%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT214^1 : 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 : n017.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 1.77s
% Output : Refutation 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT214^1 : 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 : n017.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 06:10:11 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
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : DAT214^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.46 % Domain : Data Structures
% 0.20/0.46 % Problem : Splay tree analysis 231
% 0.20/0.46 % Version : [Bla16] axioms : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Nip14] Nipkow (2014), Amortized Complexity Verified
% 0.20/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.20/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bla16]
% 0.20/0.46 % Names : splay_tree_analysis__231.p [Bla16]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.33 v9.1.0, 0.00 v7.1.0
% 0.20/0.46 % Syntax : Number of formulae : 416 ( 146 unt; 80 typ; 0 def)
% 0.20/0.46 % Number of atoms : 808 ( 320 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 19 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3902 ( 88 ~; 4 |; 24 &;3425 @)
% 0.20/0.46 % ( 0 <=>; 361 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 24 ( 6 avg)
% 0.20/0.46 % Number of types : 5 ( 4 usr)
% 0.20/0.46 % Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 79 ( 76 usr; 10 con; 0-5 aty)
% 0.20/0.46 % Number of variables : 852 ( 15 ^; 759 !; 17 ?; 852 :)
% 0.20/0.46 % ( 61 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.20/0.46 % 2016-07-13 14:50:17.933
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 %----Could-be-implicit typings (9)
% 0.20/0.46 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.20/0.46 splay_2011811431op_s_t: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Code__Numeral_Onatural,type,
% 0.20/0.46 code_natural: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.46 product_prod: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Sum__Type_Osum,type,
% 0.20/0.46 sum_sum: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Tree_Otree,type,
% 0.20/0.46 tree: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Real_Oreal,type,
% 0.20/0.46 real: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Nat_Onat,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_itself,type,
% 0.20/0.46 itself: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_a,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 %----Explicit typings (71)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Nat_Osize,type,
% 0.20/0.46 size:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oone,type,
% 0.20/0.46 one:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.20/0.46 zero:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.20/0.46 neg_numeral:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.20/0.46 group_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.20/0.46 monoid_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Transcendental_Oln,type,
% 0.20/0.46 ln:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.20/0.46 zero_neq_one:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.20/0.46 zero_less_one:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.20/0.46 semigroup_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.20/0.46 comm_semiring_1:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.20/0.46 linordered_idom:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.20/0.46 comm_monoid_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Fields_Olinordered__field,type,
% 0.20/0.46 linordered_field:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.20/0.46 ab_semigroup_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.20/0.46 linordered_semidom:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.20/0.46 cancel_semigroup_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.20/0.46 cancel1352612707id_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.20/0.46 linord219039673up_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.20/0.46 ordere216010020id_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.20/0.46 ordere779506340up_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.20/0.46 linord1659791738miring:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.20/0.46 canoni770627133id_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.20/0.46 strict797366125id_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.20/0.46 ordere236663937imp_le:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.20/0.46 ordere223160158up_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.20/0.46 strict2144017051up_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.20/0.46 ordere516151231imp_le:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.20/0.46 semiri456707255roduct:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 0.20/0.46 code_case_natural:
% 0.20/0.46 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 0.20/0.46 code_rec_natural:
% 0.20/0.46 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 0.20/0.46 code_size_natural: code_natural > nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.20/0.46 one_one:
% 0.20/0.46 !>[A: $tType] : A ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.20/0.46 plus_plus:
% 0.20/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.20/0.46 zero_zero:
% 0.20/0.46 !>[A: $tType] : A ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_HOL_Obool_Osize__bool,type,
% 0.20/0.46 size_bool: $o > nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If,type,
% 0.20/0.46 if:
% 0.20/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.20/0.46 size_size:
% 0.20/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 0.20/0.46 neg_numeral_dbl_dec:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.20/0.46 neg_numeral_dbl_inc:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.20/0.46 ord_less:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.20/0.46 ord_less_eq:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 0.20/0.46 product_rec_bool:
% 0.20/0.46 !>[T: $tType] : ( T > T > $o > T ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Pure_Otype,type,
% 0.20/0.46 type2:
% 0.20/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat,type,
% 0.20/0.46 set_fo292404081st_nat:
% 0.20/0.46 !>[A: $tType] : ( ( nat > A > A ) > nat > nat > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree_Osplay,type,
% 0.20/0.46 splay_splay:
% 0.20/0.46 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree_Osplay__max,type,
% 0.20/0.46 splay_splay_max:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 0.20/0.46 splay_914434265_splay:
% 0.20/0.46 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max,type,
% 0.20/0.46 splay_878424299ay_max:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel,type,
% 0.20/0.46 splay_1816415694ax_rel:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA,type,
% 0.20/0.46 splay_266122055elle_A:
% 0.20/0.46 !>[A: $tType] : ( A > ( tree @ A ) > real ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Transcendental_Oln__class_Oln,type,
% 0.20/0.46 ln_ln:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Transcendental_Opowr,type,
% 0.20/0.46 powr:
% 0.20/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 0.20/0.46 linorder_bst:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Opath__len,type,
% 0.20/0.46 path_len:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Opath__len__rel,type,
% 0.20/0.46 path_len_rel:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Osize1,type,
% 0.20/0.46 size1:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Otree_OLeaf,type,
% 0.20/0.46 leaf:
% 0.20/0.46 !>[A: $tType] : ( tree @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Otree_ONode,type,
% 0.20/0.46 node:
% 0.20/0.46 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Tree_Otree_Osize__tree,type,
% 0.20/0.46 size_tree:
% 0.20/0.46 !>[A: $tType] : ( ( A > nat ) > ( tree @ A ) > nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.20/0.46 accp:
% 0.20/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_b____,type,
% 0.20/0.46 b: a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_c____,type,
% 0.20/0.46 c: a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_l_H____,type,
% 0.20/0.46 l: tree @ a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_l____,type,
% 0.20/0.46 l2: tree @ a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_r_H____,type,
% 0.20/0.46 r: tree @ a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_rl____,type,
% 0.20/0.46 rl: tree @ a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_rr____,type,
% 0.20/0.46 rr: tree @ a ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_u____,type,
% 0.20/0.46 u: a ).
% 0.20/0.46
% 0.20/0.46 %----Relevant facts (253)
% 0.20/0.46 thf(fact_0__092_060open_062size_Arr_A_061_Asize_A_Isplay__max_Arr_J_092_060close_062,axiom,
% 0.20/0.46 ( ( size_size @ ( tree @ a ) @ rr )
% 0.20/0.46 = ( size_size @ ( tree @ a ) @ ( splay_splay_max @ a @ rr ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>size rr = size (splay_max rr)\<close>
% 0.20/0.46 thf(fact_1_sp,axiom,
% 0.20/0.46 ( ( splay_splay_max @ a @ rr )
% 0.20/0.46 = ( node @ a @ l @ u @ r ) ) ).
% 0.20/0.46
% 0.20/0.46 % sp
% 0.20/0.46 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062l_H_Au_Ar_H_O_Asplay__max_Arr_A_061_A_092_060langle_062l_H_M_Au_M_Ar_H_092_060rangle_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [L: tree @ a,U: a,R: tree @ a] :
% 0.20/0.46 ( ( splay_splay_max @ a @ rr )
% 0.20/0.46 != ( node @ a @ L @ U @ R ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>l' u r'. splay_max rr = \<langle>l', u, r'\<rangle> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_3__092_060open_062rr_A_092_060noteq_062_A_092_060langle_062_092_060rangle_062_092_060close_062,axiom,
% 0.20/0.46 ( rr
% 0.20/0.46 != ( leaf @ a ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>rr \<noteq> \<langle>\<rangle>\<close>
% 0.20/0.46 thf(fact_4_add__left__cancel,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.46 = ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_left_cancel
% 0.20/0.46 thf(fact_5_add__right__cancel,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.46 = ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_right_cancel
% 0.20/0.46 thf(fact_6_size__if__splay__max,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A,L2: tree @ A,U2: A,R2: tree @ A] :
% 0.20/0.46 ( ( ( splay_splay_max @ A @ T2 )
% 0.20/0.46 = ( node @ A @ L2 @ U2 @ R2 ) )
% 0.20/0.46 => ( ( size_size @ ( tree @ A ) @ T2 )
% 0.20/0.46 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ L2 ) @ ( size_size @ ( tree @ A ) @ R2 ) ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size_if_splay_max
% 0.20/0.46 thf(fact_7_one__natural_Orsp,axiom,
% 0.20/0.46 ( ( one_one @ nat )
% 0.20/0.46 = ( one_one @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % one_natural.rsp
% 0.20/0.46 thf(fact_8_size__ne__size__imp__ne,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( size @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] :
% 0.20/0.46 ( ( ( size_size @ A @ X )
% 0.20/0.46 != ( size_size @ A @ Y ) )
% 0.20/0.46 => ( X != Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size_ne_size_imp_ne
% 0.20/0.46 thf(fact_9_nat__add__left__cancel,axiom,
% 0.20/0.46 ! [K: nat,M: nat,N: nat] :
% 0.20/0.46 ( ( ( plus_plus @ nat @ K @ M )
% 0.20/0.46 = ( plus_plus @ nat @ K @ N ) )
% 0.20/0.46 = ( M = N ) ) ).
% 0.20/0.46
% 0.20/0.46 % nat_add_left_cancel
% 0.20/0.46 thf(fact_10_nat__add__right__cancel,axiom,
% 0.20/0.46 ! [M: nat,K: nat,N: nat] :
% 0.20/0.46 ( ( ( plus_plus @ nat @ M @ K )
% 0.20/0.46 = ( plus_plus @ nat @ N @ K ) )
% 0.20/0.46 = ( M = N ) ) ).
% 0.20/0.46
% 0.20/0.46 % nat_add_right_cancel
% 0.20/0.46 thf(fact_11_one__reorient,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( one @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A] :
% 0.20/0.46 ( ( ( one_one @ A )
% 0.20/0.46 = X )
% 0.20/0.46 = ( X
% 0.20/0.46 = ( one_one @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % one_reorient
% 0.20/0.46 thf(fact_12_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.20/0.46 thf(fact_13_is__num__normalize_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_num_normalize(1)
% 0.20/0.46 thf(fact_14_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linordered_field_class.sign_simps(28)
% 0.20/0.46 thf(fact_15_splay__max__Leaf__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A] :
% 0.20/0.46 ( ( ( splay_splay_max @ A @ T2 )
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 = ( T2
% 0.20/0.46 = ( leaf @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_max_Leaf_iff
% 0.20/0.46 thf(fact_16_splay__max_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [La: tree @ A,A2: A] :
% 0.20/0.46 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 0.20/0.46 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_max.simps(2)
% 0.20/0.46 thf(fact_17_splay__max_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 0.20/0.46 = ( leaf @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_max.simps(1)
% 0.20/0.46 thf(fact_18_splay__max__Leaf,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A,L2: tree @ A,A2: A,R2: tree @ A] :
% 0.20/0.46 ( ( ( splay_splay_max @ A @ T2 )
% 0.20/0.46 = ( node @ A @ L2 @ A2 @ R2 ) )
% 0.20/0.46 => ( R2
% 0.20/0.46 = ( leaf @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_max_Leaf
% 0.20/0.46 thf(fact_19_size__splay__max,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A] :
% 0.20/0.46 ( ( size_size @ ( tree @ A ) @ ( splay_splay_max @ A @ T2 ) )
% 0.20/0.46 = ( size_size @ ( tree @ A ) @ T2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size_splay_max
% 0.20/0.46 thf(fact_20_add__right__imp__eq,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.46 => ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_right_imp_eq
% 0.20/0.46 thf(fact_21_add__left__imp__eq,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.46 => ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_left_imp_eq
% 0.20/0.46 thf(fact_22_add_Oleft__commute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.left_commute
% 0.20/0.46 thf(fact_23_add_Ocommute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( plus_plus @ A )
% 0.20/0.46 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.commute
% 0.20/0.46 thf(fact_24_add_Oright__cancel,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.20/0.46 = ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.right_cancel
% 0.20/0.46 thf(fact_25_add_Oleft__cancel,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.20/0.46 = ( B = C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.left_cancel
% 0.20/0.46 thf(fact_26_add_Oassoc,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.assoc
% 0.20/0.46 thf(fact_27_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [I: A,J: A,K: A,L2: A] :
% 0.20/0.46 ( ( ( I = J )
% 0.20/0.46 & ( K = L2 ) )
% 0.20/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.20/0.46 = ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_semiring(4)
% 0.20/0.46 thf(fact_28_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linordered_field_class.sign_simps(26)
% 0.20/0.46 thf(fact_29_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( plus_plus @ A )
% 0.20/0.46 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linordered_field_class.sign_simps(27)
% 0.20/0.46 thf(fact_30__C3_Oprems_C_I2_J,axiom,
% 0.20/0.46 ( ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) )
% 0.20/0.46 != ( leaf @ a ) ) ).
% 0.20/0.46
% 0.20/0.46 % "3.prems"(2)
% 0.20/0.46 thf(fact_31_tree_Oinject,axiom,
% 0.20/0.46 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 0.20/0.46 ( ( ( node @ A @ X21 @ X22 @ X23 )
% 0.20/0.46 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 0.20/0.46 = ( ( X21 = Y21 )
% 0.20/0.46 & ( X22 = Y22 )
% 0.20/0.46 & ( X23 = Y23 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tree.inject
% 0.20/0.46 thf(fact_32_tree_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 0.20/0.46 ( ( leaf @ A )
% 0.20/0.46 != ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 0.20/0.46
% 0.20/0.46 % tree.distinct(1)
% 0.20/0.46 thf(fact_33_tree_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 0.20/0.46 ( ( P @ ( leaf @ A ) )
% 0.20/0.46 => ( ! [X1: tree @ A,X2: A,X3: tree @ A] :
% 0.20/0.46 ( ( P @ X1 )
% 0.20/0.46 => ( ( P @ X3 )
% 0.20/0.46 => ( P @ ( node @ A @ X1 @ X2 @ X3 ) ) ) )
% 0.20/0.46 => ( P @ Tree ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tree.induct
% 0.20/0.46 thf(fact_34_neq__Leaf__iff,axiom,
% 0.20/0.46 ! [A: $tType,T2: tree @ A] :
% 0.20/0.46 ( ( T2
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 = ( ? [L3: tree @ A,A3: A,R3: tree @ A] :
% 0.20/0.46 ( T2
% 0.20/0.46 = ( node @ A @ L3 @ A3 @ R3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_Leaf_iff
% 0.20/0.46 thf(fact_35_tree_Oexhaust,axiom,
% 0.20/0.46 ! [A: $tType,Y: tree @ A] :
% 0.20/0.46 ( ( Y
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ~ ! [X212: tree @ A,X222: A,X232: tree @ A] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( node @ A @ X212 @ X222 @ X232 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % tree.exhaust
% 0.20/0.46 thf(fact_36_mirror_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.20/0.46 ( ( P @ ( leaf @ A ) )
% 0.20/0.46 => ( ! [L4: tree @ A,X4: A,R4: tree @ A] :
% 0.20/0.46 ( ( P @ R4 )
% 0.20/0.46 => ( ( P @ L4 )
% 0.20/0.46 => ( P @ ( node @ A @ L4 @ X4 @ R4 ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mirror.induct
% 0.20/0.46 thf(fact_37_bst__eq_Ocases,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( node @ A @ L4 @ A4 @ R4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bst_eq.cases
% 0.20/0.46 thf(fact_38_bst__eq_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.20/0.46 ( ( P @ ( leaf @ A ) )
% 0.20/0.46 => ( ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 0.20/0.46 ( ( P @ L4 )
% 0.20/0.46 => ( ( P @ R4 )
% 0.20/0.46 => ( P @ ( node @ A @ L4 @ A4 @ R4 ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bst_eq.induct
% 0.20/0.46 thf(fact_39__092_060Phi_062_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,X: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( node @ A @ L4 @ A4 @ R4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<Phi>.cases
% 0.20/0.46 thf(fact_40__C3_Oprems_C_I1_J,axiom,
% 0.20/0.46 linorder_bst @ a @ ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) ) ).
