%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT213^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 08:45:10 AM UTC 2026
% Result : Theorem 2.97s 1.61s
% Output : Refutation 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT213^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:12:19 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : DAT213^1 : TPTP v9.2.1. Released v7.0.0.
% 0.21/0.46 % Domain : Data Structures
% 0.21/0.46 % Problem : Splay tree analysis 186
% 0.21/0.46 % Version : [Bla16] axioms : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [Nip14] Nipkow (2014), Amortized Complexity Verified
% 0.21/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.21/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Bla16]
% 0.21/0.46 % Names : splay_tree_analysis__186.p [Bla16]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.21/0.46 % Syntax : Number of formulae : 368 ( 88 unt; 60 typ; 0 def)
% 0.21/0.46 % Number of atoms : 988 ( 256 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.21/0.46 % Number of connectives : 4601 ( 113 ~; 12 |; 69 &;3855 @)
% 0.21/0.46 % ( 0 <=>; 552 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 25 ( 9 avg)
% 0.21/0.46 % Number of types : 4 ( 3 usr)
% 0.21/0.46 % Number of type conns : 222 ( 222 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 60 ( 57 usr; 5 con; 0-5 aty)
% 0.21/0.46 % Number of variables : 1181 ( 40 ^;1064 !; 23 ?;1181 :)
% 0.21/0.46 % ( 54 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.46 % SPC : TH1_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.21/0.46 % 2016-07-13 14:49:47.790
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 %----Could-be-implicit typings (6)
% 0.21/0.46 thf(ty_t_Tree_Otree,type,
% 0.21/0.46 tree: $tType > $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Real_Oreal,type,
% 0.21/0.46 real: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Set_Oset,type,
% 0.21/0.46 set: $tType > $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Nat_Onat,type,
% 0.21/0.46 nat: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_itself,type,
% 0.21/0.46 itself: $tType > $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_tf_a,type,
% 0.21/0.46 a: $tType ).
% 0.21/0.46
% 0.21/0.46 %----Explicit typings (54)
% 0.21/0.46 thf(sy_cl_HOL_Otype,type,
% 0.21/0.46 type:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Oone,type,
% 0.21/0.46 one:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.46 ord:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.21/0.46 neg_numeral:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.46 order:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.21/0.46 group_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Ono__bot,type,
% 0.21/0.46 no_bot:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Ono__top,type,
% 0.21/0.46 no_top:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Transcendental_Oln,type,
% 0.21/0.46 ln:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.46 linorder:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.21/0.46 preorder:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.21/0.46 wellorder:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.21/0.46 semigroup_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Odense__order,type,
% 0.21/0.46 dense_order:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.21/0.46 ab_semigroup_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.21/0.46 dense_linorder:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.21/0.46 linordered_semidom:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.21/0.46 cancel_semigroup_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.21/0.46 ordere779506340up_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.21/0.46 canoni770627133id_add:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.21/0.46 ordere236663937imp_le:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.21/0.46 condit1037483654norder:
% 0.21/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.21/0.46 one_one:
% 0.21/0.46 !>[A: $tType] : A ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.21/0.46 plus_plus:
% 0.21/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_If,type,
% 0.21/0.46 if:
% 0.21/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.21/0.46 ord_less:
% 0.21/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.21/0.46 ord_less_eq:
% 0.21/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Pure_Otype,type,
% 0.21/0.46 type2:
% 0.21/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_OCollect,type,
% 0.21/0.46 collect:
% 0.21/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Splay__Tree_Ois__root,type,
% 0.21/0.46 splay_is_root:
% 0.21/0.46 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Splay__Tree_Osplay,type,
% 0.21/0.47 splay_splay:
% 0.21/0.47 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Splay__Tree_Osplay__max,type,
% 0.21/0.47 splay_splay_max:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 0.21/0.47 splay_914434265_splay:
% 0.21/0.47 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA,type,
% 0.21/0.47 splay_266122055elle_A:
% 0.21/0.47 !>[A: $tType] : ( A > ( tree @ A ) > real ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Transcendental_Opowr,type,
% 0.21/0.47 powr:
% 0.21/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 0.21/0.47 linorder_bst:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Olinorder__class_Obst__eq,type,
% 0.21/0.47 linorder_bst_eq:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Omirror,type,
% 0.21/0.47 mirror:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Osubtrees,type,
% 0.21/0.47 subtrees:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( set @ ( tree @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_OLeaf,type,
% 0.21/0.47 leaf:
% 0.21/0.47 !>[A: $tType] : ( tree @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_ONode,type,
% 0.21/0.47 node:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Ocase__tree,type,
% 0.21/0.47 case_tree:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( B > ( ( tree @ A ) > A > ( tree @ A ) > B ) > ( tree @ A ) > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Ois__Leaf,type,
% 0.21/0.47 is_Leaf:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Oleft,type,
% 0.21/0.47 left:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Opred__tree,type,
% 0.21/0.47 pred_tree:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( tree @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Orec__tree,type,
% 0.21/0.47 rec_tree:
% 0.21/0.47 !>[C: $tType,A: $tType] : ( C > ( ( tree @ A ) > A > ( tree @ A ) > C > C > C ) > ( tree @ A ) > C ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Orel__tree,type,
% 0.21/0.47 rel_tree:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( tree @ A ) > ( tree @ B ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Oright,type,
% 0.21/0.47 right:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Oset__tree,type,
% 0.21/0.47 set_tree:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Tree_Otree_Oval,type,
% 0.21/0.47 val:
% 0.21/0.47 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_a,type,
% 0.21/0.47 a2: a ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_t,type,
% 0.21/0.47 t: tree @ a ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_thesis____,type,
% 0.21/0.47 thesis: $o ).
% 0.21/0.47
% 0.21/0.47 %----Relevant facts (254)
% 0.21/0.47 thf(fact_0_assms_I2_J,axiom,
% 0.21/0.47 member @ a @ a2 @ ( set_tree @ a @ t ) ).
% 0.21/0.47
% 0.21/0.47 % assms(2)
% 0.21/0.47 thf(fact_1_assms_I1_J,axiom,
% 0.21/0.47 linorder_bst @ a @ t ).
% 0.21/0.47
% 0.21/0.47 % assms(1)
% 0.21/0.47 thf(fact_2_tree_Oinject,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 0.21/0.47 ( ( ( node @ A @ X21 @ X22 @ X23 )
% 0.21/0.47 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 0.21/0.47 = ( ( X21 = Y21 )
% 0.21/0.47 & ( X22 = Y22 )
% 0.21/0.47 & ( X23 = Y23 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.inject
% 0.21/0.47 thf(fact_3_set__treeE,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,T: tree @ A] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 0.21/0.47 => ? [L: tree @ A,R: tree @ A] : ( member @ ( tree @ A ) @ ( node @ A @ L @ A2 @ R ) @ ( subtrees @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_treeE
% 0.21/0.47 thf(fact_4_in__set__tree__if,axiom,
% 0.21/0.47 ! [A: $tType,L2: tree @ A,A2: A,R2: tree @ A,T: tree @ A] :
% 0.21/0.47 ( ( member @ ( tree @ A ) @ ( node @ A @ L2 @ A2 @ R2 ) @ ( subtrees @ A @ T ) )
% 0.21/0.47 => ( member @ A @ A2 @ ( set_tree @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % in_set_tree_if
% 0.21/0.47 thf(fact_5_Node__notin__subtrees__if,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,T: tree @ A,L2: tree @ A,R2: tree @ A] :
% 0.21/0.47 ( ~ ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 0.21/0.47 => ~ ( member @ ( tree @ A ) @ ( node @ A @ L2 @ A2 @ R2 ) @ ( subtrees @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Node_notin_subtrees_if
% 0.21/0.47 thf(fact_6_tree_Oset__intros_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,Xa: A,A3: tree @ A,A1: tree @ A,A22: A] :
% 0.21/0.47 ( ( member @ A @ Xa @ ( set_tree @ A @ A3 ) )
% 0.21/0.47 => ( member @ A @ Xa @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_intros(3)
% 0.21/0.47 thf(fact_7_tree_Oset__intros_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,A22: A,A1: tree @ A,A3: tree @ A] : ( member @ A @ A22 @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_intros(2)
% 0.21/0.47 thf(fact_8_tree_Oset__intros_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X: A,A1: tree @ A,A22: A,A3: tree @ A] :
% 0.21/0.47 ( ( member @ A @ X @ ( set_tree @ A @ A1 ) )
% 0.21/0.47 => ( member @ A @ X @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_intros(1)
% 0.21/0.47 thf(fact_9_tree_Oset__cases,axiom,
% 0.21/0.47 ! [A: $tType,E: A,A2: tree @ A] :
% 0.21/0.47 ( ( member @ A @ E @ ( set_tree @ A @ A2 ) )
% 0.21/0.47 => ( ! [Z1: tree @ A] :
% 0.21/0.47 ( ? [Z2: A,Z3: tree @ A] :
% 0.21/0.47 ( A2
% 0.21/0.47 = ( node @ A @ Z1 @ Z2 @ Z3 ) )
% 0.21/0.47 => ~ ( member @ A @ E @ ( set_tree @ A @ Z1 ) ) )
% 0.21/0.47 => ( ! [Z1: tree @ A,Z3: tree @ A] :
% 0.21/0.47 ( A2
% 0.21/0.47 != ( node @ A @ Z1 @ E @ Z3 ) )
% 0.21/0.47 => ~ ! [Z1: tree @ A,Z2: A,Z3: tree @ A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( node @ A @ Z1 @ Z2 @ Z3 ) )
% 0.21/0.47 => ~ ( member @ A @ E @ ( set_tree @ A @ Z3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_cases
% 0.21/0.47 thf(fact_10_tree_Osimps_I7_J,axiom,
% 0.21/0.47 ! [C: $tType,A: $tType,F1: C,F2: ( tree @ A ) > A > ( tree @ A ) > C > C > C,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( rec_tree @ C @ A @ F1 @ F2 @ ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 = ( F2 @ X21 @ X22 @ X23 @ ( rec_tree @ C @ A @ F1 @ F2 @ X21 ) @ ( rec_tree @ C @ A @ F1 @ F2 @ X23 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.simps(7)
% 0.21/0.47 thf(fact_11_tree_Opred__inject_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,A2: tree @ A,Aa: A,Ab: tree @ A] :
% 0.21/0.47 ( ( pred_tree @ A @ P @ ( node @ A @ A2 @ Aa @ Ab ) )
% 0.21/0.47 = ( ( pred_tree @ A @ P @ A2 )
% 0.21/0.47 & ( P @ Aa )
% 0.21/0.47 & ( pred_tree @ A @ P @ Ab ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.pred_inject(2)
% 0.21/0.47 thf(fact_12_A__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.21/0.47 ( ( splay_266122055elle_A @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.21/0.47 = ( one_one @ real ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % A_simps(1)
% 0.21/0.47 thf(fact_13_tree_Osimps_I5_J,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( case_tree @ B @ A @ F1 @ F2 @ ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 = ( F2 @ X21 @ X22 @ X23 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.simps(5)
% 0.21/0.47 thf(fact_14_tree_Opred__cong,axiom,
% 0.21/0.47 ! [A: $tType,X: tree @ A,Ya: tree @ A,P: A > $o,Pa: A > $o] :
% 0.21/0.47 ( ( X = Ya )
% 0.21/0.47 => ( ! [Z: A] :
% 0.21/0.47 ( ( member @ A @ Z @ ( set_tree @ A @ Ya ) )
% 0.21/0.47 => ( ( P @ Z )
% 0.21/0.47 = ( Pa @ Z ) ) )
% 0.21/0.47 => ( ( pred_tree @ A @ P @ X )
% 0.21/0.47 = ( pred_tree @ A @ Pa @ Ya ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.pred_cong
% 0.21/0.47 thf(fact_15_tree_Opred__mono__strong,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,X: tree @ A,Pa: A > $o] :
% 0.21/0.47 ( ( pred_tree @ A @ P @ X )
% 0.21/0.47 => ( ! [Z: A] :
% 0.21/0.47 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 0.21/0.47 => ( ( P @ Z )
% 0.21/0.47 => ( Pa @ Z ) ) )
% 0.21/0.47 => ( pred_tree @ A @ Pa @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.pred_mono_strong
% 0.21/0.47 thf(fact_16_one__reorient,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( one @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ( ( ( one_one @ A )
% 0.21/0.47 = X )
% 0.21/0.47 = ( X
% 0.21/0.47 = ( one_one @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % one_reorient
% 0.21/0.47 thf(fact_17_splay__to__root,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A,T2: tree @ A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( ( ( splay_splay @ A @ A2 @ T )
% 0.21/0.47 = T2 )
% 0.21/0.47 => ( ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 0.21/0.47 = ( ? [L3: tree @ A,R3: tree @ A] :
% 0.21/0.47 ( T2
% 0.21/0.47 = ( node @ A @ L3 @ A2 @ R3 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_to_root
% 0.21/0.47 thf(fact_18_tree_Opred__set,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( pred_tree @ A )
% 0.21/0.47 = ( ^ [P2: A > $o,X2: tree @ A] :
% 0.21/0.47 ! [Y: A] :
% 0.21/0.47 ( ( member @ A @ Y @ ( set_tree @ A @ X2 ) )
% 0.21/0.47 => ( P2 @ Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.pred_set
% 0.21/0.47 thf(fact_19_tree_Osel_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( val @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 = X22 ) ).
% 0.21/0.47
% 0.21/0.47 % tree.sel(3)
% 0.21/0.47 thf(fact_20_tree_Osel_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( left @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 = X21 ) ).
% 0.21/0.47
% 0.21/0.47 % tree.sel(2)
% 0.21/0.47 thf(fact_21_tree_Osel_I5_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( right @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 = X23 ) ).
% 0.21/0.47
% 0.21/0.47 % tree.sel(5)
% 0.21/0.47 thf(fact_22_bst__eq__if__bst,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( linorder_bst_eq @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq_if_bst
% 0.21/0.47 thf(fact_23_mirror_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,L2: tree @ A,X: A,R2: tree @ A] :
% 0.21/0.47 ( ( mirror @ A @ ( node @ A @ L2 @ X @ R2 ) )
% 0.21/0.47 = ( node @ A @ ( mirror @ A @ R2 ) @ X @ ( mirror @ A @ L2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mirror.simps(2)
% 0.21/0.47 thf(fact_24_tree_Osimps_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType,F1: C,F2: ( tree @ A ) > A > ( tree @ A ) > C > C > C] :
% 0.21/0.47 ( ( rec_tree @ C @ A @ F1 @ F2 @ ( leaf @ A ) )
% 0.21/0.47 = F1 ) ).
% 0.21/0.47
% 0.21/0.47 % tree.simps(6)
% 0.21/0.47 thf(fact_25_powr__one__eq__one,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( powr @ A @ ( one_one @ A ) @ A2 )
% 0.21/0.47 = ( one_one @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_one_eq_one
% 0.21/0.47 thf(fact_26_mirror__mirror,axiom,
% 0.21/0.47 ! [A: $tType,T: tree @ A] :
% 0.21/0.47 ( ( mirror @ A @ ( mirror @ A @ T ) )
% 0.21/0.47 = T ) ).
% 0.21/0.47
% 0.21/0.47 % mirror_mirror
% 0.21/0.47 thf(fact_27_splay__Leaf__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,T: tree @ A] :
% 0.21/0.47 ( ( ( splay_splay @ A @ A2 @ T )
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 = ( T
% 0.21/0.47 = ( leaf @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_Leaf_iff
% 0.21/0.47 thf(fact_28_mirror__Leaf,axiom,
% 0.21/0.47 ! [A: $tType,T: tree @ A] :
% 0.21/0.47 ( ( ( mirror @ A @ T )
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 = ( T
% 0.21/0.47 = ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mirror_Leaf
% 0.21/0.47 thf(fact_29_tree_Osel_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( right @ A @ ( leaf @ A ) )
% 0.21/0.47 = ( leaf @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.sel(4)
% 0.21/0.47 thf(fact_30_tree_Osel_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( left @ A @ ( leaf @ A ) )
% 0.21/0.47 = ( leaf @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.sel(1)
% 0.21/0.47 thf(fact_31_mirror_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( mirror @ A @ ( leaf @ A ) )
% 0.21/0.47 = ( leaf @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % mirror.simps(1)
% 0.21/0.47 thf(fact_32_bst__eq_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( linorder_bst_eq @ A @ ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.simps(1)
% 0.21/0.47 thf(fact_33_tree_Oexhaust__sel,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A] :
% 0.21/0.47 ( ( Tree
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ( Tree
% 0.21/0.47 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.exhaust_sel
% 0.21/0.47 thf(fact_34_splay__not__Leaf,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A] :
% 0.21/0.47 ( ( T
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ? [L: tree @ A,X3: A,R: tree @ A] :
% 0.21/0.47 ( ( splay_splay @ A @ A2 @ T )
% 0.21/0.47 = ( node @ A @ L @ X3 @ R ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_not_Leaf
% 0.21/0.47 thf(fact_35_splay_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 0.21/0.47 = ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay.simps(1)
% 0.21/0.47 thf(fact_36_splay_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.21/0.47 ( ( splay_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.21/0.47 = ( node @ A @ L2 @ A2 @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay.simps(2)
% 0.21/0.47 thf(fact_37_mirror_Oelims,axiom,
% 0.21/0.47 ! [A: $tType,X: tree @ A,Y2: tree @ A] :
% 0.21/0.47 ( ( ( mirror @ A @ X )
% 0.21/0.47 = Y2 )
% 0.21/0.47 => ( ( ( X
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ( Y2
% 0.21/0.47 != ( leaf @ A ) ) )
% 0.21/0.47 => ~ ! [L: tree @ A,X3: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ X3 @ R ) )
% 0.21/0.47 => ( Y2
% 0.21/0.47 != ( node @ A @ ( mirror @ A @ R ) @ X3 @ ( mirror @ A @ L ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mirror.elims
% 0.21/0.47 thf(fact_38_tree_Osplit__sel__asm,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,Tree: tree @ A] :
% 0.21/0.47 ( ( P @ ( case_tree @ B @ A @ F1 @ F2 @ Tree ) )
% 0.21/0.47 = ( ~ ( ( ( Tree
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 & ~ ( P @ F1 ) )
% 0.21/0.47 | ( ( Tree
% 0.21/0.47 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) )
% 0.21/0.47 & ~ ( P @ ( F2 @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.split_sel_asm
% 0.21/0.47 thf(fact_39_tree_Osplit__sel,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,Tree: tree @ A] :
% 0.21/0.47 ( ( P @ ( case_tree @ B @ A @ F1 @ F2 @ Tree ) )
% 0.21/0.47 = ( ( ( Tree
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ( P @ F1 ) )
% 0.21/0.47 & ( ( Tree
% 0.21/0.47 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) )
% 0.21/0.47 => ( P @ ( F2 @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.split_sel
% 0.21/0.47 thf(fact_40_set__splay,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,T: tree @ A] :
% 0.21/0.47 ( ( set_tree @ A @ ( splay_splay @ A @ A2 @ T ) )
% 0.21/0.47 = ( set_tree @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_splay
% 0.21/0.47 thf(fact_41_bst__splay,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_splay
% 0.21/0.47 thf(fact_42_tree_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( leaf @ A )
% 0.21/0.47 != ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.distinct(1)
% 0.21/0.47 thf(fact_43_tree_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 0.21/0.47 ( ( P @ ( leaf @ A ) )
% 0.21/0.47 => ( ! [X1: tree @ A,X24: A,X32: tree @ A] :
% 0.21/0.47 ( ( P @ X1 )
% 0.21/0.47 => ( ( P @ X32 )
% 0.21/0.47 => ( P @ ( node @ A @ X1 @ X24 @ X32 ) ) ) )
% 0.21/0.47 => ( P @ Tree ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.induct
% 0.21/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,A2: A,P: A > $o] :
% 0.21/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: $tType,A4: set @ A] :
% 0.21/0.47 ( ( collect @ A
% 0.21/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.21/0.47 = A4 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_46_Collect__cong,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 = ( Q @ X3 ) )
% 0.21/0.47 => ( ( collect @ A @ P )
% 0.21/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_47_ext,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( F @ X3 )
% 0.21/0.47 = ( G @ X3 ) )
% 0.21/0.47 => ( F = G ) ) ).
% 0.21/0.47
% 0.21/0.47 % ext
% 0.21/0.47 thf(fact_48_neq__Leaf__iff,axiom,
% 0.21/0.47 ! [A: $tType,T: tree @ A] :
% 0.21/0.47 ( ( T
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 = ( ? [L3: tree @ A,A5: A,R3: tree @ A] :
% 0.21/0.47 ( T
% 0.21/0.47 = ( node @ A @ L3 @ A5 @ R3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_Leaf_iff
% 0.21/0.47 thf(fact_49_tree_Oexhaust,axiom,
% 0.21/0.47 ! [A: $tType,Y2: tree @ A] :
% 0.21/0.47 ( ( Y2
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ~ ! [X212: tree @ A,X222: A,X232: tree @ A] :
% 0.21/0.47 ( Y2
% 0.21/0.47 != ( node @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.exhaust
% 0.21/0.47 thf(fact_50_mirror_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.21/0.47 ( ( P @ ( leaf @ A ) )
% 0.21/0.47 => ( ! [L: tree @ A,X3: A,R: tree @ A] :
% 0.21/0.47 ( ( P @ R )
% 0.21/0.47 => ( ( P @ L )
% 0.21/0.47 => ( P @ ( node @ A @ L @ X3 @ R ) ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % mirror.induct
% 0.21/0.47 thf(fact_51_bst__eq_Ocases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( node @ A @ L @ A6 @ R ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.cases
% 0.21/0.47 thf(fact_52_bst__eq_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.21/0.47 ( ( P @ ( leaf @ A ) )
% 0.21/0.47 => ( ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( P @ L )
% 0.21/0.47 => ( ( P @ R )
% 0.21/0.47 => ( P @ ( node @ A @ L @ A6 @ R ) ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.induct
% 0.21/0.47 thf(fact_53_bst_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst.simps(1)
% 0.21/0.47 thf(fact_54_tree_Osimps_I4_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B] :
% 0.21/0.47 ( ( case_tree @ B @ A @ F1 @ F2 @ ( leaf @ A ) )
% 0.21/0.47 = F1 ) ).
