @ ((((binary210054475elle_T @ A) @ A3) @ Aa) @ Ab)) = ((((binary1693644968d_Tree @ A) @ P) @ A3) & ((P @ Aa) & (((binary1693644968d_Tree @ A) @ P) @ Ab))))))).
% 2.55/1.67 thf(fact_85_bot__apply, axiom, (! [C:$tType,D:$tType]: (((bot @ C) => ((bot_bot @ (D > C)) = (^ [X4:D]: ((bot_bot @ C)))))))).
% 2.55/1.67 thf(fact_86_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 2.55/1.67 thf(fact_87_Tree_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,F1:C,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > (C > (C > C)))))]: (((((((binary1929596613c_Tree @ C) @ A) @ F1) @ F22) @ (binary1746293266le_Tip @ A)) = F1)))).
% 2.55/1.67 thf(fact_88_Tree_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B)))]: (((((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ (binary1746293266le_Tip @ A)) = F1)))).
% 2.55/1.67 thf(fact_89_Tree_Opred__inject_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((((binary1693644968d_Tree @ A) @ P) @ (binary1746293266le_Tip @ A))))).
% 2.55/1.67 thf(fact_90_setOf_Osimps_I2_J, axiom, (! [A:$tType,T1:(binary1291135688e_Tree @ A),X3:A,T2:(binary1291135688e_Tree @ A)]: ((((binary1653327646_setOf @ A) @ ((((binary210054475elle_T @ A) @ T1) @ X3) @ T2)) = (((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ ((binary1653327646_setOf @ A) @ T1)) @ ((binary1653327646_setOf @ A) @ T2))) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_91_setOf_Osimps_I1_J, axiom, (! [A:$tType]: ((((binary1653327646_setOf @ A) @ (binary1746293266le_Tip @ A)) = (bot_bot @ (set @ A)))))).
% 2.55/1.67 thf(fact_92_bot_Onot__eq__extremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: (((A3 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A3)))))))).
% 2.55/1.67 thf(fact_93_bot_Oextremum__strict, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ (bot_bot @ A)))))))))).
% 2.55/1.67 thf(fact_94_Tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((binary1746293266le_Tip @ A) != ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))).
% 2.55/1.67 thf(fact_95_Tree_Oinduct, axiom, (! [A:$tType,P:((binary1291135688e_Tree @ A) > $o),Tree:(binary1291135688e_Tree @ A)]: (((P @ (binary1746293266le_Tip @ A)) => ((! [X1:(binary1291135688e_Tree @ A),X24:A,X32:(binary1291135688e_Tree @ A)]: (((P @ X1) => ((P @ X32) => (P @ ((((binary210054475elle_T @ A) @ X1) @ X24) @ X32)))))) => (P @ Tree)))))).
% 2.55/1.67 thf(fact_96_Tree_Oexhaust, axiom, (! [A:$tType,Y:(binary1291135688e_Tree @ A)]: (((Y != (binary1746293266le_Tip @ A)) => (~ ((! [X212:(binary1291135688e_Tree @ A),X222:A,X232:(binary1291135688e_Tree @ A)]: ((Y != ((((binary210054475elle_T @ A) @ X212) @ X222) @ X232)))))))))).
% 2.55/1.67 thf(fact_97_sortedTree_Osimps_I1_J, axiom, (! [A:$tType,H:(A > int)]: ((((binary1610619414edTree @ A) @ H) @ (binary1746293266le_Tip @ A))))).
% 2.55/1.67 thf(fact_98_insert__Diff__single, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = (((insert @ A) @ A3) @ A4))))).
% 2.55/1.67 thf(fact_99_Un__Diff__cancel, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((minus_minus @ (set @ A)) @ B5) @ A4)) = (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.55/1.67 thf(fact_100_Un__Diff__cancel2, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ B5) @ A4)) @ A4) = (((sup_sup @ (set @ A)) @ B5) @ A4))))).
% 2.55/1.67 thf(fact_101_Diff__insert0, axiom, (! [A:$tType,X3:A,A4:(set @ A),B5:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ B5)) = (((minus_minus @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_102_insert__Diff1, axiom, (! [A:$tType,X3:A,B5:(set @ A),A4:(set @ A)]: (((((member @ A) @ X3) @ B5) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B5) = (((minus_minus @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_103_Un__insert__left, axiom, (! [A:$tType,A3:A,B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B5)) @ C3) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B5) @ C3)))))).
% 2.55/1.67 thf(fact_104_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.55/1.67 thf(fact_105_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.55/1.67 thf(fact_106_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_107_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_108_insert__absorb2, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ X3) @ A4)) = (((insert @ A) @ X3) @ A4))))).
% 2.55/1.67 thf(fact_109_insert__iff, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) = ((A3 = B4) | (((member @ A) @ A3) @ A4)))))).
% 2.55/1.67 thf(fact_110_insertCI, axiom, (! [A:$tType,A3:A,B5:(set @ A),B4:A]: ((((~ ((((member @ A) @ A3) @ B5))) => (A3 = B4)) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B5)))))).
% 2.55/1.67 thf(fact_111_Un__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = ((((member @ A) @ C2) @ A4) | (((member @ A) @ C2) @ B5)))))).
% 2.55/1.67 thf(fact_112_UnCI, axiom, (! [A:$tType,C2:A,B5:(set @ A),A4:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B5))) => (((member @ A) @ C2) @ A4)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_113_Diff__idemp, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) @ B5) = (((minus_minus @ (set @ A)) @ A4) @ B5))))).
% 2.55/1.67 thf(fact_114_Diff__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) = ((((member @ A) @ C2) @ A4) & (~ ((((member @ A) @ C2) @ B5)))))))).
% 2.55/1.67 thf(fact_115_DiffI, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A4) => ((~ ((((member @ A) @ C2) @ B5))) => (((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B5))))))).
% 2.55/1.67 thf(fact_116_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_117_Un__empty, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A4) @ B5) = (bot_bot @ (set @ A))) = ((A4 = (bot_bot @ (set @ A))) & (B5 = (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_118_Diff__cancel, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ A4) = (bot_bot @ (set @ A)))))).
% 2.55/1.67 thf(fact_119_empty__Diff, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4) = (bot_bot @ (set @ A)))))).
% 2.55/1.67 thf(fact_120_Diff__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 2.55/1.67 thf(fact_121_Un__insert__right, axiom, (! [A:$tType,A4:(set @ A),A3:A,B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B5)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_122_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.55/1.67 thf(fact_123_not__psubset__empty, axiom, (! [A:$tType,A4:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A4) @ (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_124_ex__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A4))) = (A4 != (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_125_equals0I, axiom, (! [A:$tType,A4:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A4))))) => (A4 = (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_126_equals0D, axiom, (! [A:$tType,A4:(set @ A),A3:A]: (((A4 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A4))))))).
% 2.55/1.67 thf(fact_127_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_128_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => (? [B6:(set @ A)]: (((A4 = (((insert @ A) @ A3) @ B6)) & (~ ((((member @ A) @ A3) @ B6)))))))))).
% 2.55/1.67 thf(fact_129_insert__commute, axiom, (! [A:$tType,X3:A,Y:A,A4:(set @ A)]: (((((insert @ A) @ X3) @ (((insert @ A) @ Y) @ A4)) = (((insert @ A) @ Y) @ (((insert @ A) @ X3) @ A4)))))).
% 2.55/1.67 thf(fact_130_insert__eq__iff, axiom, (! [A:$tType,A3:A,A4:(set @ A),B4:A,B5:(set @ A)]: (((~ ((((member @ A) @ A3) @ A4))) => ((~ ((((member @ A) @ B4) @ B5))) => (((((insert @ A) @ A3) @ A4) = (((insert @ A) @ B4) @ B5)) = (((A3 = B4) => (A4 = B5)) & ((A3 != B4) => (? [C4:(set @ A)]: (((A4 = (((insert @ A) @ B4) @ C4)) & ((~ ((((member @ A) @ B4) @ C4))) & ((B5 = (((insert @ A) @ A3) @ C4)) & (~ ((((member @ A) @ A3) @ C4)))))))))))))))).
% 2.55/1.67 thf(fact_131_insert__absorb, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((insert @ A) @ A3) @ A4) = A4))))).
% 2.55/1.67 thf(fact_132_insert__ident, axiom, (! [A:$tType,X3:A,A4:(set @ A),B5:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((~ ((((member @ A) @ X3) @ B5))) => (((((insert @ A) @ X3) @ A4) = (((insert @ A) @ X3) @ B5)) = (A4 = B5))))))).
% 2.55/1.67 thf(fact_133_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((((member @ A) @ X3) @ A4) => (~ ((! [B6:(set @ A)]: (((A4 = (((insert @ A) @ X3) @ B6)) => (((member @ A) @ X3) @ B6)))))))))).
% 2.55/1.67 thf(fact_134_insertI2, axiom, (! [A:$tType,A3:A,B5:(set @ A),B4:A]: (((((member @ A) @ A3) @ B5) => (((member @ A) @ A3) @ (((insert @ A) @ B4) @ B5)))))).
% 2.55/1.67 thf(fact_135_insertI1, axiom, (! [A:$tType,A3:A,B5:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B5))))).
% 2.55/1.67 thf(fact_136_insertE, axiom, (! [A:$tType,A3:A,B4:A,A4:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B4) @ A4)) => ((A3 != B4) => (((member @ A) @ A3) @ A4)))))).
% 2.55/1.67 thf(fact_137_Un__left__commute, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C3)) = (((sup_sup @ (set @ A)) @ B5) @ (((sup_sup @ (set @ A)) @ A4) @ C3)))))).
% 2.55/1.67 thf(fact_138_Un__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.55/1.67 thf(fact_139_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: ((((sup_sup @ (set @ A)) @ B7) @ A6))))))).
% 2.55/1.67 thf(fact_140_Un__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.55/1.67 thf(fact_141_Un__assoc, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C3) = (((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C3)))))).
% 2.55/1.67 thf(fact_142_ball__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => (P @ X4)))) = ((! [X4:A]: (((((member @ A) @ X4) @ A4) => (P @ X4)))) & (! [X4:A]: (((((member @ A) @ X4) @ B5) => (P @ X4))))))))).
% 2.55/1.67 thf(fact_143_bex__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) & (P @ X4)))) = ((? [X4:A]: (((((member @ A) @ X4) @ A4) & (P @ X4)))) | (? [X4:A]: (((((member @ A) @ X4) @ B5) & (P @ X4))))))))).
% 2.55/1.67 thf(fact_144_UnI2, axiom, (! [A:$tType,C2:A,B5:(set @ A),A4:(set @ A)]: (((((member @ A) @ C2) @ B5) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_145_UnI1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.55/1.67 thf(fact_146_UnE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => ((~ ((((member @ A) @ C2) @ A4))) => (((member @ A) @ C2) @ B5)))))).
% 2.55/1.67 thf(fact_147_psubset__imp__ex__mem, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => (? [B3:A]: ((((member @ A) @ B3) @ (((minus_minus @ (set @ A)) @ B5) @ A4)))))))).
% 2.55/1.67 thf(fact_148_DiffD2, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) => (~ ((((member @ A) @ C2) @ B5))))))).
% 2.55/1.67 thf(fact_149_DiffD1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) => (((member @ A) @ C2) @ A4))))).
% 2.55/1.67 thf(fact_150_DiffE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C2) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) => (~ (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B5)))))))).
% 2.55/1.67 thf(fact_151_singleton__inject, axiom, (! [A:$tType,A3:A,B4:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) => (A3 = B4))))).
% 2.55/1.67 thf(fact_152_insert__not__empty, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((insert @ A) @ A3) @ A4) != (bot_bot @ (set @ A)))))).
% 2.55/1.67 thf(fact_153_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B4:A,C2:A,D2:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B4) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A3 = C2) & (B4 = D2)) | ((A3 = D2) & (B4 = C2))))))).
% 2.55/1.67 thf(fact_154_singleton__iff, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B4 = A3))))).
% 2.55/1.67 thf(fact_155_singletonD, axiom, (! [A:$tType,B4:A,A3:A]: (((((member @ A) @ B4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B4 = A3))))).
% 2.55/1.67 thf(fact_156_Un__empty__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 2.55/1.67 thf(fact_157_Un__empty__left, axiom, (! [A:$tType,B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B5) = B5)))).
% 2.55/1.67 thf(fact_158_insert__Diff__if, axiom, (! [A:$tType,X3:A,B5:(set @ A),A4:(set @ A)]: ((((((member @ A) @ X3) @ B5) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B5) = (((minus_minus @ (set @ A)) @ A4) @ B5))) & ((~ ((((member @ A) @ X3) @ B5))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ B5) = (((insert @ A) @ X3) @ (((minus_minus @ (set @ A)) @ A4) @ B5)))))))).
% 2.55/1.67 thf(fact_159_Un__Diff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C3) = (((sup_sup @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ C3)) @ (((minus_minus @ (set @ A)) @ B5) @ C3)))))).
% 2.55/1.67 thf(fact_160_singleton__Un__iff, axiom, (! [A:$tType,X3:A,A4:(set @ A),B5:(set @ A)]: ((((((insert @ A) @ X3) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A4) @ B5)) = (((A4 = (bot_bot @ (set @ A))) & (B5 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B5 = (bot_bot @ (set @ A)))) | ((A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B5 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 2.55/1.67 thf(fact_161_Un__singleton__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X3:A]: ((((((sup_sup @ (set @ A)) @ A4) @ B5) = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = (((A4 = (bot_bot @ (set @ A))) & (B5 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B5 = (bot_bot @ (set @ A)))) | ((A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B5 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 2.55/1.67 thf(fact_162_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))))))))).
% 2.55/1.67 thf(fact_163_Diff__insert__absorb, axiom, (! [A:$tType,X3:A,A4:(set @ A)]: (((~ ((((member @ A) @ X3) @ A4))) => ((((minus_minus @ (set @ A)) @ (((insert @ A) @ X3) @ A4)) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = A4))))).
% 2.55/1.67 thf(fact_164_Diff__insert2, axiom, (! [A:$tType,A4:(set @ A),A3:A,B5:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B5)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) @ B5))))).
% 2.55/1.67 thf(fact_165_insert__Diff, axiom, (! [A:$tType,A3:A,A4:(set @ A)]: (((((member @ A) @ A3) @ A4) => ((((insert @ A) @ A3) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) = A4))))).
% 2.55/1.67 thf(fact_166_Diff__insert, axiom, (! [A:$tType,A4:(set @ A),A3:A,B5:(set @ A)]: (((((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ A3) @ B5)) = (((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ B5)) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_167_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 2.55/1.67 thf(fact_168_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B4:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A3) @ B4)) = ((A3 = (bot_bot @ A)) & (B4 = (bot_bot @ A)))))))))).
% 2.55/1.67 thf(fact_169_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A3) = A3))))))).
% 2.55/1.67 thf(fact_170_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B4:A]: ((((((sup_sup @ A) @ A3) @ B4) = (bot_bot @ A)) = ((A3 = (bot_bot @ A)) & (B4 = (bot_bot @ A)))))))))).
% 2.55/1.67 thf(fact_171_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y:A]: ((((((sup_sup @ A) @ X3) @ Y) = (bot_bot @ A)) = ((X3 = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.55/1.67 thf(fact_172_minus__apply, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B7:(A > B),X4:A]: ((((minus_minus @ B) @ (A6 @ X4)) @ (B7 @ X4))))))))).
% 2.55/1.67 thf(fact_173_sup__apply, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F4:(A > B),G3:(A > B),X4:A]: ((((sup_sup @ B) @ (F4 @ X4)) @ (G3 @ X4))))))))).
% 2.55/1.67 thf(fact_174_sup_Oidem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ A3) = A3))))))).
% 2.55/1.67 thf(fact_175_sup__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ X3) = X3))))))).
% 2.55/1.67 thf(fact_176_sup_Oleft__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B4:A]: (((((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ A3) @ B4)) = (((sup_sup @ A) @ A3) @ B4)))))))).
% 2.55/1.67 thf(fact_177_sup__left__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y)) = (((sup_sup @ A) @ X3) @ Y)))))))).
% 2.55/1.67 thf(fact_178_sup_Oright__idem, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B4:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B4)) @ B4) = (((sup_sup @ A) @ A3) @ B4)))))))).
% 2.55/1.67 thf(fact_179_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X3) = X3))))))).
% 2.55/1.67 thf(fact_180_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ (bot_bot @ A)) = X3))))))).
% 2.55/1.67 thf(fact_181_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X3) @ Y)) = ((X3 = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.55/1.67 thf(fact_182_psubsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ B5)))))).
% 2.55/1.67 thf(fact_183_psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((ord_less @ (set @ A)) @ B5) @ C3) => (((ord_less @ (set @ A)) @ A4) @ C3)))))).
% 2.55/1.67 thf(fact_184_fun__diff__def, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B7:(A > B),X4:A]: ((((minus_minus @ B) @ (A6 @ X4)) @ (B7 @ X4))))))))).
% 2.55/1.67 thf(fact_185_inf__sup__aci_I8_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ X3) @ Y)) = (((sup_sup @ A) @ X3) @ Y)))))))).
% 2.55/1.67 thf(fact_186_inf__sup__aci_I7_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y:A,Z3:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y) @ Z3)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X3) @ Z3))))))))).
% 2.55/1.67 thf(fact_187_inf__sup__aci_I6_J, axiom, (! [A:$tType]: (((lattice @ A) => (! [X3:A,Y:A,Z3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X3) @ Y)) @ Z3) = (((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y) @ Z3))))))))).
% 2.55/1.67 thf(fact_188_inf__sup__aci_I5_J, axiom, (! [A:$tType]: (((lattice @ A) => ((sup_sup @ A) = (^ [X4:A,Y4:A]: ((((sup_sup @ A) @ Y4) @ X4)))))))).
% 2.55/1.67 thf(fact_189_sup__fun__def, axiom, (! [B:$tType,A:$tType]: (((semilattice_sup @ B) => ((sup_sup @ (A > B)) = (^ [F4:(A > B),G3:(A > B),X4:A]: ((((sup_sup @ B) @ (F4 @ X4)) @ (G3 @ X4))))))))).