% 0.20/0.46
% 0.20/0.46 % "3.prems"(1)
% 0.20/0.46 thf(fact_41_t__splay__max_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.20/0.46 ( ( P @ ( leaf @ A ) )
% 0.20/0.46 => ( ! [L4: tree @ A,B3: A] : ( P @ ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 0.20/0.46 => ( ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.20/0.46 ( ( ( Rr
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( P @ Rr ) )
% 0.20/0.46 => ( P @ ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.induct
% 0.20/0.46 thf(fact_42_t__splay__max_Ocases,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ! [L4: tree @ A,B3: A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.20/0.46 ( X
% 0.20/0.46 != ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.cases
% 0.20/0.46 thf(fact_43__092_060Phi_062_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.20/0.46 ( ( P @ ( leaf @ A ) )
% 0.20/0.46 => ( ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 0.20/0.46 ( ( P @ L4 )
% 0.20/0.46 => ( ( P @ R4 )
% 0.20/0.46 => ( P @ ( node @ A @ L4 @ A4 @ R4 ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<Phi>.induct
% 0.20/0.46 thf(fact_44_ext,axiom,
% 0.20/0.46 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 0.20/0.46 ( ! [X4: A] :
% 0.20/0.46 ( ( F @ X4 )
% 0.20/0.46 = ( G @ X4 ) )
% 0.20/0.46 => ( F = G ) ) ).
% 0.20/0.46
% 0.20/0.46 % ext
% 0.20/0.46 thf(fact_45_t__splay__max_Osimps_I3_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Rr2: tree @ A,L2: tree @ A,B: A,Rl2: tree @ A,C: A] :
% 0.20/0.46 ( ( ( Rr2
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Rr2
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.simps(3)
% 0.20/0.46 thf(fact_46_t__splay__max_Oelims,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: tree @ A,Y: nat] :
% 0.20/0.46 ( ( ( splay_878424299ay_max @ A @ X )
% 0.20/0.46 = Y )
% 0.20/0.46 => ( ( ( X
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 != ( one_one @ nat ) ) )
% 0.20/0.46 => ( ( ? [L4: tree @ A,B3: A] :
% 0.20/0.46 ( X
% 0.20/0.46 = ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 != ( one_one @ nat ) ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 = ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 0.20/0.46 => ~ ( ( ( Rr
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Rr
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.elims
% 0.20/0.46 thf(fact_47_path__len_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,L2: tree @ A,Uu: A,R2: tree @ A] :
% 0.20/0.46 ( ( path_len @ A @ ( node @ A @ L2 @ Uu @ R2 ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L2 ) @ ( size_size @ ( tree @ A ) @ L2 ) ) @ ( path_len @ A @ R2 ) ) @ ( size_size @ ( tree @ A ) @ R2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % path_len.simps(2)
% 0.20/0.46 thf(fact_48_t__splay__max_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [L2: tree @ A,B: A] :
% 0.20/0.46 ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( leaf @ A ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.simps(2)
% 0.20/0.46 thf(fact_49_size__if__splay,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,T2: tree @ A,L2: tree @ A,U2: A,R2: tree @ A] :
% 0.20/0.46 ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.20/0.46 = ( node @ A @ L2 @ U2 @ R2 ) )
% 0.20/0.46 => ( ( size_size @ ( tree @ A ) @ T2 )
% 0.20/0.46 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ L2 ) @ ( size_size @ ( tree @ A ) @ R2 ) ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size_if_splay
% 0.20/0.46 thf(fact_50_size1__def,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( size1 @ A )
% 0.20/0.46 = ( ^ [T3: tree @ A] : ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ T3 ) @ ( one_one @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size1_def
% 0.20/0.46 thf(fact_51_dbl__inc__def,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( neg_numeral_dbl_inc @ A )
% 0.20/0.46 = ( ^ [X5: A] : ( plus_plus @ A @ ( plus_plus @ A @ X5 @ X5 ) @ ( one_one @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dbl_inc_def
% 0.20/0.46 thf(fact_52_t__splay__max_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( splay_878424299ay_max @ A @ ( leaf @ A ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.simps(1)
% 0.20/0.46 thf(fact_53_splay__Leaf__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,T2: tree @ A] :
% 0.20/0.46 ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 = ( T2
% 0.20/0.46 = ( leaf @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_Leaf_iff
% 0.20/0.46 thf(fact_54_size__splay,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,T2: tree @ A] :
% 0.20/0.46 ( ( size_size @ ( tree @ A ) @ ( splay_splay @ A @ A2 @ T2 ) )
% 0.20/0.46 = ( size_size @ ( tree @ A ) @ T2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size_splay
% 0.20/0.46 thf(fact_55_size1__simps_I2_J,axiom,
% 0.20/0.46 ! [B4: $tType,L2: tree @ B4,X: B4,R2: tree @ B4] :
% 0.20/0.46 ( ( size1 @ B4 @ ( node @ B4 @ L2 @ X @ R2 ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( size1 @ B4 @ L2 ) @ ( size1 @ B4 @ R2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % size1_simps(2)
% 0.20/0.46 thf(fact_56_size1__simps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( size1 @ A @ ( leaf @ A ) )
% 0.20/0.46 = ( one_one @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % size1_simps(1)
% 0.20/0.46 thf(fact_57_bst__splay,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A,A2: A] :
% 0.20/0.46 ( ( linorder_bst @ A @ T2 )
% 0.20/0.46 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bst_splay
% 0.20/0.46 thf(fact_58_splay__max__eq__splay__ex,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A] :
% 0.20/0.46 ( ( linorder_bst @ A @ T2 )
% 0.20/0.46 => ? [A4: A] :
% 0.20/0.46 ( ( splay_splay_max @ A @ T2 )
% 0.20/0.46 = ( splay_splay @ A @ A4 @ T2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_max_eq_splay_ex
% 0.20/0.46 thf(fact_59_splay_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( splay_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.20/0.46 = ( node @ A @ L2 @ A2 @ R2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay.simps(2)
% 0.20/0.46 thf(fact_60_splay_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 0.20/0.46 = ( leaf @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay.simps(1)
% 0.20/0.46 thf(fact_61_bst_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bst.simps(1)
% 0.20/0.46 thf(fact_62_bst__splay__max,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A] :
% 0.20/0.46 ( ( linorder_bst @ A @ T2 )
% 0.20/0.46 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bst_splay_max
% 0.20/0.46 thf(fact_63_splay__not__Leaf,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [T2: tree @ A,A2: A] :
% 0.20/0.46 ( ( T2
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ? [L4: tree @ A,X4: A,R4: tree @ A] :
% 0.20/0.46 ( ( splay_splay @ A @ A2 @ T2 )
% 0.20/0.46 = ( node @ A @ L4 @ X4 @ R4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay_not_Leaf
% 0.20/0.46 thf(fact_64_path__len_Oelims,axiom,
% 0.20/0.46 ! [A: $tType,X: tree @ A,Y: nat] :
% 0.20/0.46 ( ( ( path_len @ A @ X )
% 0.20/0.46 = Y )
% 0.20/0.46 => ( ( ( X
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 != ( zero_zero @ nat ) ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,Uu2: A,R4: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 = ( node @ A @ L4 @ Uu2 @ R4 ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L4 ) @ ( size_size @ ( tree @ A ) @ L4 ) ) @ ( path_len @ A @ R4 ) ) @ ( size_size @ ( tree @ A ) @ R4 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % path_len.elims
% 0.20/0.46 thf(fact_65_A__simps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( splay_266122055elle_A @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.20/0.46 = ( one_one @ real ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % A_simps(1)
% 0.20/0.46 thf(fact_66_t__splay__max_Opelims,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: tree @ A,Y: nat] :
% 0.20/0.46 ( ( ( splay_878424299ay_max @ A @ X )
% 0.20/0.46 = Y )
% 0.20/0.46 => ( ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ X )
% 0.20/0.46 => ( ( ( X
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( Y
% 0.20/0.46 = ( one_one @ nat ) )
% 0.20/0.46 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( leaf @ A ) ) ) )
% 0.20/0.46 => ( ! [L4: tree @ A,B3: A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 = ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 0.20/0.46 => ( ( Y
% 0.20/0.46 = ( one_one @ nat ) )
% 0.20/0.46 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) ) ) )
% 0.20/0.46 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.20/0.46 ( ( X
% 0.20/0.46 = ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 0.20/0.46 => ( ( ( ( Rr
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Rr
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) )
% 0.20/0.46 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_max.pelims
% 0.20/0.46 thf(fact_67_dbl__dec__simps_I3_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 0.20/0.46 = ( one_one @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dbl_dec_simps(3)
% 0.20/0.46 thf(fact_68_dbl__inc__simps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 0.20/0.46 = ( one_one @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dbl_inc_simps(2)
% 0.20/0.46 thf(fact_69_t__splay__simps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(1)
% 0.20/0.46 thf(fact_70_splay_Osimps_I13_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,X: A,B: A,La: tree @ A,Lb: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ X )
% 0.20/0.46 => ( ( ord_less @ A @ B @ X )
% 0.20/0.46 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B @ ( leaf @ A ) ) ) )
% 0.20/0.46 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B @ ( leaf @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splay.simps(13)
% 0.20/0.46 thf(fact_71_natural_Osize_I3_J,axiom,
% 0.20/0.46 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 0.20/0.46 = ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % natural.size(3)
% 0.20/0.46 thf(fact_72_neq0__conv,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ( ( N
% 0.20/0.46 != ( zero_zero @ nat ) )
% 0.20/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq0_conv
% 0.20/0.46 thf(fact_73_nat__add__left__cancel__less,axiom,
% 0.20/0.46 ! [K: nat,M: nat,N: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.20/0.46 = ( ord_less @ nat @ M @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % nat_add_left_cancel_less
% 0.20/0.46 thf(fact_74_not__gr__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [N: A] :
% 0.20/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.20/0.46 = ( N
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_gr_zero
% 0.20/0.46 thf(fact_75_add_Oleft__neutral,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.left_neutral
% 0.20/0.46 thf(fact_76_add_Oright__neutral,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % add.right_neutral
% 0.20/0.46 thf(fact_77_double__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.20/0.46 = ( zero_zero @ A ) )
% 0.20/0.46 = ( A2
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % double_zero
% 0.20/0.46 thf(fact_78_double__zero__sym,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( ( zero_zero @ A )
% 0.20/0.46 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.20/0.46 = ( A2
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % double_zero_sym
% 0.20/0.46 thf(fact_79_add__cancel__left__left,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.20/0.46 = A2 )
% 0.20/0.46 = ( B
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_cancel_left_left
% 0.20/0.46 thf(fact_80_add__cancel__left__right,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.20/0.46 = A2 )
% 0.20/0.46 = ( B
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_cancel_left_right
% 0.20/0.46 thf(fact_81_add__cancel__right__left,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( plus_plus @ A @ B @ A2 ) )
% 0.20/0.46 = ( B
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_cancel_right_left
% 0.20/0.46 thf(fact_82_add__cancel__right__right,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( plus_plus @ A @ A2 @ B ) )
% 0.20/0.46 = ( B
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_cancel_right_right
% 0.20/0.46 thf(fact_83_add__less__cancel__left,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [C: A,A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.20/0.46 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_cancel_left
% 0.20/0.46 thf(fact_84_add__less__cancel__right,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,C: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.20/0.46 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_cancel_right
% 0.20/0.46 thf(fact_85_add__gr__0,axiom,
% 0.20/0.46 ! [M: nat,N: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ M @ N ) )
% 0.20/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.20/0.46 | ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_gr_0
% 0.20/0.46 thf(fact_86_add__is__0,axiom,
% 0.20/0.46 ! [M: nat,N: nat] :
% 0.20/0.46 ( ( ( plus_plus @ nat @ M @ N )
% 0.20/0.46 = ( zero_zero @ nat ) )
% 0.20/0.46 = ( ( M
% 0.20/0.46 = ( zero_zero @ nat ) )
% 0.20/0.46 & ( N
% 0.20/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_is_0
% 0.20/0.46 thf(fact_87_Nat_Oadd__0__right,axiom,
% 0.20/0.46 ! [M: nat] :
% 0.20/0.46 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 0.20/0.46 = M ) ).
% 0.20/0.46
% 0.20/0.46 % Nat.add_0_right
% 0.20/0.46 thf(fact_88_less__one,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.20/0.46 = ( N
% 0.20/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_one
% 0.20/0.46 thf(fact_89_add__less__same__cancel1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 0.20/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_same_cancel1
% 0.20/0.46 thf(fact_90_add__less__same__cancel2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.20/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_same_cancel2
% 0.20/0.46 thf(fact_91_less__add__same__cancel1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.20/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_add_same_cancel1
% 0.20/0.46 thf(fact_92_less__add__same__cancel2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 0.20/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_add_same_cancel2
% 0.20/0.46 thf(fact_93_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.20/0.46 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % double_add_less_zero_iff_single_add_less_zero
% 0.20/0.46 thf(fact_94_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.20/0.46 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % zero_less_double_add_iff_zero_less_single_add
% 0.20/0.46 thf(fact_95_t__splay__simps_I3_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B @ R2 ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(3)
% 0.20/0.46 thf(fact_96_t__splay__simps_I7_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,L2: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(7)
% 0.20/0.46 thf(fact_97_t__splay__simps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,R2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ R2 ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(2)
% 0.20/0.46 thf(fact_98_t__splay__simps_I6_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,L2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( leaf @ A ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(6)
% 0.20/0.46 thf(fact_99_t__splay__simps_I9_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A,Rr2: tree @ A,L2: tree @ A,Rl2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.20/0.46 => ( ( ord_less @ A @ C @ A2 )
% 0.20/0.46 => ( ( ( Rr2
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Rr2
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(9)
% 0.20/0.46 thf(fact_100_t__splay__simps_I8_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B: A,A2: A,C: A,Rl2: tree @ A,L2: tree @ A,Rr2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.20/0.46 => ( ( ord_less @ A @ A2 @ C )
% 0.20/0.46 => ( ( ( Rl2
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Rl2
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(8)
% 0.20/0.46 thf(fact_101_t__splay__simps_I5_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ( ord_less @ A @ C @ A2 )
% 0.20/0.46 => ( ( ( Lr
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Lr
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(5)
% 0.20/0.46 thf(fact_102_t__splay__simps_I4_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ( ord_less @ A @ A2 @ C )
% 0.20/0.46 => ( ( ( Ll
% 0.20/0.46 = ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 0.20/0.46 = ( one_one @ nat ) ) )
% 0.20/0.46 & ( ( Ll
% 0.20/0.46 != ( leaf @ A ) )
% 0.20/0.46 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 0.20/0.46 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % t_splay_simps(4)
% 0.20/0.46 thf(fact_103_size1__ge0,axiom,
% 0.20/0.46 ! [A: $tType,T2: tree @ A] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size1 @ A @ T2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % size1_ge0
% 0.20/0.46 thf(fact_104_less__numeral__extra_I3_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_numeral_extra(3)
% 0.20/0.46 thf(fact_105_gr0I,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ( ( N
% 0.20/0.46 != ( zero_zero @ nat ) )
% 0.20/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % gr0I
% 0.20/0.46 thf(fact_106_not__gr0,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.20/0.46 = ( N
% 0.20/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_gr0
% 0.20/0.46 thf(fact_107_not__less0,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_less0
% 0.20/0.46 thf(fact_108_less__zeroE,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_zeroE
% 0.20/0.46 thf(fact_109_gr__implies__not0,axiom,
% 0.20/0.46 ! [M: nat,N: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ M @ N )
% 0.20/0.46 => ( N
% 0.20/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % gr_implies_not0
% 0.20/0.46 thf(fact_110_zero__reorient,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( zero @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A] :
% 0.20/0.46 ( ( ( zero_zero @ A )
% 0.20/0.46 = X )
% 0.20/0.46 = ( X
% 0.20/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % zero_reorient
% 0.20/0.46 thf(fact_111_infinite__descent0,axiom,
% 0.20/0.46 ! [P: nat > $o,N: nat] :
% 0.20/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.20/0.46 => ( ! [N2: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.20/0.46 => ( ~ ( P @ N2 )
% 0.20/0.46 => ? [M2: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.20/0.46 & ~ ( P @ M2 ) ) ) )
% 0.20/0.46 => ( P @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % infinite_descent0
% 0.20/0.46 thf(fact_112_less__nat__zero__code,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nat_zero_code
% 0.20/0.46 thf(fact_113_zero__natural_Orsp,axiom,
% 0.20/0.46 ( ( zero_zero @ nat )
% 0.20/0.46 = ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % zero_natural.rsp
% 0.20/0.46 thf(fact_114_infinite__descent0__measure,axiom,
% 0.20/0.46 ! [A: $tType,V: A > nat,P: A > $o,X: A] :
% 0.20/0.46 ( ! [X4: A] :
% 0.20/0.46 ( ( ( V @ X4 )
% 0.20/0.46 = ( zero_zero @ nat ) )
% 0.20/0.46 => ( P @ X4 ) )
% 0.20/0.46 => ( ! [X4: A] :
% 0.20/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X4 ) )
% 0.20/0.46 => ( ~ ( P @ X4 )
% 0.20/0.46 => ? [Y2: A] :
% 0.20/0.46 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X4 ) )
% 0.20/0.46 & ~ ( P @ Y2 ) ) ) )
% 0.20/0.46 => ( P @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % infinite_descent0_measure
% 0.20/0.46 thf(fact_115_linordered__field__no__lb,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X6: A] :
% 0.20/0.46 ? [Y3: A] : ( ord_less @ A @ Y3 @ X6 ) ) ).