% 0.21/0.47
% 0.21/0.47 % tree.simps(4)
% 0.21/0.47 thf(fact_55_tree_Opred__inject_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] : ( pred_tree @ A @ P @ ( leaf @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.pred_inject(1)
% 0.21/0.47 thf(fact_56_is__root__splay,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( ( splay_is_root @ A @ A2 @ ( splay_splay @ A @ A2 @ T ) )
% 0.21/0.47 = ( member @ A @ A2 @ ( set_tree @ A @ T ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_root_splay
% 0.21/0.47 thf(fact_57_tree_Ocollapse_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A] :
% 0.21/0.47 ( ~ ( is_Leaf @ A @ Tree )
% 0.21/0.47 => ( ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) )
% 0.21/0.47 = Tree ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.collapse(2)
% 0.21/0.47 thf(fact_58__092_060Phi_062_Ocases,axiom,
% 0.21/0.47 ! [A: $tType,X: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( node @ A @ L @ A6 @ R ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<Phi>.cases
% 0.21/0.47 thf(fact_59__092_060Phi_062_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.21/0.47 ( ( P @ ( leaf @ A ) )
% 0.21/0.47 => ( ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( P @ L )
% 0.21/0.47 => ( ( P @ R )
% 0.21/0.47 => ( P @ ( node @ A @ L @ A6 @ R ) ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<Phi>.induct
% 0.21/0.47 thf(fact_60_t__splay__max_Ocases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ( ! [L: tree @ A,B2: A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 0.21/0.47 => ~ ! [L: tree @ A,B2: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( node @ A @ L @ B2 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_max.cases
% 0.21/0.47 thf(fact_61_t__splay__max_Oinduct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.21/0.47 ( ( P @ ( leaf @ A ) )
% 0.21/0.47 => ( ! [L: tree @ A,B2: A] : ( P @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 0.21/0.47 => ( ! [L: tree @ A,B2: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.21/0.47 ( ( ( Rr
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ( P @ Rr ) )
% 0.21/0.47 => ( P @ ( node @ A @ L @ B2 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 0.21/0.47 => ( P @ A0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_max.induct
% 0.21/0.47 thf(fact_62_tree_Ocase__eq__if,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( case_tree @ B @ A )
% 0.21/0.47 = ( ^ [F12: B,F22: ( tree @ A ) > A > ( tree @ A ) > B,Tree2: tree @ A] : ( if @ B @ ( is_Leaf @ A @ Tree2 ) @ F12 @ ( F22 @ ( left @ A @ Tree2 ) @ ( val @ A @ Tree2 ) @ ( right @ A @ Tree2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.case_eq_if
% 0.21/0.47 thf(fact_63_bst__eq_Oelims_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A] :
% 0.21/0.47 ( ( linorder_bst_eq @ A @ X )
% 0.21/0.47 => ( ( X
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.21/0.47 => ~ ( ( linorder_bst_eq @ A @ L )
% 0.21/0.47 & ( linorder_bst_eq @ A @ R )
% 0.21/0.47 & ! [X4: A] :
% 0.21/0.47 ( ( member @ A @ X4 @ ( set_tree @ A @ L ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X4 @ A6 ) )
% 0.21/0.47 & ! [X4: A] :
% 0.21/0.47 ( ( member @ A @ X4 @ ( set_tree @ A @ R ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A6 @ X4 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.elims(2)
% 0.21/0.47 thf(fact_64_bst__eq_Oelims_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A,Y2: $o] :
% 0.21/0.47 ( ( ( linorder_bst_eq @ A @ X )
% 0.21/0.47 = Y2 )
% 0.21/0.47 => ( ( ( X
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ~ Y2 )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.21/0.47 => ( Y2
% 0.21/0.47 = ( ~ ( ( linorder_bst_eq @ A @ L )
% 0.21/0.47 & ( linorder_bst_eq @ A @ R )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ L ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X2 @ A6 ) )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ R ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A6 @ X2 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.elims(1)
% 0.21/0.47 thf(fact_65_powr__mono,axiom,
% 0.21/0.47 ! [A2: real,B3: real,X: real] :
% 0.21/0.47 ( ( ord_less_eq @ real @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 0.21/0.47 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_mono
% 0.21/0.47 thf(fact_66_tree_OdiscI_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ( ( Tree
% 0.21/0.47 = ( node @ A @ X21 @ X22 @ X23 ) )
% 0.21/0.47 => ~ ( is_Leaf @ A @ Tree ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.discI(2)
% 0.21/0.47 thf(fact_67_tree_Odisc_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.21/0.47 ~ ( is_Leaf @ A @ ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.disc(2)
% 0.21/0.47 thf(fact_68_is__Leaf__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_Leaf @ A )
% 0.21/0.47 = ( ^ [Tree2: tree @ A] :
% 0.21/0.47 ( Tree2
% 0.21/0.47 = ( leaf @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_Leaf_def
% 0.21/0.47 thf(fact_69_tree_Ocollapse_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A] :
% 0.21/0.47 ( ( is_Leaf @ A @ Tree )
% 0.21/0.47 => ( Tree
% 0.21/0.47 = ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.collapse(1)
% 0.21/0.47 thf(fact_70_tree_OdiscI_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A] :
% 0.21/0.47 ( ( Tree
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ( is_Leaf @ A @ Tree ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.discI(1)
% 0.21/0.47 thf(fact_71_tree_Odisc_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] : ( is_Leaf @ A @ ( leaf @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.disc(1)
% 0.21/0.47 thf(fact_72_tree_Oset__sel_I3_J,axiom,
% 0.21/0.47 ! [A: $tType,A2: tree @ A,Xa: A] :
% 0.21/0.47 ( ~ ( is_Leaf @ A @ A2 )
% 0.21/0.47 => ( ( member @ A @ Xa @ ( set_tree @ A @ ( right @ A @ A2 ) ) )
% 0.21/0.47 => ( member @ A @ Xa @ ( set_tree @ A @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_sel(3)
% 0.21/0.47 thf(fact_73_tree_Oset__sel_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,A2: tree @ A,X: A] :
% 0.21/0.47 ( ~ ( is_Leaf @ A @ A2 )
% 0.21/0.47 => ( ( member @ A @ X @ ( set_tree @ A @ ( left @ A @ A2 ) ) )
% 0.21/0.47 => ( member @ A @ X @ ( set_tree @ A @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_sel(1)
% 0.21/0.47 thf(fact_74_tree_Oset__sel_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,A2: tree @ A] :
% 0.21/0.47 ( ~ ( is_Leaf @ A @ A2 )
% 0.21/0.47 => ( member @ A @ ( val @ A @ A2 ) @ ( set_tree @ A @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.set_sel(2)
% 0.21/0.47 thf(fact_75_bst__eq_Oelims_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A] :
% 0.21/0.47 ( ~ ( linorder_bst_eq @ A @ X )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.21/0.47 => ( ( linorder_bst_eq @ A @ L )
% 0.21/0.47 & ( linorder_bst_eq @ A @ R )
% 0.21/0.47 & ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ L ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X3 @ A6 ) )
% 0.21/0.47 & ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ R ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A6 @ X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.elims(3)
% 0.21/0.47 thf(fact_76_bst__eq_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [L2: tree @ A,A2: A,R2: tree @ A] :
% 0.21/0.47 ( ( linorder_bst_eq @ A @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.21/0.47 = ( ( linorder_bst_eq @ A @ L2 )
% 0.21/0.47 & ( linorder_bst_eq @ A @ R2 )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ L2 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X2 @ A2 ) )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ R2 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_eq.simps(2)
% 0.21/0.47 thf(fact_77_tree_Oexpand,axiom,
% 0.21/0.47 ! [A: $tType,Tree: tree @ A,Tree3: tree @ A] :
% 0.21/0.47 ( ( ( is_Leaf @ A @ Tree )
% 0.21/0.47 = ( is_Leaf @ A @ Tree3 ) )
% 0.21/0.47 => ( ( ~ ( is_Leaf @ A @ Tree )
% 0.21/0.47 => ( ~ ( is_Leaf @ A @ Tree3 )
% 0.21/0.47 => ( ( ( left @ A @ Tree )
% 0.21/0.47 = ( left @ A @ Tree3 ) )
% 0.21/0.47 & ( ( val @ A @ Tree )
% 0.21/0.47 = ( val @ A @ Tree3 ) )
% 0.21/0.47 & ( ( right @ A @ Tree )
% 0.21/0.47 = ( right @ A @ Tree3 ) ) ) ) )
% 0.21/0.47 => ( Tree = Tree3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.expand
% 0.21/0.47 thf(fact_78_order__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_refl
% 0.21/0.47 thf(fact_79_le__numeral__extra_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_numeral_extra(4)
% 0.21/0.47 thf(fact_80_splay__max__eq__splay,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ T ) )
% 0.21/0.47 => ( ord_less_eq @ A @ X3 @ A2 ) )
% 0.21/0.47 => ( ( splay_splay_max @ A @ T )
% 0.21/0.47 = ( splay_splay @ A @ A2 @ T ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_max_eq_splay
% 0.21/0.47 thf(fact_81_ex__in__set__tree,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A,A2: A] :
% 0.21/0.47 ( ( T
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ? [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ T ) )
% 0.21/0.47 & ( ( splay_splay @ A @ X3 @ T )
% 0.21/0.47 = ( splay_splay @ A @ A2 @ T ) )
% 0.21/0.47 & ( ( splay_914434265_splay @ A @ X3 @ T )
% 0.21/0.47 = ( splay_914434265_splay @ A @ A2 @ T ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ex_in_set_tree
% 0.21/0.47 thf(fact_82_bst_Oelims_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A] :
% 0.21/0.47 ( ( linorder_bst @ A @ X )
% 0.21/0.47 => ( ( X
% 0.21/0.47 != ( leaf @ A ) )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.21/0.47 => ~ ( ( linorder_bst @ A @ L )
% 0.21/0.47 & ( linorder_bst @ A @ R )
% 0.21/0.47 & ! [X4: A] :
% 0.21/0.47 ( ( member @ A @ X4 @ ( set_tree @ A @ L ) )
% 0.21/0.47 => ( ord_less @ A @ X4 @ A6 ) )
% 0.21/0.47 & ! [X4: A] :
% 0.21/0.47 ( ( member @ A @ X4 @ ( set_tree @ A @ R ) )
% 0.21/0.47 => ( ord_less @ A @ A6 @ X4 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst.elims(2)
% 0.21/0.47 thf(fact_83_bst_Oelims_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: tree @ A,Y2: $o] :
% 0.21/0.47 ( ( ( linorder_bst @ A @ X )
% 0.21/0.47 = Y2 )
% 0.21/0.47 => ( ( ( X
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ~ Y2 )
% 0.21/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.21/0.47 ( ( X
% 0.21/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.21/0.47 => ( Y2
% 0.21/0.47 = ( ~ ( ( linorder_bst @ A @ L )
% 0.21/0.47 & ( linorder_bst @ A @ R )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ L ) )
% 0.21/0.47 => ( ord_less @ A @ X2 @ A6 ) )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ R ) )
% 0.21/0.47 => ( ord_less @ A @ A6 @ X2 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst.elims(1)
% 0.21/0.47 thf(fact_84_tree_Orel__sel,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( rel_tree @ A @ B )
% 0.21/0.47 = ( ^ [R4: A > B > $o,A5: tree @ A,B4: tree @ B] :
% 0.21/0.47 ( ( ( is_Leaf @ A @ A5 )
% 0.21/0.47 = ( is_Leaf @ B @ B4 ) )
% 0.21/0.47 & ( ~ ( is_Leaf @ A @ A5 )
% 0.21/0.47 => ( ~ ( is_Leaf @ B @ B4 )
% 0.21/0.47 => ( ( rel_tree @ A @ B @ R4 @ ( left @ A @ A5 ) @ ( left @ B @ B4 ) )
% 0.21/0.47 & ( R4 @ ( val @ A @ A5 ) @ ( val @ B @ B4 ) )
% 0.21/0.47 & ( rel_tree @ A @ B @ R4 @ ( right @ A @ A5 ) @ ( right @ B @ B4 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_sel
% 0.21/0.47 thf(fact_85_powr__less__cancel__iff,axiom,
% 0.21/0.47 ! [X: real,A2: real,B3: real] :
% 0.21/0.47 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.21/0.47 => ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 0.21/0.47 = ( ord_less @ real @ A2 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_less_cancel_iff
% 0.21/0.47 thf(fact_86_t__splay__simps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.21/0.47 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_simps(1)
% 0.21/0.47 thf(fact_87_splay__max__Leaf__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A] :
% 0.21/0.47 ( ( ( splay_splay_max @ A @ T )
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 = ( T
% 0.21/0.47 = ( leaf @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_max_Leaf_iff
% 0.21/0.47 thf(fact_88_powr__le__cancel__iff,axiom,
% 0.21/0.47 ! [X: real,A2: real,B3: real] :
% 0.21/0.47 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.21/0.47 => ( ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 0.21/0.47 = ( ord_less_eq @ real @ A2 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_le_cancel_iff
% 0.21/0.47 thf(fact_89_t__splay__simps_I7_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,L2: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_simps(7)
% 0.21/0.47 thf(fact_90_t__splay__simps_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B3 @ R2 ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_simps(3)
% 0.21/0.47 thf(fact_91_t__splay__simps_I6_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,L2: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( leaf @ A ) ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_simps(6)
% 0.21/0.47 thf(fact_92_t__splay__simps_I2_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,R2: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay_simps(2)
% 0.21/0.47 thf(fact_93_leD,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Y2: A,X: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ~ ( ord_less @ A @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % leD
% 0.21/0.47 thf(fact_94_leI,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % leI
% 0.21/0.47 thf(fact_95_le__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less_eq @ A )
% 0.21/0.47 = ( ^ [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 | ( X2 = Y ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_less
% 0.21/0.47 thf(fact_96_less__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less @ A )
% 0.21/0.47 = ( ^ [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 & ( X2 != Y ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_le
% 0.21/0.47 thf(fact_97_order__le__less__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_le_less_subst1
% 0.21/0.47 thf(fact_98_order__le__less__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType] :
% 0.21/0.47 ( ( ( order @ C @ ( type2 @ C ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less @ C @ ( F @ B3 ) @ C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_le_less_subst2
% 0.21/0.47 thf(fact_99_order__less__le__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_le_subst1
% 0.21/0.47 thf(fact_100_order__less__le__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType] :
% 0.21/0.47 ( ( ( order @ C @ ( type2 @ C ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_le_subst2
% 0.21/0.47 thf(fact_101_not__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ~ ( ord_less_eq @ A @ X @ Y2 ) )
% 0.21/0.47 = ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_le
% 0.21/0.47 thf(fact_102_not__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 0.21/0.47 = ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less
% 0.21/0.47 thf(fact_103_le__neq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( A2 != B3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_neq_trans
% 0.21/0.47 thf(fact_104_less__imp__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_le
% 0.21/0.47 thf(fact_105_antisym__conv1,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 = ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv1
% 0.21/0.47 thf(fact_106_antisym__conv2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 0.21/0.47 = ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv2
% 0.21/0.47 thf(fact_107_le__less__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less @ A @ Y2 @ Z4 )
% 0.21/0.47 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_less_trans
% 0.21/0.47 thf(fact_108_less__le__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 0.21/0.47 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_le_trans
% 0.21/0.47 thf(fact_109_dense__ge,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Z4: A,Y2: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( ord_less @ A @ Z4 @ X3 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense_ge
% 0.21/0.47 thf(fact_110_dense__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Y2: A,Z4: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( ord_less @ A @ X3 @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X3 @ Z4 ) )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense_le
% 0.21/0.47 thf(fact_111_le__less__linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 | ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_less_linear
% 0.21/0.47 thf(fact_112_le__imp__less__or__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 | ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_imp_less_or_eq
% 0.21/0.47 thf(fact_113_less__le__not__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less @ A )
% 0.21/0.47 = ( ^ [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 & ~ ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_le_not_le
% 0.21/0.47 thf(fact_114_not__le__imp__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Y2: A,X: A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ( ord_less @ A @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_le_imp_less
% 0.21/0.47 thf(fact_115_order_Ostrict__trans1,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_trans1
% 0.21/0.47 thf(fact_116_order_Ostrict__trans2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_trans2
% 0.21/0.47 thf(fact_117_order_Oorder__iff__strict,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less_eq @ A )
% 0.21/0.47 = ( ^ [A5: A,B4: A] :
% 0.21/0.47 ( ( ord_less @ A @ A5 @ B4 )
% 0.21/0.47 | ( A5 = B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.order_iff_strict
% 0.21/0.47 thf(fact_118_order_Ostrict__iff__order,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less @ A )
% 0.21/0.47 = ( ^ [A5: A,B4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.21/0.47 & ( A5 != B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_iff_order
% 0.21/0.47 thf(fact_119_dual__order_Ostrict__trans1,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( ord_less @ A @ C3 @ B3 )
% 0.21/0.47 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_trans1
% 0.21/0.47 thf(fact_120_dual__order_Ostrict__trans2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.21/0.47 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_trans2
% 0.21/0.47 thf(fact_121_dense__ge__bounded,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Z4: A,X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ Z4 @ X )
% 0.21/0.47 => ( ! [W: A] :
% 0.21/0.47 ( ( ord_less @ A @ Z4 @ W )
% 0.21/0.47 => ( ( ord_less @ A @ W @ X )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense_ge_bounded
% 0.21/0.47 thf(fact_122_dense__le__bounded,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ! [W: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ W )
% 0.21/0.47 => ( ( ord_less @ A @ W @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ W @ Z4 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense_le_bounded
% 0.21/0.47 thf(fact_123_order_Ostrict__implies__order,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_implies_order
% 0.21/0.47 thf(fact_124_dual__order_Oorder__iff__strict,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less_eq @ A )
% 0.21/0.47 = ( ^ [B4: A,A5: A] :
% 0.21/0.47 ( ( ord_less @ A @ B4 @ A5 )
% 0.21/0.47 | ( A5 = B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.order_iff_strict
% 0.21/0.47 thf(fact_125_dual__order_Ostrict__iff__order,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ord_less @ A )
% 0.21/0.47 = ( ^ [B4: A,A5: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.21/0.47 & ( A5 != B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_iff_order
% 0.21/0.47 thf(fact_126_dual__order_Ostrict__implies__order,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_implies_order
% 0.21/0.47 thf(fact_127_order_Onot__eq__order__implies__strict,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( A2 != B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.not_eq_order_implies_strict
% 0.21/0.47 thf(fact_128_tree_Orel__mono,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,R5: A > B > $o,Ra: A > B > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > B > $o ) @ R5 @ Ra )
% 0.21/0.47 => ( ord_less_eq @ ( ( tree @ A ) > ( tree @ B ) > $o ) @ ( rel_tree @ A @ B @ R5 ) @ ( rel_tree @ A @ B @ Ra ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_mono
% 0.21/0.47 thf(fact_129_less__numeral__extra_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.21/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_numeral_extra(4)
% 0.21/0.47 thf(fact_130_tree_Orel__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( rel_tree @ A @ A
% 0.21/0.47 @ ^ [Y4: A,Z5: A] : ( Y4 = Z5 ) )
% 0.21/0.47 = ( ^ [Y4: tree @ A,Z5: tree @ A] : ( Y4 = Z5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_eq
% 0.21/0.47 thf(fact_131_tree_Orel__refl,axiom,
% 0.21/0.47 ! [B: $tType,Ra: B > B > $o,X: tree @ B] :
% 0.21/0.47 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.21/0.47 => ( rel_tree @ B @ B @ Ra @ X @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_refl
% 0.21/0.47 thf(fact_132_dual__order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( A2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_implies_not_eq
% 0.21/0.47 thf(fact_133_order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( A2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_implies_not_eq
% 0.21/0.47 thf(fact_134_not__less__iff__gr__or__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 0.21/0.47 = ( ( ord_less @ A @ Y2 @ X )
% 0.21/0.47 | ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_iff_gr_or_eq
% 0.21/0.47 thf(fact_135_dual__order_Ostrict__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( ord_less @ A @ C3 @ B3 )
% 0.21/0.47 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_trans
% 0.21/0.47 thf(fact_136_less__imp__not__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_less
% 0.21/0.47 thf(fact_137_order_Ostrict__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_trans
% 0.21/0.47 thf(fact_138_dual__order_Oirrefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.irrefl
% 0.21/0.47 thf(fact_139_linorder__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ( X != Y2 )
% 0.21/0.47 => ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_cases
% 0.21/0.47 thf(fact_140_less__imp__triv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,P: $o] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less @ A @ Y2 @ X )
% 0.21/0.47 => P ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_triv
% 0.21/0.47 thf(fact_141_less__imp__not__eq2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( Y2 != X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_eq2
% 0.21/0.47 thf(fact_142_antisym__conv3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Y2: A,X: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ Y2 @ X )
% 0.21/0.47 => ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 0.21/0.47 = ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv3
% 0.21/0.47 thf(fact_143_less__induct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [P: A > $o,A2: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ! [Y5: A] :
% 0.21/0.47 ( ( ord_less @ A @ Y5 @ X3 )
% 0.21/0.47 => ( P @ Y5 ) )
% 0.21/0.47 => ( P @ X3 ) )
% 0.21/0.47 => ( P @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_induct
% 0.21/0.47 thf(fact_144_less__not__sym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_sym
% 0.21/0.47 thf(fact_145_less__imp__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( X != Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_eq
% 0.21/0.47 thf(fact_146_dual__order_Oasym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.asym
% 0.21/0.47 thf(fact_147_ord__less__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( B3 = C3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_less_eq_trans
% 0.21/0.47 thf(fact_148_ord__eq__less__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( A2 = B3 )
% 0.21/0.47 => ( ( ord_less @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_less_trans
% 0.21/0.47 thf(fact_149_less__irrefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_irrefl
% 0.21/0.47 thf(fact_150_less__linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 | ( X = Y2 )
% 0.21/0.47 | ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_linear
% 0.21/0.47 thf(fact_151_less__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less @ A @ Y2 @ Z4 )
% 0.21/0.47 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_trans
% 0.21/0.47 thf(fact_152_less__asym_H,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_asym'
% 0.21/0.47 thf(fact_153_less__asym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_asym
% 0.21/0.47 thf(fact_154_less__imp__neq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( X != Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_neq
% 0.21/0.47 thf(fact_155_dense,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ? [Z: A] :
% 0.21/0.47 ( ( ord_less @ A @ X @ Z )
% 0.21/0.47 & ( ord_less @ A @ Z @ Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense
% 0.21/0.47 thf(fact_156_order_Oasym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.asym
% 0.21/0.47 thf(fact_157_neq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( X != Y2 )
% 0.21/0.47 = ( ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 | ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_iff
% 0.21/0.47 thf(fact_158_neqE,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( X != Y2 )
% 0.21/0.47 => ( ~ ( ord_less @ A @ X @ Y2 )
% 0.21/0.47 => ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neqE
% 0.21/0.47 thf(fact_159_gt__ex,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( no_top @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % gt_ex
% 0.21/0.47 thf(fact_160_lt__ex,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % lt_ex
% 0.21/0.47 thf(fact_161_order__less__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType] :
% 0.21/0.47 ( ( ( order @ C @ ( type2 @ C ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less @ C @ ( F @ B3 ) @ C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_subst2
% 0.21/0.47 thf(fact_162_order__less__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_subst1
% 0.21/0.47 thf(fact_163_ord__less__eq__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ( F @ B3 )
% 0.21/0.47 = C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_less_eq_subst
% 0.21/0.47 thf(fact_164_ord__eq__less__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_less_subst
% 0.21/0.47 thf(fact_165_powr__powr__swap,axiom,
% 0.21/0.47 ! [X: real,A2: real,B3: real] :
% 0.21/0.47 ( ( powr @ real @ ( powr @ real @ X @ A2 ) @ B3 )
% 0.21/0.47 = ( powr @ real @ ( powr @ real @ X @ B3 ) @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_powr_swap
% 0.21/0.47 thf(fact_166_tree_Orel__inject_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ B,Y22: B,Y23: tree @ B] :
% 0.21/0.47 ( ( rel_tree @ A @ B @ R5 @ ( node @ A @ X21 @ X22 @ X23 ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) )
% 0.21/0.47 = ( ( rel_tree @ A @ B @ R5 @ X21 @ Y21 )
% 0.21/0.47 & ( R5 @ X22 @ Y22 )
% 0.21/0.47 & ( rel_tree @ A @ B @ R5 @ X23 @ Y23 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_inject(2)
% 0.21/0.47 thf(fact_167_tree_Orel__intros_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,X21: tree @ A,Y21: tree @ B,X22: A,Y22: B,X23: tree @ A,Y23: tree @ B] :
% 0.21/0.47 ( ( rel_tree @ A @ B @ R5 @ X21 @ Y21 )
% 0.21/0.47 => ( ( R5 @ X22 @ Y22 )
% 0.21/0.47 => ( ( rel_tree @ A @ B @ R5 @ X23 @ Y23 )
% 0.21/0.47 => ( rel_tree @ A @ B @ R5 @ ( node @ A @ X21 @ X22 @ X23 ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_intros(2)
% 0.21/0.47 thf(fact_168_tree_Octr__transfer_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o] : ( rel_tree @ A @ B @ R5 @ ( leaf @ A ) @ ( leaf @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.ctr_transfer(1)
% 0.21/0.47 thf(fact_169_tree_Orel__refl__strong,axiom,
% 0.21/0.47 ! [A: $tType,X: tree @ A,Ra: A > A > $o] :
% 0.21/0.47 ( ! [Z: A] :
% 0.21/0.47 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 0.21/0.47 => ( Ra @ Z @ Z ) )
% 0.21/0.47 => ( rel_tree @ A @ A @ Ra @ X @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_refl_strong
% 0.21/0.47 thf(fact_170_tree_Orel__mono__strong,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,X: tree @ A,Y2: tree @ B,Ra: A > B > $o] :
% 0.21/0.47 ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 0.21/0.47 => ( ! [Z: A,Yb: B] :
% 0.21/0.47 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 0.21/0.47 => ( ( member @ B @ Yb @ ( set_tree @ B @ Y2 ) )
% 0.21/0.47 => ( ( R5 @ Z @ Yb )
% 0.21/0.47 => ( Ra @ Z @ Yb ) ) ) )
% 0.21/0.47 => ( rel_tree @ A @ B @ Ra @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_mono_strong
% 0.21/0.47 thf(fact_171_tree_Orel__cong,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,X: tree @ A,Ya: tree @ A,Y2: tree @ B,Xa: tree @ B,R5: A > B > $o,Ra: A > B > $o] :
% 0.21/0.47 ( ( X = Ya )
% 0.21/0.47 => ( ( Y2 = Xa )
% 0.21/0.47 => ( ! [Z: A,Yb: B] :
% 0.21/0.47 ( ( member @ A @ Z @ ( set_tree @ A @ Ya ) )
% 0.21/0.47 => ( ( member @ B @ Yb @ ( set_tree @ B @ Xa ) )
% 0.21/0.47 => ( ( R5 @ Z @ Yb )
% 0.21/0.47 = ( Ra @ Z @ Yb ) ) ) )
% 0.21/0.47 => ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 0.21/0.47 = ( rel_tree @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_cong
% 0.21/0.47 thf(fact_172_powr__less__mono,axiom,
% 0.21/0.47 ! [A2: real,B3: real,X: real] :
% 0.21/0.47 ( ( ord_less @ real @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.21/0.47 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_less_mono
% 0.21/0.47 thf(fact_173_powr__less__cancel,axiom,
% 0.21/0.47 ! [X: real,A2: real,B3: real] :
% 0.21/0.47 ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 0.21/0.47 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.21/0.47 => ( ord_less @ real @ A2 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % powr_less_cancel
% 0.21/0.47 thf(fact_174_t__splay_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A] :
% 0.21/0.47 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 0.21/0.47 = ( one_one @ nat ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % t_splay.simps(1)
% 0.21/0.47 thf(fact_175_splay__max_Osimps_I1_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 0.21/0.47 = ( leaf @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay_max.simps(1)
% 0.21/0.47 thf(fact_176_set__splay__max,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A] :
% 0.21/0.47 ( ( set_tree @ A @ ( splay_splay_max @ A @ T ) )
% 0.21/0.47 = ( set_tree @ A @ T ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_splay_max
% 0.21/0.47 thf(fact_177_bst__splay__max,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [T: tree @ A] :
% 0.21/0.47 ( ( linorder_bst @ A @ T )
% 0.21/0.47 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bst_splay_max
% 0.21/0.47 thf(fact_178_tree_Orel__induct,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,X: tree @ A,Y2: tree @ B,Q: ( tree @ A ) > ( tree @ B ) > $o] :
% 0.21/0.47 ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 0.21/0.47 => ( ( Q @ ( leaf @ A ) @ ( leaf @ B ) )
% 0.21/0.47 => ( ! [A21: tree @ A,A222: A,A23: tree @ A,B21: tree @ B,B22: B,B23: tree @ B] :
% 0.21/0.47 ( ( Q @ A21 @ B21 )
% 0.21/0.47 => ( ( R5 @ A222 @ B22 )
% 0.21/0.47 => ( ( Q @ A23 @ B23 )
% 0.21/0.47 => ( Q @ ( node @ A @ A21 @ A222 @ A23 ) @ ( node @ B @ B21 @ B22 @ B23 ) ) ) ) )
% 0.21/0.47 => ( Q @ X @ Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_induct
% 0.21/0.47 thf(fact_179_tree_Orel__cases,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,A2: tree @ A,B3: tree @ B] :
% 0.21/0.47 ( ( rel_tree @ A @ B @ R5 @ A2 @ B3 )
% 0.21/0.47 => ( ( ( A2
% 0.21/0.47 = ( leaf @ A ) )
% 0.21/0.47 => ( B3
% 0.21/0.47 != ( leaf @ B ) ) )
% 0.21/0.47 => ~ ! [X1: tree @ A,X24: A,X32: tree @ A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( node @ A @ X1 @ X24 @ X32 ) )
% 0.21/0.47 => ! [Y1: tree @ B,Y24: B,Y32: tree @ B] :
% 0.21/0.47 ( ( B3
% 0.21/0.47 = ( node @ B @ Y1 @ Y24 @ Y32 ) )
% 0.21/0.47 => ( ( rel_tree @ A @ B @ R5 @ X1 @ Y1 )
% 0.21/0.47 => ( ( R5 @ X24 @ Y24 )
% 0.21/0.47 => ~ ( rel_tree @ A @ B @ R5 @ X32 @ Y32 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_cases
% 0.21/0.47 thf(fact_180_tree_Orel__distinct_I1_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,Y21: tree @ B,Y22: B,Y23: tree @ B] :
% 0.21/0.47 ~ ( rel_tree @ A @ B @ R5 @ ( leaf @ A ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_distinct(1)
% 0.21/0.47 thf(fact_181_tree_Orel__distinct_I2_J,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType,R5: A > B > $o,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 0.21/0.47 ~ ( rel_tree @ A @ B @ R5 @ ( node @ A @ Y21 @ Y22 @ Y23 ) @ ( leaf @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % tree.rel_distinct(2)
% 0.21/0.47 thf(fact_182_splay_Osimps_I9_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B3 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 0.21/0.47 = ( node @ A @ ( node @ A @ Lb @ B3 @ La ) @ A2 @ Ra2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay.simps(9)