% 2.55/1.67 thf(fact_190_boolean__algebra__cancel_Osup1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A4:A,K:A,A3:A,B4:A]: (((A4 = (((sup_sup @ A) @ K) @ A3)) => ((((sup_sup @ A) @ A4) @ B4) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A3) @ B4)))))))))).
% 2.55/1.67 thf(fact_191_boolean__algebra__cancel_Osup2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B5:A,K:A,B4:A,A3:A]: (((B5 = (((sup_sup @ A) @ K) @ B4)) => ((((sup_sup @ A) @ A3) @ B5) = (((sup_sup @ A) @ K) @ (((sup_sup @ A) @ A3) @ B4)))))))))).
% 2.55/1.67 thf(fact_192_sup_Oassoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [A3:A,B4:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A3) @ B4)) @ C2) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 2.55/1.67 thf(fact_193_sup__assoc, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y:A,Z3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X3) @ Y)) @ Z3) = (((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y) @ Z3))))))))).
% 2.55/1.67 thf(fact_194_sup_Ocommute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [A2:A,B2:A]: ((((sup_sup @ A) @ B2) @ A2)))))))).
% 2.55/1.67 thf(fact_195_sup__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((sup_sup @ A) = (^ [X4:A,Y4:A]: ((((sup_sup @ A) @ Y4) @ X4)))))))).
% 2.55/1.67 thf(fact_196_sup_Oleft__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,A3:A,C2:A]: (((((sup_sup @ A) @ B4) @ (((sup_sup @ A) @ A3) @ C2)) = (((sup_sup @ A) @ A3) @ (((sup_sup @ A) @ B4) @ C2))))))))).
% 2.55/1.67 thf(fact_197_sup__left__commute, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,Y:A,Z3:A]: (((((sup_sup @ A) @ X3) @ (((sup_sup @ A) @ Y) @ Z3)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X3) @ Z3))))))))).
% 2.55/1.67 thf(fact_198_less__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,A3:A,B4:A]: (((((ord_less @ A) @ X3) @ A3) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.55/1.67 thf(fact_199_less__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,B4:A,A3:A]: (((((ord_less @ A) @ X3) @ B4) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.55/1.67 thf(fact_200_sup_Ostrict__boundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B4:A,C2:A,A3:A]: (((((ord_less @ A) @ (((sup_sup @ A) @ B4) @ C2)) @ A3) => (~ (((((ord_less @ A) @ B4) @ A3) => (~ ((((ord_less @ A) @ C2) @ A3))))))))))))).
% 2.55/1.67 thf(fact_201_sup_Ostrict__order__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less @ A) = (^ [B2:A,A2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) & (A2 != B2))))))))).
% 2.55/1.67 thf(fact_202_sup_Ostrict__coboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,A3:A,B4:A]: (((((ord_less @ A) @ C2) @ A3) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.55/1.67 thf(fact_203_sup_Ostrict__coboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C2:A,B4:A,A3:A]: (((((ord_less @ A) @ C2) @ B4) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A3) @ B4))))))))).
% 2.55/1.67 thf(fact_204_h2, axiom, ((((binary1610619414edTree @ a) @ h) @ t2) => (((binary1653327646_setOf @ a) @ ((((binary1830089824insert @ a) @ h) @ e) @ t2)) = (((sup_sup @ (set @ a)) @ (((minus_minus @ (set @ a)) @ ((binary1653327646_setOf @ a) @ t2)) @ (((binary64540844le_eqs @ a) @ h) @ e))) @ (((insert @ a) @ e) @ (bot_bot @ (set @ a))))))).
% 2.55/1.67 thf(fact_205_h1, axiom, ((((binary1610619414edTree @ a) @ h) @ t1) => (((binary1653327646_setOf @ a) @ ((((binary1830089824insert @ a) @ h) @ e) @ t1)) = (((sup_sup @ (set @ a)) @ (((minus_minus @ (set @ a)) @ ((binary1653327646_setOf @ a) @ t1)) @ (((binary64540844le_eqs @ a) @ h) @ e))) @ (((insert @ a) @ e) @ (bot_bot @ (set @ a))))))).
% 2.55/1.67 thf(fact_206__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062, axiom, ((((binary1610619414edTree @ a) @ h) @ (binary1746293266le_Tip @ a)) => (((binary1653327646_setOf @ a) @ ((((binary1830089824insert @ a) @ h) @ e) @ (binary1746293266le_Tip @ a))) = (((sup_sup @ (set @ a)) @ (((minus_minus @ (set @ a)) @ ((binary1653327646_setOf @ a) @ (binary1746293266le_Tip @ a))) @ (((binary64540844le_eqs @ a) @ h) @ e))) @ (((insert @ a) @ e) @ (bot_bot @ (set @ a))))))).
% 2.55/1.67 thf(fact_207_singleton__conv, axiom, (! [A:$tType,A3:A]: ((((collect @ A) @ (^ [X4:A]: ((X4 = A3)))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_208_singleton__conv2, axiom, (! [A:$tType,A3:A]: ((((collect @ A) @ ((^ [Y5:A,Z4:A]: ((Y5 = Z4))) @ A3)) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_209_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A6) | (((member @ A) @ X4) @ B7))))))))))).
% 2.55/1.67 thf(fact_210_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X4:A]: ($false))))))).
% 2.55/1.67 thf(fact_211_insert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A]: (((sup_sup @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: ((X4 = A2))))))))))).
% 2.55/1.67 thf(fact_212_sup__set__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: (((collect @ A) @ (((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B7))))))))))).
% 2.55/1.67 thf(fact_213_Collect__conv__if, axiom, (! [A:$tType,P:(A > $o),A3:A]: ((((P @ A3) => (((collect @ A) @ (^ [X4:A]: (((X4 = A3) & (P @ X4))))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A3))) => (((collect @ A) @ (^ [X4:A]: (((X4 = A3) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_214_Collect__disj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X4:A]: (((P @ X4) | (Q @ X4))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.55/1.67 thf(fact_215_Collect__conv__if2, axiom, (! [A:$tType,P:(A > $o),A3:A]: ((((P @ A3) => (((collect @ A) @ (^ [X4:A]: (((A3 = X4) & (P @ X4))))) = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A3))) => (((collect @ A) @ (^ [X4:A]: (((A3 = X4) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 2.55/1.67 thf(fact_216_less__set__def, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: ((((ord_less @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B7)))))))))).
% 2.55/1.67 thf(fact_217_Tree_Ocase__distrib, axiom, (! [C:$tType,B:$tType,A:$tType,H:(B > C),F1:B,F22:((binary1291135688e_Tree @ A) > (A > ((binary1291135688e_Tree @ A) > B))),Tree:(binary1291135688e_Tree @ A)]: (((H @ (((((binary536355927e_Tree @ B) @ A) @ F1) @ F22) @ Tree)) = (((((binary536355927e_Tree @ C) @ A) @ (H @ F1)) @ (^ [X12:(binary1291135688e_Tree @ A),X25:A,X33:(binary1291135688e_Tree @ A)]: ((H @ (((F22 @ X12) @ X25) @ X33))))) @ Tree))))).
% 2.55/1.67 thf(fact_218_Tree_Opred__True, axiom, (! [A:$tType]: ((((binary1693644968d_Tree @ A) @ (^ [Uu:A]: ($true))) = (^ [Uu:(binary1291135688e_Tree @ A)]: ($true)))))).
% 2.55/1.67 thf(fact_219_eqs__def, axiom, (! [A:$tType]: (((binary64540844le_eqs @ A) = (^ [H2:(A > int),X4:A]: (((collect @ A) @ (^ [Y4:A]: (((H2 @ Y4) = (H2 @ X4))))))))))).
% 2.55/1.67 thf(fact_220_insert__Collect, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((insert @ A) @ A3) @ ((collect @ A) @ P)) = ((collect @ A) @ (^ [U:A]: (((U != A3) => (P @ U))))))))).
% 2.55/1.67 thf(fact_221_minus__set__def, axiom, (! [A:$tType]: (((minus_minus @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: (((collect @ A) @ (((minus_minus @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A6)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B7))))))))))).
% 2.55/1.67 thf(fact_222_insert__compr, axiom, (! [A:$tType]: (((insert @ A) = (^ [A2:A,B7:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((X4 = A2) | (((member @ A) @ X4) @ B7))))))))))).
% 2.55/1.67 thf(fact_223_set__diff__eq, axiom, (! [A:$tType]: (((minus_minus @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A6) & (~ ((((member @ A) @ X4) @ B7))))))))))))).
% 2.55/1.67 thf(fact_224_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 2.55/1.67 thf(fact_225_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.55/1.67 thf(fact_226_sup1CI, axiom, (! [A:$tType,B5:(A > $o),X3:A,A4:(A > $o)]: ((((~ ((B5 @ X3))) => (A4 @ X3)) => ((((sup_sup @ (A > $o)) @ A4) @ B5) @ X3))))).
% 2.55/1.67 thf(fact_227_sup1E, axiom, (! [A:$tType,A4:(A > $o),B5:(A > $o),X3:A]: ((((((sup_sup @ (A > $o)) @ A4) @ B5) @ X3) => ((~ ((A4 @ X3))) => (B5 @ X3)))))).
% 2.55/1.67 thf(fact_228_sup1I1, axiom, (! [A:$tType,A4:(A > $o),X3:A,B5:(A > $o)]: (((A4 @ X3) => ((((sup_sup @ (A > $o)) @ A4) @ B5) @ X3))))).
% 2.55/1.67 thf(fact_229_sup1I2, axiom, (! [A:$tType,B5:(A > $o),X3:A,A4:(A > $o)]: (((B5 @ X3) => ((((sup_sup @ (A > $o)) @ A4) @ B5) @ X3))))).
% 2.55/1.67 thf(fact_230_sup__Un__eq, axiom, (! [A:$tType,R2:(set @ A),S:(set @ A)]: (((((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ R2)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ S)))) = (^ [X4:A]: ((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ R2) @ S)))))))).
% 2.55/1.67 thf(fact_231_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.55/1.67 thf(fact_232_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((A6 = (((insert @ A) @ ((the_elem @ A) @ A6)) @ (bot_bot @ (set @ A)))))))))).
% 2.55/1.67 thf(fact_233_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 2.55/1.67 thf(fact_234_is__singletonI_H, axiom, (! [A:$tType,A4:(set @ A)]: (((A4 != (bot_bot @ (set @ A))) => ((! [X2:A,Y2:A]: (((((member @ A) @ X2) @ A4) => ((((member @ A) @ Y2) @ A4) => (X2 = Y2))))) => ((is_singleton @ A) @ A4)))))).
% 2.55/1.67 thf(fact_235_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A6:(set @ A)]: ((? [X4:A]: ((A6 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 2.55/1.67 thf(fact_236_is__singletonE, axiom, (! [A:$tType,A4:(set @ A)]: ((((is_singleton @ A) @ A4) => (~ ((! [X2:A]: ((A4 != (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 2.55/1.67 thf(fact_237_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B4:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => (((ord_less @ A) @ (((minus_minus @ A) @ A3) @ C2)) @ (((minus_minus @ A) @ B4) @ C2))))))))).
% 2.55/1.67 thf(fact_238_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B4:A,A3:A,C2:A]: (((((ord_less @ A) @ B4) @ A3) => (((ord_less @ A) @ (((minus_minus @ A) @ C2) @ A3)) @ (((minus_minus @ A) @ C2) @ B4))))))))).
% 2.55/1.67 thf(fact_239_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A,B4:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A3) @ B4) = (((minus_minus @ A) @ C2) @ D2)) => ((A3 = B4) = (C2 = D2))))))))).
% 2.55/1.67 thf(fact_240_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A3:A,C2:A,B4:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ C2)) @ B4) = (((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ B4)) @ C2)))))))).
% 2.55/1.67 thf(fact_241_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B4:A,D2:A,C2:A]: (((((ord_less @ A) @ A3) @ B4) => ((((ord_less @ A) @ D2) @ C2) => (((ord_less @ A) @ (((minus_minus @ A) @ A3) @ C2)) @ (((minus_minus @ A) @ B4) @ D2)))))))))).
% 2.55/1.67 thf(fact_242_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B4:A,C2:A,D2:A]: ((((((minus_minus @ A) @ A3) @ B4) = (((minus_minus @ A) @ C2) @ D2)) => ((((ord_less @ A) @ A3) @ B4) = (((ord_less @ A) @ C2) @ D2))))))))).
% 2.55/1.67 thf(fact_243_remove__def, axiom, (! [A:$tType]: (((remove @ A) = (^ [X4:A,A6:(set @ A)]: ((((minus_minus @ (set @ A)) @ A6) @ (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))).
% 2.55/1.67 thf(fact_244_Tree_Osimps_I15_J, axiom, (! [A:$tType,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: ((((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)) = (((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ ((binary2130109271t_Tree @ A) @ X21)) @ (((insert @ A) @ X22) @ (bot_bot @ (set @ A))))) @ ((binary2130109271t_Tree @ A) @ X23)))))).
% 2.55/1.67 thf(fact_245_member__remove, axiom, (! [A:$tType,X3:A,Y:A,A4:(set @ A)]: (((((member @ A) @ X3) @ (((remove @ A) @ Y) @ A4)) = ((((member @ A) @ X3) @ A4) & (X3 != Y)))))).
% 2.55/1.67 thf(fact_246_Tree_Osimps_I14_J, axiom, (! [A:$tType]: ((((binary2130109271t_Tree @ A) @ (binary1746293266le_Tip @ A)) = (bot_bot @ (set @ A)))))).
% 2.55/1.67 thf(fact_247_Tree_Oset__intros_I3_J, axiom, (! [A:$tType,Ya:A,X23:(binary1291135688e_Tree @ A),X21:(binary1291135688e_Tree @ A),X22:A]: (((((member @ A) @ Ya) @ ((binary2130109271t_Tree @ A) @ X23)) => (((member @ A) @ Ya) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))))).
% 2.55/1.67 thf(fact_248_Tree_Oset__intros_I2_J, axiom, (! [A:$tType,X22:A,X21:(binary1291135688e_Tree @ A),X23:(binary1291135688e_Tree @ A)]: ((((member @ A) @ X22) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23)))))).
% 2.55/1.67 thf(fact_249_Tree_Oset__intros_I1_J, axiom, (! [A:$tType,Y:A,X21:(binary1291135688e_Tree @ A),X22:A,X23:(binary1291135688e_Tree @ A)]: (((((member @ A) @ Y) @ ((binary2130109271t_Tree @ A) @ X21)) => (((member @ A) @ Y) @ ((binary2130109271t_Tree @ A) @ ((((binary210054475elle_T @ A) @ X21) @ X22) @ X23))))))).
% 2.55/1.67 thf(fact_250_Tree_Oset__cases, axiom, (! [A:$tType,E:A,A3:(binary1291135688e_Tree @ A)]: (((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ A3)) => ((! [Z1:(binary1291135688e_Tree @ A)]: (((? [Z22:A,Z32:(binary1291135688e_Tree @ A)]: ((A3 = ((((binary210054475elle_T @ A) @ Z1) @ Z22) @ Z32)))) => (~ ((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ Z1))))))) => ((! [Z1:(binary1291135688e_Tree @ A),Z32:(binary1291135688e_Tree @ A)]: ((A3 != ((((binary210054475elle_T @ A) @ Z1) @ E) @ Z32)))) => (~ ((! [Z1:(binary1291135688e_Tree @ A),Z22:A,Z32:(binary1291135688e_Tree @ A)]: (((A3 = ((((binary210054475elle_T @ A) @ Z1) @ Z22) @ Z32)) => (~ ((((member @ A) @ E) @ ((binary2130109271t_Tree @ A) @ Z32))))))))))))))).
% 2.55/1.67 thf(fact_251_Tree_Opred__cong, axiom, (! [A:$tType,X3:(binary1291135688e_Tree @ A),Ya:(binary1291135688e_Tree @ A),P:(A > $o),Pa:(A > $o)]: (((X3 = Ya) => ((! [Z:A]: (((((member @ A) @ Z) @ ((binary2130109271t_Tree @ A) @ Ya)) => ((P @ Z) = (Pa @ Z))))) => ((((binary1693644968d_Tree @ A) @ P) @ X3) = (((binary1693644968d_Tree @ A) @ Pa) @ Ya))))))).
% 2.55/1.67 thf(fact_252_Tree_Opred__mono__strong, axiom, (! [A:$tType,P:(A > $o),X3:(binary1291135688e_Tree @ A),Pa:(A > $o)]: (((((binary1693644968d_Tree @ A) @ P) @ X3) => ((! [Z:A]: (((((member @ A) @ Z) @ ((binary2130109271t_Tree @ A) @ X3)) => ((P @ Z) => (Pa @ Z))))) => (((binary1693644968d_Tree @ A) @ Pa) @ X3)))))).
% 2.55/1.67 thf(fact_253_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A6:(set @ A)]: ((A6 = (bot_bot @ (set @ A))))))))).
% 2.55/1.67 thf(fact_254_the__elem__def, axiom, (! [A:$tType]: (((the_elem @ A) = (^ [X6:(set @ A)]: (((the @ A) @ (^ [X4:A]: ((X6 = (((insert @ A) @ X4) @ (bot_bot @ (set @ A))))))))))))).
% 2.55/1.67 thf(fact_255_psubset__insert__iff, axiom, (! [A:$tType,A4:(set @ A),X3:A,B5:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ B5)) = (((((member @ A) @ X3) @ B5) => (((ord_less @ (set @ A)) @ A4) @ B5)) & ((~ ((((member @ A) @ X3) @ B5))) => (((((member @ A) @ X3) @ A4) => (((ord_less @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A4) @ (((insert @ A) @ X3) @ (bot_bot @ (set @ A))))) @ B5)) & ((~ ((((member @ A) @ X3) @ A4))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))))))).