% 0.20/0.46
% 0.20/0.46 % linordered_field_no_lb
% 0.20/0.46 thf(fact_116_linordered__field__no__ub,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X6: A] :
% 0.20/0.46 ? [X1: A] : ( ord_less @ A @ X6 @ X1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % linordered_field_no_ub
% 0.20/0.46 thf(fact_117_gr__zeroI,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [N: A] :
% 0.20/0.46 ( ( N
% 0.20/0.46 != ( zero_zero @ A ) )
% 0.20/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % gr_zeroI
% 0.20/0.46 thf(fact_118_not__less__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [N: A] :
% 0.20/0.46 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_less_zero
% 0.20/0.46 thf(fact_119_gr__implies__not__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [M: A,N: A] :
% 0.20/0.46 ( ( ord_less @ A @ M @ N )
% 0.20/0.46 => ( N
% 0.20/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % gr_implies_not_zero
% 0.20/0.46 thf(fact_120_zero__less__iff__neq__zero,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [N: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.20/0.46 = ( N
% 0.20/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % zero_less_iff_neq_zero
% 0.20/0.46 thf(fact_121_less__imp__add__positive,axiom,
% 0.20/0.46 ! [I: nat,J: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ I @ J )
% 0.20/0.46 => ? [K2: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K2 )
% 0.20/0.46 & ( ( plus_plus @ nat @ I @ K2 )
% 0.20/0.46 = J ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_add_positive
% 0.20/0.46 thf(fact_122_less__numeral__extra_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_numeral_extra(2)
% 0.20/0.46 thf(fact_123_less__numeral__extra_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_numeral_extra(1)
% 0.20/0.46 thf(fact_124_add__neg__neg,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.20/0.46 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_neg_neg
% 0.20/0.46 thf(fact_125_add__pos__pos,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 0.20/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_pos_pos
% 0.20/0.46 thf(fact_126_pos__add__strict,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( strict797366125id_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.46 => ( ( ord_less @ A @ B @ C )
% 0.20/0.46 => ( ord_less @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pos_add_strict
% 0.20/0.46 thf(fact_127_op_092_060_094sub_062s_092_060_094sub_062t_Osize__neq,axiom,
% 0.20/0.46 ! [A: $tType,X: splay_2011811431op_s_t @ A] :
% 0.20/0.46 ( ( size_size @ ( splay_2011811431op_s_t @ A ) @ X )
% 0.20/0.46 != ( zero_zero @ nat ) ) ).
% 0.20/0.46
% 0.20/0.46 % op\<^sub>s\<^sub>t.size_neq
% 0.20/0.46 thf(fact_128_add__mono__thms__linordered__field_I5_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [I: A,J: A,K: A,L2: A] :
% 0.20/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.20/0.46 & ( ord_less @ A @ K @ L2 ) )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_field(5)
% 0.20/0.46 thf(fact_129_add__mono__thms__linordered__field_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [I: A,J: A,K: A,L2: A] :
% 0.20/0.46 ( ( ( I = J )
% 0.20/0.46 & ( ord_less @ A @ K @ L2 ) )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_field(2)
% 0.20/0.46 thf(fact_130_add__mono__thms__linordered__field_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [I: A,J: A,K: A,L2: A] :
% 0.20/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.20/0.46 & ( K = L2 ) )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_mono_thms_linordered_field(1)
% 0.20/0.46 thf(fact_131_add__strict__mono,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A,D: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ( ord_less @ A @ C @ D )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_strict_mono
% 0.20/0.46 thf(fact_132_add__strict__left__mono,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_strict_left_mono
% 0.20/0.46 thf(fact_133_add__strict__right__mono,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B: A,C: A] :
% 0.20/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_strict_right_mono
% 0.20/0.46 thf(fact_134_add__less__imp__less__left,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [C: A,A2: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.20/0.46 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_imp_less_left
% 0.20/0.46 thf(fact_135_add__less__imp__less__right,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,C: A,B: A] :
% 0.20/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.20/0.46 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_imp_less_right
% 0.20/0.46 thf(fact_136_less__numeral__extra_I4_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_numeral_extra(4)
% 0.20/0.46 thf(fact_137_add__lessD1,axiom,
% 0.20/0.46 ! [I: nat,J: nat,K: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.20/0.46 => ( ord_less @ nat @ I @ K ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_lessD1
% 0.20/0.46 thf(fact_138_add__less__mono,axiom,
% 0.20/0.46 ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ I @ J )
% 0.20/0.46 => ( ( ord_less @ nat @ K @ L2 )
% 0.20/0.46 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_mono
% 0.20/0.46 thf(fact_139_not__add__less1,axiom,
% 0.20/0.46 ! [I: nat,J: nat] :
% 0.20/0.46 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.20/0.46
% 0.20/0.46 % not_add_less1
% 0.20/0.46 thf(fact_140_not__add__less2,axiom,
% 0.20/0.46 ! [J: nat,I: nat] :
% 0.20/0.46 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.20/0.46
% 0.20/0.46 % not_add_less2
% 0.20/0.46 thf(fact_141_add__less__mono1,axiom,
% 0.20/0.46 ! [I: nat,J: nat,K: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ I @ J )
% 0.20/0.46 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % add_less_mono1
% 0.20/0.46 thf(fact_142_trans__less__add1,axiom,
% 0.20/0.46 ! [I: nat,J: nat,M: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ I @ J )
% 0.20/0.46 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % trans_less_add1
% 0.20/0.46 thf(fact_143_trans__less__add2,axiom,
% 0.20/0.46 ! [I: nat,J: nat,M: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ I @ J )
% 0.20/0.46 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % trans_less_add2
% 0.20/0.46 thf(fact_144_less__add__eq__less,axiom,
% 0.20/0.46 ! [K: nat,L2: nat,M: nat,N: nat] :
% 0.20/0.46 ( ( ord_less @ nat @ K @ L2 )
% 0.20/0.46 => ( ( ( plus_plus @ nat @ M @ L2 )
% 0.20/0.46 = ( plus_plus @ nat @ K @ N ) )
% 0.20/0.46 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_add_eq_less
% 0.20/0.46 thf(fact_145_comm__monoid__add__class_Oadd__0,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % comm_monoid_add_class.add_0
% 0.20/0.47 thf(fact_146_add_Ocomm__neutral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.comm_neutral
% 0.20/0.47 thf(fact_147_add_Ogroup__left__neutral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.group_left_neutral
% 0.20/0.47 thf(fact_148_add__eq__0__iff__both__eq__0,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ( plus_plus @ A @ X @ Y )
% 0.20/0.47 = ( zero_zero @ A ) )
% 0.20/0.47 = ( ( X
% 0.20/0.47 = ( zero_zero @ A ) )
% 0.20/0.47 & ( Y
% 0.20/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_eq_0_iff_both_eq_0
% 0.20/0.47 thf(fact_149_plus__nat_Oadd__0,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 0.20/0.47 = N ) ).
% 0.20/0.47
% 0.20/0.47 % plus_nat.add_0
% 0.20/0.47 thf(fact_150_add__eq__self__zero,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( ( plus_plus @ nat @ M @ N )
% 0.20/0.47 = M )
% 0.20/0.47 => ( N
% 0.20/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_eq_self_zero
% 0.20/0.47 thf(fact_151_splay_Osimps_I9_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A,Lb: tree @ A,La: tree @ A,Ra: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ B @ A2 )
% 0.20/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B @ ( node @ A @ La @ A2 @ Ra ) ) )
% 0.20/0.47 = ( node @ A @ ( node @ A @ Lb @ B @ La ) @ A2 @ Ra ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(9)
% 0.20/0.47 thf(fact_152_splay_Osimps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,La: tree @ A,Ra: tree @ A,Rb: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra ) @ B @ Rb ) )
% 0.20/0.47 = ( node @ A @ La @ A2 @ ( node @ A @ Ra @ B @ Rb ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(3)
% 0.20/0.47 thf(fact_153_size__0__iff__Leaf,axiom,
% 0.20/0.47 ! [A: $tType,T2: tree @ A] :
% 0.20/0.47 ( ( ( size_size @ ( tree @ A ) @ T2 )
% 0.20/0.47 = ( zero_zero @ nat ) )
% 0.20/0.47 = ( T2
% 0.20/0.47 = ( leaf @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % size_0_iff_Leaf
% 0.20/0.47 thf(fact_154_tree_Osize_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( size_size @ ( tree @ A ) @ ( leaf @ A ) )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % tree.size(3)
% 0.20/0.47 thf(fact_155_t__splay_Osimps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 0.20/0.47 = ( one_one @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % t_splay.simps(1)
% 0.20/0.47 thf(fact_156_path__len_Osimps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( path_len @ A @ ( leaf @ A ) )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % path_len.simps(1)
% 0.20/0.47 thf(fact_157_splay_Osimps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,R2: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.47 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ R2 ) )
% 0.20/0.47 = ( node @ A @ ( leaf @ A ) @ B @ R2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(4)
% 0.20/0.47 thf(fact_158_splay_Osimps_I5_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,A2: A,B: A,Ra: tree @ A,Rb: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ X @ A2 )
% 0.20/0.47 => ( ( ord_less @ A @ X @ B )
% 0.20/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra ) @ B @ Rb ) )
% 0.20/0.47 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra @ B @ Rb ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(5)
% 0.20/0.47 thf(fact_159_splay_Osimps_I7_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,B: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ X @ B )
% 0.20/0.47 => ( ( ord_less @ A @ A2 @ X )
% 0.20/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B @ Rb ) )
% 0.20/0.47 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ Rb ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(7)
% 0.20/0.47 thf(fact_160_splay_Osimps_I10_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,X: A,L2: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ A2 @ X )
% 0.20/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) )
% 0.20/0.47 = ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(10)
% 0.20/0.47 thf(fact_161_splay_Osimps_I12_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,X: A,B: A,La: tree @ A,Rb: tree @ A] :
% 0.20/0.47 ( ( ord_less @ A @ A2 @ X )
% 0.20/0.47 => ( ( ord_less @ A @ X @ B )
% 0.20/0.47 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ Rb ) ) )
% 0.20/0.47 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B @ Rb ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splay.simps(12)
% 0.20/0.47 thf(fact_162_path__len_Opelims,axiom,
% 0.20/0.47 ! [A: $tType,X: tree @ A,Y: nat] :
% 0.20/0.47 ( ( ( path_len @ A @ X )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ X )
% 0.20/0.47 => ( ( ( X
% 0.20/0.47 = ( leaf @ A ) )
% 0.20/0.47 => ( ( Y
% 0.20/0.47 = ( zero_zero @ nat ) )
% 0.20/0.47 => ~ ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ ( leaf @ A ) ) ) )
% 0.20/0.47 => ~ ! [L4: tree @ A,Uu2: A,R4: tree @ A] :
% 0.20/0.47 ( ( X
% 0.20/0.47 = ( node @ A @ L4 @ Uu2 @ R4 ) )
% 0.20/0.47 => ( ( Y
% 0.20/0.47 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L4 ) @ ( size_size @ ( tree @ A ) @ L4 ) ) @ ( path_len @ A @ R4 ) ) @ ( size_size @ ( tree @ A ) @ R4 ) ) )
% 0.20/0.47 => ~ ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ ( node @ A @ L4 @ Uu2 @ R4 ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % path_len.pelims
% 0.20/0.47 thf(fact_163_zero__less__two,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % zero_less_two
% 0.20/0.47 thf(fact_164_less__add__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_add_one
% 0.20/0.47 thf(fact_165_zero__less__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( zero_less_one @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % zero_less_one
% 0.20/0.47 thf(fact_166_not__one__less__zero,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.20/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_one_less_zero
% 0.20/0.47 thf(fact_167_bool_Osize_I4_J,axiom,
% 0.20/0.47 ( ( size_size @ $o @ $false )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.size(4)
% 0.20/0.47 thf(fact_168_bool_Osize_I3_J,axiom,
% 0.20/0.47 ( ( size_size @ $o @ $true )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.size(3)
% 0.20/0.47 thf(fact_169_nat__neq__iff,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( M != N )
% 0.20/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.20/0.47 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_neq_iff
% 0.20/0.47 thf(fact_170_less__not__refl,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.20/0.47
% 0.20/0.47 % less_not_refl
% 0.20/0.47 thf(fact_171_less__not__refl2,axiom,
% 0.20/0.47 ! [N: nat,M: nat] :
% 0.20/0.47 ( ( ord_less @ nat @ N @ M )
% 0.20/0.47 => ( M != N ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_not_refl2
% 0.20/0.47 thf(fact_172_less__not__refl3,axiom,
% 0.20/0.47 ! [S: nat,T2: nat] :
% 0.20/0.47 ( ( ord_less @ nat @ S @ T2 )
% 0.20/0.47 => ( S != T2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_not_refl3
% 0.20/0.47 thf(fact_173_measure__induct,axiom,
% 0.20/0.47 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.20/0.47 ( ! [X4: A] :
% 0.20/0.47 ( ! [Y2: A] :
% 0.20/0.47 ( ( ord_less @ nat @ ( F @ Y2 ) @ ( F @ X4 ) )
% 0.20/0.47 => ( P @ Y2 ) )
% 0.20/0.47 => ( P @ X4 ) )
% 0.20/0.47 => ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % measure_induct
% 0.20/0.47 thf(fact_174_less__irrefl__nat,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.20/0.47
% 0.20/0.47 % less_irrefl_nat
% 0.20/0.47 thf(fact_175_nat__less__induct,axiom,
% 0.20/0.47 ! [P: nat > $o,N: nat] :
% 0.20/0.47 ( ! [N2: nat] :
% 0.20/0.47 ( ! [M2: nat] :
% 0.20/0.47 ( ( ord_less @ nat @ M2 @ N2 )
% 0.20/0.47 => ( P @ M2 ) )
% 0.20/0.47 => ( P @ N2 ) )
% 0.20/0.47 => ( P @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_less_induct
% 0.20/0.47 thf(fact_176_infinite__descent,axiom,
% 0.20/0.47 ! [P: nat > $o,N: nat] :
% 0.20/0.47 ( ! [N2: nat] :
% 0.20/0.47 ( ~ ( P @ N2 )
% 0.20/0.47 => ? [M2: nat] :
% 0.20/0.47 ( ( ord_less @ nat @ M2 @ N2 )
% 0.20/0.47 & ~ ( P @ M2 ) ) )
% 0.20/0.47 => ( P @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % infinite_descent
% 0.20/0.47 thf(fact_177_linorder__neqE__nat,axiom,
% 0.20/0.47 ! [X: nat,Y: nat] :
% 0.20/0.47 ( ( X != Y )
% 0.20/0.47 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.20/0.47 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % linorder_neqE_nat
% 0.20/0.47 thf(fact_178_measure__induct__rule,axiom,
% 0.20/0.47 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.20/0.47 ( ! [X4: A] :
% 0.20/0.47 ( ! [Y2: A] :
% 0.20/0.47 ( ( ord_less @ nat @ ( F @ Y2 ) @ ( F @ X4 ) )
% 0.20/0.47 => ( P @ Y2 ) )
% 0.20/0.47 => ( P @ X4 ) )
% 0.20/0.47 => ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % measure_induct_rule
% 0.20/0.47 thf(fact_179_infinite__descent__measure,axiom,
% 0.20/0.47 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.20/0.47 ( ! [X4: A] :
% 0.20/0.47 ( ~ ( P @ X4 )
% 0.20/0.47 => ? [Y2: A] :
% 0.20/0.47 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X4 ) )
% 0.20/0.47 & ~ ( P @ Y2 ) ) )
% 0.20/0.47 => ( P @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % infinite_descent_measure
% 0.20/0.47 thf(fact_180_linorder__neqE__linordered__idom,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( X != Y )
% 0.20/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.20/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % linorder_neqE_linordered_idom
% 0.20/0.47 thf(fact_181_prod_Osize__neq,axiom,
% 0.20/0.47 ! [A: $tType,B4: $tType,X: product_prod @ A @ B4] :
% 0.20/0.47 ( ( size_size @ ( product_prod @ A @ B4 ) @ X )
% 0.20/0.47 != ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.size_neq
% 0.20/0.47 thf(fact_182_sum_Osize__neq,axiom,
% 0.20/0.47 ! [A: $tType,B4: $tType,X: sum_sum @ A @ B4] :
% 0.20/0.47 ( ( size_size @ ( sum_sum @ A @ B4 ) @ X )
% 0.20/0.47 != ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % sum.size_neq
% 0.20/0.47 thf(fact_183_size__bool,axiom,
% 0.20/0.47 ( ( size_size @ $o )
% 0.20/0.47 = ( ^ [B2: $o] : ( zero_zero @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % size_bool
% 0.20/0.47 thf(fact_184_zero__neq__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( zero_zero @ A )
% 0.20/0.47 != ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % zero_neq_one
% 0.20/0.47 thf(fact_185_natural_Osize_I1_J,axiom,
% 0.20/0.47 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % natural.size(1)
% 0.20/0.47 thf(fact_186_fold__atLeastAtMost__nat_Oinduct,axiom,
% 0.20/0.47 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A1: nat,A22: nat,A32: A] :
% 0.20/0.47 ( ! [F2: nat > A > A,A4: nat,B3: nat,Acc: A] :
% 0.20/0.47 ( ( ~ ( ord_less @ nat @ B3 @ A4 )
% 0.20/0.47 => ( P @ F2 @ ( plus_plus @ nat @ A4 @ ( one_one @ nat ) ) @ B3 @ ( F2 @ A4 @ Acc ) ) )
% 0.20/0.47 => ( P @ F2 @ A4 @ B3 @ Acc ) )
% 0.20/0.47 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ).