% 0.21/0.47 thf(fact_183_splay_Osimps_I3_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 0.21/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B3 @ Rb ) )
% 0.21/0.47 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B3 @ Rb ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % splay.simps(3)
% 0.21/0.47 thf(fact_184_dual__order_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.antisym
% 0.21/0.47 thf(fact_185_dual__order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.21/0.47 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.trans
% 0.21/0.47 thf(fact_186_linorder__wlog,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.21/0.47 ( ! [A6: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A6 @ B2 )
% 0.21/0.47 => ( P @ A6 @ B2 ) )
% 0.21/0.47 => ( ! [A6: A,B2: A] :
% 0.21/0.47 ( ( P @ B2 @ A6 )
% 0.21/0.47 => ( P @ A6 @ B2 ) )
% 0.21/0.47 => ( P @ A2 @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_wlog
% 0.21/0.47 thf(fact_187_dual__order_Orefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.refl
% 0.21/0.47 thf(fact_188_order__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 0.21/0.47 => ( ord_less_eq @ A @ X @ Z4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_trans
% 0.21/0.47 thf(fact_189_order__class_Oorder_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.21/0.47 => ( A2 = B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.antisym
% 0.21/0.47 thf(fact_190_ord__le__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( B3 = C3 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_trans
% 0.21/0.47 thf(fact_191_ord__eq__le__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( A2 = B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_trans
% 0.21/0.47 thf(fact_192_antisym__conv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [Y2: A,X: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 = ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv
% 0.21/0.47 thf(fact_193_le__cases3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A,Z4: A] :
% 0.21/0.47 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y2 @ Z4 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X @ Z4 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ X @ Z4 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z4 @ Y2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Z4 @ Y2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z4 @ X ) )
% 0.21/0.47 => ~ ( ( ord_less_eq @ A @ Z4 @ X )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases3
% 0.21/0.47 thf(fact_194_order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.trans
% 0.21/0.47 thf(fact_195_le__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases
% 0.21/0.47 thf(fact_196_eq__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( X = Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_refl
% 0.21/0.47 thf(fact_197_linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 | ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linear
% 0.21/0.47 thf(fact_198_antisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym
% 0.21/0.47 thf(fact_199_eq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.21/0.47 => ( ( ^ [Y4: A,Z5: A] : ( Y4 = Z5 ) )
% 0.21/0.47 = ( ^ [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 & ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_iff
% 0.21/0.47 thf(fact_200_ord__le__eq__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ( F @ B3 )
% 0.21/0.47 = C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_subst
% 0.21/0.47 thf(fact_201_ord__eq__le__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_subst
% 0.21/0.47 thf(fact_202_order__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C: $tType] :
% 0.21/0.47 ( ( ( order @ C @ ( type2 @ C ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 0.21/0.47 => ( ! [X3: A,Y3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst2
% 0.21/0.47 thf(fact_203_order__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.21/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.21/0.47 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.21/0.47 => ( ! [X3: B,Y3: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst1
% 0.21/0.47 thf(fact_204_le__fun__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.33/0.47 = ( ^ [F3: A > B,G2: A > B] :
% 0.33/0.47 ! [X2: A] : ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_fun_def
% 0.33/0.47 thf(fact_205_le__funI,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B] :
% 0.33/0.47 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.33/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funI
% 0.33/0.47 thf(fact_206_le__funE,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funE
% 0.33/0.47 thf(fact_207_le__funD,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.33/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_funD
% 0.33/0.47 thf(fact_208_splay__max_Osimps_I2_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [La: tree @ A,A2: A] :
% 0.33/0.47 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 0.33/0.47 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay_max.simps(2)
% 0.33/0.47 thf(fact_209_splay__max__Leaf,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: tree @ A,L2: tree @ A,A2: A,R2: tree @ A] :
% 0.33/0.47 ( ( ( splay_splay_max @ A @ T )
% 0.33/0.47 = ( node @ A @ L2 @ A2 @ R2 ) )
% 0.33/0.47 => ( R2
% 0.33/0.47 = ( leaf @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay_max_Leaf
% 0.33/0.47 thf(fact_210_splay_Osimps_I13_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,X: A,B3: A,La: tree @ A,Lb: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ X )
% 0.33/0.47 => ( ( ord_less @ A @ B3 @ X )
% 0.33/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B3 @ ( leaf @ A ) ) ) )
% 0.33/0.47 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B3 @ ( leaf @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(13)
% 0.33/0.47 thf(fact_211_splay_Osimps_I12_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,X: A,B3: A,La: tree @ A,Rb: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ X )
% 0.33/0.47 => ( ( ord_less @ A @ X @ B3 )
% 0.33/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ Rb ) ) )
% 0.33/0.47 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B3 @ Rb ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(12)
% 0.33/0.47 thf(fact_212_splay_Osimps_I10_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,X: A,L2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ X )
% 0.33/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) )
% 0.33/0.47 = ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(10)
% 0.33/0.47 thf(fact_213_splay_Osimps_I7_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X: A,B3: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ X @ B3 )
% 0.33/0.47 => ( ( ord_less @ A @ A2 @ X )
% 0.33/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B3 @ Rb ) )
% 0.33/0.47 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ Rb ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(7)
% 0.33/0.47 thf(fact_214_splay_Osimps_I5_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X: A,A2: A,B3: A,Ra2: tree @ A,Rb: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ X @ A2 )
% 0.33/0.47 => ( ( ord_less @ A @ X @ B3 )
% 0.33/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B3 @ Rb ) )
% 0.33/0.47 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B3 @ Rb ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(5)
% 0.33/0.47 thf(fact_215_splay_Osimps_I4_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,R2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) )
% 0.33/0.47 = ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay.simps(4)
% 0.33/0.47 thf(fact_216_splay__max__eq__splay__ex,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: tree @ A] :
% 0.33/0.47 ( ( linorder_bst @ A @ T )
% 0.33/0.47 => ? [A6: A] :
% 0.33/0.47 ( ( splay_splay_max @ A @ T )
% 0.33/0.47 = ( splay_splay @ A @ A6 @ T ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay_max_eq_splay_ex
% 0.33/0.47 thf(fact_217_bst_Osimps_I2_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [L2: tree @ A,A2: A,R2: tree @ A] :
% 0.33/0.47 ( ( linorder_bst @ A @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.33/0.47 = ( ( linorder_bst @ A @ L2 )
% 0.33/0.47 & ( linorder_bst @ A @ R2 )
% 0.33/0.47 & ! [X2: A] :
% 0.33/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ L2 ) )
% 0.33/0.47 => ( ord_less @ A @ X2 @ A2 ) )
% 0.33/0.47 & ! [X2: A] :
% 0.33/0.47 ( ( member @ A @ X2 @ ( set_tree @ A @ R2 ) )
% 0.33/0.47 => ( ord_less @ A @ A2 @ X2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bst.simps(2)
% 0.33/0.47 thf(fact_218_bst_Oelims_I3_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [X: tree @ A] :
% 0.33/0.47 ( ~ ( linorder_bst @ A @ X )
% 0.33/0.47 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 0.33/0.47 ( ( X
% 0.33/0.47 = ( node @ A @ L @ A6 @ R ) )
% 0.33/0.47 => ( ( linorder_bst @ A @ L )
% 0.33/0.47 & ( linorder_bst @ A @ R )
% 0.33/0.47 & ! [X3: A] :
% 0.33/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ L ) )
% 0.33/0.47 => ( ord_less @ A @ X3 @ A6 ) )
% 0.33/0.47 & ! [X3: A] :
% 0.33/0.47 ( ( member @ A @ X3 @ ( set_tree @ A @ R ) )
% 0.33/0.47 => ( ord_less @ A @ A6 @ X3 ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % bst.elims(3)
% 0.33/0.47 thf(fact_219_splay__bstR,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: tree @ A,A2: A,L2: tree @ A,E: A,R2: tree @ A,X: A] :
% 0.33/0.47 ( ( linorder_bst @ A @ T )
% 0.33/0.47 => ( ( ( splay_splay @ A @ A2 @ T )
% 0.33/0.47 = ( node @ A @ L2 @ E @ R2 ) )
% 0.33/0.47 => ( ( member @ A @ X @ ( set_tree @ A @ R2 ) )
% 0.33/0.47 => ( ord_less @ A @ A2 @ X ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay_bstR
% 0.33/0.47 thf(fact_220_splay__bstL,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: tree @ A,A2: A,L2: tree @ A,E: A,R2: tree @ A,X: A] :
% 0.33/0.47 ( ( linorder_bst @ A @ T )
% 0.33/0.47 => ( ( ( splay_splay @ A @ A2 @ T )
% 0.33/0.47 = ( node @ A @ L2 @ E @ R2 ) )
% 0.33/0.47 => ( ( member @ A @ X @ ( set_tree @ A @ L2 ) )
% 0.33/0.47 => ( ord_less @ A @ X @ A2 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % splay_bstL
% 0.33/0.47 thf(fact_221_minf_I8_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: A] :
% 0.33/0.47 ? [Z: A] :
% 0.33/0.47 ! [X4: A] :
% 0.33/0.47 ( ( ord_less @ A @ X4 @ Z )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ T @ X4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % minf(8)
% 0.33/0.47 thf(fact_222_minf_I6_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: A] :
% 0.33/0.47 ? [Z: A] :
% 0.33/0.47 ! [X4: A] :
% 0.33/0.47 ( ( ord_less @ A @ X4 @ Z )
% 0.33/0.47 => ( ord_less_eq @ A @ X4 @ T ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % minf(6)
% 0.33/0.47 thf(fact_223_pinf_I8_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: A] :
% 0.33/0.47 ? [Z: A] :
% 0.33/0.47 ! [X4: A] :
% 0.33/0.47 ( ( ord_less @ A @ Z @ X4 )
% 0.33/0.47 => ( ord_less_eq @ A @ T @ X4 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pinf(8)
% 0.33/0.47 thf(fact_224_pinf_I6_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [T: A] :
% 0.33/0.47 ? [Z: A] :
% 0.33/0.47 ! [X4: A] :
% 0.33/0.47 ( ( ord_less @ A @ Z @ X4 )
% 0.33/0.47 => ~ ( ord_less_eq @ A @ X4 @ T ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % pinf(6)
% 0.33/0.47 thf(fact_225_complete__interval,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,P: A > $o] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( P @ A2 )
% 0.33/0.47 => ( ~ ( P @ B3 )
% 0.33/0.47 => ? [C2: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.33/0.47 & ( ord_less_eq @ A @ C2 @ B3 )
% 0.33/0.47 & ! [X4: A] :
% 0.33/0.47 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 0.33/0.47 & ( ord_less @ A @ X4 @ C2 ) )
% 0.33/0.47 => ( P @ X4 ) )
% 0.33/0.47 & ! [D: A] :
% 0.33/0.47 ( ! [X3: A] :
% 0.33/0.47 ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.33/0.47 & ( ord_less @ A @ X3 @ D ) )
% 0.33/0.47 => ( P @ X3 ) )
% 0.33/0.47 => ( ord_less_eq @ A @ D @ C2 ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % complete_interval
% 0.33/0.47 thf(fact_226_t__splay__simps_I9_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A,Rr2: tree @ A,L2: tree @ A,Rl2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.33/0.47 => ( ( ord_less @ A @ C3 @ A2 )
% 0.33/0.47 => ( ( ( Rr2
% 0.33/0.47 = ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.33/0.47 = ( one_one @ nat ) ) )
% 0.33/0.47 & ( ( Rr2
% 0.33/0.47 != ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.33/0.47 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % t_splay_simps(9)
% 0.33/0.47 thf(fact_227_add__right__cancel,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ B3 @ A2 )
% 0.33/0.47 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.33/0.47 = ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_right_cancel
% 0.33/0.47 thf(fact_228_add__left__cancel,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ A2 @ B3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.33/0.47 = ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_left_cancel
% 0.33/0.47 thf(fact_229_predicate2I,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.33/0.47 ( ! [X3: A,Y3: B] :
% 0.33/0.47 ( ( P @ X3 @ Y3 )
% 0.33/0.47 => ( Q @ X3 @ Y3 ) )
% 0.33/0.47 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.33/0.47
% 0.33/0.47 % predicate2I
% 0.33/0.47 thf(fact_230_add__le__cancel__right,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,C3: A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 0.33/0.47 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_le_cancel_right
% 0.33/0.47 thf(fact_231_add__le__cancel__left,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [C3: A,A2: A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 0.33/0.47 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_le_cancel_left
% 0.33/0.47 thf(fact_232_add__less__cancel__right,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,C3: A,B3: A] :
% 0.33/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 0.33/0.47 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_less_cancel_right
% 0.33/0.47 thf(fact_233_add__less__cancel__left,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [C3: A,A2: A,B3: A] :
% 0.33/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 0.33/0.47 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_less_cancel_left
% 0.33/0.47 thf(fact_234_t__splay__simps_I4_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ord_less @ A @ A2 @ C3 )
% 0.33/0.47 => ( ( ( Ll
% 0.33/0.47 = ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 0.33/0.47 = ( one_one @ nat ) ) )
% 0.33/0.47 & ( ( Ll
% 0.33/0.47 != ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 0.33/0.47 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % t_splay_simps(4)
% 0.33/0.47 thf(fact_235_t__splay__simps_I5_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ A2 @ B3 )
% 0.33/0.47 => ( ( ord_less @ A @ C3 @ A2 )
% 0.33/0.47 => ( ( ( Lr
% 0.33/0.47 = ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 0.33/0.47 = ( one_one @ nat ) ) )
% 0.33/0.47 & ( ( Lr
% 0.33/0.47 != ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 0.33/0.47 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % t_splay_simps(5)
% 0.33/0.47 thf(fact_236_t__splay__simps_I8_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A,Rl2: tree @ A,L2: tree @ A,Rr2: tree @ A] :
% 0.33/0.47 ( ( ord_less @ A @ B3 @ A2 )
% 0.33/0.47 => ( ( ord_less @ A @ A2 @ C3 )
% 0.33/0.47 => ( ( ( Rl2
% 0.33/0.47 = ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.33/0.47 = ( one_one @ nat ) ) )
% 0.33/0.47 & ( ( Rl2
% 0.33/0.47 != ( leaf @ A ) )
% 0.33/0.47 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.33/0.47 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % t_splay_simps(8)
% 0.33/0.47 thf(fact_237_predicate2D,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y2: B] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.33/0.47 => ( ( P @ X @ Y2 )
% 0.33/0.47 => ( Q @ X @ Y2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % predicate2D
% 0.33/0.47 thf(fact_238_less__fun__def,axiom,
% 0.33/0.47 ! [B: $tType,A: $tType] :
% 0.33/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.33/0.47 => ( ( ord_less @ ( A > B ) )
% 0.33/0.47 = ( ^ [F3: A > B,G2: A > B] :
% 0.33/0.47 ( ( ord_less_eq @ ( A > B ) @ F3 @ G2 )
% 0.33/0.47 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F3 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % less_fun_def
% 0.33/0.47 thf(fact_239_rev__predicate2D,axiom,
% 0.33/0.47 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y2: B,Q: A > B > $o] :
% 0.33/0.47 ( ( P @ X @ Y2 )
% 0.33/0.47 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.33/0.47 => ( Q @ X @ Y2 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % rev_predicate2D
% 0.33/0.47 thf(fact_240_is__num__normalize_I1_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % is_num_normalize(1)
% 0.33/0.47 thf(fact_241_add__right__imp__eq,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ B3 @ A2 )
% 0.33/0.47 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.33/0.47 => ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_right_imp_eq
% 0.33/0.47 thf(fact_242_add__left__imp__eq,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ A2 @ B3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.33/0.47 => ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_left_imp_eq
% 0.33/0.47 thf(fact_243_add_Oleft__commute,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.33/0.47 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A2 @ C3 ) )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add.left_commute
% 0.33/0.47 thf(fact_244_add_Ocommute,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( ( plus_plus @ A )
% 0.33/0.47 = ( ^ [A5: A,B4: A] : ( plus_plus @ A @ B4 @ A5 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add.commute
% 0.33/0.47 thf(fact_245_add_Oright__cancel,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [B3: A,A2: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ B3 @ A2 )
% 0.33/0.47 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.33/0.47 = ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add.right_cancel
% 0.33/0.47 thf(fact_246_add_Oleft__cancel,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( ( plus_plus @ A @ A2 @ B3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.33/0.47 = ( B3 = C3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add.left_cancel
% 0.33/0.47 thf(fact_247_add_Oassoc,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add.assoc
% 0.33/0.47 thf(fact_248_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [I: A,J: A,K: A,L2: A] :
% 0.33/0.47 ( ( ( I = J )
% 0.33/0.47 & ( K = L2 ) )
% 0.33/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.33/0.47 = ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_mono_thms_linordered_semiring(4)
% 0.33/0.47 thf(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 0.33/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.33/0.47 thf(fact_250_add__le__imp__le__right,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,C3: A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_le_imp_le_right
% 0.33/0.47 thf(fact_251_add__le__imp__le__left,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [C3: A,A2: A,B3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 0.33/0.47 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_le_imp_le_left
% 0.33/0.47 thf(fact_252_le__iff__add,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( ( ord_less_eq @ A )
% 0.33/0.47 = ( ^ [A5: A,B4: A] :
% 0.33/0.47 ? [C4: A] :
% 0.33/0.47 ( B4
% 0.33/0.47 = ( plus_plus @ A @ A5 @ C4 ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % le_iff_add
% 0.33/0.47 thf(fact_253_add__right__mono,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.33/0.47 => ! [A2: A,B3: A,C3: A] :
% 0.33/0.47 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.33/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 % add_right_mono
% 0.33/0.47
% 0.33/0.47 %----Subclasses (4)
% 0.33/0.47 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( type @ A @ ( type2 @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( order @ A @ ( type2 @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.33/0.47 ! [A: $tType] :
% 0.33/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.47 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 %----Type constructors (44)
% 0.33/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.33/0.47 ! [A7: $tType,A8: $tType] :
% 0.33/0.47 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.33/0.47 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.33/0.47 ! [A7: $tType,A8: $tType] :
% 0.33/0.47 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.33/0.47 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.33/0.47 ! [A7: $tType,A8: $tType] :
% 0.33/0.47 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.33/0.47 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.33/0.47 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.33/0.47 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.33/0.47 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.33/0.47 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.33/0.47 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.33/0.47 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.33/0.47 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.33/0.47 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.33/0.47 wellorder @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.33/0.47 preorder @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.33/0.47 linorder @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.33/0.47 no_top @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.33/0.47 order @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.33/0.47 ord @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.33/0.47 one @ nat @ ( type2 @ nat ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.33/0.47 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.33/0.47 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.33/0.47 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.33/0.47 preorder @ $o @ ( type2 @ $o ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.33/0.47 linorder @ $o @ ( type2 @ $o ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.33/0.47 order @ $o @ ( type2 @ $o ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.33/0.47 ord @ $o @ ( type2 @ $o ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_11,axiom,
% 0.33/0.47 condit1037483654norder @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_12,axiom,
% 0.33/0.47 ordere236663937imp_le @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_13,axiom,
% 0.33/0.47 ordere779506340up_add @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_14,axiom,
% 0.33/0.47 cancel_semigroup_add @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_15,axiom,
% 0.33/0.47 linordered_semidom @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 0.33/0.47 dense_linorder @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_16,axiom,
% 0.33/0.47 ab_semigroup_add @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 0.33/0.47 dense_order @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_17,axiom,
% 0.33/0.47 semigroup_add @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_18,axiom,
% 0.33/0.47 preorder @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_19,axiom,
% 0.33/0.47 linorder @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 0.33/0.47 ln @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Ono__top_20,axiom,
% 0.33/0.47 no_top @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Ono__bot,axiom,
% 0.33/0.47 no_bot @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.33/0.47 group_add @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_21,axiom,
% 0.33/0.47 order @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.33/0.47 neg_numeral @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Orderings_Oord_22,axiom,
% 0.33/0.47 ord @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 thf(tcon_Real_Oreal___Groups_Oone_23,axiom,
% 0.33/0.47 one @ real @ ( type2 @ real ) ).
% 0.33/0.47
% 0.33/0.47 %----Helper facts (3)
% 0.33/0.47 thf(help_If_3_1_T,axiom,
% 0.33/0.47 ! [P: $o] :
% 0.33/0.47 ( ( P = $true )
% 0.33/0.47 | ( P = $false ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(help_If_2_1_T,axiom,
% 0.33/0.47 ! [A: $tType,X: A,Y2: A] :
% 0.33/0.47 ( ( if @ A @ $false @ X @ Y2 )
% 0.33/0.47 = Y2 ) ).
% 0.33/0.47
% 0.33/0.47 thf(help_If_1_1_T,axiom,
% 0.33/0.47 ! [A: $tType,X: A,Y2: A] :
% 0.33/0.47 ( ( if @ A @ $true @ X @ Y2 )
% 0.33/0.47 = X ) ).
% 0.33/0.47
% 0.33/0.47 %----Free types (1)
% 0.33/0.47 thf(tfree_0,hypothesis,
% 0.33/0.47 linorder @ a @ ( type2 @ a ) ).
% 0.33/0.47
% 0.33/0.47 %----Conjectures (2)
% 0.33/0.47 thf(conj_0,hypothesis,
% 0.33/0.47 ! [La2: tree @ a,Ra3: tree @ a] :
% 0.33/0.47 ( ( member @ ( tree @ a ) @ ( node @ a @ La2 @ a2 @ Ra3 ) @ ( subtrees @ a @ t ) )
% 0.33/0.47 => thesis ) ).
% 0.33/0.47
% 0.33/0.47 thf(conj_1,conjecture,
% 0.33/0.47 thesis ).
% 0.33/0.47
% 0.33/0.47 %------------------------------------------------------------------------------
% 0.33/0.47 ------------------------
% 2.61/1.47 ---- Embedded in THF ---
% 2.61/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.48 %%% Generated on Tue Feb 24 06:12:20 EST 2026
% 2.61/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.48 %%% Logic specification used:
% 2.61/1.48 %%% thf(spec, logic, $$dhol).
% 2.61/1.48
% 2.61/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2DTF23804.p
% 2.61/1.48 thf(ty_t_Tree_Otree, type, tree: ($tType > $tType)).
% 2.61/1.48 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.61/1.48 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.61/1.48 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.61/1.48 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.61/1.48 thf(ty_tf_a, type, a: $tType).
% 2.61/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Transcendental_Oln, type, ln: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.61/1.48 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.61/1.48 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.61/1.48 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.61/1.48 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.61/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.61/1.48 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.61/1.48 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.61/1.48 thf(sy_c_Splay__Tree_Ois__root, type, splay_is_root: (!> [A:$tType]: ((A > ((tree @ A) > $o))))).
% 2.61/1.48 thf(sy_c_Splay__Tree_Osplay, type, splay_splay: (!> [A:$tType]: ((A > ((tree @ A) > (tree @ A)))))).
% 2.61/1.48 thf(sy_c_Splay__Tree_Osplay__max, type, splay_splay_max: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.61/1.48 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay, type, splay_914434265_splay: (!> [A:$tType]: ((A > ((tree @ A) > nat))))).
% 2.61/1.48 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA, type, splay_266122055elle_A: (!> [A:$tType]: ((A > ((tree @ A) > real))))).
% 2.61/1.48 thf(sy_c_Transcendental_Opowr, type, powr: (!> [A:$tType]: ((A > (A > A))))).
% 2.61/1.48 thf(sy_c_Tree_Olinorder__class_Obst, type, linorder_bst: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.61/1.48 thf(sy_c_Tree_Olinorder__class_Obst__eq, type, linorder_bst_eq: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.61/1.48 thf(sy_c_Tree_Omirror, type, mirror: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.61/1.48 thf(sy_c_Tree_Osubtrees, type, subtrees: (!> [A:$tType]: (((tree @ A) > (set @ (tree @ A)))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_OLeaf, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 2.61/1.48 thf(sy_c_Tree_Otree_ONode, type, node: (!> [A:$tType]: (((tree @ A) > (A > ((tree @ A) > (tree @ A))))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Ocase__tree, type, case_tree: (!> [B:$tType,A:$tType]: ((B > (((tree @ A) > (A > ((tree @ A) > B))) > ((tree @ A) > B)))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Ois__Leaf, type, is_Leaf: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Oleft, type, left: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Opred__tree, type, pred_tree: (!> [A:$tType]: (((A > $o) > ((tree @ A) > $o))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Orec__tree, type, rec_tree: (!> [C:$tType,A:$tType]: ((C > (((tree @ A) > (A > ((tree @ A) > (C > (C > C))))) > ((tree @ A) > C)))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Orel__tree, type, rel_tree: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((tree @ A) > ((tree @ B) > $o)))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Oright, type, right: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Oset__tree, type, set_tree: (!> [A:$tType]: (((tree @ A) > (set @ A))))).
% 2.61/1.48 thf(sy_c_Tree_Otree_Oval, type, val: (!> [A:$tType]: (((tree @ A) > A)))).
% 2.61/1.48 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.61/1.48 thf(sy_v_a, type, a2: a).
% 2.61/1.48 thf(sy_v_t, type, t: (tree @ a)).
% 2.61/1.48 thf(sy_v_thesis____, type, thesis: $o).
% 2.61/1.48 thf(fact_0_assms_I2_J, axiom, (((member @ a) @ a2) @ ((set_tree @ a) @ t))).
% 2.61/1.48 thf(fact_1_assms_I1_J, axiom, ((linorder_bst @ a) @ t)).
% 2.61/1.48 thf(fact_2_tree_Oinject, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A),Y21:(tree @ A),Y22:A,Y23:(tree @ A)]: (((((((node @ A) @ X21) @ X22) @ X23) = ((((node @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.61/1.48 thf(fact_3_set__treeE, axiom, (! [A:$tType,A2:A,T:(tree @ A)]: (((((member @ A) @ A2) @ ((set_tree @ A) @ T)) => (? [L:(tree @ A),R:(tree @ A)]: ((((member @ (tree @ A)) @ ((((node @ A) @ L) @ A2) @ R)) @ ((subtrees @ A) @ T)))))))).
% 2.61/1.48 thf(fact_4_in__set__tree__if, axiom, (! [A:$tType,L2:(tree @ A),A2:A,R2:(tree @ A),T:(tree @ A)]: (((((member @ (tree @ A)) @ ((((node @ A) @ L2) @ A2) @ R2)) @ ((subtrees @ A) @ T)) => (((member @ A) @ A2) @ ((set_tree @ A) @ T)))))).
% 2.61/1.48 thf(fact_5_Node__notin__subtrees__if, axiom, (! [A:$tType,A2:A,T:(tree @ A),L2:(tree @ A),R2:(tree @ A)]: (((~ ((((member @ A) @ A2) @ ((set_tree @ A) @ T)))) => (~ ((((member @ (tree @ A)) @ ((((node @ A) @ L2) @ A2) @ R2)) @ ((subtrees @ A) @ T)))))))).
% 2.61/1.48 thf(fact_6_tree_Oset__intros_I3_J, axiom, (! [A:$tType,Xa:A,A3:(tree @ A),A1:(tree @ A),A22:A]: (((((member @ A) @ Xa) @ ((set_tree @ A) @ A3)) => (((member @ A) @ Xa) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A22) @ A3))))))).
% 2.61/1.48 thf(fact_7_tree_Oset__intros_I2_J, axiom, (! [A:$tType,A22:A,A1:(tree @ A),A3:(tree @ A)]: ((((member @ A) @ A22) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A22) @ A3)))))).
% 2.61/1.48 thf(fact_8_tree_Oset__intros_I1_J, axiom, (! [A:$tType,X:A,A1:(tree @ A),A22:A,A3:(tree @ A)]: (((((member @ A) @ X) @ ((set_tree @ A) @ A1)) => (((member @ A) @ X) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A22) @ A3))))))).
% 2.61/1.48 thf(fact_9_tree_Oset__cases, axiom, (! [A:$tType,E:A,A2:(tree @ A)]: (((((member @ A) @ E) @ ((set_tree @ A) @ A2)) => ((! [Z1:(tree @ A)]: (((? [Z2:A,Z3:(tree @ A)]: ((A2 = ((((node @ A) @ Z1) @ Z2) @ Z3)))) => (~ ((((member @ A) @ E) @ ((set_tree @ A) @ Z1))))))) => ((! [Z1:(tree @ A),Z3:(tree @ A)]: ((A2 != ((((node @ A) @ Z1) @ E) @ Z3)))) => (~ ((! [Z1:(tree @ A),Z2:A,Z3:(tree @ A)]: (((A2 = ((((node @ A) @ Z1) @ Z2) @ Z3)) => (~ ((((member @ A) @ E) @ ((set_tree @ A) @ Z3))))))))))))))).
% 2.61/1.48 thf(fact_10_tree_Osimps_I7_J, axiom, (! [C:$tType,A:$tType,F1:C,F2:((tree @ A) > (A > ((tree @ A) > (C > (C > C))))),X21:(tree @ A),X22:A,X23:(tree @ A)]: (((((((rec_tree @ C) @ A) @ F1) @ F2) @ ((((node @ A) @ X21) @ X22) @ X23)) = (((((F2 @ X21) @ X22) @ X23) @ (((((rec_tree @ C) @ A) @ F1) @ F2) @ X21)) @ (((((rec_tree @ C) @ A) @ F1) @ F2) @ X23)))))).
% 2.61/1.48 thf(fact_11_tree_Opred__inject_I2_J, axiom, (! [A:$tType,P:(A > $o),A2:(tree @ A),Aa:A,Ab:(tree @ A)]: (((((pred_tree @ A) @ P) @ ((((node @ A) @ A2) @ Aa) @ Ab)) = ((((pred_tree @ A) @ P) @ A2) & ((P @ Aa) & (((pred_tree @ A) @ P) @ Ab))))))).
% 2.61/1.48 thf(fact_12_A__simps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L2:(tree @ A),R2:(tree @ A)]: (((((splay_266122055elle_A @ A) @ A2) @ ((((node @ A) @ L2) @ A2) @ R2)) = (one_one @ real)))))))).
% 2.61/1.48 thf(fact_13_tree_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:((tree @ A) > (A > ((tree @ A) > B))),X21:(tree @ A),X22:A,X23:(tree @ A)]: (((((((case_tree @ B) @ A) @ F1) @ F2) @ ((((node @ A) @ X21) @ X22) @ X23)) = (((F2 @ X21) @ X22) @ X23))))).
% 2.61/1.48 thf(fact_14_tree_Opred__cong, axiom, (! [A:$tType,X:(tree @ A),Ya:(tree @ A),P:(A > $o),Pa:(A > $o)]: (((X = Ya) => ((! [Z:A]: (((((member @ A) @ Z) @ ((set_tree @ A) @ Ya)) => ((P @ Z) = (Pa @ Z))))) => ((((pred_tree @ A) @ P) @ X) = (((pred_tree @ A) @ Pa) @ Ya))))))).
% 2.61/1.48 thf(fact_15_tree_Opred__mono__strong, axiom, (! [A:$tType,P:(A > $o),X:(tree @ A),Pa:(A > $o)]: (((((pred_tree @ A) @ P) @ X) => ((! [Z:A]: (((((member @ A) @ Z) @ ((set_tree @ A) @ X)) => ((P @ Z) => (Pa @ Z))))) => (((pred_tree @ A) @ Pa) @ X)))))).