% 2.55/1.67 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.55/1.67 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 2.55/1.67 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounde1808546759up_bot @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: (((lattice @ A8) => (lattice @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_fun___Groups_Ominus, axiom, (! [A7:$tType,A8:$tType]: (((minus @ A8) => (minus @ (A7 > A8)))))).
% 2.55/1.67 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3, axiom, (semilattice_sup @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Rings_Olinordered__idom, axiom, (linordered_idom @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Opreorder_4, axiom, (preorder @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Olinorder, axiom, (linorder @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Ono__top, axiom, (no_top @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Ono__bot, axiom, (no_bot @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Lattices_Olattice_5, axiom, (lattice @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Groups_Ogroup__add, axiom, (group_add @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Oorder_6, axiom, (order @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Orderings_Oord_7, axiom, (ord @ int)).
% 2.55/1.67 thf(tcon_Int_Oint___Groups_Ominus_8, axiom, (minus @ int)).
% 2.55/1.67 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9, axiom, (! [A7:$tType]: ((bounde1808546759up_bot @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10, axiom, (! [A7:$tType]: ((semilattice_sup @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Orderings_Oorder__bot_11, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Orderings_Opreorder_12, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Lattices_Olattice_13, axiom, (! [A7:$tType]: ((lattice @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Orderings_Oorder_14, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Orderings_Oord_15, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Orderings_Obot_16, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 2.55/1.67 thf(tcon_Set_Oset___Groups_Ominus_17, axiom, (! [A7:$tType]: ((minus @ (set @ A7))))).
% 2.55/1.67 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_18, axiom, (bounde1808546759up_bot @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19, axiom, (semilattice_sup @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Oorder__bot_20, axiom, (order_bot @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Opreorder_21, axiom, (preorder @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Olinorder_22, axiom, (linorder @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Lattices_Olattice_23, axiom, (lattice @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Oorder_24, axiom, (order @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Oord_25, axiom, (ord @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Orderings_Obot_26, axiom, (bot @ $o)).
% 2.55/1.67 thf(tcon_HOL_Obool___Groups_Ominus_27, axiom, (minus @ $o)).
% 2.55/1.67 thf(conj_0, conjecture, (((ord_less @ int) @ (h @ w)) @ (h @ x))).
% 2.55/1.67 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2DTF13441.p
% 2.55/1.67 ------------------------
% 2.55/1.69 ---- Cleaned THF ---
% 2.55/1.69 thf(ty_t_BinaryTree__Mirabelle__pchhvghoao_OTree,type,
% 2.55/1.69 binary1291135688e_Tree: $tType > $tType ).
% 2.55/1.69
% 2.55/1.69 thf(ty_t_Set_Oset,type,
% 2.55/1.69 set: $tType > $tType ).
% 2.55/1.69
% 2.55/1.69 thf(ty_t_Int_Oint,type,
% 2.55/1.69 int: $tType ).
% 2.55/1.69
% 2.55/1.69 thf(ty_tf_a,type,
% 2.55/1.69 a: $tType ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.55/1.69 bounded_lattice:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_HOL_Otype,type,
% 2.55/1.69 type:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Groups_Ominus,type,
% 2.55/1.69 minus:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Obot,type,
% 2.55/1.69 bot:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Oord,type,
% 2.55/1.69 ord:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Oorder,type,
% 2.55/1.69 order:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Groups_Ogroup__add,type,
% 2.55/1.69 group_add:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Lattices_Olattice,type,
% 2.55/1.69 lattice:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Ono__bot,type,
% 2.55/1.69 no_bot:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Ono__top,type,
% 2.55/1.69 no_top:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Olinorder,type,
% 2.55/1.69 linorder:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Opreorder,type,
% 2.55/1.69 preorder:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.55/1.69 order_bot:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Owellorder,type,
% 2.55/1.69 wellorder:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Orderings_Odense__order,type,
% 2.55/1.69 dense_order:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.55/1.69 linordered_idom:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Fields_Olinordered__field,type,
% 2.55/1.69 linordered_field:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.55/1.69 semilattice_sup:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.55/1.69 ordered_ab_group_add:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.55/1.69 cancel146912293up_add:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.55/1.69 bounde1808546759up_bot:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 2.55/1.69 condit1656338222tinuum:
% 2.55/1.69 !>[A: $tType] : $o ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OT,type,
% 2.55/1.69 binary210054475elle_T:
% 2.55/1.69 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_OTip,type,
% 2.55/1.69 binary1746293266le_Tip:
% 2.55/1.69 !>[A: $tType] : ( binary1291135688e_Tree @ A ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Ocase__Tree,type,
% 2.55/1.69 binary536355927e_Tree:
% 2.55/1.69 !>[B: $tType,A: $tType] : ( B > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B ) > ( binary1291135688e_Tree @ A ) > B ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Opred__Tree,type,
% 2.55/1.69 binary1693644968d_Tree:
% 2.55/1.69 !>[A: $tType] : ( ( A > $o ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Orec__Tree,type,
% 2.55/1.69 binary1929596613c_Tree:
% 2.55/1.69 !>[C: $tType,A: $tType] : ( C > ( ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C ) > ( binary1291135688e_Tree @ A ) > C ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OTree_Oset__Tree,type,
% 2.55/1.69 binary2130109271t_Tree:
% 2.55/1.69 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Obinsert,type,
% 2.55/1.69 binary1830089824insert:
% 2.55/1.69 !>[A: $tType] : ( ( A > int ) > A > ( binary1291135688e_Tree @ A ) > ( binary1291135688e_Tree @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Oeqs,type,
% 2.55/1.69 binary64540844le_eqs:
% 2.55/1.69 !>[A: $tType] : ( ( A > int ) > A > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Omemb,type,
% 2.55/1.69 binary827270440e_memb:
% 2.55/1.69 !>[A: $tType] : ( ( A > int ) > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsetOf,type,
% 2.55/1.69 binary1653327646_setOf:
% 2.55/1.69 !>[A: $tType] : ( ( binary1291135688e_Tree @ A ) > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_OsortedTree,type,
% 2.55/1.69 binary1610619414edTree:
% 2.55/1.69 !>[A: $tType] : ( ( A > int ) > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_BinaryTree__Mirabelle__pchhvghoao_Osorted__distinct__pred,type,
% 2.55/1.69 binary231205461t_pred:
% 2.55/1.69 !>[A: $tType] : ( ( A > int ) > A > A > ( binary1291135688e_Tree @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.55/1.69 minus_minus:
% 2.55/1.69 !>[A: $tType] : ( A > A > A ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_HOL_OThe,type,
% 2.55/1.69 the:
% 2.55/1.69 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.55/1.69 sup_sup:
% 2.55/1.69 !>[A: $tType] : ( A > A > A ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.55/1.69 bot_bot:
% 2.55/1.69 !>[A: $tType] : A ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.55/1.69 ord_less:
% 2.55/1.69 !>[A: $tType] : ( A > A > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.55/1.69 ord_less_eq:
% 2.55/1.69 !>[A: $tType] : ( A > A > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_OCollect,type,
% 2.55/1.69 collect:
% 2.55/1.69 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_Oinsert,type,
% 2.55/1.69 insert:
% 2.55/1.69 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_Ois__empty,type,
% 2.55/1.69 is_empty:
% 2.55/1.69 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_Ois__singleton,type,
% 2.55/1.69 is_singleton:
% 2.55/1.69 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_Oremove,type,
% 2.55/1.69 remove:
% 2.55/1.69 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_Set_Othe__elem,type,
% 2.55/1.69 the_elem:
% 2.55/1.69 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_c_member,type,
% 2.55/1.69 member:
% 2.55/1.69 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_e,type,
% 2.55/1.69 e: a ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_h,type,
% 2.55/1.69 h: a > int ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_t1____,type,
% 2.55/1.69 t1: binary1291135688e_Tree @ a ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_t2____,type,
% 2.55/1.69 t2: binary1291135688e_Tree @ a ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_w____,type,
% 2.55/1.69 w: a ).
% 2.55/1.69
% 2.55/1.69 thf(sy_v_x____,type,
% 2.55/1.69 x: a ).
% 2.55/1.69
% 2.55/1.69 thf(fact_0_whSet,axiom,
% 2.55/1.69 member @ a @ w @ ( binary1653327646_setOf @ a @ t1 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_1_s,axiom,
% 2.55/1.69 binary1610619414edTree @ a @ h @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_2_s2,axiom,
% 2.55/1.69 binary1610619414edTree @ a @ h @ t2 ).
% 2.55/1.69
% 2.55/1.69 thf(fact_3_s1,axiom,
% 2.55/1.69 binary1610619414edTree @ a @ h @ t1 ).
% 2.55/1.69
% 2.55/1.69 thf(fact_4_eNotLess,axiom,
% 2.55/1.69 ~ ( ord_less @ int @ ( h @ e ) @ ( h @ x ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_5_xNotLess,axiom,
% 2.55/1.69 ~ ( ord_less @ int @ ( h @ x ) @ ( h @ e ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_6_whEq,axiom,
% 2.55/1.69 member @ a @ w @ ( binary64540844le_eqs @ a @ h @ e ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_7_xeqe,axiom,
% 2.55/1.69 ( ( h @ x )
% 2.55/1.69 = ( h @ e ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_8_Tree_Oinject,axiom,
% 2.55/1.69 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A,Y21: binary1291135688e_Tree @ A,Y22: A,Y23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( ( binary210054475elle_T @ A @ X21 @ X22 @ X23 )
% 2.55/1.69 = ( binary210054475elle_T @ A @ Y21 @ Y22 @ Y23 ) )
% 2.55/1.69 = ( ( X21 = Y21 )
% 2.55/1.69 & ( X22 = Y22 )
% 2.55/1.69 & ( X23 = Y23 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_9_calculation,axiom,
% 2.55/1.69 member @ a @ x @ ( binary64540844le_eqs @ a @ h @ e ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_10_minf_I11_J,axiom,
% 2.55/1.69 ! [C: $tType,D: $tType] :
% 2.55/1.69 ( ( ord @ C )
% 2.55/1.69 => ! [F: D] :
% 2.55/1.69 ? [Z: C] :
% 2.55/1.69 ! [X: C] :
% 2.55/1.69 ( ( ord_less @ C @ X @ Z )
% 2.55/1.69 => ( F = F ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_11_minf_I7_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ~ ( ord_less @ A @ T @ X ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_12_minf_I5_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ( ord_less @ A @ X @ T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_13_minf_I4_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ( X != T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_14_minf_I3_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ( X != T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_15_minf_I2_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.55/1.69 ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Z2 )
% 2.55/1.69 => ( ( P @ X2 )
% 2.55/1.69 = ( P2 @ X2 ) ) )
% 2.55/1.69 => ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Z2 )
% 2.55/1.69 => ( ( Q @ X2 )
% 2.55/1.69 = ( Q2 @ X2 ) ) )
% 2.55/1.69 => ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ( ( ( P @ X )
% 2.55/1.69 | ( Q @ X ) )
% 2.55/1.69 = ( ( P2 @ X )
% 2.55/1.69 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_16_minf_I1_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.55/1.69 ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Z2 )
% 2.55/1.69 => ( ( P @ X2 )
% 2.55/1.69 = ( P2 @ X2 ) ) )
% 2.55/1.69 => ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Z2 )
% 2.55/1.69 => ( ( Q @ X2 )
% 2.55/1.69 = ( Q2 @ X2 ) ) )
% 2.55/1.69 => ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ X @ Z )
% 2.55/1.69 => ( ( ( P @ X )
% 2.55/1.69 & ( Q @ X ) )
% 2.55/1.69 = ( ( P2 @ X )
% 2.55/1.69 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_17_pinf_I11_J,axiom,
% 2.55/1.69 ! [C: $tType,D: $tType] :
% 2.55/1.69 ( ( ord @ C )
% 2.55/1.69 => ! [F: D] :
% 2.55/1.69 ? [Z: C] :
% 2.55/1.69 ! [X: C] :
% 2.55/1.69 ( ( ord_less @ C @ Z @ X )
% 2.55/1.69 => ( F = F ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_18_res,axiom,
% 2.55/1.69 ( ( binary1830089824insert @ a @ h @ e @ ( binary210054475elle_T @ a @ t1 @ x @ t2 ) )
% 2.55/1.69 = ( binary210054475elle_T @ a @ t1 @ e @ t2 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_19_sortLemmaR,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 => ( binary1610619414edTree @ A @ H @ T2 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_20_sortLemmaL,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 => ( binary1610619414edTree @ A @ H @ T1 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_21_sortedTree_Osimps_I2_J,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1610619414edTree @ A @ H @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 = ( ( binary1610619414edTree @ A @ H @ T1 )
% 2.55/1.69 & ! [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T1 ) )
% 2.55/1.69 => ( ord_less @ int @ ( H @ X4 ) @ ( H @ X3 ) ) )
% 2.55/1.69 & ! [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ ( binary1653327646_setOf @ A @ T2 ) )
% 2.55/1.69 => ( ord_less @ int @ ( H @ X3 ) @ ( H @ X4 ) ) )
% 2.55/1.69 & ( binary1610619414edTree @ A @ H @ T2 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_22_pinf_I1_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.55/1.69 ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z2 @ X2 )
% 2.55/1.69 => ( ( P @ X2 )
% 2.55/1.69 = ( P2 @ X2 ) ) )
% 2.55/1.69 => ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z2 @ X2 )
% 2.55/1.69 => ( ( Q @ X2 )
% 2.55/1.69 = ( Q2 @ X2 ) ) )
% 2.55/1.69 => ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ( ( ( P @ X )
% 2.55/1.69 & ( Q @ X ) )
% 2.55/1.69 = ( ( P2 @ X )
% 2.55/1.69 & ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_23_pinf_I2_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 2.55/1.69 ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z2 @ X2 )
% 2.55/1.69 => ( ( P @ X2 )
% 2.55/1.69 = ( P2 @ X2 ) ) )
% 2.55/1.69 => ( ? [Z2: A] :
% 2.55/1.69 ! [X2: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z2 @ X2 )
% 2.55/1.69 => ( ( Q @ X2 )
% 2.55/1.69 = ( Q2 @ X2 ) ) )
% 2.55/1.69 => ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ( ( ( P @ X )
% 2.55/1.69 | ( Q @ X ) )
% 2.55/1.69 = ( ( P2 @ X )
% 2.55/1.69 | ( Q2 @ X ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_24_pinf_I3_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ( X != T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_25_pinf_I4_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ( X != T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_26_pinf_I5_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ~ ( ord_less @ A @ X @ T ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_27_pinf_I7_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [T: A] :
% 2.55/1.69 ? [Z: A] :
% 2.55/1.69 ! [X: A] :
% 2.55/1.69 ( ( ord_less @ A @ Z @ X )
% 2.55/1.69 => ( ord_less @ A @ T @ X ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_28_sorted__distinct__pred__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( binary231205461t_pred @ A )
% 2.55/1.69 = ( ^ [H2: A > int,A2: A,B2: A,T3: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( ( binary1610619414edTree @ A @ H2 @ T3 )
% 2.55/1.69 & ( member @ A @ A2 @ ( binary1653327646_setOf @ A @ T3 ) )
% 2.55/1.69 & ( member @ A @ B2 @ ( binary1653327646_setOf @ A @ T3 ) )
% 2.55/1.69 & ( ( H2 @ A2 )
% 2.55/1.69 = ( H2 @ B2 ) ) )
% 2.55/1.69 => ( A2 = B2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_29_memb__spec,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,T: binary1291135688e_Tree @ A,X3: A] :
% 2.55/1.69 ( ( binary1610619414edTree @ A @ H @ T )
% 2.55/1.69 => ( ( binary827270440e_memb @ A @ H @ X3 @ T )
% 2.55/1.69 = ( member @ A @ X3 @ ( binary1653327646_setOf @ A @ T ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_30_binsert_Osimps_I2_J,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,E: A,X3: A,T1: binary1291135688e_Tree @ A,T2: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( ( ord_less @ int @ ( H @ E ) @ ( H @ X3 ) )
% 2.55/1.69 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 = ( binary210054475elle_T @ A @ ( binary1830089824insert @ A @ H @ E @ T1 ) @ X3 @ T2 ) ) )
% 2.55/1.69 & ( ~ ( ord_less @ int @ ( H @ E ) @ ( H @ X3 ) )
% 2.55/1.69 => ( ( ( ord_less @ int @ ( H @ X3 ) @ ( H @ E ) )
% 2.55/1.69 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 = ( binary210054475elle_T @ A @ T1 @ X3 @ ( binary1830089824insert @ A @ H @ E @ T2 ) ) ) )
% 2.55/1.69 & ( ~ ( ord_less @ int @ ( H @ X3 ) @ ( H @ E ) )
% 2.55/1.69 => ( ( binary1830089824insert @ A @ H @ E @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 = ( binary210054475elle_T @ A @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_31_ex__gt__or__lt,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( condit1656338222tinuum @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ? [B3: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B3 )
% 2.55/1.69 | ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_32_linorder__neqE__linordered__idom,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linordered_idom @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( X3 != Y )
% 2.55/1.69 => ( ~ ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_33_dual__order_Ostrict__implies__not__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [B4: A,A3: A] :
% 2.55/1.69 ( ( ord_less @ A @ B4 @ A3 )
% 2.55/1.69 => ( A3 != B4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_34_linordered__field__no__ub,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linordered_field @ A )
% 2.55/1.69 => ! [X: A] :
% 2.55/1.69 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_35_linordered__field__no__lb,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linordered_field @ A )
% 2.55/1.69 => ! [X: A] :
% 2.55/1.69 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_36_order_Ostrict__implies__not__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( A3 != B4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_37_dependent__wellorder__choice,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( wellorder @ A )
% 2.55/1.69 => ! [P: ( A > B ) > A > B > $o] :
% 2.55/1.69 ( ! [R: B,F2: A > B,G: A > B,X2: A] :
% 2.55/1.69 ( ! [Y3: A] :
% 2.55/1.69 ( ( ord_less @ A @ Y3 @ X2 )
% 2.55/1.69 => ( ( F2 @ Y3 )
% 2.55/1.69 = ( G @ Y3 ) ) )
% 2.55/1.69 => ( ( P @ F2 @ X2 @ R )
% 2.55/1.69 = ( P @ G @ X2 @ R ) ) )
% 2.55/1.69 => ( ! [X2: A,F2: A > B] :
% 2.55/1.69 ( ! [Y3: A] :
% 2.55/1.69 ( ( ord_less @ A @ Y3 @ X2 )
% 2.55/1.69 => ( P @ F2 @ Y3 @ ( F2 @ Y3 ) ) )
% 2.55/1.69 => ? [X_12: B] : ( P @ F2 @ X2 @ X_12 ) )
% 2.55/1.69 => ? [F2: A > B] :
% 2.55/1.69 ! [X: A] : ( P @ F2 @ X @ ( F2 @ X ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_38_sorted__distinct,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,A3: A,B4: A,T: binary1291135688e_Tree @ A] : ( binary231205461t_pred @ A @ H @ A3 @ B4 @ T ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_39_ord__eq__less__subst,axiom,
% 2.55/1.69 ! [A: $tType,B: $tType] :
% 2.55/1.69 ( ( ( ord @ B )
% 2.55/1.69 & ( ord @ A ) )
% 2.55/1.69 => ! [A3: A,F3: B > A,B4: B,C2: B] :
% 2.55/1.69 ( ( A3
% 2.55/1.69 = ( F3 @ B4 ) )