% 0.20/0.47
% 0.20/0.47 % fold_atLeastAtMost_nat.induct
% 0.20/0.47 thf(fact_187_natural_Osimps_I4_J,axiom,
% 0.20/0.47 ! [T: $tType,F1: T,F22: code_natural > T] :
% 0.20/0.47 ( ( code_case_natural @ T @ F1 @ F22 @ ( zero_zero @ code_natural ) )
% 0.20/0.47 = F1 ) ).
% 0.20/0.47
% 0.20/0.47 % natural.simps(4)
% 0.20/0.47 thf(fact_188_bool_Osize_I1_J,axiom,
% 0.20/0.47 ( ( size_bool @ $true )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.size(1)
% 0.20/0.47 thf(fact_189_bool_Osize_I2_J,axiom,
% 0.20/0.47 ( ( size_bool @ $false )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % bool.size(2)
% 0.20/0.47 thf(fact_190_size__bool__def,axiom,
% 0.20/0.47 ( size_bool
% 0.20/0.47 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % size_bool_def
% 0.20/0.47 thf(fact_191_ind__euclid,axiom,
% 0.20/0.47 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 0.20/0.47 ( ! [A4: nat,B3: nat] :
% 0.20/0.47 ( ( P @ A4 @ B3 )
% 0.20/0.47 = ( P @ B3 @ A4 ) )
% 0.20/0.47 => ( ! [A4: nat] : ( P @ A4 @ ( zero_zero @ nat ) )
% 0.20/0.47 => ( ! [A4: nat,B3: nat] :
% 0.20/0.47 ( ( P @ A4 @ B3 )
% 0.20/0.47 => ( P @ A4 @ ( plus_plus @ nat @ A4 @ B3 ) ) )
% 0.20/0.47 => ( P @ A2 @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ind_euclid
% 0.20/0.47 thf(fact_192_size__bool__overloaded__def,axiom,
% 0.20/0.47 ( ( size_size @ $o )
% 0.20/0.47 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % size_bool_overloaded_def
% 0.20/0.47 thf(fact_193_add__0__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A] :
% 0.20/0.47 ( ( B
% 0.20/0.47 = ( plus_plus @ A @ B @ A2 ) )
% 0.20/0.47 = ( A2
% 0.20/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_0_iff
% 0.20/0.47 thf(fact_194_semiring__normalization__rules_I5_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(5)
% 0.20/0.47 thf(fact_195_semiring__normalization__rules_I20_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) )
% 0.20/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(20)
% 0.20/0.47 thf(fact_196_semiring__normalization__rules_I21_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(21)
% 0.20/0.47 thf(fact_197_semiring__normalization__rules_I22_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,C: A,D: A] :
% 0.20/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 0.20/0.47 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(22)
% 0.20/0.47 thf(fact_198_semiring__normalization__rules_I23_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A] :
% 0.20/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.20/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(23)
% 0.20/0.47 thf(fact_199_semiring__normalization__rules_I24_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( plus_plus @ A )
% 0.20/0.47 = ( ^ [A3: A,C3: A] : ( plus_plus @ A @ C3 @ A3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(24)
% 0.20/0.47 thf(fact_200_semiring__normalization__rules_I25_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,C: A,D: A] :
% 0.20/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 0.20/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ D ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(25)
% 0.20/0.47 thf(fact_201_semiring__normalization__rules_I6_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(6)
% 0.20/0.47 thf(fact_202_natural_Osimps_I6_J,axiom,
% 0.20/0.47 ! [T: $tType,F1: T,F22: code_natural > T > T] :
% 0.20/0.47 ( ( code_rec_natural @ T @ F1 @ F22 @ ( zero_zero @ code_natural ) )
% 0.20/0.47 = F1 ) ).
% 0.20/0.47
% 0.20/0.47 % natural.simps(6)
% 0.20/0.47 thf(fact_203_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( set_fo292404081st_nat @ A )
% 0.20/0.47 = ( ^ [F3: nat > A > A,A3: nat,B2: nat,Acc2: A] : ( if @ A @ ( ord_less @ nat @ B2 @ A3 ) @ Acc2 @ ( set_fo292404081st_nat @ A @ F3 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B2 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fold_atLeastAtMost_nat.simps
% 0.20/0.47 thf(fact_204_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.20/0.47 ! [A: $tType,X: nat > A > A,Xa: nat,Xb: nat,Xc: A,Y: A] :
% 0.20/0.47 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb @ Xc )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( ( ord_less @ nat @ Xb @ Xa )
% 0.20/0.47 => ( Y = Xc ) )
% 0.20/0.47 & ( ~ ( ord_less @ nat @ Xb @ Xa )
% 0.20/0.47 => ( Y
% 0.20/0.47 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fold_atLeastAtMost_nat.elims
% 0.20/0.47 thf(fact_205_ln__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( ln_ln @ A @ ( one_one @ A ) )
% 0.20/0.47 = ( zero_zero @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_one
% 0.20/0.47 thf(fact_206_tree_Osize__gen_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,X: A > nat] :
% 0.20/0.47 ( ( size_tree @ A @ X @ ( leaf @ A ) )
% 0.20/0.47 = ( zero_zero @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % tree.size_gen(1)
% 0.20/0.47 thf(fact_207_ln__less__zero__iff,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( zero_zero @ real ) )
% 0.20/0.47 = ( ord_less @ real @ X @ ( one_one @ real ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_less_zero_iff
% 0.20/0.47 thf(fact_208_ln__gt__zero__iff,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 0.20/0.47 = ( ord_less @ real @ ( one_one @ real ) @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_gt_zero_iff
% 0.20/0.47 thf(fact_209_ln__eq__zero__iff,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ( ln_ln @ real @ X )
% 0.20/0.47 = ( zero_zero @ real ) )
% 0.20/0.47 = ( X
% 0.20/0.47 = ( one_one @ real ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_eq_zero_iff
% 0.20/0.47 thf(fact_210_ln__gt__zero__imp__gt__one,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ord_less @ real @ ( one_one @ real ) @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_gt_zero_imp_gt_one
% 0.20/0.47 thf(fact_211_ln__less__zero,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ X @ ( one_one @ real ) )
% 0.20/0.47 => ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( zero_zero @ real ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_less_zero
% 0.20/0.47 thf(fact_212_ln__gt__zero,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_gt_zero
% 0.20/0.47 thf(fact_213_powr__zero__eq__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A] :
% 0.20/0.47 ( ( ( X
% 0.20/0.47 = ( zero_zero @ A ) )
% 0.20/0.47 => ( ( powr @ A @ X @ ( zero_zero @ A ) )
% 0.20/0.47 = ( zero_zero @ A ) ) )
% 0.20/0.47 & ( ( X
% 0.20/0.47 != ( zero_zero @ A ) )
% 0.20/0.47 => ( ( powr @ A @ X @ ( zero_zero @ A ) )
% 0.20/0.47 = ( one_one @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_zero_eq_one
% 0.20/0.47 thf(fact_214_powr__one__eq__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( powr @ A @ ( one_one @ A ) @ A2 )
% 0.20/0.47 = ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_one_eq_one
% 0.20/0.47 thf(fact_215_powr__gt__zero,axiom,
% 0.20/0.47 ! [X: real,A2: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( powr @ real @ X @ A2 ) )
% 0.20/0.47 = ( X
% 0.20/0.47 != ( zero_zero @ real ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_gt_zero
% 0.20/0.47 thf(fact_216_powr__less__cancel__iff,axiom,
% 0.20/0.47 ! [X: real,A2: real,B: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 0.20/0.47 = ( ord_less @ real @ A2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_less_cancel_iff
% 0.20/0.47 thf(fact_217_powr__0,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Z: A] :
% 0.20/0.47 ( ( powr @ A @ ( zero_zero @ A ) @ Z )
% 0.20/0.47 = ( zero_zero @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_0
% 0.20/0.47 thf(fact_218_powr__eq__0__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ln @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [W: A,Z: A] :
% 0.20/0.47 ( ( ( powr @ A @ W @ Z )
% 0.20/0.47 = ( zero_zero @ A ) )
% 0.20/0.47 = ( W
% 0.20/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_eq_0_iff
% 0.20/0.47 thf(fact_219_ln__inj__iff,axiom,
% 0.20/0.47 ! [X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 0.20/0.47 => ( ( ( ln_ln @ real @ X )
% 0.20/0.47 = ( ln_ln @ real @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_inj_iff
% 0.20/0.47 thf(fact_220_ln__less__cancel__iff,axiom,
% 0.20/0.47 ! [X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 0.20/0.47 => ( ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( ln_ln @ real @ Y ) )
% 0.20/0.47 = ( ord_less @ real @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_less_cancel_iff
% 0.20/0.47 thf(fact_221_ln__less__self,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ord_less @ real @ ( ln_ln @ real @ X ) @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_less_self
% 0.20/0.47 thf(fact_222_powr__less__mono2__neg,axiom,
% 0.20/0.47 ! [A2: real,X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ X @ Y )
% 0.20/0.47 => ( ord_less @ real @ ( powr @ real @ Y @ A2 ) @ ( powr @ real @ X @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_less_mono2_neg
% 0.20/0.47 thf(fact_223_powr__less__cancel,axiom,
% 0.20/0.47 ! [X: real,A2: real,B: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 0.20/0.47 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ord_less @ real @ A2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_less_cancel
% 0.20/0.47 thf(fact_224_powr__less__mono,axiom,
% 0.20/0.47 ! [A2: real,B: real,X: real] :
% 0.20/0.47 ( ( ord_less @ real @ A2 @ B )
% 0.20/0.47 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_less_mono
% 0.20/0.47 thf(fact_225_powr__inj,axiom,
% 0.20/0.47 ! [A2: real,X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.20/0.47 => ( ( A2
% 0.20/0.47 != ( one_one @ real ) )
% 0.20/0.47 => ( ( ( powr @ real @ A2 @ X )
% 0.20/0.47 = ( powr @ real @ A2 @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_inj
% 0.20/0.47 thf(fact_226_real__lbound__gt__zero,axiom,
% 0.20/0.47 ! [D1: real,D2: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ D1 )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ D2 )
% 0.20/0.47 => ? [E: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ E )
% 0.20/0.47 & ( ord_less @ real @ E @ D1 )
% 0.20/0.47 & ( ord_less @ real @ E @ D2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % real_lbound_gt_zero
% 0.20/0.47 thf(fact_227_ln__ge__zero__iff,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 0.20/0.47 = ( ord_less_eq @ real @ ( one_one @ real ) @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_ge_zero_iff
% 0.20/0.47 thf(fact_228_le__zero__eq,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.20/0.47 = ( N
% 0.20/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_zero_eq
% 0.20/0.47 thf(fact_229_add__le__cancel__left,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [C: A,A2: A,B: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_le_cancel_left
% 0.20/0.47 thf(fact_230_add__le__cancel__right,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,C: A,B: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_le_cancel_right
% 0.20/0.47 thf(fact_231_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.20/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % zero_le_double_add_iff_zero_le_single_add
% 0.20/0.47 thf(fact_232_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % double_add_le_zero_iff_single_add_le_zero
% 0.20/0.47 thf(fact_233_le__add__same__cancel2,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 0.20/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_add_same_cancel2
% 0.20/0.47 thf(fact_234_le__add__same__cancel1,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.20/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_add_same_cancel1
% 0.20/0.47 thf(fact_235_add__le__same__cancel2,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_le_same_cancel2
% 0.20/0.47 thf(fact_236_add__le__same__cancel1,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B: A,A2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_le_same_cancel1
% 0.20/0.47 thf(fact_237_ln__le__cancel__iff,axiom,
% 0.20/0.47 ! [X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( ln_ln @ real @ X ) @ ( ln_ln @ real @ Y ) )
% 0.20/0.47 = ( ord_less_eq @ real @ X @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_le_cancel_iff
% 0.20/0.47 thf(fact_238_powr__one__gt__zero__iff,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ( powr @ real @ X @ ( one_one @ real ) )
% 0.20/0.47 = X )
% 0.20/0.47 = ( ord_less_eq @ real @ ( zero_zero @ real ) @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_one_gt_zero_iff
% 0.20/0.47 thf(fact_239_powr__one,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( powr @ real @ X @ ( one_one @ real ) )
% 0.20/0.47 = X ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_one
% 0.20/0.47 thf(fact_240_powr__le__cancel__iff,axiom,
% 0.20/0.47 ! [X: real,A2: real,B: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 0.20/0.47 = ( ord_less_eq @ real @ A2 @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_le_cancel_iff
% 0.20/0.47 thf(fact_241_ln__bound,axiom,
% 0.20/0.47 ! [X: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ord_less_eq @ real @ ( ln_ln @ real @ X ) @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % ln_bound
% 0.20/0.47 thf(fact_242_powr__mono,axiom,
% 0.20/0.47 ! [A2: real,B: real,X: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ A2 @ B )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_mono
% 0.20/0.47 thf(fact_243_powr__mono2,axiom,
% 0.20/0.47 ! [A2: real,X: real,Y: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less_eq @ real @ X @ Y )
% 0.20/0.47 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ Y @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_mono2
% 0.20/0.47 thf(fact_244_powr__mono2_H,axiom,
% 0.20/0.47 ! [A2: real,X: real,Y: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.20/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less_eq @ real @ X @ Y )
% 0.20/0.47 => ( ord_less_eq @ real @ ( powr @ real @ Y @ A2 ) @ ( powr @ real @ X @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_mono2'
% 0.20/0.47 thf(fact_245_powr__ge__pzero,axiom,
% 0.20/0.47 ! [X: real,Y: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ X @ Y ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_ge_pzero
% 0.20/0.47 thf(fact_246_powr__less__mono2,axiom,
% 0.20/0.47 ! [A2: real,X: real,Y: real] :
% 0.20/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 0.20/0.47 => ( ( ord_less @ real @ X @ Y )
% 0.20/0.47 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ Y @ A2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % powr_less_mono2
% 0.20/0.47 thf(fact_247_ge__one__powr__ge__zero,axiom,
% 0.20/0.47 ! [X: real,A2: real] :
% 0.20/0.47 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 0.20/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.20/0.47 => ( ord_less_eq @ real @ ( one_one @ real ) @ ( powr @ real @ X @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ge_one_powr_ge_zero
% 0.20/0.47 thf(fact_248_less__eq__real__def,axiom,
% 0.20/0.47 ( ( ord_less_eq @ real )
% 0.20/0.47 = ( ^ [X5: real,Y4: real] :
% 0.20/0.47 ( ( ord_less @ real @ X5 @ Y4 )
% 0.20/0.47 | ( X5 = Y4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % less_eq_real_def
% 0.20/0.47 thf(fact_249_zero__le,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % zero_le
% 0.20/0.47 thf(fact_250_le__numeral__extra_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_numeral_extra(3)
% 0.20/0.47 thf(fact_251_add__less__le__mono,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.20/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.20/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.20/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_less_le_mono
% 0.20/0.47 thf(fact_252_add__le__less__mono,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.20/0.47 => ( ( ord_less @ A @ C @ D )
% 0.20/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % add_le_less_mono
% 0.20/0.47
% 0.20/0.47 %----Subclasses (1)
% 0.20/0.47 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( type @ A @ ( type2 @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %----Type constructors (77)
% 0.20/0.47 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.20/0.47 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.20/0.47 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.20/0.47 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.20/0.47 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.20/0.47 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.20/0.47 strict797366125id_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.20/0.47 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.20/0.47 linord1659791738miring @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.20/0.47 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 0.20/0.47 ordere216010020id_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.20/0.47 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.20/0.47 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.20/0.47 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.20/0.47 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.20/0.47 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.20/0.47 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.20/0.47 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 0.20/0.47 zero_less_one @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.20/0.47 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.20/0.47 linorder @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.20/0.47 monoid_add @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.20/0.47 zero @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.20/0.47 one @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.20/0.47 size @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_1,axiom,