% 2.61/1.48 thf(fact_16_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.61/1.48 thf(fact_17_splay__to__root, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A,T2:(tree @ A)]: ((((linorder_bst @ A) @ T) => (((((splay_splay @ A) @ A2) @ T) = T2) => ((((member @ A) @ A2) @ ((set_tree @ A) @ T)) = (? [L3:(tree @ A),R3:(tree @ A)]: ((T2 = ((((node @ A) @ L3) @ A2) @ R3))))))))))))).
% 2.61/1.48 thf(fact_18_tree_Opred__set, axiom, (! [A:$tType]: (((pred_tree @ A) = (^ [P2:(A > $o),X2:(tree @ A)]: ((! [Y:A]: (((((member @ A) @ Y) @ ((set_tree @ A) @ X2)) => (P2 @ Y)))))))))).
% 2.61/1.48 thf(fact_19_tree_Osel_I3_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: ((((val @ A) @ ((((node @ A) @ X21) @ X22) @ X23)) = X22)))).
% 2.61/1.48 thf(fact_20_tree_Osel_I2_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: ((((left @ A) @ ((((node @ A) @ X21) @ X22) @ X23)) = X21)))).
% 2.61/1.48 thf(fact_21_tree_Osel_I5_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: ((((right @ A) @ ((((node @ A) @ X21) @ X22) @ X23)) = X23)))).
% 2.61/1.48 thf(fact_22_bst__eq__if__bst, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A)]: ((((linorder_bst @ A) @ T) => ((linorder_bst_eq @ A) @ T)))))))).
% 2.61/1.48 thf(fact_23_mirror_Osimps_I2_J, axiom, (! [A:$tType,L2:(tree @ A),X:A,R2:(tree @ A)]: ((((mirror @ A) @ ((((node @ A) @ L2) @ X) @ R2)) = ((((node @ A) @ ((mirror @ A) @ R2)) @ X) @ ((mirror @ A) @ L2)))))).
% 2.61/1.48 thf(fact_24_tree_Osimps_I6_J, axiom, (! [A:$tType,C:$tType,F1:C,F2:((tree @ A) > (A > ((tree @ A) > (C > (C > C)))))]: (((((((rec_tree @ C) @ A) @ F1) @ F2) @ (leaf @ A)) = F1)))).
% 2.61/1.48 thf(fact_25_powr__one__eq__one, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (! [A2:A]: (((((powr @ A) @ (one_one @ A)) @ A2) = (one_one @ A)))))))).
% 2.61/1.48 thf(fact_26_mirror__mirror, axiom, (! [A:$tType,T:(tree @ A)]: ((((mirror @ A) @ ((mirror @ A) @ T)) = T)))).
% 2.61/1.48 thf(fact_27_splay__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T:(tree @ A)]: ((((((splay_splay @ A) @ A2) @ T) = (leaf @ A)) = (T = (leaf @ A))))))))).
% 2.61/1.48 thf(fact_28_mirror__Leaf, axiom, (! [A:$tType,T:(tree @ A)]: (((((mirror @ A) @ T) = (leaf @ A)) = (T = (leaf @ A)))))).
% 2.61/1.48 thf(fact_29_tree_Osel_I4_J, axiom, (! [A:$tType]: ((((right @ A) @ (leaf @ A)) = (leaf @ A))))).
% 2.61/1.48 thf(fact_30_tree_Osel_I1_J, axiom, (! [A:$tType]: ((((left @ A) @ (leaf @ A)) = (leaf @ A))))).
% 2.61/1.48 thf(fact_31_mirror_Osimps_I1_J, axiom, (! [A:$tType]: ((((mirror @ A) @ (leaf @ A)) = (leaf @ A))))).
% 2.61/1.48 thf(fact_32_bst__eq_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_bst_eq @ A) @ (leaf @ A)))))).
% 2.61/1.48 thf(fact_33_tree_Oexhaust__sel, axiom, (! [A:$tType,Tree:(tree @ A)]: (((Tree != (leaf @ A)) => (Tree = ((((node @ A) @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree))))))).
% 2.61/1.48 thf(fact_34_splay__not__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A]: (((T != (leaf @ A)) => (? [L:(tree @ A),X3:A,R:(tree @ A)]: (((((splay_splay @ A) @ A2) @ T) = ((((node @ A) @ L) @ X3) @ R))))))))))).
% 2.61/1.48 thf(fact_35_splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_splay @ A) @ A2) @ (leaf @ A)) = (leaf @ A)))))))).
% 2.61/1.48 thf(fact_36_splay_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L2:(tree @ A),R2:(tree @ A)]: (((((splay_splay @ A) @ A2) @ ((((node @ A) @ L2) @ A2) @ R2)) = ((((node @ A) @ L2) @ A2) @ R2)))))))).
% 2.61/1.48 thf(fact_37_mirror_Oelims, axiom, (! [A:$tType,X:(tree @ A),Y2:(tree @ A)]: (((((mirror @ A) @ X) = Y2) => (((X = (leaf @ A)) => (Y2 != (leaf @ A))) => (~ ((! [L:(tree @ A),X3:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ X3) @ R)) => (Y2 != ((((node @ A) @ ((mirror @ A) @ R)) @ X3) @ ((mirror @ A) @ L))))))))))))).
% 2.61/1.48 thf(fact_38_tree_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:((tree @ A) > (A > ((tree @ A) > B))),Tree:(tree @ A)]: (((P @ (((((case_tree @ B) @ A) @ F1) @ F2) @ Tree)) = (~ ((((Tree = (leaf @ A)) & (~ ((P @ F1)))) | ((Tree = ((((node @ A) @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree))) & (~ ((P @ (((F2 @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree))))))))))))).
% 2.61/1.48 thf(fact_39_tree_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:((tree @ A) > (A > ((tree @ A) > B))),Tree:(tree @ A)]: (((P @ (((((case_tree @ B) @ A) @ F1) @ F2) @ Tree)) = (((Tree = (leaf @ A)) => (P @ F1)) & ((Tree = ((((node @ A) @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree))) => (P @ (((F2 @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree))))))))).
% 2.61/1.48 thf(fact_40_set__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T:(tree @ A)]: ((((set_tree @ A) @ (((splay_splay @ A) @ A2) @ T)) = ((set_tree @ A) @ T)))))))).
% 2.61/1.48 thf(fact_41_bst__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T) => ((linorder_bst @ A) @ (((splay_splay @ A) @ A2) @ T))))))))).
% 2.61/1.48 thf(fact_42_tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: (((leaf @ A) != ((((node @ A) @ X21) @ X22) @ X23))))).
% 2.61/1.48 thf(fact_43_tree_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),Tree:(tree @ A)]: (((P @ (leaf @ A)) => ((! [X1:(tree @ A),X24:A,X32:(tree @ A)]: (((P @ X1) => ((P @ X32) => (P @ ((((node @ A) @ X1) @ X24) @ X32)))))) => (P @ Tree)))))).
% 2.61/1.48 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.61/1.48 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 2.61/1.48 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.61/1.48 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.61/1.48 thf(fact_48_neq__Leaf__iff, axiom, (! [A:$tType,T:(tree @ A)]: (((T != (leaf @ A)) = (? [L3:(tree @ A),A5:A,R3:(tree @ A)]: ((T = ((((node @ A) @ L3) @ A5) @ R3)))))))).
% 2.61/1.48 thf(fact_49_tree_Oexhaust, axiom, (! [A:$tType,Y2:(tree @ A)]: (((Y2 != (leaf @ A)) => (~ ((! [X212:(tree @ A),X222:A,X232:(tree @ A)]: ((Y2 != ((((node @ A) @ X212) @ X222) @ X232)))))))))).
% 2.61/1.48 thf(fact_50_mirror_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L:(tree @ A),X3:A,R:(tree @ A)]: (((P @ R) => ((P @ L) => (P @ ((((node @ A) @ L) @ X3) @ R)))))) => (P @ A0)))))).
% 2.61/1.48 thf(fact_51_bst__eq_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: ((X != ((((node @ A) @ L) @ A6) @ R))))))))))))).
% 2.61/1.48 thf(fact_52_bst__eq_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((P @ L) => ((P @ R) => (P @ ((((node @ A) @ L) @ A6) @ R)))))) => (P @ A0))))))))).
% 2.61/1.48 thf(fact_53_bst_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_bst @ A) @ (leaf @ A)))))).
% 2.61/1.48 thf(fact_54_tree_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:((tree @ A) > (A > ((tree @ A) > B)))]: (((((((case_tree @ B) @ A) @ F1) @ F2) @ (leaf @ A)) = F1)))).
% 2.61/1.48 thf(fact_55_tree_Opred__inject_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((((pred_tree @ A) @ P) @ (leaf @ A))))).
% 2.61/1.48 thf(fact_56_is__root__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T) => ((((splay_is_root @ A) @ A2) @ (((splay_splay @ A) @ A2) @ T)) = (((member @ A) @ A2) @ ((set_tree @ A) @ T)))))))))).
% 2.61/1.48 thf(fact_57_tree_Ocollapse_I2_J, axiom, (! [A:$tType,Tree:(tree @ A)]: (((~ (((is_Leaf @ A) @ Tree))) => (((((node @ A) @ ((left @ A) @ Tree)) @ ((val @ A) @ Tree)) @ ((right @ A) @ Tree)) = Tree))))).
% 2.61/1.48 thf(fact_58__092_060Phi_062_Ocases, axiom, (! [A:$tType,X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: ((X != ((((node @ A) @ L) @ A6) @ R)))))))))).
% 2.61/1.48 thf(fact_59__092_060Phi_062_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((P @ L) => ((P @ R) => (P @ ((((node @ A) @ L) @ A6) @ R)))))) => (P @ A0)))))).
% 2.61/1.48 thf(fact_60_t__splay__max_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => ((! [L:(tree @ A),B2:A]: ((X != ((((node @ A) @ L) @ B2) @ (leaf @ A))))) => (~ ((! [L:(tree @ A),B2:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((X != ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl) @ C2) @ Rr))))))))))))))).
% 2.61/1.48 thf(fact_61_t__splay__max_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L:(tree @ A),B2:A]: ((P @ ((((node @ A) @ L) @ B2) @ (leaf @ A))))) => ((! [L:(tree @ A),B2:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((((Rr != (leaf @ A)) => (P @ Rr)) => (P @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl) @ C2) @ Rr)))))) => (P @ A0)))))))))).
% 2.61/1.48 thf(fact_62_tree_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_tree @ B) @ A) = (^ [F12:B,F22:((tree @ A) > (A > ((tree @ A) > B))),Tree2:(tree @ A)]: (((((if @ B) @ ((is_Leaf @ A) @ Tree2)) @ F12) @ (((F22 @ ((left @ A) @ Tree2)) @ ((val @ A) @ Tree2)) @ ((right @ A) @ Tree2))))))))).
% 2.61/1.48 thf(fact_63_bst__eq_Oelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst_eq @ A) @ X) => ((X != (leaf @ A)) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (~ ((((linorder_bst_eq @ A) @ L) & (((linorder_bst_eq @ A) @ R) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L)) => (((ord_less_eq @ A) @ X4) @ A6)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R)) => (((ord_less_eq @ A) @ A6) @ X4)))))))))))))))))))))).
% 2.61/1.48 thf(fact_64_bst__eq_Oelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y2:$o]: (((((linorder_bst_eq @ A) @ X) = Y2) => (((X = (leaf @ A)) => (~ (Y2))) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (Y2 = (~ ((((linorder_bst_eq @ A) @ L) & (((linorder_bst_eq @ A) @ R) & ((! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ L)) => (((ord_less_eq @ A) @ X2) @ A6)))) & (! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ R)) => (((ord_less_eq @ A) @ A6) @ X2))))))))))))))))))))))).
% 2.61/1.48 thf(fact_65_powr__mono, axiom, (! [A2:real,B3:real,X:real]: (((((ord_less_eq @ real) @ A2) @ B3) => ((((ord_less_eq @ real) @ (one_one @ real)) @ X) => (((ord_less_eq @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B3))))))).
% 2.61/1.48 thf(fact_66_tree_OdiscI_I2_J, axiom, (! [A:$tType,Tree:(tree @ A),X21:(tree @ A),X22:A,X23:(tree @ A)]: (((Tree = ((((node @ A) @ X21) @ X22) @ X23)) => (~ (((is_Leaf @ A) @ Tree))))))).
% 2.61/1.48 thf(fact_67_tree_Odisc_I2_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: ((~ (((is_Leaf @ A) @ ((((node @ A) @ X21) @ X22) @ X23))))))).
% 2.61/1.48 thf(fact_68_is__Leaf__def, axiom, (! [A:$tType]: (((is_Leaf @ A) = (^ [Tree2:(tree @ A)]: ((Tree2 = (leaf @ A)))))))).
% 2.61/1.48 thf(fact_69_tree_Ocollapse_I1_J, axiom, (! [A:$tType,Tree:(tree @ A)]: ((((is_Leaf @ A) @ Tree) => (Tree = (leaf @ A)))))).
% 2.61/1.48 thf(fact_70_tree_OdiscI_I1_J, axiom, (! [A:$tType,Tree:(tree @ A)]: (((Tree = (leaf @ A)) => ((is_Leaf @ A) @ Tree))))).
% 2.61/1.48 thf(fact_71_tree_Odisc_I1_J, axiom, (! [A:$tType]: (((is_Leaf @ A) @ (leaf @ A))))).
% 2.61/1.48 thf(fact_72_tree_Oset__sel_I3_J, axiom, (! [A:$tType,A2:(tree @ A),Xa:A]: (((~ (((is_Leaf @ A) @ A2))) => ((((member @ A) @ Xa) @ ((set_tree @ A) @ ((right @ A) @ A2))) => (((member @ A) @ Xa) @ ((set_tree @ A) @ A2))))))).
% 2.61/1.48 thf(fact_73_tree_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(tree @ A),X:A]: (((~ (((is_Leaf @ A) @ A2))) => ((((member @ A) @ X) @ ((set_tree @ A) @ ((left @ A) @ A2))) => (((member @ A) @ X) @ ((set_tree @ A) @ A2))))))).
% 2.61/1.48 thf(fact_74_tree_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(tree @ A)]: (((~ (((is_Leaf @ A) @ A2))) => (((member @ A) @ ((val @ A) @ A2)) @ ((set_tree @ A) @ A2)))))).
% 2.61/1.48 thf(fact_75_bst__eq_Oelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst_eq @ A) @ X))) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (((linorder_bst_eq @ A) @ L) & (((linorder_bst_eq @ A) @ R) & ((! [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ L)) => (((ord_less_eq @ A) @ X3) @ A6)))) & (! [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ R)) => (((ord_less_eq @ A) @ A6) @ X3))))))))))))))))))).
% 2.61/1.48 thf(fact_76_bst__eq_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(tree @ A),A2:A,R2:(tree @ A)]: ((((linorder_bst_eq @ A) @ ((((node @ A) @ L2) @ A2) @ R2)) = (((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R2) & ((! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X2) @ A2)))) & (! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ R2)) => (((ord_less_eq @ A) @ A2) @ X2)))))))))))))).
% 2.61/1.48 thf(fact_77_tree_Oexpand, axiom, (! [A:$tType,Tree:(tree @ A),Tree3:(tree @ A)]: (((((is_Leaf @ A) @ Tree) = ((is_Leaf @ A) @ Tree3)) => (((~ (((is_Leaf @ A) @ Tree))) => ((~ (((is_Leaf @ A) @ Tree3))) => ((((left @ A) @ Tree) = ((left @ A) @ Tree3)) & ((((val @ A) @ Tree) = ((val @ A) @ Tree3)) & (((right @ A) @ Tree) = ((right @ A) @ Tree3)))))) => (Tree = Tree3)))))).
% 2.61/1.48 thf(fact_78_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.61/1.48 thf(fact_79_le__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.61/1.48 thf(fact_80_splay__max__eq__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T) => ((! [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ T)) => (((ord_less_eq @ A) @ X3) @ A2)))) => (((splay_splay_max @ A) @ T) = (((splay_splay @ A) @ A2) @ T)))))))))).
% 2.61/1.48 thf(fact_81_ex__in__set__tree, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A]: (((T != (leaf @ A)) => (((linorder_bst @ A) @ T) => (? [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ T)) & (((((splay_splay @ A) @ X3) @ T) = (((splay_splay @ A) @ A2) @ T)) & ((((splay_914434265_splay @ A) @ X3) @ T) = (((splay_914434265_splay @ A) @ A2) @ T)))))))))))))).
% 2.61/1.48 thf(fact_82_bst_Oelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst @ A) @ X) => ((X != (leaf @ A)) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (~ ((((linorder_bst @ A) @ L) & (((linorder_bst @ A) @ R) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L)) => (((ord_less @ A) @ X4) @ A6)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R)) => (((ord_less @ A) @ A6) @ X4)))))))))))))))))))))).
% 2.61/1.48 thf(fact_83_bst_Oelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y2:$o]: (((((linorder_bst @ A) @ X) = Y2) => (((X = (leaf @ A)) => (~ (Y2))) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (Y2 = (~ ((((linorder_bst @ A) @ L) & (((linorder_bst @ A) @ R) & ((! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ L)) => (((ord_less @ A) @ X2) @ A6)))) & (! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ R)) => (((ord_less @ A) @ A6) @ X2))))))))))))))))))))))).
% 2.61/1.48 thf(fact_84_tree_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((rel_tree @ A) @ B) = (^ [R4:(A > (B > $o)),A5:(tree @ A),B4:(tree @ B)]: (((((is_Leaf @ A) @ A5) = ((is_Leaf @ B) @ B4)) & ((~ (((is_Leaf @ A) @ A5))) => ((~ (((is_Leaf @ B) @ B4))) => ((((((rel_tree @ A) @ B) @ R4) @ ((left @ A) @ A5)) @ ((left @ B) @ B4)) & (((R4 @ ((val @ A) @ A5)) @ ((val @ B) @ B4)) & (((((rel_tree @ A) @ B) @ R4) @ ((right @ A) @ A5)) @ ((right @ B) @ B4))))))))))))).
% 2.61/1.48 thf(fact_85_powr__less__cancel__iff, axiom, (! [X:real,A2:real,B3:real]: (((((ord_less @ real) @ (one_one @ real)) @ X) => ((((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B3)) = (((ord_less @ real) @ A2) @ B3)))))).
% 2.61/1.48 thf(fact_86_t__splay__simps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L2:(tree @ A),R2:(tree @ A)]: (((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ A2) @ R2)) = (one_one @ nat)))))))).
% 2.61/1.48 thf(fact_87_splay__max__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A)]: (((((splay_splay_max @ A) @ T) = (leaf @ A)) = (T = (leaf @ A))))))))).
% 2.61/1.48 thf(fact_88_powr__le__cancel__iff, axiom, (! [X:real,A2:real,B3:real]: (((((ord_less @ real) @ (one_one @ real)) @ X) => ((((ord_less_eq @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B3)) = (((ord_less_eq @ real) @ A2) @ B3)))))).
% 2.61/1.48 thf(fact_89_t__splay__simps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B3:A,A2:A,L2:(tree @ A),Rl2:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B3) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ ((((node @ A) @ Rl2) @ A2) @ Rr2))) = (one_one @ nat))))))))).
% 2.61/1.48 thf(fact_90_t__splay__simps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ A2) @ Lr)) @ B3) @ R2)) = (one_one @ nat))))))))).
% 2.61/1.48 thf(fact_91_t__splay__simps_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B3:A,A2:A,L2:(tree @ A)]: (((((ord_less @ A) @ B3) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ (leaf @ A))) = (one_one @ nat))))))))).
% 2.61/1.48 thf(fact_92_t__splay__simps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B3) @ R2)) = (one_one @ nat))))))))).
% 2.61/1.48 thf(fact_93_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y2:A,X:A]: (((((ord_less_eq @ A) @ Y2) @ X) => (~ ((((ord_less @ A) @ X) @ Y2)))))))))).
% 2.61/1.48 thf(fact_94_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less @ A) @ X) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_95_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) | (X2 = Y))))))))).
% 2.61/1.48 thf(fact_96_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) & (X2 != Y))))))))).
% 2.61/1.48 thf(fact_97_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_98_order__le__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_99_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((((ord_less @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_100_order__less__le__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_101_not__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y2))) = (((ord_less @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_102_not__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less @ A) @ X) @ Y2))) = (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_103_le__neq__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((A2 != B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 2.61/1.48 thf(fact_104_less__imp__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (((ord_less_eq @ A) @ X) @ Y2)))))))).
% 2.61/1.48 thf(fact_105_antisym__conv1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less @ A) @ X) @ Y2))) => ((((ord_less_eq @ A) @ X) @ Y2) = (X = Y2))))))))).
% 2.61/1.48 thf(fact_106_antisym__conv2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((~ ((((ord_less @ A) @ X) @ Y2))) = (X = Y2))))))))).
% 2.61/1.48 thf(fact_107_le__less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less @ A) @ Y2) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 2.61/1.48 thf(fact_108_less__le__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: (((((ord_less @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 2.61/1.48 thf(fact_109_dense__ge, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z4:A,Y2:A]: (((! [X3:A]: (((((ord_less @ A) @ Z4) @ X3) => (((ord_less_eq @ A) @ Y2) @ X3)))) => (((ord_less_eq @ A) @ Y2) @ Z4)))))))).
% 2.61/1.48 thf(fact_110_dense__le, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Y2:A,Z4:A]: (((! [X3:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less_eq @ A) @ X3) @ Z4)))) => (((ord_less_eq @ A) @ Y2) @ Z4)))))))).
% 2.61/1.48 thf(fact_111_le__less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) | (((ord_less @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_112_le__imp__less__or__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less @ A) @ X) @ Y2) | (X = Y2))))))))).
% 2.61/1.48 thf(fact_113_less__le__not__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) & (~ ((((ord_less_eq @ A) @ Y) @ X2))))))))))).
% 2.61/1.48 thf(fact_114_not__le__imp__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y2:A,X:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X))) => (((ord_less @ A) @ X) @ Y2)))))))).
% 2.61/1.48 thf(fact_115_order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_116_order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_117_order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: (((((ord_less @ A) @ A5) @ B4) | (A5 = B4))))))))).
% 2.61/1.48 thf(fact_118_order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (A5 != B4))))))))).
% 2.61/1.48 thf(fact_119_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less @ A) @ C3) @ B3) => (((ord_less @ A) @ C3) @ A2))))))))).
% 2.61/1.48 thf(fact_120_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less @ A) @ C3) @ A2))))))))).
% 2.61/1.48 thf(fact_121_dense__ge__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z4:A,X:A,Y2:A]: (((((ord_less @ A) @ Z4) @ X) => ((! [W:A]: (((((ord_less @ A) @ Z4) @ W) => ((((ord_less @ A) @ W) @ X) => (((ord_less_eq @ A) @ Y2) @ W))))) => (((ord_less_eq @ A) @ Y2) @ Z4))))))))).
% 2.61/1.48 thf(fact_122_dense__le__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: (((((ord_less @ A) @ X) @ Y2) => ((! [W:A]: (((((ord_less @ A) @ X) @ W) => ((((ord_less @ A) @ W) @ Y2) => (((ord_less_eq @ A) @ W) @ Z4))))) => (((ord_less_eq @ A) @ Y2) @ Z4))))))))).
% 2.61/1.48 thf(fact_123_order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_124_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B4:A,A5:A]: (((((ord_less @ A) @ B4) @ A5) | (A5 = B4))))))))).
% 2.61/1.48 thf(fact_125_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B4:A,A5:A]: (((((ord_less_eq @ A) @ B4) @ A5) & (A5 != B4))))))))).
% 2.61/1.48 thf(fact_126_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (((ord_less_eq @ A) @ B3) @ A2)))))))).
% 2.61/1.48 thf(fact_127_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((A2 != B3) => ((((ord_less_eq @ A) @ A2) @ B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 2.61/1.48 thf(fact_128_tree_Orel__mono, axiom, (! [B:$tType,A:$tType,R5:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R5) @ Ra) => (((ord_less_eq @ ((tree @ A) > ((tree @ B) > $o))) @ (((rel_tree @ A) @ B) @ R5)) @ (((rel_tree @ A) @ B) @ Ra)))))).
% 2.61/1.48 thf(fact_129_less__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.61/1.48 thf(fact_130_tree_Orel__eq, axiom, (! [A:$tType]: (((((rel_tree @ A) @ A) @ (^ [Y4:A,Z5:A]: ((Y4 = Z5)))) = (^ [Y4:(tree @ A),Z5:(tree @ A)]: ((Y4 = Z5))))))).
% 2.61/1.48 thf(fact_131_tree_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(tree @ B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => (((((rel_tree @ B) @ B) @ Ra) @ X) @ X))))).
% 2.61/1.48 thf(fact_132_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (A2 != B3)))))))).
% 2.61/1.48 thf(fact_133_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (A2 != B3)))))))).
% 2.61/1.48 thf(fact_134_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less @ A) @ X) @ Y2))) = ((((ord_less @ A) @ Y2) @ X) | (X = Y2))))))))).
% 2.61/1.48 thf(fact_135_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ C3) @ B3) => (((ord_less @ A) @ C3) @ A2))))))))).
% 2.61/1.48 thf(fact_136_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X)))))))))).
% 2.61/1.48 thf(fact_137_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_138_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 2.61/1.48 thf(fact_139_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less @ A) @ X) @ Y2))) => ((X != Y2) => (((ord_less @ A) @ Y2) @ X))))))))).
% 2.61/1.48 thf(fact_140_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,P:$o]: (((((ord_less @ A) @ X) @ Y2) => ((((ord_less @ A) @ Y2) @ X) => P)))))))).
% 2.61/1.48 thf(fact_141_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (Y2 != X)))))))).
% 2.61/1.48 thf(fact_142_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y2:A,X:A]: (((~ ((((ord_less @ A) @ Y2) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y2))) = (X = Y2))))))))).
% 2.61/1.48 thf(fact_143_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X3) => (P @ Y5)))) => (P @ X3)))) => (P @ A2)))))))).
% 2.61/1.48 thf(fact_144_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X)))))))))).
% 2.61/1.48 thf(fact_145_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (X != Y2)))))))).
% 2.61/1.48 thf(fact_146_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (~ ((((ord_less @ A) @ A2) @ B3)))))))))).
% 2.61/1.48 thf(fact_147_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less @ A) @ A2) @ B3) => ((B3 = C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_148_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((A2 = B3) => ((((ord_less @ A) @ B3) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_149_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.61/1.48 thf(fact_150_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) | ((X = Y2) | (((ord_less @ A) @ Y2) @ X))))))))).
% 2.61/1.48 thf(fact_151_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: (((((ord_less @ A) @ X) @ Y2) => ((((ord_less @ A) @ Y2) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 2.61/1.48 thf(fact_152_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 2.61/1.48 thf(fact_153_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X)))))))))).
% 2.61/1.48 thf(fact_154_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (X != Y2)))))))).
% 2.61/1.48 thf(fact_155_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less @ A) @ X) @ Y2) => (? [Z:A]: (((((ord_less @ A) @ X) @ Z) & (((ord_less @ A) @ Z) @ Y2))))))))))).
% 2.61/1.48 thf(fact_156_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 2.61/1.48 thf(fact_157_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((X != Y2) = ((((ord_less @ A) @ X) @ Y2) | (((ord_less @ A) @ Y2) @ X))))))))).
% 2.61/1.48 thf(fact_158_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((X != Y2) => ((~ ((((ord_less @ A) @ X) @ Y2))) => (((ord_less @ A) @ Y2) @ X))))))))).
% 2.61/1.48 thf(fact_159_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X1:A]: ((((ord_less @ A) @ X) @ X1))))))))).
% 2.61/1.48 thf(fact_160_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X))))))))).
% 2.61/1.48 thf(fact_161_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_162_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((((ord_less @ A) @ A2) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_163_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > B),C3:B]: (((((ord_less @ A) @ A2) @ B3) => (((F @ B3) = C3) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ B) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_164_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((A2 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_165_powr__powr__swap, axiom, (! [X:real,A2:real,B3:real]: (((((powr @ real) @ (((powr @ real) @ X) @ A2)) @ B3) = (((powr @ real) @ (((powr @ real) @ X) @ B3)) @ A2))))).