% 2.55/1.69 => ( ( ord_less @ B @ B4 @ C2 )
% 2.55/1.69 => ( ! [X2: B,Y2: B] :
% 2.55/1.69 ( ( ord_less @ B @ X2 @ Y2 )
% 2.55/1.69 => ( ord_less @ A @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 2.55/1.69 => ( ord_less @ A @ A3 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_40_ord__less__eq__subst,axiom,
% 2.55/1.69 ! [A: $tType,B: $tType] :
% 2.55/1.69 ( ( ( ord @ B )
% 2.55/1.69 & ( ord @ A ) )
% 2.55/1.69 => ! [A3: A,B4: A,F3: A > B,C2: B] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ( ( F3 @ B4 )
% 2.55/1.69 = C2 )
% 2.55/1.69 => ( ! [X2: A,Y2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Y2 )
% 2.55/1.69 => ( ord_less @ B @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 2.55/1.69 => ( ord_less @ B @ ( F3 @ A3 ) @ C2 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_41_order__less__subst1,axiom,
% 2.55/1.69 ! [A: $tType,B: $tType] :
% 2.55/1.69 ( ( ( order @ B )
% 2.55/1.69 & ( order @ A ) )
% 2.55/1.69 => ! [A3: A,F3: B > A,B4: B,C2: B] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ ( F3 @ B4 ) )
% 2.55/1.69 => ( ( ord_less @ B @ B4 @ C2 )
% 2.55/1.69 => ( ! [X2: B,Y2: B] :
% 2.55/1.69 ( ( ord_less @ B @ X2 @ Y2 )
% 2.55/1.69 => ( ord_less @ A @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 2.55/1.69 => ( ord_less @ A @ A3 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_42_order__less__subst2,axiom,
% 2.55/1.69 ! [A: $tType,C: $tType] :
% 2.55/1.69 ( ( ( order @ C )
% 2.55/1.69 & ( order @ A ) )
% 2.55/1.69 => ! [A3: A,B4: A,F3: A > C,C2: C] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ( ord_less @ C @ ( F3 @ B4 ) @ C2 )
% 2.55/1.69 => ( ! [X2: A,Y2: A] :
% 2.55/1.69 ( ( ord_less @ A @ X2 @ Y2 )
% 2.55/1.69 => ( ord_less @ C @ ( F3 @ X2 ) @ ( F3 @ Y2 ) ) )
% 2.55/1.69 => ( ord_less @ C @ ( F3 @ A3 ) @ C2 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_43_lt__ex,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( no_bot @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ? [Y2: A] : ( ord_less @ A @ Y2 @ X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_44_gt__ex,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( no_top @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_45_mem__Collect__eq,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,P: A > $o] :
% 2.55/1.69 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.55/1.69 = ( P @ A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_46_Collect__mem__eq,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.55/1.69 = A4 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_47_Collect__cong,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.55/1.69 ( ! [X2: A] :
% 2.55/1.69 ( ( P @ X2 )
% 2.55/1.69 = ( Q @ X2 ) )
% 2.55/1.69 => ( ( collect @ A @ P )
% 2.55/1.69 = ( collect @ A @ Q ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_48_ext,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
% 2.55/1.69 ( ! [X2: A] :
% 2.55/1.69 ( ( F3 @ X2 )
% 2.55/1.69 = ( G2 @ X2 ) )
% 2.55/1.69 => ( F3 = G2 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_49_neqE,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( X3 != Y )
% 2.55/1.69 => ( ~ ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_50_neq__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( X3 != Y )
% 2.55/1.69 = ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_51_order_Oasym,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_52_dense,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( dense_order @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ? [Z: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Z )
% 2.55/1.69 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_53_less__imp__neq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( X3 != Y ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_54_less__asym,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_55_less__asym_H,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ~ ( ord_less @ A @ B4 @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_56_less__trans,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A,Z3: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( ( ord_less @ A @ Y @ Z3 )
% 2.55/1.69 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_57_less__linear,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 | ( X3 = Y )
% 2.55/1.69 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_58_less__irrefl,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_59_ord__eq__less__trans,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ord @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A] :
% 2.55/1.69 ( ( A3 = B4 )
% 2.55/1.69 => ( ( ord_less @ A @ B4 @ C2 )
% 2.55/1.69 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_60_ord__less__eq__trans,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ord @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ( B4 = C2 )
% 2.55/1.69 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_61_dual__order_Oasym,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [B4: A,A3: A] :
% 2.55/1.69 ( ( ord_less @ A @ B4 @ A3 )
% 2.55/1.69 => ~ ( ord_less @ A @ A3 @ B4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_62_less__imp__not__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( X3 != Y ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_63_less__not__sym,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_64_less__induct,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( wellorder @ A )
% 2.55/1.69 => ! [P: A > $o,A3: A] :
% 2.55/1.69 ( ! [X2: A] :
% 2.55/1.69 ( ! [Y3: A] :
% 2.55/1.69 ( ( ord_less @ A @ Y3 @ X2 )
% 2.55/1.69 => ( P @ Y3 ) )
% 2.55/1.69 => ( P @ X2 ) )
% 2.55/1.69 => ( P @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_65_antisym__conv3,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [Y: A,X3: A] :
% 2.55/1.69 ( ~ ( ord_less @ A @ Y @ X3 )
% 2.55/1.69 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 2.55/1.69 = ( X3 = Y ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_66_less__imp__not__eq2,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( Y != X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_67_less__imp__triv,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A,P: $o] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( ( ord_less @ A @ Y @ X3 )
% 2.55/1.69 => P ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_68_linorder__cases,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ~ ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ( ( X3 != Y )
% 2.55/1.69 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_69_dual__order_Oirrefl,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_70_order_Ostrict__trans,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ( ord_less @ A @ B4 @ C2 )
% 2.55/1.69 => ( ord_less @ A @ A3 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_71_less__imp__not__less,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( preorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ Y )
% 2.55/1.69 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_72_exists__least__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( wellorder @ A )
% 2.55/1.69 => ( ( ^ [P3: A > $o] :
% 2.55/1.69 ? [X5: A] : ( P3 @ X5 ) )
% 2.55/1.69 = ( ^ [P4: A > $o] :
% 2.55/1.69 ? [N: A] :
% 2.55/1.69 ( ( P4 @ N )
% 2.55/1.69 & ! [M: A] :
% 2.55/1.69 ( ( ord_less @ A @ M @ N )
% 2.55/1.69 => ~ ( P4 @ M ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_73_linorder__less__wlog,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [P: A > A > $o,A3: A,B4: A] :
% 2.55/1.69 ( ! [A5: A,B3: A] :
% 2.55/1.69 ( ( ord_less @ A @ A5 @ B3 )
% 2.55/1.69 => ( P @ A5 @ B3 ) )
% 2.55/1.69 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 2.55/1.69 => ( ! [A5: A,B3: A] :
% 2.55/1.69 ( ( P @ B3 @ A5 )
% 2.55/1.69 => ( P @ A5 @ B3 ) )
% 2.55/1.69 => ( P @ A3 @ B4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_74_dual__order_Ostrict__trans,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [B4: A,A3: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ B4 @ A3 )
% 2.55/1.69 => ( ( ord_less @ A @ C2 @ B4 )
% 2.55/1.69 => ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_75_not__less__iff__gr__or__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( linorder @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 2.55/1.69 = ( ( ord_less @ A @ Y @ X3 )
% 2.55/1.69 | ( X3 = Y ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_76_binsert_Osimps_I1_J,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int,E: A] :
% 2.55/1.69 ( ( binary1830089824insert @ A @ H @ E @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 = ( binary210054475elle_T @ A @ ( binary1746293266le_Tip @ A ) @ E @ ( binary1746293266le_Tip @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_77_verit__comp__simplify1_I1_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_78_measure__induct,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( wellorder @ B )
% 2.55/1.69 => ! [F3: A > B,P: A > $o,A3: A] :
% 2.55/1.69 ( ! [X2: A] :
% 2.55/1.69 ( ! [Y3: A] :
% 2.55/1.69 ( ( ord_less @ B @ ( F3 @ Y3 ) @ ( F3 @ X2 ) )
% 2.55/1.69 => ( P @ Y3 ) )
% 2.55/1.69 => ( P @ X2 ) )
% 2.55/1.69 => ( P @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_79_measure__induct__rule,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( wellorder @ B )
% 2.55/1.69 => ! [F3: A > B,P: A > $o,A3: A] :
% 2.55/1.69 ( ! [X2: A] :
% 2.55/1.69 ( ! [Y3: A] :
% 2.55/1.69 ( ( ord_less @ B @ ( F3 @ Y3 ) @ ( F3 @ X2 ) )
% 2.55/1.69 => ( P @ Y3 ) )
% 2.55/1.69 => ( P @ X2 ) )
% 2.55/1.69 => ( P @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_80_c2,axiom,
% 2.55/1.69 ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t2 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t2 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_81_Tree_Osimps_I5_J,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.55/1.69 = ( F22 @ X21 @ X22 @ X23 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_82_c1,axiom,
% 2.55/1.69 ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t1 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t1 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_83_Tree_Osimps_I7_J,axiom,
% 2.55/1.69 ! [C: $tType,A: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.55/1.69 = ( F22 @ X21 @ X22 @ X23 @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X21 ) @ ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ X23 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_84_Tree_Opred__inject_I2_J,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,A3: binary1291135688e_Tree @ A,Aa: A,Ab: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1693644968d_Tree @ A @ P @ ( binary210054475elle_T @ A @ A3 @ Aa @ Ab ) )
% 2.55/1.69 = ( ( binary1693644968d_Tree @ A @ P @ A3 )
% 2.55/1.69 & ( P @ Aa )
% 2.55/1.69 & ( binary1693644968d_Tree @ A @ P @ Ab ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_85_bot__apply,axiom,
% 2.55/1.69 ! [C: $tType,D: $tType] :
% 2.55/1.69 ( ( bot @ C )
% 2.55/1.69 => ( ( bot_bot @ ( D > C ) )
% 2.55/1.69 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_86_bot__fun__def,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( bot @ B )
% 2.55/1.69 => ( ( bot_bot @ ( A > B ) )
% 2.55/1.69 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_87_Tree_Osimps_I6_J,axiom,
% 2.55/1.69 ! [A: $tType,C: $tType,F1: C,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > C > C > C] :
% 2.55/1.69 ( ( binary1929596613c_Tree @ C @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 = F1 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_88_Tree_Osimps_I4_J,axiom,
% 2.55/1.69 ! [A: $tType,B: $tType,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B] :
% 2.55/1.69 ( ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 = F1 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_89_Tree_Opred__inject_I1_J,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o] : ( binary1693644968d_Tree @ A @ P @ ( binary1746293266le_Tip @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_90_setOf_Osimps_I2_J,axiom,
% 2.55/1.69 ! [A: $tType,T1: binary1291135688e_Tree @ A,X3: A,T2: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1653327646_setOf @ A @ ( binary210054475elle_T @ A @ T1 @ X3 @ T2 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary1653327646_setOf @ A @ T1 ) @ ( binary1653327646_setOf @ A @ T2 ) ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_91_setOf_Osimps_I1_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( binary1653327646_setOf @ A @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_92_bot_Onot__eq__extremum,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order_bot @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ( ( A3
% 2.55/1.69 != ( bot_bot @ A ) )
% 2.55/1.69 = ( ord_less @ A @ ( bot_bot @ A ) @ A3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_93_bot_Oextremum__strict,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( order_bot @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ~ ( ord_less @ A @ A3 @ ( bot_bot @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_94_Tree_Odistinct_I1_J,axiom,
% 2.55/1.69 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary1746293266le_Tip @ A )
% 2.55/1.69 != ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_95_Tree_Oinduct,axiom,
% 2.55/1.69 ! [A: $tType,P: ( binary1291135688e_Tree @ A ) > $o,Tree: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( P @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 => ( ! [X1: binary1291135688e_Tree @ A,X24: A,X32: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( P @ X1 )
% 2.55/1.69 => ( ( P @ X32 )
% 2.55/1.69 => ( P @ ( binary210054475elle_T @ A @ X1 @ X24 @ X32 ) ) ) )
% 2.55/1.69 => ( P @ Tree ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_96_Tree_Oexhaust,axiom,
% 2.55/1.69 ! [A: $tType,Y: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( Y
% 2.55/1.69 != ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 => ~ ! [X212: binary1291135688e_Tree @ A,X222: A,X232: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( Y
% 2.55/1.69 != ( binary210054475elle_T @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_97_sortedTree_Osimps_I1_J,axiom,
% 2.55/1.69 ! [A: $tType,H: A > int] : ( binary1610619414edTree @ A @ H @ ( binary1746293266le_Tip @ A ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_98_insert__Diff__single,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A] :
% 2.55/1.69 ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 = ( insert @ A @ A3 @ A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_99_Un__Diff__cancel,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_100_Un__Diff__cancel2,axiom,
% 2.55/1.69 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) @ A4 )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_101_Diff__insert0,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ~ ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B5 ) )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_102_insert__Diff1,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,B5: set @ A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_103_Un__insert__left,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B5: set @ A,C3: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B5 ) @ C3 )
% 2.55/1.69 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_104_empty__Collect__eq,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o] :
% 2.55/1.69 ( ( ( bot_bot @ ( set @ A ) )
% 2.55/1.69 = ( collect @ A @ P ) )
% 2.55/1.69 = ( ! [X4: A] :
% 2.55/1.69 ~ ( P @ X4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_105_Collect__empty__eq,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o] :
% 2.55/1.69 ( ( ( collect @ A @ P )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = ( ! [X4: A] :
% 2.55/1.69 ~ ( P @ X4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_106_all__not__in__conv,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( ! [X4: A] :
% 2.55/1.69 ~ ( member @ A @ X4 @ A4 ) )
% 2.55/1.69 = ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_107_empty__iff,axiom,
% 2.55/1.69 ! [A: $tType,C2: A] :
% 2.55/1.69 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_108_insert__absorb2,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A] :
% 2.55/1.69 ( ( insert @ A @ X3 @ ( insert @ A @ X3 @ A4 ) )
% 2.55/1.69 = ( insert @ A @ X3 @ A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_109_insert__iff,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 2.55/1.69 = ( ( A3 = B4 )
% 2.55/1.69 | ( member @ A @ A3 @ A4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_110_insertCI,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 2.55/1.69 ( ( ~ ( member @ A @ A3 @ B5 )
% 2.55/1.69 => ( A3 = B4 ) )
% 2.55/1.69 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_111_Un__iff,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 = ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 | ( member @ A @ C2 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_112_UnCI,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 2.55/1.69 ( ( ~ ( member @ A @ C2 @ B5 )
% 2.55/1.69 => ( member @ A @ C2 @ A4 ) )
% 2.55/1.69 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_113_Diff__idemp,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) @ B5 )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_114_Diff__iff,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 = ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 & ~ ( member @ A @ C2 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_115_DiffI,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 => ( ~ ( member @ A @ C2 @ B5 )
% 2.55/1.69 => ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_116_singletonI,axiom,
% 2.55/1.69 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_117_Un__empty,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = ( ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_118_Diff__cancel,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ A4 @ A4 )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_119_empty__Diff,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_120_Diff__empty,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = A4 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_121_Un__insert__right,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 2.55/1.69 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_122_bot__set__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bot_bot @ ( set @ A ) )
% 2.55/1.69 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_123_not__psubset__empty,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ~ ( ord_less @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_124_ex__in__conv,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( ? [X4: A] : ( member @ A @ X4 @ A4 ) )
% 2.55/1.69 = ( A4
% 2.55/1.69 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_125_equals0I,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ! [Y2: A] :
% 2.55/1.69 ~ ( member @ A @ Y2 @ A4 )
% 2.55/1.69 => ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_126_equals0D,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,A3: A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 => ~ ( member @ A @ A3 @ A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_127_emptyE,axiom,
% 2.55/1.69 ! [A: $tType,A3: A] :
% 2.55/1.69 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_128_mk__disjoint__insert,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ A3 @ A4 )
% 2.55/1.69 => ? [B6: set @ A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 = ( insert @ A @ A3 @ B6 ) )
% 2.55/1.69 & ~ ( member @ A @ A3 @ B6 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_129_insert__commute,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 2.55/1.69 ( ( insert @ A @ X3 @ ( insert @ A @ Y @ A4 ) )
% 2.55/1.69 = ( insert @ A @ Y @ ( insert @ A @ X3 @ A4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_130_insert__eq__iff,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A,B4: A,B5: set @ A] :
% 2.55/1.69 ( ~ ( member @ A @ A3 @ A4 )
% 2.55/1.69 => ( ~ ( member @ A @ B4 @ B5 )
% 2.55/1.69 => ( ( ( insert @ A @ A3 @ A4 )
% 2.55/1.69 = ( insert @ A @ B4 @ B5 ) )
% 2.55/1.69 = ( ( ( A3 = B4 )
% 2.55/1.69 => ( A4 = B5 ) )
% 2.55/1.69 & ( ( A3 != B4 )
% 2.55/1.69 => ? [C4: set @ A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 = ( insert @ A @ B4 @ C4 ) )
% 2.55/1.69 & ~ ( member @ A @ B4 @ C4 )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( insert @ A @ A3 @ C4 ) )