% 0.20/0.47 linorder @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Nat_Osize_2,axiom,
% 0.20/0.47 size @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_3,axiom,
% 0.20/0.47 semiri456707255roduct @ real @ ( type2 @ real ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4,axiom,
% 0.20/0.47 ordere516151231imp_le @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_5,axiom,
% 0.31/0.47 strict2144017051up_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_6,axiom,
% 0.31/0.47 ordere223160158up_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_7,axiom,
% 0.31/0.47 ordere236663937imp_le @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_8,axiom,
% 0.31/0.47 strict797366125id_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_9,axiom,
% 0.31/0.47 linord1659791738miring @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_10,axiom,
% 0.31/0.47 ordere779506340up_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_11,axiom,
% 0.31/0.47 ordere216010020id_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.31/0.47 linord219039673up_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_12,axiom,
% 0.31/0.47 cancel1352612707id_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_13,axiom,
% 0.31/0.47 cancel_semigroup_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_14,axiom,
% 0.31/0.47 linordered_semidom @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_15,axiom,
% 0.31/0.47 ab_semigroup_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 0.31/0.47 linordered_field @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_16,axiom,
% 0.31/0.47 comm_monoid_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.31/0.47 linordered_idom @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_17,axiom,
% 0.31/0.47 comm_semiring_1 @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_18,axiom,
% 0.31/0.47 semigroup_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Ozero__less__one_19,axiom,
% 0.31/0.47 zero_less_one @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_20,axiom,
% 0.31/0.47 zero_neq_one @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_21,axiom,
% 0.31/0.47 linorder @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 0.31/0.47 ln @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__add_22,axiom,
% 0.31/0.47 monoid_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.31/0.47 group_add @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.31/0.47 neg_numeral @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Ozero_23,axiom,
% 0.31/0.47 zero @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Real_Oreal___Groups_Oone_24,axiom,
% 0.31/0.47 one @ real @ ( type2 @ real ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Tree_Otree___Nat_Osize_25,axiom,
% 0.31/0.47 ! [A5: $tType] : ( size @ ( tree @ A5 ) @ ( type2 @ ( tree @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Sum__Type_Osum___Nat_Osize_26,axiom,
% 0.31/0.47 ! [A5: $tType,A6: $tType] : ( size @ ( sum_sum @ A5 @ A6 ) @ ( type2 @ ( sum_sum @ A5 @ A6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Product__Type_Oprod___Nat_Osize_27,axiom,
% 0.31/0.47 ! [A5: $tType,A6: $tType] : ( size @ ( product_prod @ A5 @ A6 ) @ ( type2 @ ( product_prod @ A5 @ A6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_28,axiom,
% 0.31/0.47 ordere516151231imp_le @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_29,axiom,
% 0.31/0.47 strict2144017051up_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_30,axiom,
% 0.31/0.47 ordere223160158up_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add__imp__le_31,axiom,
% 0.31/0.47 ordere236663937imp_le @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_32,axiom,
% 0.31/0.47 strict797366125id_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_33,axiom,
% 0.31/0.47 ordere779506340up_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__comm__monoid__add_34,axiom,
% 0.31/0.47 ordere216010020id_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_35,axiom,
% 0.31/0.47 cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_36,axiom,
% 0.31/0.47 cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_37,axiom,
% 0.31/0.47 ab_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_38,axiom,
% 0.31/0.47 comm_monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_39,axiom,
% 0.31/0.47 comm_semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_40,axiom,
% 0.31/0.47 semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_41,axiom,
% 0.31/0.47 zero_neq_one @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Orderings_Olinorder_42,axiom,
% 0.31/0.47 linorder @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_43,axiom,
% 0.31/0.47 monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_44,axiom,
% 0.31/0.47 zero @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Groups_Oone_45,axiom,
% 0.31/0.47 one @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Code__Numeral_Onatural___Nat_Osize_46,axiom,
% 0.31/0.47 size @ code_natural @ ( type2 @ code_natural ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t___Nat_Osize_47,axiom,
% 0.31/0.47 ! [A5: $tType] : ( size @ ( splay_2011811431op_s_t @ A5 ) @ ( type2 @ ( splay_2011811431op_s_t @ A5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %----Helper facts (3)
% 0.31/0.47 thf(help_If_3_1_T,axiom,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_2_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_T,axiom,
% 0.31/0.47 ! [A: $tType,X: A,Y: A] :
% 0.31/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 %----Free types (1)
% 0.31/0.47 thf(tfree_0,hypothesis,
% 0.31/0.47 linorder @ a @ ( type2 @ a ) ).
% 0.31/0.47
% 0.31/0.47 %----Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( size_size @ ( tree @ a ) @ rr )
% 0.31/0.47 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ a ) @ l ) @ ( size_size @ ( tree @ a ) @ r ) ) @ ( one_one @ nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.75/1.56 ---- Embedded in THF ---
% 2.75/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.75/1.56 %%% Generated on Tue Feb 24 06:10:12 EST 2026
% 2.75/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.75/1.56 %%% Logic specification used:
% 2.75/1.56 %%% thf(spec, logic, $$dhol).
% 2.75/1.56
% 2.75/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2DTF30178.p
% 2.75/1.56 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t, type, splay_2011811431op_s_t: ($tType > $tType)).
% 2.75/1.56 thf(ty_t_Code__Numeral_Onatural, type, code_natural: $tType).
% 2.75/1.56 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.75/1.56 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 2.75/1.56 thf(ty_t_Tree_Otree, type, tree: ($tType > $tType)).
% 2.75/1.56 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.75/1.56 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.75/1.56 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.75/1.56 thf(ty_tf_a, type, a: $tType).
% 2.75/1.56 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Transcendental_Oln, type, ln: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add, type, strict797366125id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.75/1.56 thf(sy_c_Code__Numeral_Onatural_Ocase__natural, type, code_case_natural: (!> [T:$tType]: ((T > ((code_natural > T) > (code_natural > T)))))).
% 2.75/1.56 thf(sy_c_Code__Numeral_Onatural_Orec__natural, type, code_rec_natural: (!> [T:$tType]: ((T > ((code_natural > (T > T)) > (code_natural > T)))))).
% 2.75/1.56 thf(sy_c_Code__Numeral_Onatural_Osize__natural, type, code_size_natural: (code_natural > nat)).
% 2.75/1.56 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.75/1.56 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.75/1.56 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.75/1.56 thf(sy_c_HOL_Obool_Osize__bool, type, size_bool: ($o > nat)).
% 2.75/1.56 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.75/1.56 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.75/1.56 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec, type, neg_numeral_dbl_dec: (!> [A:$tType]: ((A > A)))).
% 2.75/1.56 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc, type, neg_numeral_dbl_inc: (!> [A:$tType]: ((A > A)))).
% 2.75/1.56 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.75/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.75/1.56 thf(sy_c_Product__Type_Oold_Obool_Orec__bool, type, product_rec_bool: (!> [T:$tType]: ((T > (T > ($o > T)))))).
% 2.75/1.56 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.75/1.56 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat, type, set_fo292404081st_nat: (!> [A:$tType]: (((nat > (A > A)) > (nat > (nat > (A > A))))))).
% 2.75/1.56 thf(sy_c_Splay__Tree_Osplay, type, splay_splay: (!> [A:$tType]: ((A > ((tree @ A) > (tree @ A)))))).
% 2.75/1.56 thf(sy_c_Splay__Tree_Osplay__max, type, splay_splay_max: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.75/1.56 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay, type, splay_914434265_splay: (!> [A:$tType]: ((A > ((tree @ A) > nat))))).
% 2.75/1.56 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max, type, splay_878424299ay_max: (!> [A:$tType]: (((tree @ A) > nat)))).
% 2.75/1.56 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel, type, splay_1816415694ax_rel: (!> [A:$tType]: (((tree @ A) > ((tree @ A) > $o))))).
% 2.75/1.56 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA, type, splay_266122055elle_A: (!> [A:$tType]: ((A > ((tree @ A) > real))))).
% 2.75/1.56 thf(sy_c_Transcendental_Oln__class_Oln, type, ln_ln: (!> [A:$tType]: ((A > A)))).
% 2.75/1.56 thf(sy_c_Transcendental_Opowr, type, powr: (!> [A:$tType]: ((A > (A > A))))).
% 2.75/1.56 thf(sy_c_Tree_Olinorder__class_Obst, type, linorder_bst: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.75/1.56 thf(sy_c_Tree_Opath__len, type, path_len: (!> [A:$tType]: (((tree @ A) > nat)))).
% 2.75/1.56 thf(sy_c_Tree_Opath__len__rel, type, path_len_rel: (!> [A:$tType]: (((tree @ A) > ((tree @ A) > $o))))).
% 2.75/1.56 thf(sy_c_Tree_Osize1, type, size1: (!> [A:$tType]: (((tree @ A) > nat)))).
% 2.75/1.56 thf(sy_c_Tree_Otree_OLeaf, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 2.75/1.56 thf(sy_c_Tree_Otree_ONode, type, node: (!> [A:$tType]: (((tree @ A) > (A > ((tree @ A) > (tree @ A))))))).
% 2.75/1.56 thf(sy_c_Tree_Otree_Osize__tree, type, size_tree: (!> [A:$tType]: (((A > nat) > ((tree @ A) > nat))))).
% 2.75/1.56 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.75/1.56 thf(sy_v_b____, type, b: a).
% 2.75/1.56 thf(sy_v_c____, type, c: a).
% 2.75/1.56 thf(sy_v_l_H____, type, l: (tree @ a)).
% 2.75/1.56 thf(sy_v_l____, type, l2: (tree @ a)).
% 2.75/1.56 thf(sy_v_r_H____, type, r: (tree @ a)).
% 2.75/1.56 thf(sy_v_rl____, type, rl: (tree @ a)).
% 2.75/1.56 thf(sy_v_rr____, type, rr: (tree @ a)).
% 2.75/1.56 thf(sy_v_u____, type, u: a).
% 2.75/1.56 thf(fact_0__092_060open_062size_Arr_A_061_Asize_A_Isplay__max_Arr_J_092_060close_062, axiom, (((size_size @ (tree @ a)) @ rr) = ((size_size @ (tree @ a)) @ ((splay_splay_max @ a) @ rr)))).
% 2.75/1.56 thf(fact_1_sp, axiom, (((splay_splay_max @ a) @ rr) = ((((node @ a) @ l) @ u) @ r))).
% 2.75/1.56 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062l_H_Au_Ar_H_O_Asplay__max_Arr_A_061_A_092_060langle_062l_H_M_Au_M_Ar_H_092_060rangle_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [L:(tree @ a),U:a,R:(tree @ a)]: ((((splay_splay_max @ a) @ rr) != ((((node @ a) @ L) @ U) @ R))))))).
% 2.75/1.56 thf(fact_3__092_060open_062rr_A_092_060noteq_062_A_092_060langle_062_092_060rangle_062_092_060close_062, axiom, (rr != (leaf @ a))).
% 2.75/1.56 thf(fact_4_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.75/1.56 thf(fact_5_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.75/1.56 thf(fact_6_size__if__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),L2:(tree @ A),U2:A,R2:(tree @ A)]: (((((splay_splay_max @ A) @ T2) = ((((node @ A) @ L2) @ U2) @ R2)) => (((size_size @ (tree @ A)) @ T2) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((size_size @ (tree @ A)) @ L2)) @ ((size_size @ (tree @ A)) @ R2))) @ (one_one @ nat)))))))))).
% 2.75/1.56 thf(fact_7_one__natural_Orsp, axiom, ((one_one @ nat) = (one_one @ nat))).
% 2.75/1.56 thf(fact_8_size__ne__size__imp__ne, axiom, (! [A:$tType]: ((((size @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y)) => (X != Y)))))))).
% 2.75/1.56 thf(fact_9_nat__add__left__cancel, axiom, (! [K:nat,M:nat,N:nat]: ((((((plus_plus @ nat) @ K) @ M) = (((plus_plus @ nat) @ K) @ N)) = (M = N))))).
% 2.75/1.56 thf(fact_10_nat__add__right__cancel, axiom, (! [M:nat,K:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ K) = (((plus_plus @ nat) @ N) @ K)) = (M = N))))).
% 2.75/1.56 thf(fact_11_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.75/1.56 thf(fact_12_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_13_is__num__normalize_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_14_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_15_splay__max__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: (((((splay_splay_max @ A) @ T2) = (leaf @ A)) = (T2 = (leaf @ A))))))))).
% 2.75/1.56 thf(fact_16_splay__max_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [La:(tree @ A),A2:A]: ((((splay_splay_max @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) = ((((node @ A) @ La) @ A2) @ (leaf @ A))))))))).
% 2.75/1.56 thf(fact_17_splay__max_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((splay_splay_max @ A) @ (leaf @ A)) = (leaf @ A)))))).
% 2.75/1.56 thf(fact_18_splay__max__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),L2:(tree @ A),A2:A,R2:(tree @ A)]: (((((splay_splay_max @ A) @ T2) = ((((node @ A) @ L2) @ A2) @ R2)) => (R2 = (leaf @ A))))))))).
% 2.75/1.56 thf(fact_19_size__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((size_size @ (tree @ A)) @ ((splay_splay_max @ A) @ T2)) = ((size_size @ (tree @ A)) @ T2)))))))).
% 2.75/1.56 thf(fact_20_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B = C)))))))).
% 2.75/1.56 thf(fact_21_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) => (B = C)))))))).
% 2.75/1.56 thf(fact_22_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_23_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,B2:A]: ((((plus_plus @ A) @ B2) @ A3)))))))).
% 2.75/1.56 thf(fact_24_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.75/1.56 thf(fact_25_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.75/1.56 thf(fact_26_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_27_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$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))))))))).
% 2.75/1.56 thf(fact_28_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.56 thf(fact_29_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,B2:A]: ((((plus_plus @ A) @ B2) @ A3)))))))).
% 2.75/1.56 thf(fact_30__C3_Oprems_C_I2_J, axiom, (((((node @ a) @ l2) @ b) @ ((((node @ a) @ rl) @ c) @ rr)) != (leaf @ a))).
% 2.75/1.56 thf(fact_31_tree_Oinject, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A),Y21:(tree @ A),Y22:A,Y23:(tree @ A)]: (((((((node @ A) @ X21) @ X22) @ X23) = ((((node @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X22 = Y22) & (X23 = Y23))))))).
% 2.75/1.56 thf(fact_32_tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:(tree @ A),X22:A,X23:(tree @ A)]: (((leaf @ A) != ((((node @ A) @ X21) @ X22) @ X23))))).
% 2.75/1.56 thf(fact_33_tree_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),Tree:(tree @ A)]: (((P @ (leaf @ A)) => ((! [X1:(tree @ A),X2:A,X3:(tree @ A)]: (((P @ X1) => ((P @ X3) => (P @ ((((node @ A) @ X1) @ X2) @ X3)))))) => (P @ Tree)))))).
% 2.75/1.56 thf(fact_34_neq__Leaf__iff, axiom, (! [A:$tType,T2:(tree @ A)]: (((T2 != (leaf @ A)) = (? [L3:(tree @ A),A3:A,R3:(tree @ A)]: ((T2 = ((((node @ A) @ L3) @ A3) @ R3)))))))).
% 2.75/1.56 thf(fact_35_tree_Oexhaust, axiom, (! [A:$tType,Y:(tree @ A)]: (((Y != (leaf @ A)) => (~ ((! [X212:(tree @ A),X222:A,X232:(tree @ A)]: ((Y != ((((node @ A) @ X212) @ X222) @ X232)))))))))).
% 2.75/1.56 thf(fact_36_mirror_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L4:(tree @ A),X4:A,R4:(tree @ A)]: (((P @ R4) => ((P @ L4) => (P @ ((((node @ A) @ L4) @ X4) @ R4)))))) => (P @ A0)))))).