% 2.61/1.48 thf(fact_166_tree_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),X21:(tree @ A),X22:A,X23:(tree @ A),Y21:(tree @ B),Y22:B,Y23:(tree @ B)]: (((((((rel_tree @ A) @ B) @ R5) @ ((((node @ A) @ X21) @ X22) @ X23)) @ ((((node @ B) @ Y21) @ Y22) @ Y23)) = ((((((rel_tree @ A) @ B) @ R5) @ X21) @ Y21) & (((R5 @ X22) @ Y22) & (((((rel_tree @ A) @ B) @ R5) @ X23) @ Y23))))))).
% 2.61/1.48 thf(fact_167_tree_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),X21:(tree @ A),Y21:(tree @ B),X22:A,Y22:B,X23:(tree @ A),Y23:(tree @ B)]: (((((((rel_tree @ A) @ B) @ R5) @ X21) @ Y21) => (((R5 @ X22) @ Y22) => ((((((rel_tree @ A) @ B) @ R5) @ X23) @ Y23) => (((((rel_tree @ A) @ B) @ R5) @ ((((node @ A) @ X21) @ X22) @ X23)) @ ((((node @ B) @ Y21) @ Y22) @ Y23)))))))).
% 2.61/1.48 thf(fact_168_tree_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o))]: ((((((rel_tree @ A) @ B) @ R5) @ (leaf @ A)) @ (leaf @ B))))).
% 2.61/1.48 thf(fact_169_tree_Orel__refl__strong, axiom, (! [A:$tType,X:(tree @ A),Ra:(A > (A > $o))]: (((! [Z:A]: (((((member @ A) @ Z) @ ((set_tree @ A) @ X)) => ((Ra @ Z) @ Z)))) => (((((rel_tree @ A) @ A) @ Ra) @ X) @ X))))).
% 2.61/1.48 thf(fact_170_tree_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),X:(tree @ A),Y2:(tree @ B),Ra:(A > (B > $o))]: (((((((rel_tree @ A) @ B) @ R5) @ X) @ Y2) => ((! [Z:A,Yb:B]: (((((member @ A) @ Z) @ ((set_tree @ A) @ X)) => ((((member @ B) @ Yb) @ ((set_tree @ B) @ Y2)) => (((R5 @ Z) @ Yb) => ((Ra @ Z) @ Yb)))))) => (((((rel_tree @ A) @ B) @ Ra) @ X) @ Y2)))))).
% 2.61/1.48 thf(fact_171_tree_Orel__cong, axiom, (! [A:$tType,B:$tType,X:(tree @ A),Ya:(tree @ A),Y2:(tree @ B),Xa:(tree @ B),R5:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya) => ((Y2 = Xa) => ((! [Z:A,Yb:B]: (((((member @ A) @ Z) @ ((set_tree @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((set_tree @ B) @ Xa)) => (((R5 @ Z) @ Yb) = ((Ra @ Z) @ Yb)))))) => ((((((rel_tree @ A) @ B) @ R5) @ X) @ Y2) = (((((rel_tree @ A) @ B) @ Ra) @ Ya) @ Xa)))))))).
% 2.61/1.48 thf(fact_172_powr__less__mono, axiom, (! [A2:real,B3:real,X:real]: (((((ord_less @ real) @ A2) @ B3) => ((((ord_less @ real) @ (one_one @ real)) @ X) => (((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B3))))))).
% 2.61/1.48 thf(fact_173_powr__less__cancel, axiom, (! [X:real,A2:real,B3:real]: (((((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B3)) => ((((ord_less @ real) @ (one_one @ real)) @ X) => (((ord_less @ real) @ A2) @ B3)))))).
% 2.61/1.48 thf(fact_174_t__splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_914434265_splay @ A) @ A2) @ (leaf @ A)) = (one_one @ nat)))))))).
% 2.61/1.48 thf(fact_175_splay__max_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((splay_splay_max @ A) @ (leaf @ A)) = (leaf @ A)))))).
% 2.61/1.48 thf(fact_176_set__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A)]: ((((set_tree @ A) @ ((splay_splay_max @ A) @ T)) = ((set_tree @ A) @ T)))))))).
% 2.61/1.48 thf(fact_177_bst__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A)]: ((((linorder_bst @ A) @ T) => ((linorder_bst @ A) @ ((splay_splay_max @ A) @ T))))))))).
% 2.61/1.48 thf(fact_178_tree_Orel__induct, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),X:(tree @ A),Y2:(tree @ B),Q:((tree @ A) > ((tree @ B) > $o))]: (((((((rel_tree @ A) @ B) @ R5) @ X) @ Y2) => (((Q @ (leaf @ A)) @ (leaf @ B)) => ((! [A21:(tree @ A),A222:A,A23:(tree @ A),B21:(tree @ B),B22:B,B23:(tree @ B)]: ((((Q @ A21) @ B21) => (((R5 @ A222) @ B22) => (((Q @ A23) @ B23) => ((Q @ ((((node @ A) @ A21) @ A222) @ A23)) @ ((((node @ B) @ B21) @ B22) @ B23))))))) => ((Q @ X) @ Y2))))))).
% 2.61/1.48 thf(fact_179_tree_Orel__cases, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),A2:(tree @ A),B3:(tree @ B)]: (((((((rel_tree @ A) @ B) @ R5) @ A2) @ B3) => (((A2 = (leaf @ A)) => (B3 != (leaf @ B))) => (~ ((! [X1:(tree @ A),X24:A,X32:(tree @ A)]: (((A2 = ((((node @ A) @ X1) @ X24) @ X32)) => (! [Y1:(tree @ B),Y24:B,Y32:(tree @ B)]: (((B3 = ((((node @ B) @ Y1) @ Y24) @ Y32)) => ((((((rel_tree @ A) @ B) @ R5) @ X1) @ Y1) => (((R5 @ X24) @ Y24) => (~ ((((((rel_tree @ A) @ B) @ R5) @ X32) @ Y32)))))))))))))))))).
% 2.61/1.48 thf(fact_180_tree_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),Y21:(tree @ B),Y22:B,Y23:(tree @ B)]: ((~ ((((((rel_tree @ A) @ B) @ R5) @ (leaf @ A)) @ ((((node @ B) @ Y21) @ Y22) @ Y23))))))).
% 2.61/1.48 thf(fact_181_tree_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R5:(A > (B > $o)),Y21:(tree @ A),Y22:A,Y23:(tree @ A)]: ((~ ((((((rel_tree @ A) @ B) @ R5) @ ((((node @ A) @ Y21) @ Y22) @ Y23)) @ (leaf @ B))))))).
% 2.61/1.48 thf(fact_182_splay_Osimps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B3:A,A2:A,Lb:(tree @ A),La:(tree @ A),Ra2:(tree @ A)]: (((((ord_less @ A) @ B3) @ A2) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ Lb) @ B3) @ ((((node @ A) @ La) @ A2) @ Ra2))) = ((((node @ A) @ ((((node @ A) @ Lb) @ B3) @ La)) @ A2) @ Ra2))))))))).
% 2.61/1.48 thf(fact_183_splay_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,La:(tree @ A),Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Ra2)) @ B3) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Ra2) @ B3) @ Rb)))))))))).
% 2.61/1.48 thf(fact_184_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 2.61/1.48 thf(fact_185_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.61/1.48 thf(fact_186_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A6:A,B2:A]: (((((ord_less_eq @ A) @ A6) @ B2) => ((P @ A6) @ B2)))) => ((! [A6:A,B2:A]: ((((P @ B2) @ A6) => ((P @ A6) @ B2)))) => ((P @ A2) @ B3))))))))).
% 2.61/1.48 thf(fact_187_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.61/1.48 thf(fact_188_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z4) => (((ord_less_eq @ A) @ X) @ Z4))))))))).
% 2.61/1.48 thf(fact_189_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ A2) => (A2 = B3))))))))).
% 2.61/1.48 thf(fact_190_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((B3 = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_191_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((A2 = B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_192_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y2:A,X:A]: (((((ord_less_eq @ A) @ Y2) @ X) => ((((ord_less_eq @ A) @ X) @ Y2) = (X = Y2))))))))).
% 2.61/1.48 thf(fact_193_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A,Z4:A]: ((((((ord_less_eq @ A) @ X) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z4)))) => (((((ord_less_eq @ A) @ Y2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z4)))) => (((((ord_less_eq @ A) @ X) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ Y2)))) => (((((ord_less_eq @ A) @ Z4) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X)))) => (((((ord_less_eq @ A) @ Y2) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ X)))) => (~ (((((ord_less_eq @ A) @ Z4) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y2))))))))))))))))).
% 2.61/1.48 thf(fact_194_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.61/1.48 thf(fact_195_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_196_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((X = Y2) => (((ord_less_eq @ A) @ X) @ Y2)))))))).
% 2.61/1.48 thf(fact_197_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 2.61/1.48 thf(fact_198_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X) => (X = Y2))))))))).
% 2.61/1.48 thf(fact_199_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y4:A,Z5:A]: ((Y4 = Z5))) = (^ [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) & (((ord_less_eq @ A) @ Y) @ X2))))))))).
% 2.61/1.48 thf(fact_200_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > B),C3:B]: (((((ord_less_eq @ A) @ A2) @ B3) => (((F @ B3) = C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_201_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((A2 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_202_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C3)))))))))).
% 2.61/1.48 thf(fact_203_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C3))))))))))).
% 2.61/1.48 thf(fact_204_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F3 @ X2)) @ (G2 @ X2))))))))))).
% 2.61/1.48 thf(fact_205_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.61/1.48 thf(fact_206_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.61/1.48 thf(fact_207_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.61/1.48 thf(fact_208_splay__max_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [La:(tree @ A),A2:A]: ((((splay_splay_max @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) = ((((node @ A) @ La) @ A2) @ (leaf @ A))))))))).
% 2.61/1.48 thf(fact_209_splay__max__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),L2:(tree @ A),A2:A,R2:(tree @ A)]: (((((splay_splay_max @ A) @ T) = ((((node @ A) @ L2) @ A2) @ R2)) => (R2 = (leaf @ A))))))))).
% 2.61/1.48 thf(fact_210_splay_Osimps_I13_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B3:A,La:(tree @ A),Lb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ B3) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Lb) @ B3) @ (leaf @ A)))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Lb)) @ B3) @ (leaf @ A))))))))))).
% 2.61/1.48 thf(fact_211_splay_Osimps_I12_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B3:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ X) @ B3) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B3) @ Rb))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B3) @ Rb)))))))))).
% 2.61/1.48 thf(fact_212_splay_Osimps_I10_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,L2:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ L2) @ A2) @ (leaf @ A))) = ((((node @ A) @ L2) @ A2) @ (leaf @ A)))))))))).
% 2.61/1.48 thf(fact_213_splay_Osimps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,B3:A,A2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ B3) => ((((ord_less @ A) @ A2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B3) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B3) @ Rb))))))))))).
% 2.61/1.48 thf(fact_214_splay_Osimps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,A2:A,B3:A,Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ A2) => ((((ord_less @ A) @ X) @ B3) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ (leaf @ A)) @ A2) @ Ra2)) @ B3) @ Rb)) = ((((node @ A) @ (leaf @ A)) @ A2) @ ((((node @ A) @ Ra2) @ B3) @ Rb))))))))))).
% 2.61/1.48 thf(fact_215_splay_Osimps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B3) @ R2)) = ((((node @ A) @ (leaf @ A)) @ B3) @ R2))))))))).
% 2.61/1.48 thf(fact_216_splay__max__eq__splay__ex, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A)]: ((((linorder_bst @ A) @ T) => (? [A6:A]: ((((splay_splay_max @ A) @ T) = (((splay_splay @ A) @ A6) @ T))))))))))).
% 2.61/1.48 thf(fact_217_bst_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(tree @ A),A2:A,R2:(tree @ A)]: ((((linorder_bst @ A) @ ((((node @ A) @ L2) @ A2) @ R2)) = (((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R2) & ((! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X2) @ A2)))) & (! [X2:A]: (((((member @ A) @ X2) @ ((set_tree @ A) @ R2)) => (((ord_less @ A) @ A2) @ X2)))))))))))))).
% 2.61/1.48 thf(fact_218_bst_Oelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst @ A) @ X))) => (~ ((! [L:(tree @ A),A6:A,R:(tree @ A)]: (((X = ((((node @ A) @ L) @ A6) @ R)) => (((linorder_bst @ A) @ L) & (((linorder_bst @ A) @ R) & ((! [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ L)) => (((ord_less @ A) @ X3) @ A6)))) & (! [X3:A]: (((((member @ A) @ X3) @ ((set_tree @ A) @ R)) => (((ord_less @ A) @ A6) @ X3))))))))))))))))))).
% 2.61/1.48 thf(fact_219_splay__bstR, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A,L2:(tree @ A),E:A,R2:(tree @ A),X:A]: ((((linorder_bst @ A) @ T) => (((((splay_splay @ A) @ A2) @ T) = ((((node @ A) @ L2) @ E) @ R2)) => ((((member @ A) @ X) @ ((set_tree @ A) @ R2)) => (((ord_less @ A) @ A2) @ X)))))))))).
% 2.61/1.48 thf(fact_220_splay__bstL, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:(tree @ A),A2:A,L2:(tree @ A),E:A,R2:(tree @ A),X:A]: ((((linorder_bst @ A) @ T) => (((((splay_splay @ A) @ A2) @ T) = ((((node @ A) @ L2) @ E) @ R2)) => ((((member @ A) @ X) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X) @ A2)))))))))).
% 2.61/1.48 thf(fact_221_minf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => (~ ((((ord_less_eq @ A) @ T) @ X4)))))))))))))).
% 2.61/1.48 thf(fact_222_minf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ X4) @ Z) => (((ord_less_eq @ A) @ X4) @ T)))))))))))).
% 2.61/1.48 thf(fact_223_pinf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => (((ord_less_eq @ A) @ T) @ X4)))))))))))).
% 2.61/1.48 thf(fact_224_pinf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X4:A]: (((((ord_less @ A) @ Z) @ X4) => (~ ((((ord_less_eq @ A) @ X4) @ T)))))))))))))).
% 2.61/1.48 thf(fact_225_complete__interval, axiom, (! [A:$tType]: ((((condit1037483654norder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B3) => ((P @ A2) => ((~ ((P @ B3))) => (? [C2:A]: (((((ord_less_eq @ A) @ A2) @ C2) & ((((ord_less_eq @ A) @ C2) @ B3) & ((! [X4:A]: ((((((ord_less_eq @ A) @ A2) @ X4) & (((ord_less @ A) @ X4) @ C2)) => (P @ X4)))) & (! [D:A]: (((! [X3:A]: ((((((ord_less_eq @ A) @ A2) @ X3) & (((ord_less @ A) @ X3) @ D)) => (P @ X3)))) => (((ord_less_eq @ A) @ D) @ C2)))))))))))))))))).
% 2.61/1.48 thf(fact_226_t__splay__simps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A,Rr2:(tree @ A),L2:(tree @ A),Rl2:(tree @ A)]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ C3) @ A2) => (((Rr2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (one_one @ nat))) & ((Rr2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rr2)) @ (one_one @ nat))))))))))))).
% 2.61/1.48 thf(fact_227_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B3) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B3 = C3)))))))).
% 2.61/1.48 thf(fact_228_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ A2) @ C3)) = (B3 = C3)))))))).
% 2.61/1.48 thf(fact_229_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X3:A,Y3:B]: ((((P @ X3) @ Y3) => ((Q @ X3) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.61/1.48 thf(fact_230_add__le__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B3) @ C3)) = (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_231_add__le__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B3)) = (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_232_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B3) @ C3)) = (((ord_less @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_233_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B3)) = (((ord_less @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_234_t__splay__simps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ A2) @ C3) => (((Ll = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B3) @ R2)) = (one_one @ nat))) & ((Ll != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B3) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Ll)) @ (one_one @ nat))))))))))))).
% 2.61/1.48 thf(fact_235_t__splay__simps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A,Lr:(tree @ A),Ll:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ C3) @ A2) => (((Lr = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B3) @ R2)) = (one_one @ nat))) & ((Lr != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B3) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Lr)) @ (one_one @ nat))))))))))))).
% 2.61/1.48 thf(fact_236_t__splay__simps_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A,Rl2:(tree @ A),L2:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ A2) @ C3) => (((Rl2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (one_one @ nat))) & ((Rl2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B3) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rl2)) @ (one_one @ nat))))))))))))).
% 2.61/1.48 thf(fact_237_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X:A,Y2:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X) @ Y2) => ((Q @ X) @ Y2)))))).
% 2.61/1.48 thf(fact_238_less__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less @ (A > B)) = (^ [F3:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F3) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F3))))))))))).
% 2.61/1.48 thf(fact_239_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Y2:B,Q:(A > (B > $o))]: ((((P @ X) @ Y2) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X) @ Y2)))))).
% 2.61/1.48 thf(fact_240_is__num__normalize_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C3))))))))).
% 2.61/1.48 thf(fact_241_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B3) @ A2) = (((plus_plus @ A) @ C3) @ A2)) => (B3 = C3)))))))).
% 2.61/1.48 thf(fact_242_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ A2) @ C3)) => (B3 = C3)))))))).
% 2.61/1.48 thf(fact_243_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: (((((plus_plus @ A) @ B3) @ (((plus_plus @ A) @ A2) @ C3)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C3))))))))).
% 2.61/1.48 thf(fact_244_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A5:A,B4:A]: ((((plus_plus @ A) @ B4) @ A5)))))))).
% 2.61/1.48 thf(fact_245_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B3) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B3 = C3)))))))).
% 2.61/1.48 thf(fact_246_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ A2) @ C3)) = (B3 = C3)))))))).
% 2.61/1.48 thf(fact_247_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C3))))))))).
% 2.61/1.48 thf(fact_248_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L2:A]: ((((I = J) & (K = L2)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L2))))))))).
% 2.61/1.48 thf(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C3))))))))).
% 2.61/1.48 thf(fact_250_add__le__imp__le__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B3) @ C3)) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_251_add__le__imp__le__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B3)) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 2.61/1.48 thf(fact_252_le__iff__add, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: ((? [C4:A]: ((B4 = (((plus_plus @ A) @ A5) @ C4))))))))))).
% 2.61/1.48 thf(fact_253_add__right__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B3) @ C3))))))))).
% 2.61/1.48 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((type @ A) @ (type2 @ A)))))).
% 2.61/1.48 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord @ A) @ (type2 @ A)))))).
% 2.61/1.48 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((order @ A) @ (type2 @ A)))))).
% 2.61/1.48 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((preorder @ A) @ (type2 @ A)))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.61/1.48 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, ((condit1037483654norder @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.61/1.48 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.61/1.48 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.61/1.48 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Olinorder_8, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.61/1.48 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_11, axiom, ((condit1037483654norder @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_12, axiom, ((ordere236663937imp_le @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_13, axiom, ((ordere779506340up_add @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_14, axiom, ((cancel_semigroup_add @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_15, axiom, ((linordered_semidom @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Odense__linorder, axiom, ((dense_linorder @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_16, axiom, ((ab_semigroup_add @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Odense__order, axiom, ((dense_order @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Osemigroup__add_17, axiom, ((semigroup_add @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Opreorder_18, axiom, ((preorder @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Olinorder_19, axiom, ((linorder @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Transcendental_Oln, axiom, ((ln @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Ono__top_20, axiom, ((no_top @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Ono__bot, axiom, ((no_bot @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, ((group_add @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Oorder_21, axiom, ((order @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, ((neg_numeral @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Oord_22, axiom, ((ord @ real) @ (type2 @ real))).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Oone_23, axiom, ((one @ real) @ (type2 @ real))).
% 2.61/1.48 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.61/1.48 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y2:A]: ((((((if @ A) @ $false) @ X) @ Y2) = Y2)))).
% 2.61/1.48 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y2:A]: ((((((if @ A) @ $true) @ X) @ Y2) = X)))).
% 2.61/1.48 thf(tfree_0, hypothesis, ((linorder @ a) @ (type2 @ a))).
% 2.61/1.48 thf(conj_0, hypothesis, (! [La2:(tree @ a),Ra3:(tree @ a)]: (((((member @ (tree @ a)) @ ((((node @ a) @ La2) @ a2) @ Ra3)) @ ((subtrees @ a) @ t)) => thesis)))).
% 2.61/1.48 thf(conj_1, conjecture, thesis).
% 2.61/1.48 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2DTF23804.p
% 2.61/1.48 ------------------------
% 2.91/1.53 ---- Cleaned THF ---
% 2.91/1.53 thf(ty_t_Tree_Otree,type,
% 2.91/1.53 tree: $tType > $tType ).
% 2.91/1.53
% 2.91/1.53 thf(ty_t_Real_Oreal,type,
% 2.91/1.53 real: $tType ).
% 2.91/1.53
% 2.91/1.53 thf(ty_t_Set_Oset,type,
% 2.91/1.53 set: $tType > $tType ).
% 2.91/1.53
% 2.91/1.53 thf(ty_t_Nat_Onat,type,
% 2.91/1.53 nat: $tType ).
% 2.91/1.53
% 2.91/1.53 thf(ty_t_itself,type,
% 2.91/1.53 itself: $tType > $tType ).
% 2.91/1.53
% 2.91/1.53 thf(ty_tf_a,type,
% 2.91/1.53 a: $tType ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_HOL_Otype,type,
% 2.91/1.53 type:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Oone,type,
% 2.91/1.53 one:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Oord,type,
% 2.91/1.53 ord:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Num_Oneg__numeral,type,
% 2.91/1.53 neg_numeral:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Oorder,type,
% 2.91/1.53 order:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Ogroup__add,type,
% 2.91/1.53 group_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Ono__bot,type,
% 2.91/1.53 no_bot:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Ono__top,type,
% 2.91/1.53 no_top:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Transcendental_Oln,type,
% 2.91/1.53 ln:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Olinorder,type,
% 2.91/1.53 linorder:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Opreorder,type,
% 2.91/1.53 preorder:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Owellorder,type,
% 2.91/1.53 wellorder:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.91/1.53 semigroup_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Odense__order,type,
% 2.91/1.53 dense_order:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.91/1.53 ab_semigroup_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Orderings_Odense__linorder,type,
% 2.91/1.53 dense_linorder:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.91/1.53 linordered_semidom:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.91/1.53 cancel_semigroup_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.91/1.53 ordere779506340up_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.91/1.53 canoni770627133id_add:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.91/1.53 ordere236663937imp_le:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 2.91/1.53 condit1037483654norder:
% 2.91/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.91/1.53 one_one:
% 2.91/1.53 !>[A: $tType] : A ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.91/1.53 plus_plus:
% 2.91/1.53 !>[A: $tType] : ( A > A > A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_If,type,
% 2.91/1.53 if:
% 2.91/1.53 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.91/1.53 ord_less:
% 2.91/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.91/1.53 ord_less_eq:
% 2.91/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Pure_Otype,type,
% 2.91/1.53 type2:
% 2.91/1.53 !>[A: $tType] : ( itself @ A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Set_OCollect,type,
% 2.91/1.53 collect:
% 2.91/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Splay__Tree_Ois__root,type,
% 2.91/1.53 splay_is_root:
% 2.91/1.53 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Splay__Tree_Osplay,type,
% 2.91/1.53 splay_splay:
% 2.91/1.53 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Splay__Tree_Osplay__max,type,
% 2.91/1.53 splay_splay_max:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 2.91/1.53 splay_914434265_splay:
% 2.91/1.53 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA,type,
% 2.91/1.53 splay_266122055elle_A:
% 2.91/1.53 !>[A: $tType] : ( A > ( tree @ A ) > real ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Transcendental_Opowr,type,
% 2.91/1.53 powr:
% 2.91/1.53 !>[A: $tType] : ( A > A > A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 2.91/1.53 linorder_bst:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Olinorder__class_Obst__eq,type,
% 2.91/1.53 linorder_bst_eq:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Omirror,type,
% 2.91/1.53 mirror:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Osubtrees,type,
% 2.91/1.53 subtrees:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( set @ ( tree @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_OLeaf,type,
% 2.91/1.53 leaf:
% 2.91/1.53 !>[A: $tType] : ( tree @ A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_ONode,type,
% 2.91/1.53 node:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Ocase__tree,type,
% 2.91/1.53 case_tree:
% 2.91/1.53 !>[B: $tType,A: $tType] : ( B > ( ( tree @ A ) > A > ( tree @ A ) > B ) > ( tree @ A ) > B ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Ois__Leaf,type,
% 2.91/1.53 is_Leaf:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Oleft,type,
% 2.91/1.53 left:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Opred__tree,type,
% 2.91/1.53 pred_tree:
% 2.91/1.53 !>[A: $tType] : ( ( A > $o ) > ( tree @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Orec__tree,type,
% 2.91/1.53 rec_tree:
% 2.91/1.53 !>[C: $tType,A: $tType] : ( C > ( ( tree @ A ) > A > ( tree @ A ) > C > C > C ) > ( tree @ A ) > C ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Orel__tree,type,
% 2.91/1.53 rel_tree:
% 2.91/1.53 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( tree @ A ) > ( tree @ B ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Oright,type,
% 2.91/1.53 right:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Oset__tree,type,
% 2.91/1.53 set_tree:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > ( set @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_Tree_Otree_Oval,type,
% 2.91/1.53 val:
% 2.91/1.53 !>[A: $tType] : ( ( tree @ A ) > A ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_c_member,type,
% 2.91/1.53 member:
% 2.91/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.91/1.53
% 2.91/1.53 thf(sy_v_a,type,
% 2.91/1.53 a2: a ).
% 2.91/1.53
% 2.91/1.53 thf(sy_v_t,type,
% 2.91/1.53 t: tree @ a ).
% 2.91/1.53
% 2.91/1.53 thf(sy_v_thesis____,type,
% 2.91/1.53 thesis: $o ).
% 2.91/1.53
% 2.91/1.53 thf(fact_0_assms_I2_J,axiom,
% 2.91/1.53 member @ a @ a2 @ ( set_tree @ a @ t ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_1_assms_I1_J,axiom,
% 2.91/1.53 linorder_bst @ a @ t ).