% 2.55/1.69 & ~ ( member @ A @ A3 @ C4 ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_131_insert__absorb,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ A3 @ A4 )
% 2.55/1.69 => ( ( insert @ A @ A3 @ A4 )
% 2.55/1.69 = A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_132_insert__ident,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ~ ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ( ~ ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ( ( insert @ A @ X3 @ A4 )
% 2.55/1.69 = ( insert @ A @ X3 @ B5 ) )
% 2.55/1.69 = ( A4 = B5 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_133_Set_Oset__insert,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ~ ! [B6: set @ A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 = ( insert @ A @ X3 @ B6 ) )
% 2.55/1.69 => ( member @ A @ X3 @ B6 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_134_insertI2,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B5: set @ A,B4: A] :
% 2.55/1.69 ( ( member @ A @ A3 @ B5 )
% 2.55/1.69 => ( member @ A @ A3 @ ( insert @ A @ B4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_135_insertI1,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B5: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_136_insertE,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B4: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ A3 @ ( insert @ A @ B4 @ A4 ) )
% 2.55/1.69 => ( ( A3 != B4 )
% 2.55/1.69 => ( member @ A @ A3 @ A4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_137_Un__left__commute,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_138_Un__left__absorb,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_139_Un__commute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A6 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_140_Un__absorb,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 2.55/1.69 = A4 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_141_Un__assoc,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_142_ball__Un,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.55/1.69 ( ( ! [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 => ( P @ X4 ) ) )
% 2.55/1.69 = ( ! [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ A4 )
% 2.55/1.69 => ( P @ X4 ) )
% 2.55/1.69 & ! [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ B5 )
% 2.55/1.69 => ( P @ X4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_143_bex__Un,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.55/1.69 ( ( ? [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 & ( P @ X4 ) ) )
% 2.55/1.69 = ( ? [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ A4 )
% 2.55/1.69 & ( P @ X4 ) )
% 2.55/1.69 | ? [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ B5 )
% 2.55/1.69 & ( P @ X4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_144_UnI2,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,B5: set @ A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ B5 )
% 2.55/1.69 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_145_UnI1,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_146_UnE,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 => ( ~ ( member @ A @ C2 @ A4 )
% 2.55/1.69 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_147_psubset__imp__ex__mem,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.69 => ? [B3: A] : ( member @ A @ B3 @ ( minus_minus @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_148_DiffD2,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 => ~ ( member @ A @ C2 @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_149_DiffD1,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 => ( member @ A @ C2 @ A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_150_DiffE,axiom,
% 2.55/1.69 ! [A: $tType,C2: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( member @ A @ C2 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 => ~ ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_151_singleton__inject,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B4: A] :
% 2.55/1.69 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 => ( A3 = B4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_152_insert__not__empty,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A] :
% 2.55/1.69 ( ( insert @ A @ A3 @ A4 )
% 2.55/1.69 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_153_doubleton__eq__iff,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,B4: A,C2: A,D2: A] :
% 2.55/1.69 ( ( ( insert @ A @ A3 @ ( insert @ A @ B4 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 = ( ( ( A3 = C2 )
% 2.55/1.69 & ( B4 = D2 ) )
% 2.55/1.69 | ( ( A3 = D2 )
% 2.55/1.69 & ( B4 = C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_154_singleton__iff,axiom,
% 2.55/1.69 ! [A: $tType,B4: A,A3: A] :
% 2.55/1.69 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 = ( B4 = A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_155_singletonD,axiom,
% 2.55/1.69 ! [A: $tType,B4: A,A3: A] :
% 2.55/1.69 ( ( member @ A @ B4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 => ( B4 = A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_156_Un__empty__right,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = A4 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_157_Un__empty__left,axiom,
% 2.55/1.69 ! [A: $tType,B5: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B5 )
% 2.55/1.69 = B5 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_158_insert__Diff__if,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,B5: set @ A,A4: set @ A] :
% 2.55/1.69 ( ( ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) )
% 2.55/1.69 & ( ~ ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ B5 )
% 2.55/1.69 = ( insert @ A @ X3 @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_159_Un__Diff,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C3 )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ C3 ) @ ( minus_minus @ ( set @ A ) @ B5 @ C3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_160_singleton__Un__iff,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A,B5: set @ A] :
% 2.55/1.69 ( ( ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 = ( ( ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 | ( ( A4
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 | ( ( A4
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_161_Un__singleton__iff,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,X3: A] :
% 2.55/1.69 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 = ( ( ( A4
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 | ( ( A4
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 | ( ( A4
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 & ( B5
% 2.55/1.69 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_162_insert__is__Un,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( insert @ A )
% 2.55/1.69 = ( ^ [A2: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_163_Diff__insert__absorb,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,A4: set @ A] :
% 2.55/1.69 ( ~ ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ( ( minus_minus @ ( set @ A ) @ ( insert @ A @ X3 @ A4 ) @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 = A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_164_Diff__insert2,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B5 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_165_insert__Diff,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ A3 @ A4 )
% 2.55/1.69 => ( ( insert @ A @ A3 @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 = A4 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_166_Diff__insert,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,A3: A,B5: set @ A] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ A3 @ B5 ) )
% 2.55/1.69 = ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ B5 ) @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_167_sup__bot_Oright__neutral,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 2.55/1.69 = A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_168_sup__bot_Oneutr__eq__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( ( bot_bot @ A )
% 2.55/1.69 = ( sup_sup @ A @ A3 @ B4 ) )
% 2.55/1.69 = ( ( A3
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 & ( B4
% 2.55/1.69 = ( bot_bot @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_169_sup__bot_Oleft__neutral,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 2.55/1.69 = A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_170_sup__bot_Oeq__neutr__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( ( sup_sup @ A @ A3 @ B4 )
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 = ( ( A3
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 & ( B4
% 2.55/1.69 = ( bot_bot @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_171_sup__eq__bot__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ( sup_sup @ A @ X3 @ Y )
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 = ( ( X3
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 & ( Y
% 2.55/1.69 = ( bot_bot @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_172_minus__apply,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( minus @ B )
% 2.55/1.69 => ( ( minus_minus @ ( A > B ) )
% 2.55/1.69 = ( ^ [A6: A > B,B7: A > B,X4: A] : ( minus_minus @ B @ ( A6 @ X4 ) @ ( B7 @ X4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_173_sup__apply,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ B )
% 2.55/1.69 => ( ( sup_sup @ ( A > B ) )
% 2.55/1.69 = ( ^ [F4: A > B,G3: A > B,X4: A] : ( sup_sup @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_174_sup_Oidem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [A3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ A3 @ A3 )
% 2.55/1.69 = A3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_175_sup__idem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ X3 )
% 2.55/1.69 = X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_176_sup_Oleft__idem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( sup_sup @ A @ A3 @ ( sup_sup @ A @ A3 @ B4 ) )
% 2.55/1.69 = ( sup_sup @ A @ A3 @ B4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_177_sup__left__idem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y ) )
% 2.55/1.69 = ( sup_sup @ A @ X3 @ Y ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_178_sup_Oright__idem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [A3: A,B4: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B4 ) @ B4 )
% 2.55/1.69 = ( sup_sup @ A @ A3 @ B4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_179_sup__bot__left,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 2.55/1.69 = X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_180_sup__bot__right,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [X3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 2.55/1.69 = X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_181_bot__eq__sup__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bounde1808546759up_bot @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( ( bot_bot @ A )
% 2.55/1.69 = ( sup_sup @ A @ X3 @ Y ) )
% 2.55/1.69 = ( ( X3
% 2.55/1.69 = ( bot_bot @ A ) )
% 2.55/1.69 & ( Y
% 2.55/1.69 = ( bot_bot @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_182_psubsetD,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,C2: A] :
% 2.55/1.69 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.69 => ( ( member @ A @ C2 @ A4 )
% 2.55/1.69 => ( member @ A @ C2 @ B5 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_183_psubset__trans,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,B5: set @ A,C3: set @ A] :
% 2.55/1.69 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 2.55/1.69 => ( ( ord_less @ ( set @ A ) @ B5 @ C3 )
% 2.55/1.69 => ( ord_less @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_184_fun__diff__def,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( minus @ B )
% 2.55/1.69 => ( ( minus_minus @ ( A > B ) )
% 2.55/1.69 = ( ^ [A6: A > B,B7: A > B,X4: A] : ( minus_minus @ B @ ( A6 @ X4 ) @ ( B7 @ X4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_185_inf__sup__aci_I8_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( lattice @ A )
% 2.55/1.69 => ! [X3: A,Y: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ X3 @ Y ) )
% 2.55/1.69 = ( sup_sup @ A @ X3 @ Y ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_186_inf__sup__aci_I7_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( lattice @ A )
% 2.55/1.69 => ! [X3: A,Y: A,Z3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) )
% 2.55/1.69 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X3 @ Z3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_187_inf__sup__aci_I6_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( lattice @ A )
% 2.55/1.69 => ! [X3: A,Y: A,Z3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y ) @ Z3 )
% 2.55/1.69 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_188_inf__sup__aci_I5_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( lattice @ A )
% 2.55/1.69 => ( ( sup_sup @ A )
% 2.55/1.69 = ( ^ [X4: A,Y4: A] : ( sup_sup @ A @ Y4 @ X4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_189_sup__fun__def,axiom,
% 2.55/1.69 ! [B: $tType,A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ B )
% 2.55/1.69 => ( ( sup_sup @ ( A > B ) )
% 2.55/1.69 = ( ^ [F4: A > B,G3: A > B,X4: A] : ( sup_sup @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_190_boolean__algebra__cancel_Osup1,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [A4: A,K: A,A3: A,B4: A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 = ( sup_sup @ A @ K @ A3 ) )
% 2.55/1.69 => ( ( sup_sup @ A @ A4 @ B4 )
% 2.55/1.69 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_191_boolean__algebra__cancel_Osup2,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [B5: A,K: A,B4: A,A3: A] :
% 2.55/1.69 ( ( B5
% 2.55/1.69 = ( sup_sup @ A @ K @ B4 ) )
% 2.55/1.69 => ( ( sup_sup @ A @ A3 @ B5 )
% 2.55/1.69 = ( sup_sup @ A @ K @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_192_sup_Oassoc,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( sup_sup @ A @ A3 @ B4 ) @ C2 )
% 2.55/1.69 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_193_sup__assoc,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A,Y: A,Z3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ ( sup_sup @ A @ X3 @ Y ) @ Z3 )
% 2.55/1.69 = ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_194_sup_Ocommute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ( ( sup_sup @ A )
% 2.55/1.69 = ( ^ [A2: A,B2: A] : ( sup_sup @ A @ B2 @ A2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_195_sup__commute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ( ( sup_sup @ A )
% 2.55/1.69 = ( ^ [X4: A,Y4: A] : ( sup_sup @ A @ Y4 @ X4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_196_sup_Oleft__commute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [B4: A,A3: A,C2: A] :
% 2.55/1.69 ( ( sup_sup @ A @ B4 @ ( sup_sup @ A @ A3 @ C2 ) )
% 2.55/1.69 = ( sup_sup @ A @ A3 @ ( sup_sup @ A @ B4 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_197_sup__left__commute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A,Y: A,Z3: A] :
% 2.55/1.69 ( ( sup_sup @ A @ X3 @ ( sup_sup @ A @ Y @ Z3 ) )
% 2.55/1.69 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X3 @ Z3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_198_less__supI1,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A,A3: A,B4: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ A3 )
% 2.55/1.69 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_199_less__supI2,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [X3: A,B4: A,A3: A] :
% 2.55/1.69 ( ( ord_less @ A @ X3 @ B4 )
% 2.55/1.69 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_200_sup_Ostrict__boundedE,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [B4: A,C2: A,A3: A] :
% 2.55/1.69 ( ( ord_less @ A @ ( sup_sup @ A @ B4 @ C2 ) @ A3 )
% 2.55/1.69 => ~ ( ( ord_less @ A @ B4 @ A3 )
% 2.55/1.69 => ~ ( ord_less @ A @ C2 @ A3 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_201_sup_Ostrict__order__iff,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ( ( ord_less @ A )
% 2.55/1.69 = ( ^ [B2: A,A2: A] :
% 2.55/1.69 ( ( A2
% 2.55/1.69 = ( sup_sup @ A @ A2 @ B2 ) )
% 2.55/1.69 & ( A2 != B2 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_202_sup_Ostrict__coboundedI1,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [C2: A,A3: A,B4: A] :
% 2.55/1.69 ( ( ord_less @ A @ C2 @ A3 )
% 2.55/1.69 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_203_sup_Ostrict__coboundedI2,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A )
% 2.55/1.69 => ! [C2: A,B4: A,A3: A] :
% 2.55/1.69 ( ( ord_less @ A @ C2 @ B4 )
% 2.55/1.69 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A3 @ B4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_204_h2,axiom,
% 2.55/1.69 ( ( binary1610619414edTree @ a @ h @ t2 )
% 2.55/1.69 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t2 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t2 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_205_h1,axiom,
% 2.55/1.69 ( ( binary1610619414edTree @ a @ h @ t1 )
% 2.55/1.69 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ t1 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ t1 ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_206__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,axiom,
% 2.55/1.69 ( ( binary1610619414edTree @ a @ h @ ( binary1746293266le_Tip @ a ) )
% 2.55/1.69 => ( ( binary1653327646_setOf @ a @ ( binary1830089824insert @ a @ h @ e @ ( binary1746293266le_Tip @ a ) ) )
% 2.55/1.69 = ( sup_sup @ ( set @ a ) @ ( minus_minus @ ( set @ a ) @ ( binary1653327646_setOf @ a @ ( binary1746293266le_Tip @ a ) ) @ ( binary64540844le_eqs @ a @ h @ e ) ) @ ( insert @ a @ e @ ( bot_bot @ ( set @ a ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_207_singleton__conv,axiom,
% 2.55/1.69 ! [A: $tType,A3: A] :
% 2.55/1.69 ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] : ( X4 = A3 ) )
% 2.55/1.69 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_208_singleton__conv2,axiom,
% 2.55/1.69 ! [A: $tType,A3: A] :
% 2.55/1.69 ( ( collect @ A
% 2.55/1.69 @ ( ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 2.55/1.69 @ A3 ) )
% 2.55/1.69 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_209_Un__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ A6 )
% 2.55/1.69 | ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_210_empty__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bot_bot @ ( set @ A ) )
% 2.55/1.69 = ( collect @ A
% 2.55/1.69 @ ^ [X4: A] : $false ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_211_insert__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( insert @ A )
% 2.55/1.69 = ( ^ [A2: A] :
% 2.55/1.69 ( sup_sup @ ( set @ A )
% 2.55/1.69 @ ( collect @ A
% 2.55/1.69 @ ^ [X4: A] : ( X4 = A2 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_212_sup__set__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( sup_sup @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ( sup_sup @ ( A > $o )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_213_Collect__conv__if,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,A3: A] :
% 2.55/1.69 ( ( ( P @ A3 )
% 2.55/1.69 => ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( X4 = A3 )
% 2.55/1.69 & ( P @ X4 ) ) )
% 2.55/1.69 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 & ( ~ ( P @ A3 )
% 2.55/1.69 => ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( X4 = A3 )
% 2.55/1.69 & ( P @ X4 ) ) )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_214_Collect__disj__eq,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.55/1.69 ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( P @ X4 )
% 2.55/1.69 | ( Q @ X4 ) ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_215_Collect__conv__if2,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,A3: A] :
% 2.55/1.69 ( ( ( P @ A3 )
% 2.55/1.69 => ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( A3 = X4 )
% 2.55/1.69 & ( P @ X4 ) ) )
% 2.55/1.69 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.55/1.69 & ( ~ ( P @ A3 )
% 2.55/1.69 => ( ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( A3 = X4 )
% 2.55/1.69 & ( P @ X4 ) ) )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_216_less__set__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ord_less @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.55/1.69 ( ord_less @ ( A > $o )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_217_Tree_Ocase__distrib,axiom,