% 2.75/1.56 thf(fact_37_bst__eq_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L4:(tree @ A),A4:A,R4:(tree @ A)]: ((X != ((((node @ A) @ L4) @ A4) @ R4))))))))))))).
% 2.75/1.56 thf(fact_38_bst__eq_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L4:(tree @ A),A4:A,R4:(tree @ A)]: (((P @ L4) => ((P @ R4) => (P @ ((((node @ A) @ L4) @ A4) @ R4)))))) => (P @ A0))))))))).
% 2.75/1.56 thf(fact_39__092_060Phi_062_Ocases, axiom, (! [A:$tType,X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L4:(tree @ A),A4:A,R4:(tree @ A)]: ((X != ((((node @ A) @ L4) @ A4) @ R4)))))))))).
% 2.75/1.56 thf(fact_40__C3_Oprems_C_I1_J, axiom, ((linorder_bst @ a) @ ((((node @ a) @ l2) @ b) @ ((((node @ a) @ rl) @ c) @ rr)))).
% 2.75/1.56 thf(fact_41_t__splay__max_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L4:(tree @ A),B3:A]: ((P @ ((((node @ A) @ L4) @ B3) @ (leaf @ A))))) => ((! [L4:(tree @ A),B3:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((((Rr != (leaf @ A)) => (P @ Rr)) => (P @ ((((node @ A) @ L4) @ B3) @ ((((node @ A) @ Rl) @ C2) @ Rr)))))) => (P @ A0)))))))))).
% 2.75/1.56 thf(fact_42_t__splay__max_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => ((! [L4:(tree @ A),B3:A]: ((X != ((((node @ A) @ L4) @ B3) @ (leaf @ A))))) => (~ ((! [L4:(tree @ A),B3:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((X != ((((node @ A) @ L4) @ B3) @ ((((node @ A) @ Rl) @ C2) @ Rr))))))))))))))).
% 2.75/1.56 thf(fact_43__092_060Phi_062_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L4:(tree @ A),A4:A,R4:(tree @ A)]: (((P @ L4) => ((P @ R4) => (P @ ((((node @ A) @ L4) @ A4) @ R4)))))) => (P @ A0)))))).
% 2.75/1.56 thf(fact_44_ext, axiom, (! [B4:$tType,A:$tType,F:(A > B4),G:(A > B4)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.75/1.56 thf(fact_45_t__splay__max_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Rr2:(tree @ A),L2:(tree @ A),B:A,Rl2:(tree @ A),C:A]: ((((Rr2 = (leaf @ A)) => (((splay_878424299ay_max @ A) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (one_one @ nat))) & ((Rr2 != (leaf @ A)) => (((splay_878424299ay_max @ A) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (((plus_plus @ nat) @ ((splay_878424299ay_max @ A) @ Rr2)) @ (one_one @ nat))))))))))).
% 2.75/1.56 thf(fact_46_t__splay__max_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:nat]: (((((splay_878424299ay_max @ A) @ X) = Y) => (((X = (leaf @ A)) => (Y != (one_one @ nat))) => (((? [L4:(tree @ A),B3:A]: ((X = ((((node @ A) @ L4) @ B3) @ (leaf @ A))))) => (Y != (one_one @ nat))) => (~ ((! [L4:(tree @ A),B3:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: (((X = ((((node @ A) @ L4) @ B3) @ ((((node @ A) @ Rl) @ C2) @ Rr))) => (~ ((((Rr = (leaf @ A)) => (Y = (one_one @ nat))) & ((Rr != (leaf @ A)) => (Y = (((plus_plus @ nat) @ ((splay_878424299ay_max @ A) @ Rr)) @ (one_one @ nat))))))))))))))))))))).
% 2.75/1.56 thf(fact_47_path__len_Osimps_I2_J, axiom, (! [A:$tType,L2:(tree @ A),Uu:A,R2:(tree @ A)]: ((((path_len @ A) @ ((((node @ A) @ L2) @ Uu) @ R2)) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((path_len @ A) @ L2)) @ ((size_size @ (tree @ A)) @ L2))) @ ((path_len @ A) @ R2))) @ ((size_size @ (tree @ A)) @ R2)))))).
% 2.75/1.56 thf(fact_48_t__splay__max_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(tree @ A),B:A]: ((((splay_878424299ay_max @ A) @ ((((node @ A) @ L2) @ B) @ (leaf @ A))) = (one_one @ nat)))))))).
% 2.75/1.56 thf(fact_49_size__if__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A),L2:(tree @ A),U2:A,R2:(tree @ A)]: ((((((splay_splay @ A) @ A2) @ T2) = ((((node @ A) @ L2) @ U2) @ R2)) => (((size_size @ (tree @ A)) @ T2) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((size_size @ (tree @ A)) @ L2)) @ ((size_size @ (tree @ A)) @ R2))) @ (one_one @ nat)))))))))).
% 2.75/1.56 thf(fact_50_size1__def, axiom, (! [A:$tType]: (((size1 @ A) = (^ [T3:(tree @ A)]: ((((plus_plus @ nat) @ ((size_size @ (tree @ A)) @ T3)) @ (one_one @ nat)))))))).
% 2.75/1.56 thf(fact_51_dbl__inc__def, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((neg_numeral_dbl_inc @ A) = (^ [X5:A]: ((((plus_plus @ A) @ (((plus_plus @ A) @ X5) @ X5)) @ (one_one @ A))))))))).
% 2.75/1.56 thf(fact_52_t__splay__max_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((splay_878424299ay_max @ A) @ (leaf @ A)) = (one_one @ nat)))))).
% 2.75/1.56 thf(fact_53_splay__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: ((((((splay_splay @ A) @ A2) @ T2) = (leaf @ A)) = (T2 = (leaf @ A))))))))).
% 2.75/1.56 thf(fact_54_size__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: ((((size_size @ (tree @ A)) @ (((splay_splay @ A) @ A2) @ T2)) = ((size_size @ (tree @ A)) @ T2)))))))).
% 2.75/1.56 thf(fact_55_size1__simps_I2_J, axiom, (! [B4:$tType,L2:(tree @ B4),X:B4,R2:(tree @ B4)]: ((((size1 @ B4) @ ((((node @ B4) @ L2) @ X) @ R2)) = (((plus_plus @ nat) @ ((size1 @ B4) @ L2)) @ ((size1 @ B4) @ R2)))))).
% 2.75/1.56 thf(fact_56_size1__simps_I1_J, axiom, (! [A:$tType]: ((((size1 @ A) @ (leaf @ A)) = (one_one @ nat))))).
% 2.75/1.56 thf(fact_57_bst__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ (((splay_splay @ A) @ A2) @ T2))))))))).
% 2.75/1.56 thf(fact_58_splay__max__eq__splay__ex, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => (? [A4:A]: ((((splay_splay_max @ A) @ T2) = (((splay_splay @ A) @ A4) @ T2))))))))))).
% 2.75/1.56 thf(fact_59_splay_Osimps_I2_J, axiom, (! [A:$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)))))))).
% 2.75/1.56 thf(fact_60_splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_splay @ A) @ A2) @ (leaf @ A)) = (leaf @ A)))))))).
% 2.75/1.56 thf(fact_61_bst_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_bst @ A) @ (leaf @ A)))))).
% 2.75/1.56 thf(fact_62_bst__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ ((splay_splay_max @ A) @ T2))))))))).
% 2.75/1.57 thf(fact_63_splay__not__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: (((T2 != (leaf @ A)) => (? [L4:(tree @ A),X4:A,R4:(tree @ A)]: (((((splay_splay @ A) @ A2) @ T2) = ((((node @ A) @ L4) @ X4) @ R4))))))))))).
% 2.75/1.57 thf(fact_64_path__len_Oelims, axiom, (! [A:$tType,X:(tree @ A),Y:nat]: (((((path_len @ A) @ X) = Y) => (((X = (leaf @ A)) => (Y != (zero_zero @ nat))) => (~ ((! [L4:(tree @ A),Uu2:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L4) @ Uu2) @ R4)) => (Y != (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((path_len @ A) @ L4)) @ ((size_size @ (tree @ A)) @ L4))) @ ((path_len @ A) @ R4))) @ ((size_size @ (tree @ A)) @ R4))))))))))))).
% 2.75/1.57 thf(fact_65_A__simps_I1_J, axiom, (! [A:$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)))))))).
% 2.75/1.57 thf(fact_66_t__splay__max_Opelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:nat]: (((((splay_878424299ay_max @ A) @ X) = Y) => ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ X) => (((X = (leaf @ A)) => ((Y = (one_one @ nat)) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ (leaf @ A)))))) => ((! [L4:(tree @ A),B3:A]: (((X = ((((node @ A) @ L4) @ B3) @ (leaf @ A))) => ((Y = (one_one @ nat)) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ ((((node @ A) @ L4) @ B3) @ (leaf @ A))))))))) => (~ ((! [L4:(tree @ A),B3:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: (((X = ((((node @ A) @ L4) @ B3) @ ((((node @ A) @ Rl) @ C2) @ Rr))) => ((((Rr = (leaf @ A)) => (Y = (one_one @ nat))) & ((Rr != (leaf @ A)) => (Y = (((plus_plus @ nat) @ ((splay_878424299ay_max @ A) @ Rr)) @ (one_one @ nat))))) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ ((((node @ A) @ L4) @ B3) @ ((((node @ A) @ Rl) @ C2) @ Rr))))))))))))))))))))).
% 2.75/1.57 thf(fact_67_dbl__dec__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_dec @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 2.75/1.57 thf(fact_68_dbl__inc__simps_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_inc @ A) @ (zero_zero @ A)) = (one_one @ A)))))).
% 2.75/1.57 thf(fact_69_t__splay__simps_I1_J, axiom, (! [A:$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)))))))).
% 2.75/1.57 thf(fact_70_splay_Osimps_I13_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B:A,La:(tree @ A),Lb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ B) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Lb) @ B) @ (leaf @ A)))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Lb)) @ B) @ (leaf @ A))))))))))).
% 2.75/1.57 thf(fact_71_natural_Osize_I3_J, axiom, (((size_size @ code_natural) @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_72_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.75/1.57 thf(fact_73_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.75/1.57 thf(fact_74_not__gr__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_75_add_Oleft__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.75/1.57 thf(fact_76_add_Oright__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.75/1.57 thf(fact_77_double__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_78_double__zero__sym, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_79_add__cancel__left__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [B:A,A2:A]: ((((((plus_plus @ A) @ B) @ A2) = A2) = (B = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_80_add__cancel__left__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: ((((((plus_plus @ A) @ A2) @ B) = A2) = (B = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_81_add__cancel__right__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((A2 = (((plus_plus @ A) @ B) @ A2)) = (B = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_82_add__cancel__right__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((A2 = (((plus_plus @ A) @ A2) @ B)) = (B = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_83_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_84_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_85_add__gr__0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((plus_plus @ nat) @ M) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) | (((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))).
% 2.75/1.57 thf(fact_86_add__is__0, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) & (N = (zero_zero @ nat))))))).
% 2.75/1.57 thf(fact_87_Nat_Oadd__0__right, axiom, (! [M:nat]: (((((plus_plus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.75/1.57 thf(fact_88_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.75/1.57 thf(fact_89_add__less__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ B) @ A2)) @ B) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_90_add__less__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_91_less__add__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B)) = (((ord_less @ A) @ (zero_zero @ A)) @ B)))))))).
% 2.75/1.57 thf(fact_92_less__add__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ B) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B)))))))).
% 2.75/1.57 thf(fact_93_double__add__less__zero__iff__single__add__less__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_94_zero__less__double__add__iff__zero__less__single__add, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.75/1.57 thf(fact_95_t__splay__simps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ A2) @ Lr)) @ B) @ R2)) = (one_one @ nat))))))))).
% 2.75/1.57 thf(fact_96_t__splay__simps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B:A,A2:A,L2:(tree @ A),Rl2:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ A2) @ Rr2))) = (one_one @ nat))))))))).
% 2.75/1.57 thf(fact_97_t__splay__simps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B) @ R2)) = (one_one @ nat))))))))).
% 2.75/1.57 thf(fact_98_t__splay__simps_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B:A,A2:A,L2:(tree @ A)]: (((((ord_less @ A) @ B) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ (leaf @ A))) = (one_one @ nat))))))))).
% 2.75/1.57 thf(fact_99_t__splay__simps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A,Rr2:(tree @ A),L2:(tree @ A),Rl2:(tree @ A)]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ C) @ A2) => (((Rr2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (one_one @ nat))) & ((Rr2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rr2)) @ (one_one @ nat))))))))))))).
% 2.75/1.57 thf(fact_100_t__splay__simps_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B:A,A2:A,C:A,Rl2:(tree @ A),L2:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ A2) @ C) => (((Rl2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (one_one @ nat))) & ((Rl2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L2) @ B) @ ((((node @ A) @ Rl2) @ C) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rl2)) @ (one_one @ nat))))))))))))).
% 2.75/1.57 thf(fact_101_t__splay__simps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,Lr:(tree @ A),Ll:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ A2) => (((Lr = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C) @ Lr)) @ B) @ R2)) = (one_one @ nat))) & ((Lr != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C) @ Lr)) @ B) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Lr)) @ (one_one @ nat))))))))))))).
% 2.75/1.57 thf(fact_102_t__splay__simps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ A2) @ C) => (((Ll = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C) @ Lr)) @ B) @ R2)) = (one_one @ nat))) & ((Ll != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C) @ Lr)) @ B) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Ll)) @ (one_one @ nat))))))))))))).
% 2.75/1.57 thf(fact_103_size1__ge0, axiom, (! [A:$tType,T2:(tree @ A)]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size1 @ A) @ T2))))).
% 2.75/1.57 thf(fact_104_less__numeral__extra_I3_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.75/1.57 thf(fact_105_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.75/1.57 thf(fact_106_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.75/1.57 thf(fact_107_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.75/1.57 thf(fact_108_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.75/1.57 thf(fact_109_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.75/1.57 thf(fact_110_zero__reorient, axiom, (! [A:$tType]: ((((zero @ A) @ (type2 @ A)) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_111_infinite__descent0, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2)))))))))) => (P @ N)))))).
% 2.75/1.57 thf(fact_112_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.75/1.57 thf(fact_113_zero__natural_Orsp, axiom, ((zero_zero @ nat) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_114_infinite__descent0__measure, axiom, (! [A:$tType,V:(A > nat),P:(A > $o),X:A]: (((! [X4:A]: ((((V @ X4) = (zero_zero @ nat)) => (P @ X4)))) => ((! [X4:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V @ X4)) => ((~ ((P @ X4))) => (? [Y2:A]: (((((ord_less @ nat) @ (V @ Y2)) @ (V @ X4)) & (~ ((P @ Y2)))))))))) => (P @ X)))))).
% 2.75/1.57 thf(fact_115_linordered__field__no__lb, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X6:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X6))))))))).
% 2.75/1.57 thf(fact_116_linordered__field__no__ub, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X6:A]: ((? [X1:A]: ((((ord_less @ A) @ X6) @ X1))))))))).
% 2.75/1.57 thf(fact_117_gr__zeroI, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.75/1.57 thf(fact_118_not__less__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.75/1.57 thf(fact_119_gr__implies__not__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_120_zero__less__iff__neq__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_121_less__imp__add__positive, axiom, (! [I:nat,J:nat]: (((((ord_less @ nat) @ I) @ J) => (? [K2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K2) & ((((plus_plus @ nat) @ I) @ K2) = J)))))))).
% 2.75/1.57 thf(fact_122_less__numeral__extra_I2_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.75/1.57 thf(fact_123_less__numeral__extra_I1_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.75/1.57 thf(fact_124_add__neg__neg, axiom, (! [A:$tType]: ((((ordere216010020id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B)) @ (zero_zero @ A)))))))))).
% 2.75/1.57 thf(fact_125_add__pos__pos, axiom, (! [A:$tType]: ((((ordere216010020id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B)))))))))).
% 2.75/1.57 thf(fact_126_pos__add__strict, axiom, (! [A:$tType]: ((((strict797366125id_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B) @ C) => (((ord_less @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 2.75/1.57 thf(fact_127_op_092_060_094sub_062s_092_060_094sub_062t_Osize__neq, axiom, (! [A:$tType,X:(splay_2011811431op_s_t @ A)]: ((((size_size @ (splay_2011811431op_s_t @ A)) @ X) != (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_128_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L2:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L2)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L2))))))))).
% 2.75/1.57 thf(fact_129_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L2:A]: ((((I = J) & (((ord_less @ A) @ K) @ L2)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L2))))))))).