% 2.91/1.53
% 2.91/1.53 thf(fact_2_tree_Oinject,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 2.91/1.53 ( ( ( node @ A @ X21 @ X22 @ X23 )
% 2.91/1.53 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 2.91/1.53 = ( ( X21 = Y21 )
% 2.91/1.53 & ( X22 = Y22 )
% 2.91/1.53 & ( X23 = Y23 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_3_set__treeE,axiom,
% 2.91/1.53 ! [A: $tType,A2: A,T: tree @ A] :
% 2.91/1.53 ( ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 2.91/1.53 => ? [L: tree @ A,R: tree @ A] : ( member @ ( tree @ A ) @ ( node @ A @ L @ A2 @ R ) @ ( subtrees @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_4_in__set__tree__if,axiom,
% 2.91/1.53 ! [A: $tType,L2: tree @ A,A2: A,R2: tree @ A,T: tree @ A] :
% 2.91/1.53 ( ( member @ ( tree @ A ) @ ( node @ A @ L2 @ A2 @ R2 ) @ ( subtrees @ A @ T ) )
% 2.91/1.53 => ( member @ A @ A2 @ ( set_tree @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_5_Node__notin__subtrees__if,axiom,
% 2.91/1.53 ! [A: $tType,A2: A,T: tree @ A,L2: tree @ A,R2: tree @ A] :
% 2.91/1.53 ( ~ ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 2.91/1.53 => ~ ( member @ ( tree @ A ) @ ( node @ A @ L2 @ A2 @ R2 ) @ ( subtrees @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_6_tree_Oset__intros_I3_J,axiom,
% 2.91/1.53 ! [A: $tType,Xa: A,A3: tree @ A,A1: tree @ A,A22: A] :
% 2.91/1.53 ( ( member @ A @ Xa @ ( set_tree @ A @ A3 ) )
% 2.91/1.53 => ( member @ A @ Xa @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_7_tree_Oset__intros_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,A22: A,A1: tree @ A,A3: tree @ A] : ( member @ A @ A22 @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_8_tree_Oset__intros_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,X: A,A1: tree @ A,A22: A,A3: tree @ A] :
% 2.91/1.53 ( ( member @ A @ X @ ( set_tree @ A @ A1 ) )
% 2.91/1.53 => ( member @ A @ X @ ( set_tree @ A @ ( node @ A @ A1 @ A22 @ A3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_9_tree_Oset__cases,axiom,
% 2.91/1.53 ! [A: $tType,E: A,A2: tree @ A] :
% 2.91/1.53 ( ( member @ A @ E @ ( set_tree @ A @ A2 ) )
% 2.91/1.53 => ( ! [Z1: tree @ A] :
% 2.91/1.53 ( ? [Z2: A,Z3: tree @ A] :
% 2.91/1.53 ( A2
% 2.91/1.53 = ( node @ A @ Z1 @ Z2 @ Z3 ) )
% 2.91/1.53 => ~ ( member @ A @ E @ ( set_tree @ A @ Z1 ) ) )
% 2.91/1.53 => ( ! [Z1: tree @ A,Z3: tree @ A] :
% 2.91/1.53 ( A2
% 2.91/1.53 != ( node @ A @ Z1 @ E @ Z3 ) )
% 2.91/1.53 => ~ ! [Z1: tree @ A,Z2: A,Z3: tree @ A] :
% 2.91/1.53 ( ( A2
% 2.91/1.53 = ( node @ A @ Z1 @ Z2 @ Z3 ) )
% 2.91/1.53 => ~ ( member @ A @ E @ ( set_tree @ A @ Z3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_10_tree_Osimps_I7_J,axiom,
% 2.91/1.53 ! [C: $tType,A: $tType,F1: C,F2: ( tree @ A ) > A > ( tree @ A ) > C > C > C,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( rec_tree @ C @ A @ F1 @ F2 @ ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 = ( F2 @ X21 @ X22 @ X23 @ ( rec_tree @ C @ A @ F1 @ F2 @ X21 ) @ ( rec_tree @ C @ A @ F1 @ F2 @ X23 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_11_tree_Opred__inject_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,P: A > $o,A2: tree @ A,Aa: A,Ab: tree @ A] :
% 2.91/1.53 ( ( pred_tree @ A @ P @ ( node @ A @ A2 @ Aa @ Ab ) )
% 2.91/1.53 = ( ( pred_tree @ A @ P @ A2 )
% 2.91/1.53 & ( P @ Aa )
% 2.91/1.53 & ( pred_tree @ A @ P @ Ab ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_12_A__simps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.91/1.53 ( ( splay_266122055elle_A @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 = ( one_one @ real ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_13_tree_Osimps_I5_J,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( case_tree @ B @ A @ F1 @ F2 @ ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 = ( F2 @ X21 @ X22 @ X23 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_14_tree_Opred__cong,axiom,
% 2.91/1.53 ! [A: $tType,X: tree @ A,Ya: tree @ A,P: A > $o,Pa: A > $o] :
% 2.91/1.53 ( ( X = Ya )
% 2.91/1.53 => ( ! [Z: A] :
% 2.91/1.53 ( ( member @ A @ Z @ ( set_tree @ A @ Ya ) )
% 2.91/1.53 => ( ( P @ Z )
% 2.91/1.53 = ( Pa @ Z ) ) )
% 2.91/1.53 => ( ( pred_tree @ A @ P @ X )
% 2.91/1.53 = ( pred_tree @ A @ Pa @ Ya ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_15_tree_Opred__mono__strong,axiom,
% 2.91/1.53 ! [A: $tType,P: A > $o,X: tree @ A,Pa: A > $o] :
% 2.91/1.53 ( ( pred_tree @ A @ P @ X )
% 2.91/1.53 => ( ! [Z: A] :
% 2.91/1.53 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 2.91/1.53 => ( ( P @ Z )
% 2.91/1.53 => ( Pa @ Z ) ) )
% 2.91/1.53 => ( pred_tree @ A @ Pa @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_16_one__reorient,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( one @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A] :
% 2.91/1.53 ( ( ( one_one @ A )
% 2.91/1.53 = X )
% 2.91/1.53 = ( X
% 2.91/1.53 = ( one_one @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_17_splay__to__root,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A,T2: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( ( ( splay_splay @ A @ A2 @ T )
% 2.91/1.53 = T2 )
% 2.91/1.53 => ( ( member @ A @ A2 @ ( set_tree @ A @ T ) )
% 2.91/1.53 = ( ? [L3: tree @ A,R3: tree @ A] :
% 2.91/1.53 ( T2
% 2.91/1.53 = ( node @ A @ L3 @ A2 @ R3 ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_18_tree_Opred__set,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( pred_tree @ A )
% 2.91/1.53 = ( ^ [P2: A > $o,X2: tree @ A] :
% 2.91/1.53 ! [Y: A] :
% 2.91/1.53 ( ( member @ A @ Y @ ( set_tree @ A @ X2 ) )
% 2.91/1.53 => ( P2 @ Y ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_19_tree_Osel_I3_J,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( val @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 = X22 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_20_tree_Osel_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( left @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 = X21 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_21_tree_Osel_I5_J,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( right @ A @ ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 = X23 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_22_bst__eq__if__bst,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( linorder_bst_eq @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_23_mirror_Osimps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,L2: tree @ A,X: A,R2: tree @ A] :
% 2.91/1.53 ( ( mirror @ A @ ( node @ A @ L2 @ X @ R2 ) )
% 2.91/1.53 = ( node @ A @ ( mirror @ A @ R2 ) @ X @ ( mirror @ A @ L2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_24_tree_Osimps_I6_J,axiom,
% 2.91/1.53 ! [A: $tType,C: $tType,F1: C,F2: ( tree @ A ) > A > ( tree @ A ) > C > C > C] :
% 2.91/1.53 ( ( rec_tree @ C @ A @ F1 @ F2 @ ( leaf @ A ) )
% 2.91/1.53 = F1 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_25_powr__one__eq__one,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( ln @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A] :
% 2.91/1.53 ( ( powr @ A @ ( one_one @ A ) @ A2 )
% 2.91/1.53 = ( one_one @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_26_mirror__mirror,axiom,
% 2.91/1.53 ! [A: $tType,T: tree @ A] :
% 2.91/1.53 ( ( mirror @ A @ ( mirror @ A @ T ) )
% 2.91/1.53 = T ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_27_splay__Leaf__iff,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,T: tree @ A] :
% 2.91/1.53 ( ( ( splay_splay @ A @ A2 @ T )
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 = ( T
% 2.91/1.53 = ( leaf @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_28_mirror__Leaf,axiom,
% 2.91/1.53 ! [A: $tType,T: tree @ A] :
% 2.91/1.53 ( ( ( mirror @ A @ T )
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 = ( T
% 2.91/1.53 = ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_29_tree_Osel_I4_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( right @ A @ ( leaf @ A ) )
% 2.91/1.53 = ( leaf @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_30_tree_Osel_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( left @ A @ ( leaf @ A ) )
% 2.91/1.53 = ( leaf @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_31_mirror_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( mirror @ A @ ( leaf @ A ) )
% 2.91/1.53 = ( leaf @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_32_bst__eq_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( linorder_bst_eq @ A @ ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_33_tree_Oexhaust__sel,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A] :
% 2.91/1.53 ( ( Tree
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ( Tree
% 2.91/1.53 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_34_splay__not__Leaf,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A] :
% 2.91/1.53 ( ( T
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ? [L: tree @ A,X3: A,R: tree @ A] :
% 2.91/1.53 ( ( splay_splay @ A @ A2 @ T )
% 2.91/1.53 = ( node @ A @ L @ X3 @ R ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_35_splay_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A] :
% 2.91/1.53 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 2.91/1.53 = ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_36_splay_Osimps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.91/1.53 ( ( splay_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 = ( node @ A @ L2 @ A2 @ R2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_37_mirror_Oelims,axiom,
% 2.91/1.53 ! [A: $tType,X: tree @ A,Y2: tree @ A] :
% 2.91/1.53 ( ( ( mirror @ A @ X )
% 2.91/1.53 = Y2 )
% 2.91/1.53 => ( ( ( X
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ( Y2
% 2.91/1.53 != ( leaf @ A ) ) )
% 2.91/1.53 => ~ ! [L: tree @ A,X3: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ X3 @ R ) )
% 2.91/1.53 => ( Y2
% 2.91/1.53 != ( node @ A @ ( mirror @ A @ R ) @ X3 @ ( mirror @ A @ L ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_38_tree_Osplit__sel__asm,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,Tree: tree @ A] :
% 2.91/1.53 ( ( P @ ( case_tree @ B @ A @ F1 @ F2 @ Tree ) )
% 2.91/1.53 = ( ~ ( ( ( Tree
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 & ~ ( P @ F1 ) )
% 2.91/1.53 | ( ( Tree
% 2.91/1.53 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) )
% 2.91/1.53 & ~ ( P @ ( F2 @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_39_tree_Osplit__sel,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B,Tree: tree @ A] :
% 2.91/1.53 ( ( P @ ( case_tree @ B @ A @ F1 @ F2 @ Tree ) )
% 2.91/1.53 = ( ( ( Tree
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ( P @ F1 ) )
% 2.91/1.53 & ( ( Tree
% 2.91/1.53 = ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) )
% 2.91/1.53 => ( P @ ( F2 @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_40_set__splay,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,T: tree @ A] :
% 2.91/1.53 ( ( set_tree @ A @ ( splay_splay @ A @ A2 @ T ) )
% 2.91/1.53 = ( set_tree @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_41_bst__splay,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_42_tree_Odistinct_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( leaf @ A )
% 2.91/1.53 != ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_43_tree_Oinduct,axiom,
% 2.91/1.53 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 2.91/1.53 ( ( P @ ( leaf @ A ) )
% 2.91/1.53 => ( ! [X1: tree @ A,X24: A,X32: tree @ A] :
% 2.91/1.53 ( ( P @ X1 )
% 2.91/1.53 => ( ( P @ X32 )
% 2.91/1.53 => ( P @ ( node @ A @ X1 @ X24 @ X32 ) ) ) )
% 2.91/1.53 => ( P @ Tree ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_44_mem__Collect__eq,axiom,
% 2.91/1.53 ! [A: $tType,A2: A,P: A > $o] :
% 2.91/1.53 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.91/1.53 = ( P @ A2 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_45_Collect__mem__eq,axiom,
% 2.91/1.53 ! [A: $tType,A4: set @ A] :
% 2.91/1.53 ( ( collect @ A
% 2.91/1.53 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 2.91/1.53 = A4 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_46_Collect__cong,axiom,
% 2.91/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.91/1.53 ( ! [X3: A] :
% 2.91/1.53 ( ( P @ X3 )
% 2.91/1.53 = ( Q @ X3 ) )
% 2.91/1.53 => ( ( collect @ A @ P )
% 2.91/1.53 = ( collect @ A @ Q ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_47_ext,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.91/1.53 ( ! [X3: A] :
% 2.91/1.53 ( ( F @ X3 )
% 2.91/1.53 = ( G @ X3 ) )
% 2.91/1.53 => ( F = G ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_48_neq__Leaf__iff,axiom,
% 2.91/1.53 ! [A: $tType,T: tree @ A] :
% 2.91/1.53 ( ( T
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 = ( ? [L3: tree @ A,A5: A,R3: tree @ A] :
% 2.91/1.53 ( T
% 2.91/1.53 = ( node @ A @ L3 @ A5 @ R3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_49_tree_Oexhaust,axiom,
% 2.91/1.53 ! [A: $tType,Y2: tree @ A] :
% 2.91/1.53 ( ( Y2
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ~ ! [X212: tree @ A,X222: A,X232: tree @ A] :
% 2.91/1.53 ( Y2
% 2.91/1.53 != ( node @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_50_mirror_Oinduct,axiom,
% 2.91/1.53 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.91/1.53 ( ( P @ ( leaf @ A ) )
% 2.91/1.53 => ( ! [L: tree @ A,X3: A,R: tree @ A] :
% 2.91/1.53 ( ( P @ R )
% 2.91/1.53 => ( ( P @ L )
% 2.91/1.53 => ( P @ ( node @ A @ L @ X3 @ R ) ) ) )
% 2.91/1.53 => ( P @ A0 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_51_bst__eq_Ocases,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( X
% 2.91/1.53 != ( node @ A @ L @ A6 @ R ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_52_bst__eq_Oinduct,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.91/1.53 ( ( P @ ( leaf @ A ) )
% 2.91/1.53 => ( ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( P @ L )
% 2.91/1.53 => ( ( P @ R )
% 2.91/1.53 => ( P @ ( node @ A @ L @ A6 @ R ) ) ) )
% 2.91/1.53 => ( P @ A0 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_53_bst_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_54_tree_Osimps_I4_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,F1: B,F2: ( tree @ A ) > A > ( tree @ A ) > B] :
% 2.91/1.53 ( ( case_tree @ B @ A @ F1 @ F2 @ ( leaf @ A ) )
% 2.91/1.53 = F1 ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_55_tree_Opred__inject_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,P: A > $o] : ( pred_tree @ A @ P @ ( leaf @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_56_is__root__splay,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( ( splay_is_root @ A @ A2 @ ( splay_splay @ A @ A2 @ T ) )
% 2.91/1.53 = ( member @ A @ A2 @ ( set_tree @ A @ T ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_57_tree_Ocollapse_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A] :
% 2.91/1.53 ( ~ ( is_Leaf @ A @ Tree )
% 2.91/1.53 => ( ( node @ A @ ( left @ A @ Tree ) @ ( val @ A @ Tree ) @ ( right @ A @ Tree ) )
% 2.91/1.53 = Tree ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_58__092_060Phi_062_Ocases,axiom,
% 2.91/1.53 ! [A: $tType,X: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( X
% 2.91/1.53 != ( node @ A @ L @ A6 @ R ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_59__092_060Phi_062_Oinduct,axiom,
% 2.91/1.53 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.91/1.53 ( ( P @ ( leaf @ A ) )
% 2.91/1.53 => ( ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( P @ L )
% 2.91/1.53 => ( ( P @ R )
% 2.91/1.53 => ( P @ ( node @ A @ L @ A6 @ R ) ) ) )
% 2.91/1.53 => ( P @ A0 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_60_t__splay__max_Ocases,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ( ! [L: tree @ A,B2: A] :
% 2.91/1.53 ( X
% 2.91/1.53 != ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 2.91/1.53 => ~ ! [L: tree @ A,B2: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.91/1.53 ( X
% 2.91/1.53 != ( node @ A @ L @ B2 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_61_t__splay__max_Oinduct,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.91/1.53 ( ( P @ ( leaf @ A ) )
% 2.91/1.53 => ( ! [L: tree @ A,B2: A] : ( P @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 2.91/1.53 => ( ! [L: tree @ A,B2: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.91/1.53 ( ( ( Rr
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ( P @ Rr ) )
% 2.91/1.53 => ( P @ ( node @ A @ L @ B2 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 2.91/1.53 => ( P @ A0 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_62_tree_Ocase__eq__if,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( case_tree @ B @ A )
% 2.91/1.53 = ( ^ [F12: B,F22: ( tree @ A ) > A > ( tree @ A ) > B,Tree2: tree @ A] : ( if @ B @ ( is_Leaf @ A @ Tree2 ) @ F12 @ ( F22 @ ( left @ A @ Tree2 ) @ ( val @ A @ Tree2 ) @ ( right @ A @ Tree2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_63_bst__eq_Oelims_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ( linorder_bst_eq @ A @ X )
% 2.91/1.53 => ( ( X
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ~ ( ( linorder_bst_eq @ A @ L )
% 2.91/1.53 & ( linorder_bst_eq @ A @ R )
% 2.91/1.53 & ! [X4: A] :
% 2.91/1.53 ( ( member @ A @ X4 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less_eq @ A @ X4 @ A6 ) )
% 2.91/1.53 & ! [X4: A] :
% 2.91/1.53 ( ( member @ A @ X4 @ ( set_tree @ A @ R ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A6 @ X4 ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_64_bst__eq_Oelims_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A,Y2: $o] :
% 2.91/1.53 ( ( ( linorder_bst_eq @ A @ X )
% 2.91/1.53 = Y2 )
% 2.91/1.53 => ( ( ( X
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ~ Y2 )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ( Y2
% 2.91/1.53 = ( ~ ( ( linorder_bst_eq @ A @ L )
% 2.91/1.53 & ( linorder_bst_eq @ A @ R )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less_eq @ A @ X2 @ A6 ) )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ R ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A6 @ X2 ) ) ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_65_powr__mono,axiom,
% 2.91/1.53 ! [A2: real,B3: real,X: real] :
% 2.91/1.53 ( ( ord_less_eq @ real @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 2.91/1.53 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_66_tree_OdiscI_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ( ( Tree
% 2.91/1.53 = ( node @ A @ X21 @ X22 @ X23 ) )
% 2.91/1.53 => ~ ( is_Leaf @ A @ Tree ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_67_tree_Odisc_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.91/1.53 ~ ( is_Leaf @ A @ ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_68_is__Leaf__def,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( is_Leaf @ A )
% 2.91/1.53 = ( ^ [Tree2: tree @ A] :
% 2.91/1.53 ( Tree2
% 2.91/1.53 = ( leaf @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_69_tree_Ocollapse_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A] :
% 2.91/1.53 ( ( is_Leaf @ A @ Tree )
% 2.91/1.53 => ( Tree
% 2.91/1.53 = ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_70_tree_OdiscI_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A] :
% 2.91/1.53 ( ( Tree
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ( is_Leaf @ A @ Tree ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_71_tree_Odisc_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] : ( is_Leaf @ A @ ( leaf @ A ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_72_tree_Oset__sel_I3_J,axiom,
% 2.91/1.53 ! [A: $tType,A2: tree @ A,Xa: A] :
% 2.91/1.53 ( ~ ( is_Leaf @ A @ A2 )
% 2.91/1.53 => ( ( member @ A @ Xa @ ( set_tree @ A @ ( right @ A @ A2 ) ) )
% 2.91/1.53 => ( member @ A @ Xa @ ( set_tree @ A @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_73_tree_Oset__sel_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,A2: tree @ A,X: A] :
% 2.91/1.53 ( ~ ( is_Leaf @ A @ A2 )
% 2.91/1.53 => ( ( member @ A @ X @ ( set_tree @ A @ ( left @ A @ A2 ) ) )
% 2.91/1.53 => ( member @ A @ X @ ( set_tree @ A @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_74_tree_Oset__sel_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,A2: tree @ A] :
% 2.91/1.53 ( ~ ( is_Leaf @ A @ A2 )
% 2.91/1.53 => ( member @ A @ ( val @ A @ A2 ) @ ( set_tree @ A @ A2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_75_bst__eq_Oelims_I3_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ~ ( linorder_bst_eq @ A @ X )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ( ( linorder_bst_eq @ A @ L )
% 2.91/1.53 & ( linorder_bst_eq @ A @ R )
% 2.91/1.53 & ! [X3: A] :
% 2.91/1.53 ( ( member @ A @ X3 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less_eq @ A @ X3 @ A6 ) )
% 2.91/1.53 & ! [X3: A] :
% 2.91/1.53 ( ( member @ A @ X3 @ ( set_tree @ A @ R ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A6 @ X3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_76_bst__eq_Osimps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [L2: tree @ A,A2: A,R2: tree @ A] :
% 2.91/1.53 ( ( linorder_bst_eq @ A @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 = ( ( linorder_bst_eq @ A @ L2 )
% 2.91/1.53 & ( linorder_bst_eq @ A @ R2 )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ L2 ) )
% 2.91/1.53 => ( ord_less_eq @ A @ X2 @ A2 ) )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ R2 ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ X2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_77_tree_Oexpand,axiom,
% 2.91/1.53 ! [A: $tType,Tree: tree @ A,Tree3: tree @ A] :
% 2.91/1.53 ( ( ( is_Leaf @ A @ Tree )
% 2.91/1.53 = ( is_Leaf @ A @ Tree3 ) )
% 2.91/1.53 => ( ( ~ ( is_Leaf @ A @ Tree )
% 2.91/1.53 => ( ~ ( is_Leaf @ A @ Tree3 )
% 2.91/1.53 => ( ( ( left @ A @ Tree )
% 2.91/1.53 = ( left @ A @ Tree3 ) )
% 2.91/1.53 & ( ( val @ A @ Tree )
% 2.91/1.53 = ( val @ A @ Tree3 ) )
% 2.91/1.53 & ( ( right @ A @ Tree )
% 2.91/1.53 = ( right @ A @ Tree3 ) ) ) ) )
% 2.91/1.53 => ( Tree = Tree3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_78_order__refl,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_79_le__numeral__extra_I4_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_80_splay__max__eq__splay,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( ! [X3: A] :
% 2.91/1.53 ( ( member @ A @ X3 @ ( set_tree @ A @ T ) )
% 2.91/1.53 => ( ord_less_eq @ A @ X3 @ A2 ) )
% 2.91/1.53 => ( ( splay_splay_max @ A @ T )
% 2.91/1.53 = ( splay_splay @ A @ A2 @ T ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_81_ex__in__set__tree,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,A2: A] :
% 2.91/1.53 ( ( T
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ? [X3: A] :
% 2.91/1.53 ( ( member @ A @ X3 @ ( set_tree @ A @ T ) )
% 2.91/1.53 & ( ( splay_splay @ A @ X3 @ T )
% 2.91/1.53 = ( splay_splay @ A @ A2 @ T ) )
% 2.91/1.53 & ( ( splay_914434265_splay @ A @ X3 @ T )
% 2.91/1.53 = ( splay_914434265_splay @ A @ A2 @ T ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_82_bst_Oelims_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ X )
% 2.91/1.53 => ( ( X
% 2.91/1.53 != ( leaf @ A ) )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ~ ( ( linorder_bst @ A @ L )
% 2.91/1.53 & ( linorder_bst @ A @ R )
% 2.91/1.53 & ! [X4: A] :
% 2.91/1.53 ( ( member @ A @ X4 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less @ A @ X4 @ A6 ) )
% 2.91/1.53 & ! [X4: A] :
% 2.91/1.53 ( ( member @ A @ X4 @ ( set_tree @ A @ R ) )
% 2.91/1.53 => ( ord_less @ A @ A6 @ X4 ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_83_bst_Oelims_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A,Y2: $o] :
% 2.91/1.53 ( ( ( linorder_bst @ A @ X )
% 2.91/1.53 = Y2 )
% 2.91/1.53 => ( ( ( X
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ~ Y2 )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ( Y2
% 2.91/1.53 = ( ~ ( ( linorder_bst @ A @ L )
% 2.91/1.53 & ( linorder_bst @ A @ R )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less @ A @ X2 @ A6 ) )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ R ) )
% 2.91/1.53 => ( ord_less @ A @ A6 @ X2 ) ) ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_84_tree_Orel__sel,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType] :
% 2.91/1.53 ( ( rel_tree @ A @ B )
% 2.91/1.53 = ( ^ [R4: A > B > $o,A5: tree @ A,B4: tree @ B] :
% 2.91/1.53 ( ( ( is_Leaf @ A @ A5 )
% 2.91/1.53 = ( is_Leaf @ B @ B4 ) )
% 2.91/1.53 & ( ~ ( is_Leaf @ A @ A5 )
% 2.91/1.53 => ( ~ ( is_Leaf @ B @ B4 )
% 2.91/1.53 => ( ( rel_tree @ A @ B @ R4 @ ( left @ A @ A5 ) @ ( left @ B @ B4 ) )
% 2.91/1.53 & ( R4 @ ( val @ A @ A5 ) @ ( val @ B @ B4 ) )
% 2.91/1.53 & ( rel_tree @ A @ B @ R4 @ ( right @ A @ A5 ) @ ( right @ B @ B4 ) ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_85_powr__less__cancel__iff,axiom,
% 2.91/1.53 ! [X: real,A2: real,B3: real] :
% 2.91/1.53 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.91/1.53 => ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 2.91/1.53 = ( ord_less @ real @ A2 @ B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_86_t__splay__simps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.91/1.53 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_87_splay__max__Leaf__iff,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A] :
% 2.91/1.53 ( ( ( splay_splay_max @ A @ T )
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 = ( T
% 2.91/1.53 = ( leaf @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_88_powr__le__cancel__iff,axiom,
% 2.91/1.53 ! [X: real,A2: real,B3: real] :
% 2.91/1.53 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.91/1.53 => ( ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 2.91/1.53 = ( ord_less_eq @ real @ A2 @ B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_89_t__splay__simps_I7_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,L2: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_90_t__splay__simps_I3_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B3 @ R2 ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_91_t__splay__simps_I6_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,L2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( leaf @ A ) ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_92_t__splay__simps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,R2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_93_leD,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Y2: A,X: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ Y2 @ X )
% 2.91/1.53 => ~ ( ord_less @ A @ X @ Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_94_leI,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ~ ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_95_le__less,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less_eq @ A )
% 2.91/1.53 = ( ^ [X2: A,Y: A] :
% 2.91/1.53 ( ( ord_less @ A @ X2 @ Y )
% 2.91/1.53 | ( X2 = Y ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_96_less__le,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less @ A )
% 2.91/1.53 = ( ^ [X2: A,Y: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.53 & ( X2 != Y ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_97_order__le__less__subst1,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_98_order__le__less__subst2,axiom,
% 2.91/1.53 ! [A: $tType,C: $tType] :
% 2.91/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less @ C @ ( F @ B3 ) @ C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_99_order__less__le__subst1,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_100_order__less__le__subst2,axiom,
% 2.91/1.53 ! [A: $tType,C: $tType] :
% 2.91/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_101_not__le,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ~ ( ord_less_eq @ A @ X @ Y2 ) )
% 2.91/1.53 = ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_102_not__less,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 2.91/1.53 = ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_103_le__neq__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( A2 != B3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_104_less__imp__le,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_105_antisym__conv1,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ~ ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 = ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_106_antisym__conv2,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 2.91/1.53 = ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_107_le__less__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less @ A @ Y2 @ Z4 )
% 2.91/1.53 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_108_less__le__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 2.91/1.53 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_109_dense__ge,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Z4: A,Y2: A] :
% 2.91/1.53 ( ! [X3: A] :
% 2.91/1.53 ( ( ord_less @ A @ Z4 @ X3 )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ X3 ) )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_110_dense__le,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Y2: A,Z4: A] :
% 2.91/1.53 ( ! [X3: A] :
% 2.91/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ X3 @ Z4 ) )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_111_le__less__linear,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 | ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_112_le__imp__less__or__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 | ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_113_less__le__not__le,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less @ A )
% 2.91/1.53 = ( ^ [X2: A,Y: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.53 & ~ ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_114_not__le__imp__less,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Y2: A,X: A] :
% 2.91/1.53 ( ~ ( ord_less_eq @ A @ Y2 @ X )
% 2.91/1.53 => ( ord_less @ A @ X @ Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_115_order_Ostrict__trans1,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_116_order_Ostrict__trans2,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_117_order_Oorder__iff__strict,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less_eq @ A )
% 2.91/1.53 = ( ^ [A5: A,B4: A] :
% 2.91/1.53 ( ( ord_less @ A @ A5 @ B4 )
% 2.91/1.53 | ( A5 = B4 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_118_order_Ostrict__iff__order,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less @ A )
% 2.91/1.53 = ( ^ [A5: A,B4: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A5 @ B4 )
% 2.91/1.53 & ( A5 != B4 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_119_dual__order_Ostrict__trans1,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( ord_less @ A @ C3 @ B3 )
% 2.91/1.53 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_120_dual__order_Ostrict__trans2,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 2.91/1.53 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_121_dense__ge__bounded,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Z4: A,X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ Z4 @ X )
% 2.91/1.53 => ( ! [W: A] :
% 2.91/1.53 ( ( ord_less @ A @ Z4 @ W )
% 2.91/1.53 => ( ( ord_less @ A @ W @ X )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ W ) ) )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_122_dense__le__bounded,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ! [W: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ W )
% 2.91/1.53 => ( ( ord_less @ A @ W @ Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ W @ Z4 ) ) )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_123_order_Ostrict__implies__order,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_124_dual__order_Oorder__iff__strict,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less_eq @ A )
% 2.91/1.53 = ( ^ [B4: A,A5: A] :
% 2.91/1.53 ( ( ord_less @ A @ B4 @ A5 )
% 2.91/1.53 | ( A5 = B4 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_125_dual__order_Ostrict__iff__order,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ord_less @ A )
% 2.91/1.53 = ( ^ [B4: A,A5: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ B4 @ A5 )
% 2.91/1.53 & ( A5 != B4 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_126_dual__order_Ostrict__implies__order,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_127_order_Onot__eq__order__implies__strict,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( A2 != B3 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_128_tree_Orel__mono,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType,R5: A > B > $o,Ra: A > B > $o] :
% 2.91/1.53 ( ( ord_less_eq @ ( A > B > $o ) @ R5 @ Ra )
% 2.91/1.53 => ( ord_less_eq @ ( ( tree @ A ) > ( tree @ B ) > $o ) @ ( rel_tree @ A @ B @ R5 ) @ ( rel_tree @ A @ B @ Ra ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_129_less__numeral__extra_I4_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.91/1.53 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_130_tree_Orel__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( rel_tree @ A @ A
% 2.91/1.53 @ ^ [Y4: A,Z5: A] : ( Y4 = Z5 ) )
% 2.91/1.53 = ( ^ [Y4: tree @ A,Z5: tree @ A] : ( Y4 = Z5 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_131_tree_Orel__refl,axiom,
% 2.91/1.53 ! [B: $tType,Ra: B > B > $o,X: tree @ B] :
% 2.91/1.53 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 2.91/1.53 => ( rel_tree @ B @ B @ Ra @ X @ X ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_132_dual__order_Ostrict__implies__not__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( A2 != B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_133_order_Ostrict__implies__not__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( A2 != B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_134_not__less__iff__gr__or__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 2.91/1.53 = ( ( ord_less @ A @ Y2 @ X )
% 2.91/1.53 | ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_135_dual__order_Ostrict__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( ord_less @ A @ C3 @ B3 )
% 2.91/1.53 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_136_less__imp__not__less,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_137_order_Ostrict__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_138_dual__order_Oirrefl,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A] :
% 2.91/1.53 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_139_linorder__cases,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ~ ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ( X != Y2 )