% 2.55/1.69 ! [C: $tType,B: $tType,A: $tType,H: B > C,F1: B,F22: ( binary1291135688e_Tree @ A ) > A > ( binary1291135688e_Tree @ A ) > B,Tree: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( H @ ( binary536355927e_Tree @ B @ A @ F1 @ F22 @ Tree ) )
% 2.55/1.69 = ( binary536355927e_Tree @ C @ A @ ( H @ F1 )
% 2.55/1.69 @ ^ [X12: binary1291135688e_Tree @ A,X25: A,X33: binary1291135688e_Tree @ A] : ( H @ ( F22 @ X12 @ X25 @ X33 ) )
% 2.55/1.69 @ Tree ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_218_Tree_Opred__True,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( binary1693644968d_Tree @ A
% 2.55/1.69 @ ^ [Uu: A] : $true )
% 2.55/1.69 = ( ^ [Uu: binary1291135688e_Tree @ A] : $true ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_219_eqs__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( binary64540844le_eqs @ A )
% 2.55/1.69 = ( ^ [H2: A > int,X4: A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ^ [Y4: A] :
% 2.55/1.69 ( ( H2 @ Y4 )
% 2.55/1.69 = ( H2 @ X4 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_220_insert__Collect,axiom,
% 2.55/1.69 ! [A: $tType,A3: A,P: A > $o] :
% 2.55/1.69 ( ( insert @ A @ A3 @ ( collect @ A @ P ) )
% 2.55/1.69 = ( collect @ A
% 2.55/1.69 @ ^ [U: A] :
% 2.55/1.69 ( ( U != A3 )
% 2.55/1.69 => ( P @ U ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_221_minus__set__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ( minus_minus @ ( A > $o )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ A6 )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_222_insert__compr,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( insert @ A )
% 2.55/1.69 = ( ^ [A2: A,B7: set @ A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( X4 = A2 )
% 2.55/1.69 | ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_223_set__diff__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( minus_minus @ ( set @ A ) )
% 2.55/1.69 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.55/1.69 ( collect @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( ( member @ A @ X4 @ A6 )
% 2.55/1.69 & ~ ( member @ A @ X4 @ B7 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_224_the__elem__eq,axiom,
% 2.55/1.69 ! [A: $tType,X3: A] :
% 2.55/1.69 ( ( the_elem @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.55/1.69 = X3 ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_225_bot__empty__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( bot_bot @ ( A > $o ) )
% 2.55/1.69 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_226_sup1CI,axiom,
% 2.55/1.69 ! [A: $tType,B5: A > $o,X3: A,A4: A > $o] :
% 2.55/1.69 ( ( ~ ( B5 @ X3 )
% 2.55/1.69 => ( A4 @ X3 ) )
% 2.55/1.69 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_227_sup1E,axiom,
% 2.55/1.69 ! [A: $tType,A4: A > $o,B5: A > $o,X3: A] :
% 2.55/1.69 ( ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 )
% 2.55/1.69 => ( ~ ( A4 @ X3 )
% 2.55/1.69 => ( B5 @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_228_sup1I1,axiom,
% 2.55/1.69 ! [A: $tType,A4: A > $o,X3: A,B5: A > $o] :
% 2.55/1.69 ( ( A4 @ X3 )
% 2.55/1.69 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_229_sup1I2,axiom,
% 2.55/1.69 ! [A: $tType,B5: A > $o,X3: A,A4: A > $o] :
% 2.55/1.69 ( ( B5 @ X3 )
% 2.55/1.69 => ( sup_sup @ ( A > $o ) @ A4 @ B5 @ X3 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_230_sup__Un__eq,axiom,
% 2.55/1.69 ! [A: $tType,R2: set @ A,S: set @ A] :
% 2.55/1.69 ( ( sup_sup @ ( A > $o )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ R2 )
% 2.55/1.69 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 2.55/1.69 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R2 @ S ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_231_Collect__empty__eq__bot,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o] :
% 2.55/1.69 ( ( ( collect @ A @ P )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 = ( P
% 2.55/1.69 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_232_is__singleton__the__elem,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( is_singleton @ A )
% 2.55/1.69 = ( ^ [A6: set @ A] :
% 2.55/1.69 ( A6
% 2.55/1.69 = ( insert @ A @ ( the_elem @ A @ A6 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_233_is__singletonI,axiom,
% 2.55/1.69 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_234_is__singletonI_H,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( A4
% 2.55/1.69 != ( bot_bot @ ( set @ A ) ) )
% 2.55/1.69 => ( ! [X2: A,Y2: A] :
% 2.55/1.69 ( ( member @ A @ X2 @ A4 )
% 2.55/1.69 => ( ( member @ A @ Y2 @ A4 )
% 2.55/1.69 => ( X2 = Y2 ) ) )
% 2.55/1.69 => ( is_singleton @ A @ A4 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_235_is__singleton__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( is_singleton @ A )
% 2.55/1.69 = ( ^ [A6: set @ A] :
% 2.55/1.69 ? [X4: A] :
% 2.55/1.69 ( A6
% 2.55/1.69 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_236_is__singletonE,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A] :
% 2.55/1.69 ( ( is_singleton @ A @ A4 )
% 2.55/1.69 => ~ ! [X2: A] :
% 2.55/1.69 ( A4
% 2.55/1.69 != ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_237_diff__strict__right__mono,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ordered_ab_group_add @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ C2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_238_diff__strict__left__mono,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ordered_ab_group_add @ A )
% 2.55/1.69 => ! [B4: A,A3: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ B4 @ A3 )
% 2.55/1.69 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A3 ) @ ( minus_minus @ A @ C2 @ B4 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_239_diff__eq__diff__eq,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( group_add @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A,D2: A] :
% 2.55/1.69 ( ( ( minus_minus @ A @ A3 @ B4 )
% 2.55/1.69 = ( minus_minus @ A @ C2 @ D2 ) )
% 2.55/1.69 => ( ( A3 = B4 )
% 2.55/1.69 = ( C2 = D2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_240_diff__right__commute,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( cancel146912293up_add @ A )
% 2.55/1.69 => ! [A3: A,C2: A,B4: A] :
% 2.55/1.69 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C2 ) @ B4 )
% 2.55/1.69 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B4 ) @ C2 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_241_diff__strict__mono,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ordered_ab_group_add @ A )
% 2.55/1.69 => ! [A3: A,B4: A,D2: A,C2: A] :
% 2.55/1.69 ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 => ( ( ord_less @ A @ D2 @ C2 )
% 2.55/1.69 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C2 ) @ ( minus_minus @ A @ B4 @ D2 ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_242_diff__eq__diff__less,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( ordered_ab_group_add @ A )
% 2.55/1.69 => ! [A3: A,B4: A,C2: A,D2: A] :
% 2.55/1.69 ( ( ( minus_minus @ A @ A3 @ B4 )
% 2.55/1.69 = ( minus_minus @ A @ C2 @ D2 ) )
% 2.55/1.69 => ( ( ord_less @ A @ A3 @ B4 )
% 2.55/1.69 = ( ord_less @ A @ C2 @ D2 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_243_remove__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( remove @ A )
% 2.55/1.69 = ( ^ [X4: A,A6: set @ A] : ( minus_minus @ ( set @ A ) @ A6 @ ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_244_Tree_Osimps_I15_J,axiom,
% 2.55/1.69 ! [A: $tType,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) )
% 2.55/1.69 = ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ ( binary2130109271t_Tree @ A @ X21 ) @ ( insert @ A @ X22 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( binary2130109271t_Tree @ A @ X23 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_245_member__remove,axiom,
% 2.55/1.69 ! [A: $tType,X3: A,Y: A,A4: set @ A] :
% 2.55/1.69 ( ( member @ A @ X3 @ ( remove @ A @ Y @ A4 ) )
% 2.55/1.69 = ( ( member @ A @ X3 @ A4 )
% 2.55/1.69 & ( X3 != Y ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_246_Tree_Osimps_I14_J,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( binary2130109271t_Tree @ A @ ( binary1746293266le_Tip @ A ) )
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_247_Tree_Oset__intros_I3_J,axiom,
% 2.55/1.69 ! [A: $tType,Ya: A,X23: binary1291135688e_Tree @ A,X21: binary1291135688e_Tree @ A,X22: A] :
% 2.55/1.69 ( ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ X23 ) )
% 2.55/1.69 => ( member @ A @ Ya @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_248_Tree_Oset__intros_I2_J,axiom,
% 2.55/1.69 ! [A: $tType,X22: A,X21: binary1291135688e_Tree @ A,X23: binary1291135688e_Tree @ A] : ( member @ A @ X22 @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_249_Tree_Oset__intros_I1_J,axiom,
% 2.55/1.69 ! [A: $tType,Y: A,X21: binary1291135688e_Tree @ A,X22: A,X23: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ X21 ) )
% 2.55/1.69 => ( member @ A @ Y @ ( binary2130109271t_Tree @ A @ ( binary210054475elle_T @ A @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_250_Tree_Oset__cases,axiom,
% 2.55/1.69 ! [A: $tType,E: A,A3: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( member @ A @ E @ ( binary2130109271t_Tree @ A @ A3 ) )
% 2.55/1.69 => ( ! [Z1: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ? [Z22: A,Z32: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( A3
% 2.55/1.69 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 2.55/1.69 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z1 ) ) )
% 2.55/1.69 => ( ! [Z1: binary1291135688e_Tree @ A,Z32: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( A3
% 2.55/1.69 != ( binary210054475elle_T @ A @ Z1 @ E @ Z32 ) )
% 2.55/1.69 => ~ ! [Z1: binary1291135688e_Tree @ A,Z22: A,Z32: binary1291135688e_Tree @ A] :
% 2.55/1.69 ( ( A3
% 2.55/1.69 = ( binary210054475elle_T @ A @ Z1 @ Z22 @ Z32 ) )
% 2.55/1.69 => ~ ( member @ A @ E @ ( binary2130109271t_Tree @ A @ Z32 ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_251_Tree_Opred__cong,axiom,
% 2.55/1.69 ! [A: $tType,X3: binary1291135688e_Tree @ A,Ya: binary1291135688e_Tree @ A,P: A > $o,Pa: A > $o] :
% 2.55/1.69 ( ( X3 = Ya )
% 2.55/1.69 => ( ! [Z: A] :
% 2.55/1.69 ( ( member @ A @ Z @ ( binary2130109271t_Tree @ A @ Ya ) )
% 2.55/1.69 => ( ( P @ Z )
% 2.55/1.69 = ( Pa @ Z ) ) )
% 2.55/1.69 => ( ( binary1693644968d_Tree @ A @ P @ X3 )
% 2.55/1.69 = ( binary1693644968d_Tree @ A @ Pa @ Ya ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_252_Tree_Opred__mono__strong,axiom,
% 2.55/1.69 ! [A: $tType,P: A > $o,X3: binary1291135688e_Tree @ A,Pa: A > $o] :
% 2.55/1.69 ( ( binary1693644968d_Tree @ A @ P @ X3 )
% 2.55/1.69 => ( ! [Z: A] :
% 2.55/1.69 ( ( member @ A @ Z @ ( binary2130109271t_Tree @ A @ X3 ) )
% 2.55/1.69 => ( ( P @ Z )
% 2.55/1.69 => ( Pa @ Z ) ) )
% 2.55/1.69 => ( binary1693644968d_Tree @ A @ Pa @ X3 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_253_Set_Ois__empty__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( is_empty @ A )
% 2.55/1.69 = ( ^ [A6: set @ A] :
% 2.55/1.69 ( A6
% 2.55/1.69 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_254_the__elem__def,axiom,
% 2.55/1.69 ! [A: $tType] :
% 2.55/1.69 ( ( the_elem @ A )
% 2.55/1.69 = ( ^ [X6: set @ A] :
% 2.55/1.69 ( the @ A
% 2.55/1.69 @ ^ [X4: A] :
% 2.55/1.69 ( X6
% 2.55/1.69 = ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(fact_255_psubset__insert__iff,axiom,
% 2.55/1.69 ! [A: $tType,A4: set @ A,X3: A,B5: set @ A] :
% 2.55/1.69 ( ( ord_less @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ B5 ) )
% 2.55/1.69 = ( ( ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) )
% 2.55/1.69 & ( ~ ( member @ A @ X3 @ B5 )
% 2.55/1.69 => ( ( ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ( ord_less @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A4 @ ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) @ B5 ) )
% 2.55/1.69 & ( ~ ( member @ A @ X3 @ A4 )
% 2.55/1.69 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ) ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.55/1.69 bounded_lattice @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.55/1.69 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( bounded_lattice @ A8 )
% 2.55/1.69 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( bounded_lattice @ A8 )
% 2.55/1.69 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( semilattice_sup @ A8 )
% 2.55/1.69 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( order_bot @ A8 )
% 2.55/1.69 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( preorder @ A8 )
% 2.55/1.69 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( lattice @ A8 )
% 2.55/1.69 => ( lattice @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( order @ A8 )
% 2.55/1.69 => ( order @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Orderings_Oord,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( ord @ A8 )
% 2.55/1.69 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Orderings_Obot,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( bot @ A8 )
% 2.55/1.69 => ( bot @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_fun___Groups_Ominus,axiom,
% 2.55/1.69 ! [A7: $tType,A8: $tType] :
% 2.55/1.69 ( ( minus @ A8 )
% 2.55/1.69 => ( minus @ ( A7 > A8 ) ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.55/1.69 cancel146912293up_add @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 2.55/1.69 ordered_ab_group_add @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Lattices_Osemilattice__sup_3,axiom,
% 2.55/1.69 semilattice_sup @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 2.55/1.69 linordered_idom @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Opreorder_4,axiom,
% 2.55/1.69 preorder @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 2.55/1.69 linorder @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Ono__top,axiom,
% 2.55/1.69 no_top @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Ono__bot,axiom,
% 2.55/1.69 no_bot @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Lattices_Olattice_5,axiom,
% 2.55/1.69 lattice @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 2.55/1.69 group_add @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Oorder_6,axiom,
% 2.55/1.69 order @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Orderings_Oord_7,axiom,
% 2.55/1.69 ord @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Int_Oint___Groups_Ominus_8,axiom,
% 2.55/1.69 minus @ int ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 2.55/1.69 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 2.55/1.69 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 2.55/1.69 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 2.55/1.69 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Lattices_Olattice_13,axiom,
% 2.55/1.69 ! [A7: $tType] : ( lattice @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Orderings_Oorder_14,axiom,
% 2.55/1.69 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Orderings_Oord_15,axiom,
% 2.55/1.69 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Orderings_Obot_16,axiom,
% 2.55/1.69 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_Set_Oset___Groups_Ominus_17,axiom,
% 2.55/1.69 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_18,axiom,
% 2.55/1.69 bounde1808546759up_bot @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_19,axiom,
% 2.55/1.69 semilattice_sup @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Oorder__bot_20,axiom,
% 2.55/1.69 order_bot @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Opreorder_21,axiom,
% 2.55/1.69 preorder @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Olinorder_22,axiom,
% 2.55/1.69 linorder @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Lattices_Olattice_23,axiom,
% 2.55/1.69 lattice @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Oorder_24,axiom,
% 2.55/1.69 order @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Oord_25,axiom,
% 2.55/1.69 ord @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Orderings_Obot_26,axiom,
% 2.55/1.69 bot @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(tcon_HOL_Obool___Groups_Ominus_27,axiom,
% 2.55/1.69 minus @ $o ).
% 2.55/1.69
% 2.55/1.69 thf(conj_0,conjecture,
% 2.55/1.69 ord_less @ int @ ( h @ w ) @ ( h @ x ) ).
% 2.55/1.69 ------------------------
% 2.80/1.71 % (13693)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_13441 for (2999ds/275Mi)
% 2.80/1.71 % (13689)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_13441 for (2999ds/4Mi)
% 2.80/1.71 % (13692)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_13441 for (2999ds/2Mi)
% 2.80/1.71 % (13688)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/183Mi)
% 2.80/1.71 % (13691)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/2Mi)
% 2.80/1.71 % (13694)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/18Mi)
% 2.80/1.71 % (13691)Instruction limit reached!
% 2.80/1.71 % (13691)------------------------------
% 2.80/1.71 % (13691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.71 % (13691)Termination reason: Unknown
% 2.80/1.71 % (13691)Termination phase: shuffling
% 2.80/1.71
% 2.80/1.71 % (13691)Memory used [KB]: 1407
% 2.80/1.71 % (13691)Time elapsed: 0.002 s
% 2.80/1.71 % (13691)Instructions burned: 2 (million)
% 2.80/1.71 % (13691)------------------------------
% 2.80/1.71 % (13691)------------------------------
% 2.80/1.71 % (13692)Instruction limit reached!
% 2.80/1.71 % (13692)------------------------------
% 2.80/1.71 % (13692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.71 % (13692)Termination reason: Unknown
% 2.80/1.71 % (13692)Termination phase: shuffling
% 2.80/1.71
% 2.80/1.71 % (13692)Memory used [KB]: 1407
% 2.80/1.71 % (13692)Time elapsed: 0.002 s
% 2.80/1.71 % (13692)Instructions burned: 2 (million)
% 2.80/1.71 % (13692)------------------------------
% 2.80/1.71 % (13692)------------------------------
% 2.80/1.71 % (13689)Instruction limit reached!
% 2.80/1.71 % (13689)------------------------------
% 2.80/1.71 % (13689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.71 % (13689)Termination reason: Unknown
% 2.80/1.71 % (13689)Termination phase: shuffling
% 2.80/1.71
% 2.80/1.71 % (13689)Memory used [KB]: 1407
% 2.80/1.71 % (13689)Time elapsed: 0.003 s
% 2.80/1.71 % (13689)Instructions burned: 5 (million)
% 2.80/1.71 % (13689)------------------------------
% 2.80/1.71 % (13689)------------------------------
% 2.80/1.72 % (13694)Instruction limit reached!
% 2.80/1.72 % (13694)------------------------------
% 2.80/1.72 % (13694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.72 % (13694)Termination reason: Unknown
% 2.80/1.72 % (13694)Termination phase: Property scanning
% 2.80/1.72
% 2.80/1.72 % (13694)Memory used [KB]: 1791
% 2.80/1.72 % (13694)Time elapsed: 0.008 s
% 2.80/1.72 % (13694)Instructions burned: 21 (million)
% 2.80/1.72 % (13694)------------------------------
% 2.80/1.72 % (13694)------------------------------
% 2.80/1.72 % (13690)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_13441 for (2999ds/27Mi)
% 2.80/1.72 % (13698)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/3Mi)
% 2.80/1.72 % (13699)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_13441 for (2999ds/37Mi)
% 2.80/1.72 % (13700)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_13441 for (2999ds/15Mi)
% 2.80/1.72 % (13698)Instruction limit reached!
% 2.80/1.72 % (13698)------------------------------
% 2.80/1.72 % (13698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.72 % (13698)Termination reason: Unknown
% 2.80/1.72 % (13698)Termination phase: shuffling
% 2.80/1.72
% 2.80/1.72 % (13698)Memory used [KB]: 1407
% 2.80/1.72 % (13698)Time elapsed: 0.002 s
% 2.80/1.72 % (13698)Instructions burned: 3 (million)
% 2.80/1.72 % (13698)------------------------------
% 2.80/1.72 % (13698)------------------------------
% 2.80/1.72 % (13693)Refutation not found, incomplete strategy
% 2.80/1.72 % (13693)------------------------------
% 2.80/1.72 % (13693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.72 % (13693)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.72
% 2.80/1.72
% 2.80/1.72 % (13693)Memory used [KB]: 6524
% 2.80/1.72 % (13693)Time elapsed: 0.016 s
% 2.80/1.72 % (13693)Instructions burned: 47 (million)
% 2.80/1.72 % (13693)------------------------------
% 2.80/1.72 % (13693)------------------------------
% 2.80/1.73 % (13700)Instruction limit reached!