% 2.75/1.57 thf(fact_130_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L2:A]: ((((((ord_less @ A) @ I) @ J) & (K = L2)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L2))))))))).
% 2.75/1.57 thf(fact_131_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.75/1.57 thf(fact_132_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B))))))))).
% 2.75/1.57 thf(fact_133_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.57 thf(fact_134_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_135_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_136_less__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.75/1.57 thf(fact_137_add__lessD1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K) => (((ord_less @ nat) @ I) @ K))))).
% 2.75/1.57 thf(fact_138_add__less__mono, axiom, (! [I:nat,J:nat,K:nat,L2:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K) @ L2) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L2))))))).
% 2.75/1.57 thf(fact_139_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.75/1.57 thf(fact_140_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.75/1.57 thf(fact_141_add__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.75/1.57 thf(fact_142_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.75/1.57 thf(fact_143_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.75/1.57 thf(fact_144_less__add__eq__less, axiom, (! [K:nat,L2:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K) @ L2) => (((((plus_plus @ nat) @ M) @ L2) = (((plus_plus @ nat) @ K) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 2.75/1.57 thf(fact_145_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.75/1.57 thf(fact_146_add_Ocomm__neutral, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.75/1.57 thf(fact_147_add_Ogroup__left__neutral, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.75/1.57 thf(fact_148_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.75/1.57 thf(fact_149_plus__nat_Oadd__0, axiom, (! [N:nat]: (((((plus_plus @ nat) @ (zero_zero @ nat)) @ N) = N)))).
% 2.75/1.57 thf(fact_150_add__eq__self__zero, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = M) => (N = (zero_zero @ nat)))))).
% 2.75/1.57 thf(fact_151_splay_Osimps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B:A,A2:A,Lb:(tree @ A),La:(tree @ A),Ra:(tree @ A)]: (((((ord_less @ A) @ B) @ A2) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ Lb) @ B) @ ((((node @ A) @ La) @ A2) @ Ra))) = ((((node @ A) @ ((((node @ A) @ Lb) @ B) @ La)) @ A2) @ Ra))))))))).
% 2.75/1.57 thf(fact_152_splay_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,La:(tree @ A),Ra:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Ra)) @ B) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Ra) @ B) @ Rb)))))))))).
% 2.75/1.57 thf(fact_153_size__0__iff__Leaf, axiom, (! [A:$tType,T2:(tree @ A)]: (((((size_size @ (tree @ A)) @ T2) = (zero_zero @ nat)) = (T2 = (leaf @ A)))))).
% 2.75/1.57 thf(fact_154_tree_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (tree @ A)) @ (leaf @ A)) = (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_155_t__splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_914434265_splay @ A) @ A2) @ (leaf @ A)) = (one_one @ nat)))))))).
% 2.75/1.57 thf(fact_156_path__len_Osimps_I1_J, axiom, (! [A:$tType]: ((((path_len @ A) @ (leaf @ A)) = (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_157_splay_Osimps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B) @ R2)) = ((((node @ A) @ (leaf @ A)) @ B) @ R2))))))))).
% 2.75/1.57 thf(fact_158_splay_Osimps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,A2:A,B:A,Ra:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ A2) => ((((ord_less @ A) @ X) @ B) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ (leaf @ A)) @ A2) @ Ra)) @ B) @ Rb)) = ((((node @ A) @ (leaf @ A)) @ A2) @ ((((node @ A) @ Ra) @ B) @ Rb))))))))))).
% 2.75/1.57 thf(fact_159_splay_Osimps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,B:A,A2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ B) => ((((ord_less @ A) @ A2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B) @ Rb))))))))))).
% 2.75/1.57 thf(fact_160_splay_Osimps_I10_J, axiom, (! [A:$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)))))))))).
% 2.75/1.57 thf(fact_161_splay_Osimps_I12_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ X) @ B) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B) @ Rb))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B) @ Rb)))))))))).
% 2.75/1.57 thf(fact_162_path__len_Opelims, axiom, (! [A:$tType,X:(tree @ A),Y:nat]: (((((path_len @ A) @ X) = Y) => ((((accp @ (tree @ A)) @ (path_len_rel @ A)) @ X) => (((X = (leaf @ A)) => ((Y = (zero_zero @ nat)) => (~ ((((accp @ (tree @ A)) @ (path_len_rel @ A)) @ (leaf @ A)))))) => (~ ((! [L4:(tree @ A),Uu2:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L4) @ Uu2) @ R4)) => ((Y = (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((path_len @ A) @ L4)) @ ((size_size @ (tree @ A)) @ L4))) @ ((path_len @ A) @ R4))) @ ((size_size @ (tree @ A)) @ R4))) => (~ ((((accp @ (tree @ A)) @ (path_len_rel @ A)) @ ((((node @ A) @ L4) @ Uu2) @ R4)))))))))))))))).
% 2.75/1.57 thf(fact_163_zero__less__two, axiom, (! [A:$tType]: ((((linord1659791738miring @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A))))))).
% 2.75/1.57 thf(fact_164_less__add__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 2.75/1.57 thf(fact_165_zero__less__one, axiom, (! [A:$tType]: ((((zero_less_one @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.75/1.57 thf(fact_166_not__one__less__zero, axiom, (! [A:$tType]: ((((linord1659791738miring @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.75/1.57 thf(fact_167_bool_Osize_I4_J, axiom, (((size_size @ $o) @ $false) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_168_bool_Osize_I3_J, axiom, (((size_size @ $o) @ $true) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_169_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.75/1.57 thf(fact_170_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.75/1.57 thf(fact_171_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.75/1.57 thf(fact_172_less__not__refl3, axiom, (! [S:nat,T2:nat]: (((((ord_less @ nat) @ S) @ T2) => (S != T2))))).
% 2.75/1.57 thf(fact_173_measure__induct, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y2:A]: (((((ord_less @ nat) @ (F @ Y2)) @ (F @ X4)) => (P @ Y2)))) => (P @ X4)))) => (P @ A2))))).
% 2.75/1.57 thf(fact_174_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.75/1.57 thf(fact_175_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.75/1.57 thf(fact_176_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.75/1.57 thf(fact_177_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 2.75/1.57 thf(fact_178_measure__induct__rule, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y2:A]: (((((ord_less @ nat) @ (F @ Y2)) @ (F @ X4)) => (P @ Y2)))) => (P @ X4)))) => (P @ A2))))).
% 2.75/1.57 thf(fact_179_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X:A]: (((! [X4:A]: (((~ ((P @ X4))) => (? [Y2:A]: (((((ord_less @ nat) @ (V @ Y2)) @ (V @ X4)) & (~ ((P @ Y2))))))))) => (P @ X))))).
% 2.75/1.57 thf(fact_180_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.75/1.57 thf(fact_181_prod_Osize__neq, axiom, (! [A:$tType,B4:$tType,X:((product_prod @ A) @ B4)]: ((((size_size @ ((product_prod @ A) @ B4)) @ X) != (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_182_sum_Osize__neq, axiom, (! [A:$tType,B4:$tType,X:((sum_sum @ A) @ B4)]: ((((size_size @ ((sum_sum @ A) @ B4)) @ X) != (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_183_size__bool, axiom, ((size_size @ $o) = (^ [B2:$o]: ((zero_zero @ nat))))).
% 2.75/1.57 thf(fact_184_zero__neq__one, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.75/1.57 thf(fact_185_natural_Osize_I1_J, axiom, ((code_size_natural @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_186_fold__atLeastAtMost__nat_Oinduct, axiom, (! [A:$tType,P:((nat > (A > A)) > (nat > (nat > (A > $o)))),A0:(nat > (A > A)),A1:nat,A22:nat,A32:A]: (((! [F2:(nat > (A > A)),A4:nat,B3:nat,Acc:A]: ((((~ ((((ord_less @ nat) @ B3) @ A4))) => ((((P @ F2) @ (((plus_plus @ nat) @ A4) @ (one_one @ nat))) @ B3) @ ((F2 @ A4) @ Acc))) => ((((P @ F2) @ A4) @ B3) @ Acc)))) => ((((P @ A0) @ A1) @ A22) @ A32))))).
% 2.75/1.57 thf(fact_187_natural_Osimps_I4_J, axiom, (! [T:$tType,F1:T,F22:(code_natural > T)]: ((((((code_case_natural @ T) @ F1) @ F22) @ (zero_zero @ code_natural)) = F1)))).
% 2.75/1.57 thf(fact_188_bool_Osize_I1_J, axiom, ((size_bool @ $true) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_189_bool_Osize_I2_J, axiom, ((size_bool @ $false) = (zero_zero @ nat))).
% 2.75/1.57 thf(fact_190_size__bool__def, axiom, (size_bool = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 2.75/1.57 thf(fact_191_ind__euclid, axiom, (! [P:(nat > (nat > $o)),A2:nat,B:nat]: (((! [A4:nat,B3:nat]: ((((P @ A4) @ B3) = ((P @ B3) @ A4)))) => ((! [A4:nat]: (((P @ A4) @ (zero_zero @ nat)))) => ((! [A4:nat,B3:nat]: ((((P @ A4) @ B3) => ((P @ A4) @ (((plus_plus @ nat) @ A4) @ B3))))) => ((P @ A2) @ B))))))).
% 2.75/1.57 thf(fact_192_size__bool__overloaded__def, axiom, ((size_size @ $o) = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 2.75/1.57 thf(fact_193_add__0__iff, axiom, (! [A:$tType]: ((((semiri456707255roduct @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((B = (((plus_plus @ A) @ B) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_194_semiring__normalization__rules_I5_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 2.75/1.57 thf(fact_195_semiring__normalization__rules_I20_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D))))))))).
% 2.75/1.57 thf(fact_196_semiring__normalization__rules_I21_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.75/1.57 thf(fact_197_semiring__normalization__rules_I22_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ C) @ (((plus_plus @ A) @ A2) @ D))))))))).
% 2.75/1.57 thf(fact_198_semiring__normalization__rules_I23_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B)))))))).
% 2.75/1.57 thf(fact_199_semiring__normalization__rules_I24_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,C3:A]: ((((plus_plus @ A) @ C3) @ A3)))))))).
% 2.75/1.57 thf(fact_200_semiring__normalization__rules_I25_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A,C:A,D:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ C) @ D)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ D)))))))).
% 2.75/1.57 thf(fact_201_semiring__normalization__rules_I6_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.75/1.57 thf(fact_202_natural_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F22:(code_natural > (T > T))]: ((((((code_rec_natural @ T) @ F1) @ F22) @ (zero_zero @ code_natural)) = F1)))).
% 2.75/1.57 thf(fact_203_fold__atLeastAtMost__nat_Osimps, axiom, (! [A:$tType]: (((set_fo292404081st_nat @ A) = (^ [F3:(nat > (A > A)),A3:nat,B2:nat,Acc2:A]: (((((if @ A) @ (((ord_less @ nat) @ B2) @ A3)) @ Acc2) @ (((((set_fo292404081st_nat @ A) @ F3) @ (((plus_plus @ nat) @ A3) @ (one_one @ nat))) @ B2) @ ((F3 @ A3) @ Acc2))))))))).
% 2.75/1.57 thf(fact_204_fold__atLeastAtMost__nat_Oelims, axiom, (! [A:$tType,X:(nat > (A > A)),Xa:nat,Xb:nat,Xc:A,Y:A]: ((((((((set_fo292404081st_nat @ A) @ X) @ Xa) @ Xb) @ Xc) = Y) => (((((ord_less @ nat) @ Xb) @ Xa) => (Y = Xc)) & ((~ ((((ord_less @ nat) @ Xb) @ Xa))) => (Y = (((((set_fo292404081st_nat @ A) @ X) @ (((plus_plus @ nat) @ Xa) @ (one_one @ nat))) @ Xb) @ ((X @ Xa) @ Xc))))))))).
% 2.75/1.57 thf(fact_205_ln__one, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (((ln_ln @ A) @ (one_one @ A)) = (zero_zero @ A)))))).
% 2.75/1.57 thf(fact_206_tree_Osize__gen_I1_J, axiom, (! [A:$tType,X:(A > nat)]: (((((size_tree @ A) @ X) @ (leaf @ A)) = (zero_zero @ nat))))).
% 2.75/1.57 thf(fact_207_ln__less__zero__iff, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ ((ln_ln @ real) @ X)) @ (zero_zero @ real)) = (((ord_less @ real) @ X) @ (one_one @ real))))))).
% 2.75/1.57 thf(fact_208_ln__gt__zero__iff, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ (zero_zero @ real)) @ ((ln_ln @ real) @ X)) = (((ord_less @ real) @ (one_one @ real)) @ X)))))).
% 2.75/1.57 thf(fact_209_ln__eq__zero__iff, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ln_ln @ real) @ X) = (zero_zero @ real)) = (X = (one_one @ real))))))).
% 2.75/1.57 thf(fact_210_ln__gt__zero__imp__gt__one, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ ((ln_ln @ real) @ X)) => ((((ord_less @ real) @ (zero_zero @ real)) @ X) => (((ord_less @ real) @ (one_one @ real)) @ X)))))).
% 2.75/1.57 thf(fact_211_ln__less__zero, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ X) @ (one_one @ real)) => (((ord_less @ real) @ ((ln_ln @ real) @ X)) @ (zero_zero @ real))))))).
% 2.75/1.57 thf(fact_212_ln__gt__zero, axiom, (! [X:real]: (((((ord_less @ real) @ (one_one @ real)) @ X) => (((ord_less @ real) @ (zero_zero @ real)) @ ((ln_ln @ real) @ X)))))).
% 2.75/1.57 thf(fact_213_powr__zero__eq__one, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (! [X:A]: ((((X = (zero_zero @ A)) => ((((powr @ A) @ X) @ (zero_zero @ A)) = (zero_zero @ A))) & ((X != (zero_zero @ A)) => ((((powr @ A) @ X) @ (zero_zero @ A)) = (one_one @ A)))))))))).
% 2.75/1.57 thf(fact_214_powr__one__eq__one, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (! [A2:A]: (((((powr @ A) @ (one_one @ A)) @ A2) = (one_one @ A)))))))).
% 2.75/1.57 thf(fact_215_powr__gt__zero, axiom, (! [X:real,A2:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ (((powr @ real) @ X) @ A2)) = (X != (zero_zero @ real)))))).
% 2.75/1.57 thf(fact_216_powr__less__cancel__iff, axiom, (! [X:real,A2:real,B:real]: (((((ord_less @ real) @ (one_one @ real)) @ X) => ((((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B)) = (((ord_less @ real) @ A2) @ B)))))).
% 2.75/1.57 thf(fact_217_powr__0, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (! [Z:A]: (((((powr @ A) @ (zero_zero @ A)) @ Z) = (zero_zero @ A)))))))).
% 2.75/1.57 thf(fact_218_powr__eq__0__iff, axiom, (! [A:$tType]: ((((ln @ A) @ (type2 @ A)) => (! [W:A,Z:A]: ((((((powr @ A) @ W) @ Z) = (zero_zero @ A)) = (W = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_219_ln__inj__iff, axiom, (! [X:real,Y:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ (zero_zero @ real)) @ Y) => ((((ln_ln @ real) @ X) = ((ln_ln @ real) @ Y)) = (X = Y))))))).
% 2.75/1.57 thf(fact_220_ln__less__cancel__iff, axiom, (! [X:real,Y:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ (zero_zero @ real)) @ Y) => ((((ord_less @ real) @ ((ln_ln @ real) @ X)) @ ((ln_ln @ real) @ Y)) = (((ord_less @ real) @ X) @ Y))))))).
% 2.75/1.57 thf(fact_221_ln__less__self, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => (((ord_less @ real) @ ((ln_ln @ real) @ X)) @ X))))).
% 2.75/1.57 thf(fact_222_powr__less__mono2__neg, axiom, (! [A2:real,X:real,Y:real]: (((((ord_less @ real) @ A2) @ (zero_zero @ real)) => ((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ X) @ Y) => (((ord_less @ real) @ (((powr @ real) @ Y) @ A2)) @ (((powr @ real) @ X) @ A2)))))))).
% 2.75/1.57 thf(fact_223_powr__less__cancel, axiom, (! [X:real,A2:real,B:real]: (((((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B)) => ((((ord_less @ real) @ (one_one @ real)) @ X) => (((ord_less @ real) @ A2) @ B)))))).
% 2.75/1.57 thf(fact_224_powr__less__mono, axiom, (! [A2:real,B:real,X:real]: (((((ord_less @ real) @ A2) @ B) => ((((ord_less @ real) @ (one_one @ real)) @ X) => (((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B))))))).