% 2.91/1.53 => ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_140_less__imp__triv,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,P: $o] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less @ A @ Y2 @ X )
% 2.91/1.53 => P ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_141_less__imp__not__eq2,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( Y2 != X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_142_antisym__conv3,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Y2: A,X: A] :
% 2.91/1.53 ( ~ ( ord_less @ A @ Y2 @ X )
% 2.91/1.53 => ( ( ~ ( ord_less @ A @ X @ Y2 ) )
% 2.91/1.53 = ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_143_less__induct,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [P: A > $o,A2: A] :
% 2.91/1.53 ( ! [X3: A] :
% 2.91/1.53 ( ! [Y5: A] :
% 2.91/1.53 ( ( ord_less @ A @ Y5 @ X3 )
% 2.91/1.53 => ( P @ Y5 ) )
% 2.91/1.53 => ( P @ X3 ) )
% 2.91/1.53 => ( P @ A2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_144_less__not__sym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_145_less__imp__not__eq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( X != Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_146_dual__order_Oasym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_147_ord__less__eq__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( B3 = C3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_148_ord__eq__less__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( A2 = B3 )
% 2.91/1.53 => ( ( ord_less @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_149_less__irrefl,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A] :
% 2.91/1.53 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_150_less__linear,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 | ( X = Y2 )
% 2.91/1.53 | ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_151_less__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less @ A @ Y2 @ Z4 )
% 2.91/1.53 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_152_less__asym_H,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_153_less__asym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ~ ( ord_less @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_154_less__imp__neq,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( X != Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_155_dense,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ? [Z: A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ Z )
% 2.91/1.53 & ( ord_less @ A @ Z @ Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_156_order_Oasym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_157_neq__iff,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( X != Y2 )
% 2.91/1.53 = ( ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 | ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_158_neqE,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( X != Y2 )
% 2.91/1.53 => ( ~ ( ord_less @ A @ X @ Y2 )
% 2.91/1.53 => ( ord_less @ A @ Y2 @ X ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_159_gt__ex,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( no_top @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A] :
% 2.91/1.53 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_160_lt__ex,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A] :
% 2.91/1.53 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_161_order__less__subst2,axiom,
% 2.91/1.53 ! [A: $tType,C: $tType] :
% 2.91/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less @ C @ ( F @ B3 ) @ C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_162_order__less__subst1,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_163_ord__less__eq__subst,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ( F @ B3 )
% 2.91/1.53 = C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_164_ord__eq__less__subst,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( A2
% 2.91/1.53 = ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_165_powr__powr__swap,axiom,
% 2.91/1.53 ! [X: real,A2: real,B3: real] :
% 2.91/1.53 ( ( powr @ real @ ( powr @ real @ X @ A2 ) @ B3 )
% 2.91/1.53 = ( powr @ real @ ( powr @ real @ X @ B3 ) @ A2 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_166_tree_Orel__inject_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ B,Y22: B,Y23: tree @ B] :
% 2.91/1.53 ( ( rel_tree @ A @ B @ R5 @ ( node @ A @ X21 @ X22 @ X23 ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) )
% 2.91/1.53 = ( ( rel_tree @ A @ B @ R5 @ X21 @ Y21 )
% 2.91/1.53 & ( R5 @ X22 @ Y22 )
% 2.91/1.53 & ( rel_tree @ A @ B @ R5 @ X23 @ Y23 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_167_tree_Orel__intros_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,X21: tree @ A,Y21: tree @ B,X22: A,Y22: B,X23: tree @ A,Y23: tree @ B] :
% 2.91/1.53 ( ( rel_tree @ A @ B @ R5 @ X21 @ Y21 )
% 2.91/1.53 => ( ( R5 @ X22 @ Y22 )
% 2.91/1.53 => ( ( rel_tree @ A @ B @ R5 @ X23 @ Y23 )
% 2.91/1.53 => ( rel_tree @ A @ B @ R5 @ ( node @ A @ X21 @ X22 @ X23 ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_168_tree_Octr__transfer_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o] : ( rel_tree @ A @ B @ R5 @ ( leaf @ A ) @ ( leaf @ B ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_169_tree_Orel__refl__strong,axiom,
% 2.91/1.53 ! [A: $tType,X: tree @ A,Ra: A > A > $o] :
% 2.91/1.53 ( ! [Z: A] :
% 2.91/1.53 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 2.91/1.53 => ( Ra @ Z @ Z ) )
% 2.91/1.53 => ( rel_tree @ A @ A @ Ra @ X @ X ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_170_tree_Orel__mono__strong,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,X: tree @ A,Y2: tree @ B,Ra: A > B > $o] :
% 2.91/1.53 ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 2.91/1.53 => ( ! [Z: A,Yb: B] :
% 2.91/1.53 ( ( member @ A @ Z @ ( set_tree @ A @ X ) )
% 2.91/1.53 => ( ( member @ B @ Yb @ ( set_tree @ B @ Y2 ) )
% 2.91/1.53 => ( ( R5 @ Z @ Yb )
% 2.91/1.53 => ( Ra @ Z @ Yb ) ) ) )
% 2.91/1.53 => ( rel_tree @ A @ B @ Ra @ X @ Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_171_tree_Orel__cong,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,X: tree @ A,Ya: tree @ A,Y2: tree @ B,Xa: tree @ B,R5: A > B > $o,Ra: A > B > $o] :
% 2.91/1.53 ( ( X = Ya )
% 2.91/1.53 => ( ( Y2 = Xa )
% 2.91/1.53 => ( ! [Z: A,Yb: B] :
% 2.91/1.53 ( ( member @ A @ Z @ ( set_tree @ A @ Ya ) )
% 2.91/1.53 => ( ( member @ B @ Yb @ ( set_tree @ B @ Xa ) )
% 2.91/1.53 => ( ( R5 @ Z @ Yb )
% 2.91/1.53 = ( Ra @ Z @ Yb ) ) ) )
% 2.91/1.53 => ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 2.91/1.53 = ( rel_tree @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_172_powr__less__mono,axiom,
% 2.91/1.53 ! [A2: real,B3: real,X: real] :
% 2.91/1.53 ( ( ord_less @ real @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.91/1.53 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_173_powr__less__cancel,axiom,
% 2.91/1.53 ! [X: real,A2: real,B3: real] :
% 2.91/1.53 ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B3 ) )
% 2.91/1.53 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.91/1.53 => ( ord_less @ real @ A2 @ B3 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_174_t__splay_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A] :
% 2.91/1.53 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 2.91/1.53 = ( one_one @ nat ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_175_splay__max_Osimps_I1_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 2.91/1.53 = ( leaf @ A ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_176_set__splay__max,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A] :
% 2.91/1.53 ( ( set_tree @ A @ ( splay_splay_max @ A @ T ) )
% 2.91/1.53 = ( set_tree @ A @ T ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_177_bst__splay__max,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_178_tree_Orel__induct,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,X: tree @ A,Y2: tree @ B,Q: ( tree @ A ) > ( tree @ B ) > $o] :
% 2.91/1.53 ( ( rel_tree @ A @ B @ R5 @ X @ Y2 )
% 2.91/1.53 => ( ( Q @ ( leaf @ A ) @ ( leaf @ B ) )
% 2.91/1.53 => ( ! [A21: tree @ A,A222: A,A23: tree @ A,B21: tree @ B,B22: B,B23: tree @ B] :
% 2.91/1.53 ( ( Q @ A21 @ B21 )
% 2.91/1.53 => ( ( R5 @ A222 @ B22 )
% 2.91/1.53 => ( ( Q @ A23 @ B23 )
% 2.91/1.53 => ( Q @ ( node @ A @ A21 @ A222 @ A23 ) @ ( node @ B @ B21 @ B22 @ B23 ) ) ) ) )
% 2.91/1.53 => ( Q @ X @ Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_179_tree_Orel__cases,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,A2: tree @ A,B3: tree @ B] :
% 2.91/1.53 ( ( rel_tree @ A @ B @ R5 @ A2 @ B3 )
% 2.91/1.53 => ( ( ( A2
% 2.91/1.53 = ( leaf @ A ) )
% 2.91/1.53 => ( B3
% 2.91/1.53 != ( leaf @ B ) ) )
% 2.91/1.53 => ~ ! [X1: tree @ A,X24: A,X32: tree @ A] :
% 2.91/1.53 ( ( A2
% 2.91/1.53 = ( node @ A @ X1 @ X24 @ X32 ) )
% 2.91/1.53 => ! [Y1: tree @ B,Y24: B,Y32: tree @ B] :
% 2.91/1.53 ( ( B3
% 2.91/1.53 = ( node @ B @ Y1 @ Y24 @ Y32 ) )
% 2.91/1.53 => ( ( rel_tree @ A @ B @ R5 @ X1 @ Y1 )
% 2.91/1.53 => ( ( R5 @ X24 @ Y24 )
% 2.91/1.53 => ~ ( rel_tree @ A @ B @ R5 @ X32 @ Y32 ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_180_tree_Orel__distinct_I1_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,Y21: tree @ B,Y22: B,Y23: tree @ B] :
% 2.91/1.53 ~ ( rel_tree @ A @ B @ R5 @ ( leaf @ A ) @ ( node @ B @ Y21 @ Y22 @ Y23 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_181_tree_Orel__distinct_I2_J,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType,R5: A > B > $o,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 2.91/1.53 ~ ( rel_tree @ A @ B @ R5 @ ( node @ A @ Y21 @ Y22 @ Y23 ) @ ( leaf @ B ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_182_splay_Osimps_I9_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B3 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 2.91/1.53 = ( node @ A @ ( node @ A @ Lb @ B3 @ La ) @ A2 @ Ra2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_183_splay_Osimps_I3_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B3 @ Rb ) )
% 2.91/1.53 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B3 @ Rb ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_184_dual__order_Oantisym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( A2 = B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_185_dual__order_Otrans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 2.91/1.53 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_186_linorder__wlog,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [P: A > A > $o,A2: A,B3: A] :
% 2.91/1.53 ( ! [A6: A,B2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A6 @ B2 )
% 2.91/1.53 => ( P @ A6 @ B2 ) )
% 2.91/1.53 => ( ! [A6: A,B2: A] :
% 2.91/1.53 ( ( P @ B2 @ A6 )
% 2.91/1.53 => ( P @ A6 @ B2 ) )
% 2.91/1.53 => ( P @ A2 @ B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_187_dual__order_Orefl,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_188_order__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 2.91/1.53 => ( ord_less_eq @ A @ X @ Z4 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_189_order__class_Oorder_Oantisym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.91/1.53 => ( A2 = B3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_190_ord__le__eq__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( B3 = C3 )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_191_ord__eq__le__trans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( ord @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( A2 = B3 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_192_antisym__conv,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [Y2: A,X: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ Y2 @ X )
% 2.91/1.53 => ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 = ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_193_le__cases3,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A,Z4: A] :
% 2.91/1.53 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ Y2 @ Z4 ) )
% 2.91/1.53 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ X @ Z4 ) )
% 2.91/1.53 => ( ( ( ord_less_eq @ A @ X @ Z4 )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ Z4 @ Y2 ) )
% 2.91/1.53 => ( ( ( ord_less_eq @ A @ Z4 @ Y2 )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 2.91/1.53 => ( ( ( ord_less_eq @ A @ Y2 @ Z4 )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ Z4 @ X ) )
% 2.91/1.53 => ~ ( ( ord_less_eq @ A @ Z4 @ X )
% 2.91/1.53 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_194_order_Otrans,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_195_le__cases,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_196_eq__refl,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( preorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( X = Y2 )
% 2.91/1.53 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_197_linear,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 | ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_198_antisym,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,Y2: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X @ Y2 )
% 2.91/1.53 => ( ( ord_less_eq @ A @ Y2 @ X )
% 2.91/1.53 => ( X = Y2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_199_eq__iff,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( order @ A @ ( type2 @ A ) )
% 2.91/1.53 => ( ( ^ [Y4: A,Z5: A] : ( Y4 = Z5 ) )
% 2.91/1.53 = ( ^ [X2: A,Y: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.91/1.53 & ( ord_less_eq @ A @ Y @ X2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_200_ord__le__eq__subst,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > B,C3: B] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ( F @ B3 )
% 2.91/1.53 = C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less_eq @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_201_ord__eq__le__subst,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( ord @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( A2
% 2.91/1.53 = ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_202_order__subst2,axiom,
% 2.91/1.53 ! [A: $tType,C: $tType] :
% 2.91/1.53 ( ( ( order @ C @ ( type2 @ C ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,B3: A,F: A > C,C3: C] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 2.91/1.53 => ( ! [X3: A,Y3: A] :
% 2.91/1.53 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ C @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less_eq @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_203_order__subst1,axiom,
% 2.91/1.53 ! [A: $tType,B: $tType] :
% 2.91/1.53 ( ( ( order @ B @ ( type2 @ B ) )
% 2.91/1.53 & ( order @ A @ ( type2 @ A ) ) )
% 2.91/1.53 => ! [A2: A,F: B > A,B3: B,C3: B] :
% 2.91/1.53 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 2.91/1.53 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.91/1.53 => ( ! [X3: B,Y3: B] :
% 2.91/1.53 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.91/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.91/1.53 => ( ord_less_eq @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_204_le__fun__def,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType] :
% 2.91/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 => ( ( ord_less_eq @ ( A > B ) )
% 2.91/1.53 = ( ^ [F3: A > B,G2: A > B] :
% 2.91/1.53 ! [X2: A] : ( ord_less_eq @ B @ ( F3 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_205_le__funI,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType] :
% 2.91/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 => ! [F: A > B,G: A > B] :
% 2.91/1.53 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.91/1.53 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_206_le__funE,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType] :
% 2.91/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 => ! [F: A > B,G: A > B,X: A] :
% 2.91/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.91/1.53 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_207_le__funD,axiom,
% 2.91/1.53 ! [B: $tType,A: $tType] :
% 2.91/1.53 ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.53 => ! [F: A > B,G: A > B,X: A] :
% 2.91/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.91/1.53 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_208_splay__max_Osimps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [La: tree @ A,A2: A] :
% 2.91/1.53 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 2.91/1.53 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_209_splay__max__Leaf,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A,L2: tree @ A,A2: A,R2: tree @ A] :
% 2.91/1.53 ( ( ( splay_splay_max @ A @ T )
% 2.91/1.53 = ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 => ( R2
% 2.91/1.53 = ( leaf @ A ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_210_splay_Osimps_I13_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,X: A,B3: A,La: tree @ A,Lb: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ X )
% 2.91/1.53 => ( ( ord_less @ A @ B3 @ X )
% 2.91/1.53 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B3 @ ( leaf @ A ) ) ) )
% 2.91/1.53 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B3 @ ( leaf @ A ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_211_splay_Osimps_I12_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,X: A,B3: A,La: tree @ A,Rb: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ X )
% 2.91/1.53 => ( ( ord_less @ A @ X @ B3 )
% 2.91/1.53 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ Rb ) ) )
% 2.91/1.53 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B3 @ Rb ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_212_splay_Osimps_I10_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,X: A,L2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ X )
% 2.91/1.53 => ( ( splay_splay @ A @ X @ ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) )
% 2.91/1.53 = ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_213_splay_Osimps_I7_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,B3: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ B3 )
% 2.91/1.53 => ( ( ord_less @ A @ A2 @ X )
% 2.91/1.53 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B3 @ Rb ) )
% 2.91/1.53 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ Rb ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_214_splay_Osimps_I5_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: A,A2: A,B3: A,Ra2: tree @ A,Rb: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ X @ A2 )
% 2.91/1.53 => ( ( ord_less @ A @ X @ B3 )
% 2.91/1.53 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B3 @ Rb ) )
% 2.91/1.53 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B3 @ Rb ) ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_215_splay_Osimps_I4_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [A2: A,B3: A,R2: tree @ A] :
% 2.91/1.53 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.53 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) )
% 2.91/1.53 = ( node @ A @ ( leaf @ A ) @ B3 @ R2 ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_216_splay__max__eq__splay__ex,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [T: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ T )
% 2.91/1.53 => ? [A6: A] :
% 2.91/1.53 ( ( splay_splay_max @ A @ T )
% 2.91/1.53 = ( splay_splay @ A @ A6 @ T ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_217_bst_Osimps_I2_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [L2: tree @ A,A2: A,R2: tree @ A] :
% 2.91/1.53 ( ( linorder_bst @ A @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.91/1.53 = ( ( linorder_bst @ A @ L2 )
% 2.91/1.53 & ( linorder_bst @ A @ R2 )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ L2 ) )
% 2.91/1.53 => ( ord_less @ A @ X2 @ A2 ) )
% 2.91/1.53 & ! [X2: A] :
% 2.91/1.53 ( ( member @ A @ X2 @ ( set_tree @ A @ R2 ) )
% 2.91/1.53 => ( ord_less @ A @ A2 @ X2 ) ) ) ) ) ).
% 2.91/1.53
% 2.91/1.53 thf(fact_218_bst_Oelims_I3_J,axiom,
% 2.91/1.53 ! [A: $tType] :
% 2.91/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.53 => ! [X: tree @ A] :
% 2.91/1.53 ( ~ ( linorder_bst @ A @ X )
% 2.91/1.53 => ~ ! [L: tree @ A,A6: A,R: tree @ A] :
% 2.91/1.53 ( ( X
% 2.91/1.53 = ( node @ A @ L @ A6 @ R ) )
% 2.91/1.53 => ( ( linorder_bst @ A @ L )
% 2.91/1.53 & ( linorder_bst @ A @ R )
% 2.91/1.53 & ! [X3: A] :
% 2.91/1.53 ( ( member @ A @ X3 @ ( set_tree @ A @ L ) )
% 2.91/1.53 => ( ord_less @ A @ X3 @ A6 ) )
% 2.91/1.54 & ! [X3: A] :
% 2.91/1.54 ( ( member @ A @ X3 @ ( set_tree @ A @ R ) )
% 2.91/1.54 => ( ord_less @ A @ A6 @ X3 ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_219_splay__bstR,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: tree @ A,A2: A,L2: tree @ A,E: A,R2: tree @ A,X: A] :
% 2.91/1.54 ( ( linorder_bst @ A @ T )
% 2.91/1.54 => ( ( ( splay_splay @ A @ A2 @ T )
% 2.91/1.54 = ( node @ A @ L2 @ E @ R2 ) )
% 2.91/1.54 => ( ( member @ A @ X @ ( set_tree @ A @ R2 ) )
% 2.91/1.54 => ( ord_less @ A @ A2 @ X ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_220_splay__bstL,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: tree @ A,A2: A,L2: tree @ A,E: A,R2: tree @ A,X: A] :
% 2.91/1.54 ( ( linorder_bst @ A @ T )
% 2.91/1.54 => ( ( ( splay_splay @ A @ A2 @ T )
% 2.91/1.54 = ( node @ A @ L2 @ E @ R2 ) )
% 2.91/1.54 => ( ( member @ A @ X @ ( set_tree @ A @ L2 ) )
% 2.91/1.54 => ( ord_less @ A @ X @ A2 ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_221_minf_I8_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: A] :
% 2.91/1.54 ? [Z: A] :
% 2.91/1.54 ! [X4: A] :
% 2.91/1.54 ( ( ord_less @ A @ X4 @ Z )
% 2.91/1.54 => ~ ( ord_less_eq @ A @ T @ X4 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_222_minf_I6_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: A] :
% 2.91/1.54 ? [Z: A] :
% 2.91/1.54 ! [X4: A] :
% 2.91/1.54 ( ( ord_less @ A @ X4 @ Z )
% 2.91/1.54 => ( ord_less_eq @ A @ X4 @ T ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_223_pinf_I8_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: A] :
% 2.91/1.54 ? [Z: A] :
% 2.91/1.54 ! [X4: A] :
% 2.91/1.54 ( ( ord_less @ A @ Z @ X4 )
% 2.91/1.54 => ( ord_less_eq @ A @ T @ X4 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_224_pinf_I6_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [T: A] :
% 2.91/1.54 ? [Z: A] :
% 2.91/1.54 ! [X4: A] :
% 2.91/1.54 ( ( ord_less @ A @ Z @ X4 )
% 2.91/1.54 => ~ ( ord_less_eq @ A @ X4 @ T ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_225_complete__interval,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,P: A > $o] :
% 2.91/1.54 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.54 => ( ( P @ A2 )
% 2.91/1.54 => ( ~ ( P @ B3 )
% 2.91/1.54 => ? [C2: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ A2 @ C2 )
% 2.91/1.54 & ( ord_less_eq @ A @ C2 @ B3 )
% 2.91/1.54 & ! [X4: A] :
% 2.91/1.54 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 2.91/1.54 & ( ord_less @ A @ X4 @ C2 ) )
% 2.91/1.54 => ( P @ X4 ) )
% 2.91/1.54 & ! [D: A] :
% 2.91/1.54 ( ! [X3: A] :
% 2.91/1.54 ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 2.91/1.54 & ( ord_less @ A @ X3 @ D ) )
% 2.91/1.54 => ( P @ X3 ) )
% 2.91/1.54 => ( ord_less_eq @ A @ D @ C2 ) ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_226_t__splay__simps_I9_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A,Rr2: tree @ A,L2: tree @ A,Rl2: tree @ A] :
% 2.91/1.54 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.54 => ( ( ord_less @ A @ C3 @ A2 )
% 2.91/1.54 => ( ( ( Rr2
% 2.91/1.54 = ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.91/1.54 = ( one_one @ nat ) ) )
% 2.91/1.54 & ( ( Rr2
% 2.91/1.54 != ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.91/1.54 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_227_add__right__cancel,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ B3 @ A2 )
% 2.91/1.54 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.91/1.54 = ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_228_add__left__cancel,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ A2 @ B3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.91/1.54 = ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_229_predicate2I,axiom,
% 2.91/1.54 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 2.91/1.54 ( ! [X3: A,Y3: B] :
% 2.91/1.54 ( ( P @ X3 @ Y3 )
% 2.91/1.54 => ( Q @ X3 @ Y3 ) )
% 2.91/1.54 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_230_add__le__cancel__right,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,C3: A,B3: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 2.91/1.54 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_231_add__le__cancel__left,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [C3: A,A2: A,B3: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 2.91/1.54 = ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_232_add__less__cancel__right,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,C3: A,B3: A] :
% 2.91/1.54 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 2.91/1.54 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_233_add__less__cancel__left,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [C3: A,A2: A,B3: A] :
% 2.91/1.54 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 2.91/1.54 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_234_t__splay__simps_I4_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.91/1.54 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.54 => ( ( ord_less @ A @ A2 @ C3 )
% 2.91/1.54 => ( ( ( Ll
% 2.91/1.54 = ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 2.91/1.54 = ( one_one @ nat ) ) )
% 2.91/1.54 & ( ( Ll
% 2.91/1.54 != ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 2.91/1.54 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_235_t__splay__simps_I5_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 2.91/1.54 ( ( ord_less @ A @ A2 @ B3 )
% 2.91/1.54 => ( ( ord_less @ A @ C3 @ A2 )
% 2.91/1.54 => ( ( ( Lr
% 2.91/1.54 = ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 2.91/1.54 = ( one_one @ nat ) ) )
% 2.91/1.54 & ( ( Lr
% 2.91/1.54 != ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B3 @ R2 ) )
% 2.91/1.54 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_236_t__splay__simps_I8_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A,Rl2: tree @ A,L2: tree @ A,Rr2: tree @ A] :
% 2.91/1.54 ( ( ord_less @ A @ B3 @ A2 )
% 2.91/1.54 => ( ( ord_less @ A @ A2 @ C3 )
% 2.91/1.54 => ( ( ( Rl2
% 2.91/1.54 = ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.91/1.54 = ( one_one @ nat ) ) )
% 2.91/1.54 & ( ( Rl2
% 2.91/1.54 != ( leaf @ A ) )
% 2.91/1.54 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B3 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.91/1.54 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_237_predicate2D,axiom,
% 2.91/1.54 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y2: B] :
% 2.91/1.54 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.91/1.54 => ( ( P @ X @ Y2 )
% 2.91/1.54 => ( Q @ X @ Y2 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_238_less__fun__def,axiom,
% 2.91/1.54 ! [B: $tType,A: $tType] :
% 2.91/1.54 ( ( ord @ B @ ( type2 @ B ) )
% 2.91/1.54 => ( ( ord_less @ ( A > B ) )
% 2.91/1.54 = ( ^ [F3: A > B,G2: A > B] :
% 2.91/1.54 ( ( ord_less_eq @ ( A > B ) @ F3 @ G2 )
% 2.91/1.54 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F3 ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_239_rev__predicate2D,axiom,
% 2.91/1.54 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y2: B,Q: A > B > $o] :
% 2.91/1.54 ( ( P @ X @ Y2 )
% 2.91/1.54 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.91/1.54 => ( Q @ X @ Y2 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_240_is__num__normalize_I1_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_241_add__right__imp__eq,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ B3 @ A2 )
% 2.91/1.54 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.91/1.54 => ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_242_add__left__imp__eq,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ A2 @ B3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.91/1.54 => ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_243_add_Oleft__commute,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.54 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A2 @ C3 ) )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_244_add_Ocommute,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( ( plus_plus @ A )
% 2.91/1.54 = ( ^ [A5: A,B4: A] : ( plus_plus @ A @ B4 @ A5 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_245_add_Oright__cancel,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [B3: A,A2: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ B3 @ A2 )
% 2.91/1.54 = ( plus_plus @ A @ C3 @ A2 ) )
% 2.91/1.54 = ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_246_add_Oleft__cancel,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( ( plus_plus @ A @ A2 @ B3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ C3 ) )
% 2.91/1.54 = ( B3 = C3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_247_add_Oassoc,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_248_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [I: A,J: A,K: A,L2: A] :
% 2.91/1.54 ( ( ( I = J )
% 2.91/1.54 & ( K = L2 ) )
% 2.91/1.54 => ( ( plus_plus @ A @ I @ K )
% 2.91/1.54 = ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C3 )
% 2.91/1.54 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_250_add__le__imp__le__right,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,C3: A,B3: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) )
% 2.91/1.54 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_251_add__le__imp__le__left,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [C3: A,A2: A,B3: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B3 ) )
% 2.91/1.54 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_252_le__iff__add,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( ( ord_less_eq @ A )
% 2.91/1.54 = ( ^ [A5: A,B4: A] :
% 2.91/1.54 ? [C4: A] :
% 2.91/1.54 ( B4
% 2.91/1.54 = ( plus_plus @ A @ A5 @ C4 ) ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(fact_253_add__right__mono,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.91/1.54 => ! [A2: A,B3: A,C3: A] :
% 2.91/1.54 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.91/1.54 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B3 @ C3 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( type @ A @ ( type2 @ A ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( order @ A @ ( type2 @ A ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.91/1.54 ! [A: $tType] :
% 2.91/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 2.91/1.54 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.91/1.54 ! [A7: $tType,A8: $tType] :
% 2.91/1.54 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 2.91/1.54 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.91/1.54 ! [A7: $tType,A8: $tType] :
% 2.91/1.54 ( ( order @ A8 @ ( type2 @ A8 ) )
% 2.91/1.54 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_fun___Orderings_Oord,axiom,
% 2.91/1.54 ! [A7: $tType,A8: $tType] :
% 2.91/1.54 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 2.91/1.54 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 2.91/1.54 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.91/1.54 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.91/1.54 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.91/1.54 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.91/1.54 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.91/1.54 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.91/1.54 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.91/1.54 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.91/1.54 wellorder @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.91/1.54 preorder @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.91/1.54 linorder @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.91/1.54 no_top @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.91/1.54 order @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.91/1.54 ord @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.91/1.54 one @ nat @ ( type2 @ nat ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 2.91/1.54 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.91/1.54 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.91/1.54 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.91/1.54 preorder @ $o @ ( type2 @ $o ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 2.91/1.54 linorder @ $o @ ( type2 @ $o ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.91/1.54 order @ $o @ ( type2 @ $o ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.91/1.54 ord @ $o @ ( type2 @ $o ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_11,axiom,
% 2.91/1.54 condit1037483654norder @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_12,axiom,
% 2.91/1.54 ordere236663937imp_le @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_13,axiom,
% 2.91/1.54 ordere779506340up_add @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_14,axiom,
% 2.91/1.54 cancel_semigroup_add @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_15,axiom,
% 2.91/1.54 linordered_semidom @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 2.91/1.54 dense_linorder @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_16,axiom,
% 2.91/1.54 ab_semigroup_add @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 2.91/1.54 dense_order @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Osemigroup__add_17,axiom,
% 2.91/1.54 semigroup_add @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Opreorder_18,axiom,
% 2.91/1.54 preorder @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Olinorder_19,axiom,
% 2.91/1.54 linorder @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 2.91/1.54 ln @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Ono__top_20,axiom,
% 2.91/1.54 no_top @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Ono__bot,axiom,
% 2.91/1.54 no_bot @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 2.91/1.54 group_add @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Oorder_21,axiom,
% 2.91/1.54 order @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 2.91/1.54 neg_numeral @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Orderings_Oord_22,axiom,
% 2.91/1.54 ord @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(tcon_Real_Oreal___Groups_Oone_23,axiom,
% 2.91/1.54 one @ real @ ( type2 @ real ) ).