% 2.80/1.73 % (13700)------------------------------
% 2.80/1.73 % (13700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.73 % (13700)Termination reason: Unknown
% 2.80/1.73 % (13700)Termination phase: shuffling
% 2.80/1.73
% 2.80/1.73 % (13700)Memory used [KB]: 1663
% 2.80/1.73 % (13700)Time elapsed: 0.006 s
% 2.80/1.73 % (13700)Instructions burned: 15 (million)
% 2.80/1.73 % (13700)------------------------------
% 2.80/1.73 % (13700)------------------------------
% 2.80/1.73 % (13702)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_13441 for (2999ds/3Mi)
% 2.80/1.73 % (13702)Instruction limit reached!
% 2.80/1.73 % (13702)------------------------------
% 2.80/1.73 % (13702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.73 % (13702)Termination reason: Unknown
% 2.80/1.73 % (13702)Termination phase: shuffling
% 2.80/1.73
% 2.80/1.73 % (13702)Memory used [KB]: 1407
% 2.80/1.73 % (13702)Time elapsed: 0.002 s
% 2.80/1.73 % (13702)Instructions burned: 3 (million)
% 2.80/1.73 % (13702)------------------------------
% 2.80/1.73 % (13702)------------------------------
% 2.80/1.73 % (13705)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_13441 for (2999ds/1041Mi)
% 2.80/1.73 % (13699)Instruction limit reached!
% 2.80/1.73 % (13699)------------------------------
% 2.80/1.73 % (13699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.73 % (13699)Termination reason: Unknown
% 2.80/1.73 % (13699)Termination phase: Property scanning
% 2.80/1.73
% 2.80/1.73 % (13699)Memory used [KB]: 2174
% 2.80/1.73 % (13699)Time elapsed: 0.012 s
% 2.80/1.73 % (13699)Instructions burned: 38 (million)
% 2.80/1.73 % (13699)------------------------------
% 2.80/1.73 % (13699)------------------------------
% 2.80/1.73 % (13707)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/7Mi)
% 2.80/1.73 % (13708)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/16Mi)
% 2.80/1.73 % (13690)Instruction limit reached!
% 2.80/1.73 % (13690)------------------------------
% 2.80/1.73 % (13690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.73 % (13690)Termination reason: Unknown
% 2.80/1.73 % (13690)Termination phase: Property scanning
% 2.80/1.73
% 2.80/1.73 % (13690)Memory used [KB]: 1791
% 2.80/1.73 % (13690)Time elapsed: 0.018 s
% 2.80/1.73 % (13690)Instructions burned: 27 (million)
% 2.80/1.73 % (13690)------------------------------
% 2.80/1.73 % (13690)------------------------------
% 2.80/1.74 % (13710)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_13441 for (2999ds/3Mi)
% 2.80/1.74 % (13710)Instruction limit reached!
% 2.80/1.74 % (13710)------------------------------
% 2.80/1.74 % (13710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.74 % (13710)Termination reason: Unknown
% 2.80/1.74 % (13710)Termination phase: shuffling
% 2.80/1.74
% 2.80/1.74 % (13710)Memory used [KB]: 1407
% 2.80/1.74 % (13710)Time elapsed: 0.002 s
% 2.80/1.74 % (13710)Instructions burned: 3 (million)
% 2.80/1.74 % (13710)------------------------------
% 2.80/1.74 % (13710)------------------------------
% 2.80/1.74 % (13707)Instruction limit reached!
% 2.80/1.74 % (13707)------------------------------
% 2.80/1.74 % (13707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.74 % (13707)Termination reason: Unknown
% 2.80/1.74 % (13707)Termination phase: shuffling
% 2.80/1.74
% 2.80/1.74 % (13707)Memory used [KB]: 1535
% 2.80/1.74 % (13707)Time elapsed: 0.004 s
% 2.80/1.74 % (13707)Instructions burned: 9 (million)
% 2.80/1.74 % (13707)------------------------------
% 2.80/1.74 % (13707)------------------------------
% 2.80/1.74 % (13713)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_13441 for (2999ds/3Mi)
% 2.80/1.74 % (13708)Instruction limit reached!
% 2.80/1.74 % (13708)------------------------------
% 2.80/1.74 % (13708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.74 % (13708)Termination reason: Unknown
% 2.80/1.74 % (13708)Termination phase: shuffling
% 2.80/1.74
% 2.80/1.74 % (13708)Memory used [KB]: 1663
% 2.80/1.74 % (13708)Time elapsed: 0.007 s
% 2.80/1.74 % (13708)Instructions burned: 18 (million)
% 2.80/1.74 % (13708)------------------------------
% 2.80/1.74 % (13708)------------------------------
% 2.80/1.74 % (13713)Instruction limit reached!
% 2.80/1.74 % (13713)------------------------------
% 2.80/1.74 % (13713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.74 % (13713)Termination reason: Unknown
% 2.80/1.74 % (13713)Termination phase: shuffling
% 2.80/1.74
% 2.80/1.74 % (13713)Memory used [KB]: 1407
% 2.80/1.74 % (13713)Time elapsed: 0.002 s
% 2.80/1.74 % (13713)Instructions burned: 3 (million)
% 2.80/1.74 % (13713)------------------------------
% 2.80/1.74 % (13713)------------------------------
% 2.80/1.75 % (13717)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/3Mi)
% 2.80/1.75 % (13718)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/4Mi)
% 2.80/1.75 % (13717)Instruction limit reached!
% 2.80/1.75 % (13717)------------------------------
% 2.80/1.75 % (13717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.75 % (13717)Termination reason: Unknown
% 2.80/1.75 % (13717)Termination phase: shuffling
% 2.80/1.75
% 2.80/1.75 % (13717)Memory used [KB]: 1407
% 2.80/1.75 % (13717)Time elapsed: 0.002 s
% 2.80/1.75 % (13717)Instructions burned: 4 (million)
% 2.80/1.75 % (13717)------------------------------
% 2.80/1.75 % (13717)------------------------------
% 2.80/1.75 % (13718)Instruction limit reached!
% 2.80/1.75 % (13718)------------------------------
% 2.80/1.75 % (13718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.75 % (13718)Termination reason: Unknown
% 2.80/1.75 % (13718)Termination phase: shuffling
% 2.80/1.75
% 2.80/1.75 % (13718)Memory used [KB]: 1407
% 2.80/1.75 % (13718)Time elapsed: 0.002 s
% 2.80/1.75 % (13718)Instructions burned: 4 (million)
% 2.80/1.75 % (13718)------------------------------
% 2.80/1.75 % (13718)------------------------------
% 2.80/1.75 % (13720)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/18Mi)
% 2.80/1.75 % (13721)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/710Mi)
% 2.80/1.75 % (13716)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/7Mi)
% 2.80/1.76 % (13720)Instruction limit reached!
% 2.80/1.76 % (13720)------------------------------
% 2.80/1.76 % (13720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.76 % (13720)Termination reason: Unknown
% 2.80/1.76 % (13720)Termination phase: shuffling
% 2.80/1.76
% 2.80/1.76 % (13720)Memory used [KB]: 1791
% 2.80/1.76 % (13720)Time elapsed: 0.007 s
% 2.80/1.76 % (13720)Instructions burned: 18 (million)
% 2.80/1.76 % (13720)------------------------------
% 2.80/1.76 % (13720)------------------------------
% 2.80/1.76 % (13716)Instruction limit reached!
% 2.80/1.76 % (13716)------------------------------
% 2.80/1.76 % (13716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.76 % (13716)Termination reason: Unknown
% 2.80/1.76 % (13716)Termination phase: shuffling
% 2.80/1.76
% 2.80/1.76 % (13716)Memory used [KB]: 1535
% 2.80/1.76 % (13716)Time elapsed: 0.006 s
% 2.80/1.76 % (13716)Instructions burned: 7 (million)
% 2.80/1.76 % (13716)------------------------------
% 2.80/1.76 % (13716)------------------------------
% 2.80/1.76 % (13724)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/6Mi)
% 2.80/1.76 % (13726)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_13441 for (2999ds/902Mi)
% 2.80/1.76 % (13724)Instruction limit reached!
% 2.80/1.76 % (13724)------------------------------
% 2.80/1.76 % (13724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.76 % (13724)Termination reason: Unknown
% 2.80/1.76 % (13724)Termination phase: shuffling
% 2.80/1.76
% 2.80/1.76 % (13724)Memory used [KB]: 1407
% 2.80/1.76 % (13724)Time elapsed: 0.003 s
% 2.80/1.76 % (13724)Instructions burned: 6 (million)
% 2.80/1.76 % (13724)------------------------------
% 2.80/1.76 % (13724)------------------------------
% 2.80/1.76 % (13688)Instruction limit reached!
% 2.80/1.76 % (13688)------------------------------
% 2.80/1.76 % (13688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.76 % (13688)Termination reason: Unknown
% 2.80/1.76 % (13688)Termination phase: Saturation
% 2.80/1.76
% 2.80/1.76 % (13688)Memory used [KB]: 7164
% 2.80/1.76 % (13688)Time elapsed: 0.056 s
% 2.80/1.76 % (13688)Instructions burned: 184 (million)
% 2.80/1.76 % (13688)------------------------------
% 2.80/1.76 % (13688)------------------------------
% 2.80/1.77 % (13730)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_13441 for (2999ds/21Mi)
% 2.80/1.77 % (13732)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_13441 for (2999ds/6Mi)
% 2.80/1.77 % (13732)Instruction limit reached!
% 2.80/1.77 % (13732)------------------------------
% 2.80/1.77 % (13732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.77 % (13732)Termination reason: Unknown
% 2.80/1.77 % (13732)Termination phase: shuffling
% 2.80/1.77
% 2.80/1.77 % (13732)Memory used [KB]: 1407
% 2.80/1.77 % (13732)Time elapsed: 0.003 s
% 2.80/1.77 % (13732)Instructions burned: 7 (million)
% 2.80/1.77 % (13732)------------------------------
% 2.80/1.77 % (13732)------------------------------
% 2.80/1.77 % (13730)Instruction limit reached!
% 2.80/1.77 % (13730)------------------------------
% 2.80/1.77 % (13730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.77 % (13730)Termination reason: Unknown
% 2.80/1.77 % (13730)Termination phase: shuffling
% 2.80/1.77
% 2.80/1.77 % (13730)Memory used [KB]: 1791
% 2.80/1.77 % (13730)Time elapsed: 0.008 s
% 2.80/1.77 % (13730)Instructions burned: 21 (million)
% 2.80/1.77 % (13730)------------------------------
% 2.80/1.77 % (13730)------------------------------
% 2.80/1.77 % (13734)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/377Mi)
% 2.80/1.78 % (13731)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/5Mi)
% 2.80/1.78 % (13731)Instruction limit reached!
% 2.80/1.78 % (13731)------------------------------
% 2.80/1.78 % (13731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.78 % (13731)Termination reason: Unknown
% 2.80/1.78 % (13731)Termination phase: shuffling
% 2.80/1.78
% 2.80/1.78 % (13731)Memory used [KB]: 1407
% 2.80/1.78 % (13731)Time elapsed: 0.004 s
% 2.80/1.78 % (13731)Instructions burned: 6 (million)
% 2.80/1.78 % (13731)------------------------------
% 2.80/1.78 % (13731)------------------------------
% 2.80/1.78 % (13736)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_13441 for (2999ds/779Mi)
% 2.80/1.78 % (13738)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_13441 for (2999ds/19Mi)
% 2.80/1.79 % (13738)Instruction limit reached!
% 2.80/1.79 % (13738)------------------------------
% 2.80/1.79 % (13738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.79 % (13738)Termination reason: Unknown
% 2.80/1.79 % (13738)Termination phase: shuffling
% 2.80/1.79
% 2.80/1.79 % (13738)Memory used [KB]: 1791
% 2.80/1.79 % (13738)Time elapsed: 0.008 s
% 2.80/1.79 % (13738)Instructions burned: 22 (million)
% 2.80/1.79 % (13738)------------------------------
% 2.80/1.79 % (13738)------------------------------
% 2.80/1.79 % (13741)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/879Mi)
% 2.80/1.80 % (13744)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/17Mi)
% 2.80/1.80 % (13744)Instruction limit reached!
% 2.80/1.80 % (13744)------------------------------
% 2.80/1.80 % (13744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.80 % (13744)Termination reason: Unknown
% 2.80/1.80 % (13744)Termination phase: shuffling
% 2.80/1.80
% 2.80/1.80 % (13744)Memory used [KB]: 1663
% 2.80/1.80 % (13744)Time elapsed: 0.007 s
% 2.80/1.80 % (13744)Instructions burned: 17 (million)
% 2.80/1.80 % (13744)------------------------------
% 2.80/1.80 % (13744)------------------------------
% 2.80/1.81 % (13747)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13441 for (2999ds/3Mi)
% 2.80/1.81 % (13747)Instruction limit reached!
% 2.80/1.81 % (13747)------------------------------
% 2.80/1.81 % (13747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.81 % (13747)Termination reason: Unknown
% 2.80/1.81 % (13747)Termination phase: shuffling
% 2.80/1.81
% 2.80/1.81 % (13747)Memory used [KB]: 1407
% 2.80/1.81 % (13747)Time elapsed: 0.002 s
% 2.80/1.81 % (13747)Instructions burned: 3 (million)
% 2.80/1.81 % (13747)------------------------------
% 2.80/1.81 % (13747)------------------------------
% 2.80/1.82 % (13751)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13441 for (2998ds/30Mi)
% 2.80/1.83 % (13751)Instruction limit reached!
% 2.80/1.83 % (13751)------------------------------
% 2.80/1.83 % (13751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.83 % (13751)Termination reason: Unknown
% 2.80/1.83 % (13751)Termination phase: Property scanning
% 2.80/1.83
% 2.80/1.83 % (13751)Memory used [KB]: 1918
% 2.80/1.83 % (13751)Time elapsed: 0.011 s
% 2.80/1.83 % (13751)Instructions burned: 32 (million)
% 2.80/1.83 % (13751)------------------------------
% 2.80/1.83 % (13751)------------------------------
% 2.80/1.84 % (13756)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13441 for (2998ds/127Mi)
% 2.80/1.88 % (13756)Instruction limit reached!
% 2.80/1.88 % (13756)------------------------------
% 2.80/1.88 % (13756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.88 % (13756)Termination reason: Unknown
% 2.80/1.88 % (13756)Termination phase: Saturation
% 2.80/1.88
% 2.80/1.88 % (13756)Memory used [KB]: 6780
% 2.80/1.88 % (13756)Time elapsed: 0.040 s
% 2.80/1.88 % (13756)Instructions burned: 130 (million)
% 2.80/1.88 % (13756)------------------------------
% 2.80/1.88 % (13756)------------------------------
% 2.80/1.89 % (13734)Instruction limit reached!
% 2.80/1.89 % (13734)------------------------------
% 2.80/1.89 % (13734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.89 % (13734)Termination reason: Unknown
% 2.80/1.89 % (13734)Termination phase: Saturation
% 2.80/1.89
% 2.80/1.89 % (13734)Memory used [KB]: 7547
% 2.80/1.89 % (13734)Time elapsed: 0.115 s
% 2.80/1.89 % (13734)Instructions burned: 378 (million)
% 2.80/1.89 % (13734)------------------------------
% 2.80/1.89 % (13734)------------------------------
% 2.80/1.89 % (13766)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13441 for (2998ds/100Mi)
% 2.80/1.90 % (13768)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/3Mi)
% 2.80/1.90 % (13768)Instruction limit reached!
% 2.80/1.90 % (13768)------------------------------
% 2.80/1.90 % (13768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.90 % (13768)Termination reason: Unknown
% 2.80/1.90 % (13768)Termination phase: shuffling
% 2.80/1.90
% 2.80/1.90 % (13768)Memory used [KB]: 1407
% 2.80/1.90 % (13768)Time elapsed: 0.003 s
% 2.80/1.90 % (13768)Instructions burned: 6 (million)
% 2.80/1.90 % (13768)------------------------------
% 2.80/1.90 % (13768)------------------------------
% 2.80/1.91 % (13776)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/20Mi)
% 2.80/1.92 % (13776)Instruction limit reached!
% 2.80/1.92 % (13776)------------------------------
% 2.80/1.92 % (13776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.92 % (13776)Termination reason: Unknown
% 2.80/1.92 % (13776)Termination phase: Property scanning
% 2.80/1.92
% 2.80/1.92 % (13776)Memory used [KB]: 1791
% 2.80/1.92 % (13776)Time elapsed: 0.008 s
% 2.80/1.92 % (13776)Instructions burned: 22 (million)
% 2.80/1.92 % (13776)------------------------------
% 2.80/1.92 % (13776)------------------------------
% 2.80/1.92 % (13766)Instruction limit reached!
% 2.80/1.92 % (13766)------------------------------
% 2.80/1.92 % (13766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.92 % (13766)Termination reason: Unknown
% 2.80/1.92 % (13766)Termination phase: Saturation
% 2.80/1.92
% 2.80/1.92 % (13766)Memory used [KB]: 6780
% 2.80/1.92 % (13766)Time elapsed: 0.028 s
% 2.80/1.92 % (13766)Instructions burned: 100 (million)
% 2.80/1.92 % (13766)------------------------------
% 2.80/1.92 % (13766)------------------------------
% 2.80/1.92 % (13786)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/86Mi)
% 2.80/1.93 % (13789)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/107Mi)
% 2.80/1.95 % (13786)Instruction limit reached!
% 2.80/1.95 % (13786)------------------------------
% 2.80/1.95 % (13786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.95 % (13786)Termination reason: Unknown
% 2.80/1.95 % (13786)Termination phase: Saturation
% 2.80/1.95
% 2.80/1.95 % (13786)Memory used [KB]: 6652
% 2.80/1.95 % (13786)Time elapsed: 0.027 s
% 2.80/1.95 % (13786)Instructions burned: 87 (million)
% 2.80/1.95 % (13786)------------------------------
% 2.80/1.95 % (13786)------------------------------
% 2.80/1.96 % (13805)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/39Mi)
% 2.80/1.96 % (13789)Instruction limit reached!