% 2.91/1.54
% 2.91/1.54 thf(help_If_3_1_T,axiom,
% 2.91/1.54 ! [P: $o] :
% 2.91/1.54 ( ( P = $true )
% 2.91/1.54 | ( P = $false ) ) ).
% 2.91/1.54
% 2.91/1.54 thf(help_If_2_1_T,axiom,
% 2.91/1.54 ! [A: $tType,X: A,Y2: A] :
% 2.91/1.54 ( ( if @ A @ $false @ X @ Y2 )
% 2.91/1.54 = Y2 ) ).
% 2.91/1.54
% 2.91/1.54 thf(help_If_1_1_T,axiom,
% 2.91/1.54 ! [A: $tType,X: A,Y2: A] :
% 2.91/1.54 ( ( if @ A @ $true @ X @ Y2 )
% 2.91/1.54 = X ) ).
% 2.91/1.54
% 2.91/1.54 thf(tfree_0,hypothesis,
% 2.91/1.54 linorder @ a @ ( type2 @ a ) ).
% 2.91/1.54
% 2.91/1.54 thf(conj_0,hypothesis,
% 2.91/1.54 ! [La2: tree @ a,Ra3: tree @ a] :
% 2.91/1.54 ( ( member @ ( tree @ a ) @ ( node @ a @ La2 @ a2 @ Ra3 ) @ ( subtrees @ a @ t ) )
% 2.91/1.54 => thesis ) ).
% 2.91/1.54
% 2.91/1.54 thf(conj_1,conjecture,
% 2.91/1.54 thesis ).
% 2.91/1.54 ------------------------
% 2.91/1.56 % (24135)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/2Mi)
% 2.91/1.56 % (24134)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_23804 for (2999ds/27Mi)
% 2.91/1.56 % (24136)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_23804 for (2999ds/2Mi)
% 2.91/1.56 % (24135)Instruction limit reached!
% 2.91/1.56 % (24135)------------------------------
% 2.91/1.56 % (24135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.56 % (24135)Termination reason: Unknown
% 2.91/1.56 % (24135)Termination phase: shuffling
% 2.91/1.56
% 2.91/1.56 % (24135)Memory used [KB]: 1407
% 2.91/1.56 % (24135)Time elapsed: 0.002 s
% 2.91/1.56 % (24135)Instructions burned: 3 (million)
% 2.91/1.56 % (24135)------------------------------
% 2.91/1.56 % (24135)------------------------------
% 2.91/1.56 % (24136)Instruction limit reached!
% 2.91/1.56 % (24136)------------------------------
% 2.91/1.56 % (24136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.56 % (24136)Termination reason: Unknown
% 2.91/1.56 % (24136)Termination phase: shuffling
% 2.91/1.56
% 2.91/1.56 % (24136)Memory used [KB]: 1407
% 2.91/1.56 % (24136)Time elapsed: 0.002 s
% 2.91/1.56 % (24136)Instructions burned: 2 (million)
% 2.91/1.56 % (24136)------------------------------
% 2.91/1.56 % (24136)------------------------------
% 2.91/1.56 % (24132)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/183Mi)
% 2.91/1.56 % (24133)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_23804 for (2999ds/4Mi)
% 2.91/1.56 % (24137)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_23804 for (2999ds/275Mi)
% 2.91/1.56 % (24138)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/18Mi)
% 2.91/1.57 % (24134)Instruction limit reached!
% 2.91/1.57 % (24134)------------------------------
% 2.91/1.57 % (24134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (24134)Termination reason: Unknown
% 2.91/1.57 % (24134)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (24134)Memory used [KB]: 2046
% 2.91/1.57 % (24134)Time elapsed: 0.010 s
% 2.91/1.57 % (24134)Instructions burned: 27 (million)
% 2.91/1.57 % (24134)------------------------------
% 2.91/1.57 % (24134)------------------------------
% 2.91/1.57 % (24133)Instruction limit reached!
% 2.91/1.57 % (24133)------------------------------
% 2.91/1.57 % (24133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (24133)Termination reason: Unknown
% 2.91/1.57 % (24133)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (24133)Memory used [KB]: 1535
% 2.91/1.57 % (24133)Time elapsed: 0.005 s
% 2.91/1.57 % (24133)Instructions burned: 5 (million)
% 2.91/1.57 % (24133)------------------------------
% 2.91/1.57 % (24133)------------------------------
% 2.91/1.57 % (24139)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/3Mi)
% 2.91/1.57 % (24140)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_23804 for (2999ds/37Mi)
% 2.91/1.57 % (24139)Instruction limit reached!
% 2.91/1.57 % (24139)------------------------------
% 2.91/1.57 % (24139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (24139)Termination reason: Unknown
% 2.91/1.57 % (24139)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (24139)Memory used [KB]: 1407
% 2.91/1.57 % (24139)Time elapsed: 0.002 s
% 2.91/1.57 % (24139)Instructions burned: 3 (million)
% 2.91/1.57 % (24139)------------------------------
% 2.91/1.57 % (24139)------------------------------
% 2.91/1.57 % (24141)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_23804 for (2999ds/15Mi)
% 2.91/1.58 % (24138)Instruction limit reached!
% 2.91/1.58 % (24138)------------------------------
% 2.91/1.58 % (24138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (24138)Termination reason: Unknown
% 2.91/1.58 % (24138)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (24138)Memory used [KB]: 1791
% 2.91/1.58 % (24138)Time elapsed: 0.014 s
% 2.91/1.58 % (24138)Instructions burned: 18 (million)
% 2.91/1.58 % (24138)------------------------------
% 2.91/1.58 % (24138)------------------------------
% 2.91/1.58 % (24143)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_23804 for (2999ds/1041Mi)
% 2.91/1.58 % (24140)Instruction limit reached!
% 2.91/1.58 % (24140)------------------------------
% 2.91/1.58 % (24140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (24140)Termination reason: Unknown
% 2.91/1.58 % (24140)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (24140)Memory used [KB]: 2174
% 2.91/1.58 % (24140)Time elapsed: 0.013 s
% 2.91/1.58 % (24140)Instructions burned: 37 (million)
% 2.91/1.58 % (24140)------------------------------
% 2.91/1.58 % (24140)------------------------------
% 2.91/1.58 % (24141)Instruction limit reached!
% 2.91/1.58 % (24141)------------------------------
% 2.91/1.58 % (24141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (24141)Termination reason: Unknown
% 2.91/1.58 % (24141)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (24141)Memory used [KB]: 1663
% 2.91/1.58 % (24141)Time elapsed: 0.006 s
% 2.91/1.58 % (24141)Instructions burned: 15 (million)
% 2.91/1.58 % (24141)------------------------------
% 2.91/1.58 % (24141)------------------------------
% 2.91/1.58 % (24142)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_23804 for (2999ds/3Mi)
% 2.91/1.59 % (24142)Instruction limit reached!
% 2.91/1.59 % (24142)------------------------------
% 2.91/1.59 % (24142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.59 % (24142)Termination reason: Unknown
% 2.91/1.59 % (24142)Termination phase: shuffling
% 2.91/1.59
% 2.91/1.59 % (24142)Memory used [KB]: 1407
% 2.91/1.59 % (24142)Time elapsed: 0.004 s
% 2.91/1.59 % (24142)Instructions burned: 3 (million)
% 2.91/1.59 % (24142)------------------------------
% 2.91/1.59 % (24142)------------------------------
% 2.91/1.59 % (24146)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_23804 for (2999ds/3Mi)
% 2.91/1.59 % (24145)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/16Mi)
% 2.91/1.59 % (24146)Instruction limit reached!
% 2.91/1.59 % (24146)------------------------------
% 2.91/1.59 % (24146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.59 % (24146)Termination reason: Unknown
% 2.91/1.59 % (24146)Termination phase: shuffling
% 2.91/1.59
% 2.91/1.59 % (24146)Memory used [KB]: 1407
% 2.91/1.59 % (24146)Time elapsed: 0.002 s
% 2.91/1.59 % (24146)Instructions burned: 3 (million)
% 2.91/1.59 % (24146)------------------------------
% 2.91/1.59 % (24146)------------------------------
% 2.91/1.59 % (24144)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/7Mi)
% 2.91/1.60 % (24145)Instruction limit reached!
% 2.91/1.60 % (24145)------------------------------
% 2.91/1.60 % (24145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (24145)Termination reason: Unknown
% 2.91/1.60 % (24145)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (24145)Memory used [KB]: 1791
% 2.91/1.60 % (24145)Time elapsed: 0.008 s
% 2.91/1.60 % (24145)Instructions burned: 17 (million)
% 2.91/1.60 % (24145)------------------------------
% 2.91/1.60 % (24145)------------------------------
% 2.97/1.60 % (24144)Instruction limit reached!
% 2.97/1.60 % (24144)------------------------------
% 2.97/1.60 % (24144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.60 % (24144)Termination reason: Unknown
% 2.97/1.60 % (24144)Termination phase: shuffling
% 2.97/1.60
% 2.97/1.60 % (24144)Memory used [KB]: 1535
% 2.97/1.60 % (24144)Time elapsed: 0.007 s
% 2.97/1.60 % (24144)Instructions burned: 7 (million)
% 2.97/1.60 % (24144)------------------------------
% 2.97/1.60 % (24144)------------------------------
% 2.97/1.60 % (24148)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/7Mi)
% 2.97/1.60 % (24148)Instruction limit reached!
% 2.97/1.60 % (24148)------------------------------
% 2.97/1.60 % (24148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.60 % (24148)Termination reason: Unknown
% 2.97/1.60 % (24148)Termination phase: shuffling
% 2.97/1.60
% 2.97/1.60 % (24148)Memory used [KB]: 1535
% 2.97/1.60 % (24148)Time elapsed: 0.004 s
% 2.97/1.60 % (24148)Instructions burned: 8 (million)
% 2.97/1.60 % (24148)------------------------------
% 2.97/1.60 % (24148)------------------------------
% 2.97/1.60 % (24147)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_23804 for (2999ds/3Mi)
% 2.97/1.61 % (24149)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23804 for (2999ds/3Mi)
% 2.97/1.61 % (24147)Instruction limit reached!
% 2.97/1.61 % (24147)------------------------------
% 2.97/1.61 % (24147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (24147)Termination reason: Unknown
% 2.97/1.61 % (24147)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (24147)Memory used [KB]: 1407
% 2.97/1.61 % (24147)Time elapsed: 0.004 s
% 2.97/1.61 % (24147)Instructions burned: 3 (million)
% 2.97/1.61 % (24147)------------------------------
% 2.97/1.61 % (24147)------------------------------
% 2.97/1.61 % (24137)First to succeed.
% 2.97/1.61 % (24149)Instruction limit reached!
% 2.97/1.61 % (24149)------------------------------
% 2.97/1.61 % (24149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (24149)Termination reason: Unknown
% 2.97/1.61 % (24149)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (24149)Memory used [KB]: 1535
% 2.97/1.61 % (24149)Time elapsed: 0.003 s
% 2.97/1.61 % (24149)Instructions burned: 5 (million)
% 2.97/1.61 % (24149)------------------------------
% 2.97/1.61 % (24149)------------------------------
% 2.97/1.61 % (24137)Refutation found. Thanks to Tanya!
% 2.97/1.61 % SZS status Theorem for DTF2THF_23804
% 2.97/1.61 % SZS output start Proof for DTF2THF_23804
% 2.97/1.61 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.97/1.61 thf(type_def_7, type, set: ($tType) > $tType).
% 2.97/1.61 thf(type_def_8, type, tree: ($tType) > $tType).
% 2.97/1.61 thf(type_def_9, type, nat: $tType).
% 2.97/1.61 thf(type_def_10, type, real: $tType).
% 2.97/1.61 thf(type_def_11, type, a: $tType).
% 2.97/1.61 thf(func_def_0, type, tree: ($tType) > $tType).
% 2.97/1.61 thf(func_def_1, type, real: $tType).
% 2.97/1.61 thf(func_def_2, type, set: ($tType) > $tType).
% 2.97/1.61 thf(func_def_3, type, nat: $tType).
% 2.97/1.61 thf(func_def_4, type, itself: ($tType) > $tType).
% 2.97/1.61 thf(func_def_5, type, a: $tType).
% 2.97/1.61 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_7, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_9, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_11, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_12, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_13, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_14, type, ln: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_15, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_16, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_17, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_18, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_19, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_20, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_21, type, dense_linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_22, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_23, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_24, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_26, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_27, type, condit1037483654norder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.61 thf(func_def_28, type, one_one: !>[X0: $tType]:(X0)).
% 2.97/1.61 thf(func_def_29, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_30, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_31, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.97/1.61 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.97/1.61 thf(func_def_33, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.97/1.61 thf(func_def_34, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.97/1.61 thf(func_def_35, type, splay_is_root: !>[X0: $tType]:(X0 > tree @ X0 > $o)).
% 2.97/1.61 thf(func_def_36, type, splay_splay: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_37, type, splay_splay_max: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_38, type, splay_914434265_splay: !>[X0: $tType]:(X0 > tree @ X0 > nat)).
% 2.97/1.61 thf(func_def_39, type, splay_266122055elle_A: !>[X0: $tType]:(X0 > tree @ X0 > real)).
% 2.97/1.61 thf(func_def_40, type, powr: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_41, type, linorder_bst: !>[X0: $tType]:(tree @ X0 > $o)).
% 2.97/1.61 thf(func_def_42, type, linorder_bst_eq: !>[X0: $tType]:(tree @ X0 > $o)).
% 2.97/1.61 thf(func_def_43, type, mirror: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_44, type, subtrees: !>[X0: $tType]:(tree @ X0 > set @ tree @ X0)).
% 2.97/1.61 thf(func_def_45, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 2.97/1.61 thf(func_def_46, type, node: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_47, type, case_tree: !>[X0: $tType, X1: $tType]:(X0 > (tree @ X1 > X1 > tree @ X1 > X0) > tree @ X1 > X0)).
% 2.97/1.61 thf(func_def_48, type, is_Leaf: !>[X0: $tType]:(tree @ X0 > $o)).
% 2.97/1.61 thf(func_def_49, type, left: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_50, type, pred_tree: !>[X0: $tType]:((X0 > $o) > tree @ X0 > $o)).
% 2.97/1.61 thf(func_def_51, type, rec_tree: !>[X0: $tType, X1: $tType]:(X0 > (tree @ X1 > X1 > tree @ X1 > X0 > X0 > X0) > tree @ X1 > X0)).
% 2.97/1.61 thf(func_def_52, type, rel_tree: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tree @ X0 > tree @ X1 > $o)).
% 2.97/1.61 thf(func_def_53, type, right: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_54, type, set_tree: !>[X0: $tType]:(tree @ X0 > set @ X0)).
% 2.97/1.61 thf(func_def_55, type, val: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_56, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.97/1.61 thf(func_def_57, type, a2: a).
% 2.97/1.61 thf(func_def_58, type, t: tree @ a).
% 2.97/1.61 thf(func_def_74, type, sP0: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0 > $o > $o)).
% 2.97/1.61 thf(func_def_75, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.97/1.61 thf(func_def_76, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.97/1.61 thf(func_def_77, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.97/1.61 thf(func_def_78, type, sK4: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.61 thf(func_def_79, type, sK5: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_80, type, sK6: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_81, type, sK7: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_82, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.97/1.61 thf(func_def_83, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.97/1.61 thf(func_def_84, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.97/1.61 thf(func_def_85, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.97/1.61 thf(func_def_86, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_87, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_88, type, sK14: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.61 thf(func_def_89, type, sK15: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_90, type, sK16: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_91, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_92, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_93, type, sK19: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.61 thf(func_def_94, type, sK20: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_95, type, sK21: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_96, type, sK22: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_97, type, sK23: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_98, type, sK24: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_99, type, sK25: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_100, type, sK26: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_101, type, sK27: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_102, type, sK28: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_103, type, sK29: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_104, type, sK30: !>[X0: $tType]:($o > tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_105, type, sK31: !>[X0: $tType]:($o > tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_106, type, sK32: !>[X0: $tType]:($o > tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_107, type, sK33: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_108, type, sK34: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_109, type, sK35: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_110, type, sK36: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_111, type, sK37: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.61 thf(func_def_112, type, sK38: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_113, type, sK39: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_114, type, sK40: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 2.97/1.61 thf(func_def_115, type, sK41: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 2.97/1.61 thf(func_def_116, type, sK42: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_117, type, sK43: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_118, type, sK44: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.61 thf(func_def_119, type, sK45: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_120, type, sK46: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_121, type, sK47: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_122, type, sK48: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_123, type, sK49: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_124, type, sK50: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.97/1.61 thf(func_def_125, type, sK51: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_126, type, sK52: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_127, type, sK53: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_128, type, sK54: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_129, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.97/1.61 thf(func_def_130, type, sK56: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 2.97/1.61 thf(func_def_131, type, sK57: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 2.97/1.61 thf(func_def_133, type, ph59: !>[X0: $tType]:(X0)).
% 2.97/1.61 thf(f1310,plain,(
% 2.97/1.61 $false),
% 2.97/1.61 inference(avatar_sat_refutation,[status(thm)],[f1301,f1302,f1308])).
% 2.97/1.61 thf(f1308,plain,(
% 2.97/1.61 ~spl58_2),
% 2.97/1.61 inference(avatar_contradiction_clause,[status(thm)],[f1307])).
% 2.97/1.61 thf(f1307,plain,(
% 2.97/1.61 $false | ~spl58_2),
% 2.97/1.61 inference(subsumption_resolution,[status(thm)],[f1306,f1255])).
% 2.97/1.61 thf(f1255,plain,(
% 2.97/1.61 ((member @ a @ a2 @ (set_tree @ a @ t)) = $true)),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f592])).
% 2.97/1.61 thf(f592,plain,(
% 2.97/1.61 ((member @ a @ a2 @ (set_tree @ a @ t)) = $true)),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f591])).
% 2.97/1.61 thf(f591,plain,(
% 2.97/1.61 (member @ a @ a2 @ (set_tree @ a @ t))),
% 2.97/1.61 inference(rectify,[status(thm)],[f1])).
% 2.97/1.61 thf(f1,axiom,(
% 2.97/1.61 (member @ a @ a2 @ (set_tree @ a @ t))),
% 2.97/1.61 file('/export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2THF_23804.p',fact_0_assms_I2_J)).
% 2.97/1.61 thf(f1306,plain,(
% 2.97/1.61 ((member @ a @ a2 @ (set_tree @ a @ t)) != $true) | ~spl58_2),
% 2.97/1.61 inference(trivial_inequality_removal,[status(thm)],[f1305])).
% 2.97/1.61 thf(f1305,plain,(
% 2.97/1.61 ($true != $true) | ((member @ a @ a2 @ (set_tree @ a @ t)) != $true) | ~spl58_2),
% 2.97/1.61 inference(superposition,[status(thm)],[f1300,f1192])).
% 2.97/1.61 thf(f1192,plain,(
% 2.97/1.61 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((member @ tree @ X0 @ (node @ X0 @ (sK33 @ X0 @ X2 @ X1) @ X1 @ (sK34 @ X0 @ X2 @ X1)) @ (subtrees @ X0 @ X2)) = $true) | ($true != (member @ X0 @ X1 @ (set_tree @ X0 @ X2)))) )),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f1071])).
% 2.97/1.61 thf(f1071,plain,(
% 2.97/1.61 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : (((member @ tree @ X0 @ (node @ X0 @ (sK33 @ X0 @ X2 @ X1) @ X1 @ (sK34 @ X0 @ X2 @ X1)) @ (subtrees @ X0 @ X2)) = $true) | ($true != (member @ X0 @ X1 @ (set_tree @ X0 @ X2))))),
% 2.97/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f937,f1070])).
% 2.97/1.61 thf(f1070,plain,(
% 2.97/1.61 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : (? [X3 : tree @ X0,X4 : tree @ X0] : ($true = (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2))) => ((member @ tree @ X0 @ (node @ X0 @ (sK33 @ X0 @ X2 @ X1) @ X1 @ (sK34 @ X0 @ X2 @ X1)) @ (subtrees @ X0 @ X2)) = $true))),
% 2.97/1.61 introduced(definition,[],[choice_axiom])).
% 2.97/1.61 thf(f937,plain,(
% 2.97/1.61 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : (? [X3 : tree @ X0,X4 : tree @ X0] : ($true = (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2))) | ($true != (member @ X0 @ X1 @ (set_tree @ X0 @ X2))))),
% 2.97/1.61 inference(ennf_transformation,[status(thm)],[f456])).
% 2.97/1.61 thf(f456,plain,(
% 2.97/1.61 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : (($true = (member @ X0 @ X1 @ (set_tree @ X0 @ X2))) => ? [X3 : tree @ X0,X4 : tree @ X0] : ($true = (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2))))),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f455])).
% 2.97/1.61 thf(f455,plain,(
% 2.97/1.61 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : ((member @ X0 @ X1 @ (set_tree @ X0 @ X2)) => ? [X3 : tree @ X0,X4 : tree @ X0] : (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2)))),
% 2.97/1.61 inference(rectify,[status(thm)],[f4])).
% 2.97/1.61 thf(f4,axiom,(
% 2.97/1.61 ! [X0 : $tType,X9 : X0,X10 : tree @ X0] : ((member @ X0 @ X9 @ (set_tree @ X0 @ X10)) => ? [X11 : tree @ X0,X12 : tree @ X0] : (member @ tree @ X0 @ (node @ X0 @ X11 @ X9 @ X12) @ (subtrees @ X0 @ X10)))),
% 2.97/1.61 file('/export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2THF_23804.p',fact_3_set__treeE)).
% 2.97/1.61 thf(f1300,plain,(
% 2.97/1.61 ( ! [X0 : tree @ a,X1 : tree @ a] : (($true != (member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t)))) ) | ~spl58_2),
% 2.97/1.61 inference(avatar_component_clause,[status(thm)],[f1299])).
% 2.97/1.61 thf(f1299,definition,(
% 2.97/1.61 spl58_2 <=> ! [X0 : tree @ a,X1 : tree @ a] : ($true != (member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t)))),
% 2.97/1.61 introduced(definition,[new_symbols(naming,[spl58_2])],[avatar_definition])).
% 2.97/1.61 thf(f1302,plain,(
% 2.97/1.61 ~spl58_1),
% 2.97/1.61 inference(avatar_split_clause,[status(thm)],[f1234,f1295])).
% 2.97/1.61 thf(f1295,definition,(
% 2.97/1.61 spl58_1 <=> (thesis = $true)),
% 2.97/1.61 introduced(definition,[new_symbols(naming,[spl58_1])],[avatar_definition])).
% 2.97/1.61 thf(f1234,plain,(
% 2.97/1.61 (thesis != $true)),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f885])).
% 2.97/1.61 thf(f885,plain,(
% 2.97/1.61 (thesis != $true)),
% 2.97/1.61 inference(flattening,[status(thm)],[f712])).
% 2.97/1.61 thf(f712,plain,(
% 2.97/1.61 ~(thesis = $true)),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f711])).
% 2.97/1.61 thf(f711,plain,(
% 2.97/1.61 ~thesis),
% 2.97/1.61 inference(rectify,[status(thm)],[f309])).
% 2.97/1.61 thf(f309,negated_conjecture,(
% 2.97/1.61 ~thesis),
% 2.97/1.61 inference(negated_conjecture,[status(cth)],[f308])).
% 2.97/1.61 thf(f308,conjecture,(
% 2.97/1.61 thesis),
% 2.97/1.61 file('/export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2THF_23804.p',conj_1)).
% 2.97/1.61 thf(f1301,plain,(
% 2.97/1.61 spl58_1 | spl58_2),
% 2.97/1.61 inference(avatar_split_clause,[status(thm)],[f1216,f1299,f1295])).
% 2.97/1.61 thf(f1216,plain,(
% 2.97/1.61 ( ! [X0 : tree @ a,X1 : tree @ a] : (($true != (member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) | (thesis = $true)) )),
% 2.97/1.61 inference(cnf_transformation,[status(thm)],[f979])).
% 2.97/1.61 thf(f979,plain,(
% 2.97/1.61 ! [X0 : tree @ a,X1 : tree @ a] : (($true != (member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) | (thesis = $true))),
% 2.97/1.61 inference(ennf_transformation,[status(thm)],[f876])).
% 2.97/1.61 thf(f876,plain,(
% 2.97/1.61 ! [X0 : tree @ a,X1 : tree @ a] : (($true = (member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) => (thesis = $true))),
% 2.97/1.61 inference(fool_elimination,[status(thm)],[f875])).
% 2.97/1.61 thf(f875,plain,(
% 2.97/1.61 ! [X0 : tree @ a,X1 : tree @ a] : ((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t)) => thesis)),
% 2.97/1.61 inference(rectify,[status(thm)],[f307])).
% 2.97/1.61 thf(f307,axiom,(
% 2.97/1.61 ! [X102 : tree @ a,X103 : tree @ a] : ((member @ tree @ a @ (node @ a @ X102 @ a2 @ X103) @ (subtrees @ a @ t)) => thesis)),
% 2.97/1.61 file('/export/starexec/sandbox/tmp/tmp.mXAZ2pKHsw/DTF2THF_23804.p',conj_0)).
% 2.97/1.61 % SZS output end Proof for DTF2THF_23804
% 2.97/1.61 % (24137)------------------------------
% 2.97/1.61 % (24137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (24137)Termination reason: Refutation
% 2.97/1.61
% 2.97/1.61 % (24137)Memory used [KB]: 6908
% 2.97/1.61 % (24137)Time elapsed: 0.045 s
% 2.97/1.61 % (24137)Instructions burned: 88 (million)
% 2.97/1.61 % (24137)------------------------------
% 2.97/1.61 % (24137)------------------------------
% 2.97/1.61 % (24131)Success in time 0.065 s
%------------------------------------------------------------------------------