% 2.80/1.96 % (13789)------------------------------
% 2.80/1.96 % (13789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.96 % (13789)Termination reason: Unknown
% 2.80/1.96 % (13789)Termination phase: Saturation
% 2.80/1.96
% 2.80/1.96 % (13789)Memory used [KB]: 6780
% 2.80/1.96 % (13789)Time elapsed: 0.034 s
% 2.80/1.96 % (13789)Instructions burned: 110 (million)
% 2.80/1.96 % (13789)------------------------------
% 2.80/1.96 % (13789)------------------------------
% 2.80/1.97 % (13721)Instruction limit reached!
% 2.80/1.97 % (13721)------------------------------
% 2.80/1.97 % (13721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.97 % (13721)Termination reason: Unknown
% 2.80/1.97 % (13721)Termination phase: Saturation
% 2.80/1.97
% 2.80/1.97 % (13721)Memory used [KB]: 8059
% 2.80/1.97 % (13721)Time elapsed: 0.218 s
% 2.80/1.97 % (13721)Instructions burned: 712 (million)
% 2.80/1.97 % (13721)------------------------------
% 2.80/1.97 % (13721)------------------------------
% 2.80/1.97 % (13807)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/448Mi)
% 2.80/1.97 % (13805)Instruction limit reached!
% 2.80/1.97 % (13805)------------------------------
% 2.80/1.97 % (13805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.97 % (13805)Termination reason: Unknown
% 2.80/1.97 % (13805)Termination phase: Property scanning
% 2.80/1.97
% 2.80/1.97 % (13805)Memory used [KB]: 2174
% 2.80/1.97 % (13805)Time elapsed: 0.012 s
% 2.80/1.97 % (13805)Instructions burned: 39 (million)
% 2.80/1.97 % (13805)------------------------------
% 2.80/1.97 % (13805)------------------------------
% 2.80/1.98 % (13810)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/46Mi)
% 2.80/1.98 % (13813)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_13441 for (2997ds/98Mi)
% 2.80/1.99 % (13810)Instruction limit reached!
% 2.80/1.99 % (13810)------------------------------
% 2.80/1.99 % (13810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.99 % (13810)Termination reason: Unknown
% 2.80/1.99 % (13810)Termination phase: Preprocessing 3
% 2.80/1.99
% 2.80/1.99 % (13810)Memory used [KB]: 2046
% 2.80/1.99 % (13810)Time elapsed: 0.016 s
% 2.80/1.99 % (13810)Instructions burned: 47 (million)
% 2.80/1.99 % (13810)------------------------------
% 2.80/1.99 % (13810)------------------------------
% 2.80/1.99 % (13741)First to succeed.
% 2.80/1.99 % (13741)Refutation found. Thanks to Tanya!
% 2.80/1.99 % SZS status Theorem for DTF2THF_13441
% 2.80/1.99 % SZS output start Proof for DTF2THF_13441
% 2.80/1.99 thf(type_def_5, type, binary1291135688e_Tree: ($tType) > $tType).
% 2.80/1.99 thf(type_def_7, type, set: ($tType) > $tType).
% 2.80/1.99 thf(type_def_8, type, int: $tType).
% 2.80/1.99 thf(type_def_9, type, a: $tType).
% 2.80/1.99 thf(func_def_0, type, binary1291135688e_Tree: ($tType) > $tType).
% 2.80/1.99 thf(func_def_1, type, set: ($tType) > $tType).
% 2.80/1.99 thf(func_def_2, type, int: $tType).
% 2.80/1.99 thf(func_def_3, type, a: $tType).
% 2.80/1.99 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_6, type, minus: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_7, type, bot: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_10, type, group_add: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_11, type, lattice: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_12, type, no_bot: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_13, type, no_top: !>[X0: $tType]:($o)).
% 2.80/1.99 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_16, type, order_bot: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_17, type, wellorder: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_18, type, dense_order: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_19, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_21, type, semilattice_sup: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_23, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_24, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_25, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 2.80/2.00 thf(func_def_26, type, binary210054475elle_T: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0)).
% 2.80/2.00 thf(func_def_27, type, binary1746293266le_Tip: !>[X0: $tType]:(binary1291135688e_Tree @ X0)).
% 2.80/2.00 thf(func_def_28, type, binary536355927e_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0) > binary1291135688e_Tree @ X1 > X0)).
% 2.80/2.00 thf(func_def_29, type, binary1693644968d_Tree: !>[X0: $tType]:((X0 > $o) > binary1291135688e_Tree @ X0 > $o)).
% 2.80/2.00 thf(func_def_30, type, binary1929596613c_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0 > X0 > X0) > binary1291135688e_Tree @ X1 > X0)).
% 2.80/2.00 thf(func_def_31, type, binary2130109271t_Tree: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > set @ X0)).
% 2.80/2.00 thf(func_def_32, type, binary1830089824insert: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0)).
% 2.80/2.00 thf(func_def_33, type, binary64540844le_eqs: !>[X0: $tType]:((X0 > int) > X0 > set @ X0)).
% 2.80/2.00 thf(func_def_34, type, binary827270440e_memb: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree @ X0 > $o)).
% 2.80/2.00 thf(func_def_35, type, binary1653327646_setOf: !>[X0: $tType]:(binary1291135688e_Tree @ X0 > set @ X0)).
% 2.80/2.00 thf(func_def_36, type, binary1610619414edTree: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree @ X0 > $o)).
% 2.80/2.00 thf(func_def_37, type, binary231205461t_pred: !>[X0: $tType]:((X0 > int) > X0 > X0 > binary1291135688e_Tree @ X0 > $o)).
% 2.80/2.00 thf(func_def_38, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.80/2.00 thf(func_def_39, type, the: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.80/2.00 thf(func_def_40, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.80/2.00 thf(func_def_41, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.80/2.00 thf(func_def_42, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.80/2.00 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.80/2.00 thf(func_def_44, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.80/2.00 thf(func_def_45, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.80/2.00 thf(func_def_46, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.80/2.00 thf(func_def_47, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.80/2.00 thf(func_def_48, type, remove: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.80/2.00 thf(func_def_49, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.80/2.00 thf(func_def_50, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.80/2.00 thf(func_def_51, type, e: a).
% 2.80/2.00 thf(func_def_52, type, h: a > int).
% 2.80/2.00 thf(func_def_53, type, t1: binary1291135688e_Tree @ a).
% 2.80/2.00 thf(func_def_54, type, t2: binary1291135688e_Tree @ a).
% 2.80/2.00 thf(func_def_55, type, w: a).
% 2.80/2.00 thf(func_def_56, type, x: a).
% 2.80/2.00 thf(func_def_72, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.80/2.00 thf(func_def_74, type, sK2: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree @ X0 > X0)).
% 2.80/2.00 thf(func_def_75, type, sK3: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree @ X0 > X0 > X0)).
% 2.80/2.00 thf(func_def_76, type, ph4: !>[X0: $tType]:(X0)).
% 2.80/2.00 thf(f1600,plain,(
% 2.80/2.00 $false),
% 2.80/2.00 inference(subsumption_resolution,[status(thm)],[f1599,f947])).
% 2.80/2.00 thf(f947,plain,(
% 2.80/2.00 ((ord_less @ int @ (h @ w) @ (h @ e)) != $true)),
% 2.80/2.00 inference(forward_demodulation,[status(thm)],[f860,f879])).
% 2.80/2.00 thf(f879,plain,(
% 2.80/2.00 ((h @ e) = (h @ x))),
% 2.80/2.00 inference(cnf_transformation,[status(thm)],[f8])).
% 2.80/2.00 thf(f8,axiom,(
% 2.80/2.00 ((h @ e) = (h @ x))),
% 2.80/2.00 file('/export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2THF_13441.p',fact_7_xeqe)).
% 2.80/2.00 thf(f860,plain,(
% 2.80/2.00 ((ord_less @ int @ (h @ w) @ (h @ x)) != $true)),
% 2.80/2.00 inference(cnf_transformation,[status(thm)],[f822])).
% 2.80/2.00 thf(f822,plain,(
% 2.80/2.00 ((ord_less @ int @ (h @ w) @ (h @ x)) != $true)),
% 2.80/2.00 inference(flattening,[status(thm)],[f433])).
% 2.80/2.00 thf(f433,plain,(
% 2.80/2.00 ~((ord_less @ int @ (h @ w) @ (h @ x)) = $true)),
% 2.80/2.00 inference(fool_elimination,[status(thm)],[f432])).
% 2.80/2.00 thf(f432,plain,(
% 2.80/2.00 ~(ord_less @ int @ (h @ w) @ (h @ x))),
% 2.80/2.00 inference(rectify,[status(thm)],[f302])).
% 2.80/2.00 thf(f302,negated_conjecture,(
% 2.80/2.00 ~(ord_less @ int @ (h @ w) @ (h @ x))),
% 2.80/2.00 inference(negated_conjecture,[status(cth)],[f301])).
% 2.80/2.00 thf(f301,conjecture,(
% 2.80/2.00 (ord_less @ int @ (h @ w) @ (h @ x))),
% 2.80/2.00 file('/export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2THF_13441.p',conj_0)).
% 2.80/2.00 thf(f1599,plain,(
% 2.80/2.00 ((ord_less @ int @ (h @ w) @ (h @ e)) = $true)),
% 2.80/2.00 inference(trivial_inequality_removal,[status(thm)],[f1595])).
% 2.80/2.00 thf(f1595,plain,(
% 2.80/2.00 ($false = $true) | ((ord_less @ int @ (h @ w) @ (h @ e)) = $true)),
% 2.80/2.00 inference(superposition,[status(thm)],[f850,f1587])).
% 2.80/2.00 thf(f1587,plain,(
% 2.80/2.00 ( ! [X0 : a] : (($false = (member @ a @ X0 @ (binary1653327646_setOf @ a @ t1))) | ($true = (ord_less @ int @ (h @ X0) @ (h @ e)))) )),
% 2.80/2.00 inference(forward_demodulation,[status(thm)],[f1586,f879])).
% 2.80/2.00 thf(f1586,plain,(
% 2.80/2.00 ( ! [X0 : a] : (($true = (ord_less @ int @ (h @ X0) @ (h @ x))) | ($false = (member @ a @ X0 @ (binary1653327646_setOf @ a @ t1)))) )),
% 2.80/2.00 inference(trivial_inequality_removal,[status(thm)],[f1581])).
% 2.80/2.00 thf(f1581,plain,(
% 2.80/2.00 ( ! [X0 : a] : (($true = (ord_less @ int @ (h @ X0) @ (h @ x))) | ($false = $true) | ($false = (member @ a @ X0 @ (binary1653327646_setOf @ a @ t1)))) )),
% 2.80/2.00 inference(superposition,[status(thm)],[f919,f844])).
% 2.80/2.00 thf(f844,plain,(
% 2.80/2.00 ((binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2)) = $true)),
% 2.80/2.00 inference(cnf_transformation,[status(thm)],[f387])).
% 2.80/2.00 thf(f387,plain,(
% 2.80/2.00 ((binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2)) = $true)),
% 2.80/2.00 inference(fool_elimination,[status(thm)],[f386])).
% 2.80/2.00 thf(f386,plain,(
% 2.80/2.00 (binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))),
% 2.80/2.00 inference(rectify,[status(thm)],[f2])).
% 2.80/2.00 thf(f2,axiom,(
% 2.80/2.00 (binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))),
% 2.80/2.00 file('/export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2THF_13441.p',fact_1_s)).
% 2.80/2.00 thf(f919,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0,X5 : X0] : (($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) | ($false = (member @ X0 @ X5 @ (binary1653327646_setOf @ X0 @ X2))) | ($true = (ord_less @ int @ (X1 @ X5) @ (X1 @ X3)))) )),
% 2.80/2.00 inference(binary_proxy_clausification,[status(thm)],[f918])).
% 2.80/2.00 thf(f918,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0,X5 : X0] : (($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) | ($true = ((member @ X0 @ X5 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ X5) @ (X1 @ X3))))) )),
% 2.80/2.00 inference(beta_eta_normalization,[status(thm)],[f917])).
% 2.80/2.00 thf(f917,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0,X5 : X0] : (($true = ((^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))) @ X5)) | ($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))) )),
% 2.80/2.00 inference(pi_clausification,[status(thm)],[f915])).
% 2.80/2.00 thf(f915,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0] : (((!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3))))) = $true) | ($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))) )),
% 2.80/2.00 inference(binary_proxy_clausification,[status(thm)],[f914])).
% 2.80/2.00 thf(f914,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0] : ((((binary1610619414edTree @ X0 @ X1 @ X4) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))))) = $true) | ($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))) )),
% 2.80/2.00 inference(binary_proxy_clausification,[status(thm)],[f912])).
% 2.80/2.00 thf(f912,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0] : (($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) | ($true = (((binary1610619414edTree @ X0 @ X1 @ X4) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))))) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X4)) => (ord_less @ int @ (X1 @ X3) @ (X1 @ Y0)))))))) )),
% 2.80/2.00 inference(binary_proxy_clausification,[status(thm)],[f896])).
% 2.80/2.00 thf(f896,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0] : (($true = ((((binary1610619414edTree @ X0 @ X1 @ X4) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))))) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X4)) => (ord_less @ int @ (X1 @ X3) @ (X1 @ Y0)))))) & (binary1610619414edTree @ X0 @ X1 @ X2))) | ($false = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))) )),
% 2.80/2.00 inference(binary_proxy_clausification,[status(thm)],[f864])).
% 2.80/2.00 thf(f864,plain,(
% 2.80/2.00 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree @ X0] : ((((((binary1610619414edTree @ X0 @ X1 @ X4) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))))) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X4)) => (ord_less @ int @ (X1 @ X3) @ (X1 @ Y0)))))) & (binary1610619414edTree @ X0 @ X1 @ X2)) = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))) )),
% 2.80/2.00 inference(cnf_transformation,[status(thm)],[f795])).
% 2.80/2.00 thf(f795,plain,(
% 2.80/2.00 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : (((((binary1610619414edTree @ X0 @ X1 @ X4) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ Y0) @ (X1 @ X3)))))) & (!! @ X0 @ (^[Y0 : X0]: ((member @ X0 @ Y0 @ (binary1653327646_setOf @ X0 @ X4)) => (ord_less @ int @ (X1 @ X3) @ (X1 @ Y0)))))) & (binary1610619414edTree @ X0 @ X1 @ X2)) = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))),
% 2.80/2.00 inference(fool_elimination,[status(thm)],[f794])).
% 2.80/2.00 thf(f794,plain,(
% 2.80/2.00 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : ((binary1610619414edTree @ X0 @ X1 @ X2) & ! [X5 : X0] : ((member @ X0 @ X5 @ (binary1653327646_setOf @ X0 @ X4)) => (ord_less @ int @ (X1 @ X3) @ (X1 @ X5))) & ! [X6 : X0] : ((member @ X0 @ X6 @ (binary1653327646_setOf @ X0 @ X2)) => (ord_less @ int @ (X1 @ X6) @ (X1 @ X3))) & (binary1610619414edTree @ X0 @ X1 @ X4) = (binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)))),
% 2.80/2.00 inference(rectify,[status(thm)],[f22])).
% 2.80/2.00 thf(f22,axiom,(
% 2.80/2.00 ! [X0 : $tType,X20 : X0 > int,X21 : binary1291135688e_Tree @ X0,X22 : X0,X23 : binary1291135688e_Tree @ X0] : ((binary1610619414edTree @ X0 @ X20 @ X21) & ! [X24 : X0] : ((member @ X0 @ X24 @ (binary1653327646_setOf @ X0 @ X23)) => (ord_less @ int @ (X20 @ X22) @ (X20 @ X24))) & ! [X24 : X0] : ((member @ X0 @ X24 @ (binary1653327646_setOf @ X0 @ X21)) => (ord_less @ int @ (X20 @ X24) @ (X20 @ X22))) & (binary1610619414edTree @ X0 @ X20 @ X23) = (binary1610619414edTree @ X0 @ X20 @ (binary210054475elle_T @ X0 @ X21 @ X22 @ X23)))),
% 2.80/2.00 file('/export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2THF_13441.p',fact_21_sortedTree_Osimps_I2_J)).
% 2.80/2.00 thf(f850,plain,(
% 2.80/2.00 ((member @ a @ w @ (binary1653327646_setOf @ a @ t1)) = $true)),
% 2.80/2.00 inference(cnf_transformation,[status(thm)],[f659])).
% 2.80/2.00 thf(f659,plain,(
% 2.80/2.00 ((member @ a @ w @ (binary1653327646_setOf @ a @ t1)) = $true)),
% 2.80/2.00 inference(fool_elimination,[status(thm)],[f658])).
% 2.80/2.00 thf(f658,plain,(
% 2.80/2.00 (member @ a @ w @ (binary1653327646_setOf @ a @ t1))),
% 2.80/2.00 inference(rectify,[status(thm)],[f1])).
% 2.80/2.00 thf(f1,axiom,(
% 2.80/2.00 (member @ a @ w @ (binary1653327646_setOf @ a @ t1))),
% 2.80/2.00 file('/export/starexec/sandbox/tmp/tmp.2ytiupHN7C/DTF2THF_13441.p',fact_0_whSet)).
% 2.80/2.00 % SZS output end Proof for DTF2THF_13441
% 2.80/2.00 % (13741)------------------------------
% 2.80/2.00 % (13741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/2.00 % (13741)Termination reason: Refutation
% 2.80/2.00
% 2.80/2.00 % (13741)Memory used [KB]: 7675
% 2.80/2.00 % (13741)Time elapsed: 0.225 s
% 2.80/2.00 % (13741)Instructions burned: 646 (million)
% 2.80/2.00 % (13741)------------------------------
% 2.80/2.00 % (13741)------------------------------
% 2.80/2.00 % (13685)Success in time 0.305 s
%------------------------------------------------------------------------------