% 2.75/1.57 thf(fact_225_powr__inj, axiom, (! [A2:real,X:real,Y:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ A2) => ((A2 != (one_one @ real)) => (((((powr @ real) @ A2) @ X) = (((powr @ real) @ A2) @ Y)) = (X = Y))))))).
% 2.75/1.57 thf(fact_226_real__lbound__gt__zero, axiom, (! [D1:real,D2:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ D1) => ((((ord_less @ real) @ (zero_zero @ real)) @ D2) => (? [E:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ E) & ((((ord_less @ real) @ E) @ D1) & (((ord_less @ real) @ E) @ D2)))))))))).
% 2.75/1.57 thf(fact_227_ln__ge__zero__iff, axiom, (! [X:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ ((ln_ln @ real) @ X)) = (((ord_less_eq @ real) @ (one_one @ real)) @ X)))))).
% 2.75/1.57 thf(fact_228_le__zero__eq, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_229_add__le__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_230_add__le__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.75/1.57 thf(fact_231_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.75/1.57 thf(fact_232_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_233_le__add__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ B) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B)))))))).
% 2.75/1.57 thf(fact_234_le__add__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B)))))))).
% 2.75/1.57 thf(fact_235_add__le__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_236_add__le__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B) @ A2)) @ B) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.75/1.57 thf(fact_237_ln__le__cancel__iff, axiom, (! [X:real,Y:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ (zero_zero @ real)) @ Y) => ((((ord_less_eq @ real) @ ((ln_ln @ real) @ X)) @ ((ln_ln @ real) @ Y)) = (((ord_less_eq @ real) @ X) @ Y))))))).
% 2.75/1.57 thf(fact_238_powr__one__gt__zero__iff, axiom, (! [X:real]: ((((((powr @ real) @ X) @ (one_one @ real)) = X) = (((ord_less_eq @ real) @ (zero_zero @ real)) @ X))))).
% 2.75/1.57 thf(fact_239_powr__one, axiom, (! [X:real]: (((((ord_less_eq @ real) @ (zero_zero @ real)) @ X) => ((((powr @ real) @ X) @ (one_one @ real)) = X))))).
% 2.75/1.57 thf(fact_240_powr__le__cancel__iff, axiom, (! [X:real,A2:real,B:real]: (((((ord_less @ real) @ (one_one @ real)) @ X) => ((((ord_less_eq @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B)) = (((ord_less_eq @ real) @ A2) @ B)))))).
% 2.75/1.57 thf(fact_241_ln__bound, axiom, (! [X:real]: (((((ord_less_eq @ real) @ (one_one @ real)) @ X) => (((ord_less_eq @ real) @ ((ln_ln @ real) @ X)) @ X))))).
% 2.75/1.57 thf(fact_242_powr__mono, axiom, (! [A2:real,B:real,X:real]: (((((ord_less_eq @ real) @ A2) @ B) => ((((ord_less_eq @ real) @ (one_one @ real)) @ X) => (((ord_less_eq @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ X) @ B))))))).
% 2.75/1.57 thf(fact_243_powr__mono2, axiom, (! [A2:real,X:real,Y:real]: (((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ X) => ((((ord_less_eq @ real) @ X) @ Y) => (((ord_less_eq @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ Y) @ A2)))))))).
% 2.75/1.57 thf(fact_244_powr__mono2_H, axiom, (! [A2:real,X:real,Y:real]: (((((ord_less_eq @ real) @ A2) @ (zero_zero @ real)) => ((((ord_less @ real) @ (zero_zero @ real)) @ X) => ((((ord_less_eq @ real) @ X) @ Y) => (((ord_less_eq @ real) @ (((powr @ real) @ Y) @ A2)) @ (((powr @ real) @ X) @ A2)))))))).
% 2.75/1.57 thf(fact_245_powr__ge__pzero, axiom, (! [X:real,Y:real]: ((((ord_less_eq @ real) @ (zero_zero @ real)) @ (((powr @ real) @ X) @ Y))))).
% 2.75/1.57 thf(fact_246_powr__less__mono2, axiom, (! [A2:real,X:real,Y:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ A2) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ X) => ((((ord_less @ real) @ X) @ Y) => (((ord_less @ real) @ (((powr @ real) @ X) @ A2)) @ (((powr @ real) @ Y) @ A2)))))))).
% 2.75/1.57 thf(fact_247_ge__one__powr__ge__zero, axiom, (! [X:real,A2:real]: (((((ord_less_eq @ real) @ (one_one @ real)) @ X) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => (((ord_less_eq @ real) @ (one_one @ real)) @ (((powr @ real) @ X) @ A2))))))).
% 2.75/1.57 thf(fact_248_less__eq__real__def, axiom, ((ord_less_eq @ real) = (^ [X5:real,Y4:real]: (((((ord_less @ real) @ X5) @ Y4) | (X5 = Y4)))))).
% 2.75/1.57 thf(fact_249_zero__le, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.75/1.57 thf(fact_250_le__numeral__extra_I3_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.75/1.57 thf(fact_251_add__less__le__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.75/1.57 thf(fact_252_add__le__less__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.75/1.57 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((type @ A) @ (type2 @ A)))))).
% 2.75/1.57 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, ((semiri456707255roduct @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, ((ordere516151231imp_le @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, ((ordere223160158up_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add, axiom, ((strict797366125id_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, ((linord1659791738miring @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, axiom, ((ordere216010020id_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, ((cancel1352612707id_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, ((comm_monoid_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Rings_Ozero__less__one, axiom, ((zero_less_one @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, ((zero_neq_one @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, ((monoid_add @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Ozero, axiom, ((zero @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_Nat_Onat___Nat_Osize, axiom, ((size @ nat) @ (type2 @ nat))).
% 2.75/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder_1, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.75/1.57 thf(tcon_HOL_Obool___Nat_Osize_2, axiom, ((size @ $o) @ (type2 @ $o))).
% 2.75/1.57 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_3, axiom, ((semiri456707255roduct @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4, axiom, ((ordere516151231imp_le @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_5, axiom, ((strict2144017051up_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_6, axiom, ((ordere223160158up_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_7, axiom, ((ordere236663937imp_le @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_8, axiom, ((strict797366125id_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_9, axiom, ((linord1659791738miring @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_10, axiom, ((ordere779506340up_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_11, axiom, ((ordere216010020id_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add, axiom, ((linord219039673up_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_12, axiom, ((cancel1352612707id_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_13, axiom, ((cancel_semigroup_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_14, axiom, ((linordered_semidom @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_15, axiom, ((ab_semigroup_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Fields_Olinordered__field, axiom, ((linordered_field @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_16, axiom, ((comm_monoid_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Olinordered__idom, axiom, ((linordered_idom @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_17, axiom, ((comm_semiring_1 @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Osemigroup__add_18, axiom, ((semigroup_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Ozero__less__one_19, axiom, ((zero_less_one @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_20, axiom, ((zero_neq_one @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Orderings_Olinorder_21, axiom, ((linorder @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Transcendental_Oln, axiom, ((ln @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Omonoid__add_22, axiom, ((monoid_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, ((group_add @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, ((neg_numeral @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Ozero_23, axiom, ((zero @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Real_Oreal___Groups_Oone_24, axiom, ((one @ real) @ (type2 @ real))).
% 2.75/1.57 thf(tcon_Tree_Otree___Nat_Osize_25, axiom, (! [A5:$tType]: (((size @ (tree @ A5)) @ (type2 @ (tree @ A5)))))).
% 2.75/1.57 thf(tcon_Sum__Type_Osum___Nat_Osize_26, axiom, (! [A5:$tType,A6:$tType]: (((size @ ((sum_sum @ A5) @ A6)) @ (type2 @ ((sum_sum @ A5) @ A6)))))).
% 2.75/1.57 thf(tcon_Product__Type_Oprod___Nat_Osize_27, axiom, (! [A5:$tType,A6:$tType]: (((size @ ((product_prod @ A5) @ A6)) @ (type2 @ ((product_prod @ A5) @ A6)))))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_28, axiom, ((ordere516151231imp_le @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_29, axiom, ((strict2144017051up_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_30, axiom, ((ordere223160158up_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add__imp__le_31, axiom, ((ordere236663937imp_le @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_32, axiom, ((strict797366125id_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_33, axiom, ((ordere779506340up_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__comm__monoid__add_34, axiom, ((ordere216010020id_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_35, axiom, ((cancel1352612707id_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_36, axiom, ((cancel_semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_37, axiom, ((ab_semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_38, axiom, ((comm_monoid_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_39, axiom, ((comm_semiring_1 @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_40, axiom, ((semigroup_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_41, axiom, ((zero_neq_one @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Orderings_Olinorder_42, axiom, ((linorder @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_43, axiom, ((monoid_add @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_44, axiom, ((zero @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Groups_Oone_45, axiom, ((one @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Code__Numeral_Onatural___Nat_Osize_46, axiom, ((size @ code_natural) @ (type2 @ code_natural))).
% 2.75/1.57 thf(tcon_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t___Nat_Osize_47, axiom, (! [A5:$tType]: (((size @ (splay_2011811431op_s_t @ A5)) @ (type2 @ (splay_2011811431op_s_t @ A5)))))).
% 2.75/1.57 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.75/1.57 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.75/1.57 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.75/1.57 thf(tfree_0, hypothesis, ((linorder @ a) @ (type2 @ a))).
% 2.75/1.57 thf(conj_0, conjecture, (((size_size @ (tree @ a)) @ rr) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((size_size @ (tree @ a)) @ l)) @ ((size_size @ (tree @ a)) @ r))) @ (one_one @ nat)))).
% 2.75/1.57 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2DTF30178.p
% 2.75/1.57 ------------------------
% 2.93/1.61 ---- Cleaned THF ---
% 2.93/1.61 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.93/1.61 splay_2011811431op_s_t: $tType > $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Code__Numeral_Onatural,type,
% 2.93/1.61 code_natural: $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Product__Type_Oprod,type,
% 2.93/1.61 product_prod: $tType > $tType > $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Sum__Type_Osum,type,
% 2.93/1.61 sum_sum: $tType > $tType > $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Tree_Otree,type,
% 2.93/1.61 tree: $tType > $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Real_Oreal,type,
% 2.93/1.61 real: $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_Nat_Onat,type,
% 2.93/1.61 nat: $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_t_itself,type,
% 2.93/1.61 itself: $tType > $tType ).
% 2.93/1.61
% 2.93/1.61 thf(ty_tf_a,type,
% 2.93/1.61 a: $tType ).
% 2.93/1.61
% 2.93/1.61 thf(sy_cl_HOL_Otype,type,
% 2.93/1.61 type:
% 2.93/1.61 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.61
% 2.93/1.61 thf(sy_cl_Nat_Osize,type,
% 2.93/1.61 size:
% 2.93/1.61 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.61
% 2.93/1.61 thf(sy_cl_Groups_Oone,type,
% 2.93/1.61 one:
% 2.93/1.61 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.61
% 2.93/1.61 thf(sy_cl_Groups_Ozero,type,
% 2.93/1.61 zero:
% 2.93/1.61 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.61
% 2.93/1.61 thf(sy_cl_Num_Oneg__numeral,type,
% 2.93/1.61 neg_numeral:
% 2.93/1.61 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ogroup__add,type,
% 2.93/1.62 group_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Omonoid__add,type,
% 2.93/1.62 monoid_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Transcendental_Oln,type,
% 2.93/1.62 ln:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Orderings_Olinorder,type,
% 2.93/1.62 linorder:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.93/1.62 zero_neq_one:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Ozero__less__one,type,
% 2.93/1.62 zero_less_one:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.93/1.62 semigroup_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.93/1.62 comm_semiring_1:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.93/1.62 linordered_idom:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.93/1.62 comm_monoid_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Fields_Olinordered__field,type,
% 2.93/1.62 linordered_field:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.93/1.62 ab_semigroup_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.93/1.62 linordered_semidom:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.93/1.62 cancel_semigroup_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.93/1.62 cancel1352612707id_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.93/1.62 linord219039673up_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.93/1.62 ordere216010020id_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.93/1.62 ordere779506340up_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.93/1.62 linord1659791738miring:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.93/1.62 canoni770627133id_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 2.93/1.62 strict797366125id_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.93/1.62 ordere236663937imp_le:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.93/1.62 ordere223160158up_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.93/1.62 strict2144017051up_add:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.93/1.62 ordere516151231imp_le:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 2.93/1.62 semiri456707255roduct:
% 2.93/1.62 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 2.93/1.62 code_case_natural:
% 2.93/1.62 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 2.93/1.62 code_rec_natural:
% 2.93/1.62 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 2.93/1.62 code_size_natural: code_natural > nat ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.93/1.62 one_one:
% 2.93/1.62 !>[A: $tType] : A ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.93/1.62 plus_plus:
% 2.93/1.62 !>[A: $tType] : ( A > A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.93/1.62 zero_zero:
% 2.93/1.62 !>[A: $tType] : A ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_HOL_Obool_Osize__bool,type,
% 2.93/1.62 size_bool: $o > nat ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_If,type,
% 2.93/1.62 if:
% 2.93/1.62 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.93/1.62 size_size:
% 2.93/1.62 !>[A: $tType] : ( A > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 2.93/1.62 neg_numeral_dbl_dec:
% 2.93/1.62 !>[A: $tType] : ( A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 2.93/1.62 neg_numeral_dbl_inc:
% 2.93/1.62 !>[A: $tType] : ( A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.93/1.62 ord_less:
% 2.93/1.62 !>[A: $tType] : ( A > A > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.93/1.62 ord_less_eq:
% 2.93/1.62 !>[A: $tType] : ( A > A > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 2.93/1.62 product_rec_bool:
% 2.93/1.62 !>[T: $tType] : ( T > T > $o > T ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Pure_Otype,type,
% 2.93/1.62 type2:
% 2.93/1.62 !>[A: $tType] : ( itself @ A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat,type,
% 2.93/1.62 set_fo292404081st_nat:
% 2.93/1.62 !>[A: $tType] : ( ( nat > A > A ) > nat > nat > A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree_Osplay,type,
% 2.93/1.62 splay_splay:
% 2.93/1.62 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree_Osplay__max,type,
% 2.93/1.62 splay_splay_max:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 2.93/1.62 splay_914434265_splay:
% 2.93/1.62 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max,type,
% 2.93/1.62 splay_878424299ay_max:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel,type,
% 2.93/1.62 splay_1816415694ax_rel:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Splay__Tree__Analysis__Mirabelle__pcaxyvimtd_OA,type,
% 2.93/1.62 splay_266122055elle_A:
% 2.93/1.62 !>[A: $tType] : ( A > ( tree @ A ) > real ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Transcendental_Oln__class_Oln,type,
% 2.93/1.62 ln_ln:
% 2.93/1.62 !>[A: $tType] : ( A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Transcendental_Opowr,type,
% 2.93/1.62 powr:
% 2.93/1.62 !>[A: $tType] : ( A > A > A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 2.93/1.62 linorder_bst:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Opath__len,type,
% 2.93/1.62 path_len:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Opath__len__rel,type,
% 2.93/1.62 path_len_rel:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Osize1,type,
% 2.93/1.62 size1:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Otree_OLeaf,type,
% 2.93/1.62 leaf:
% 2.93/1.62 !>[A: $tType] : ( tree @ A ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Otree_ONode,type,
% 2.93/1.62 node:
% 2.93/1.62 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Tree_Otree_Osize__tree,type,
% 2.93/1.62 size_tree:
% 2.93/1.62 !>[A: $tType] : ( ( A > nat ) > ( tree @ A ) > nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_c_Wellfounded_Oaccp,type,
% 2.93/1.62 accp:
% 2.93/1.62 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_b____,type,
% 2.93/1.62 b: a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_c____,type,
% 2.93/1.62 c: a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_l_H____,type,
% 2.93/1.62 l: tree @ a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_l____,type,
% 2.93/1.62 l2: tree @ a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_r_H____,type,
% 2.93/1.62 r: tree @ a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_rl____,type,
% 2.93/1.62 rl: tree @ a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_rr____,type,
% 2.93/1.62 rr: tree @ a ).
% 2.93/1.62
% 2.93/1.62 thf(sy_v_u____,type,
% 2.93/1.62 u: a ).
% 2.93/1.62
% 2.93/1.62 thf(fact_0__092_060open_062size_Arr_A_061_Asize_A_Isplay__max_Arr_J_092_060close_062,axiom,
% 2.93/1.62 ( ( size_size @ ( tree @ a ) @ rr )
% 2.93/1.62 = ( size_size @ ( tree @ a ) @ ( splay_splay_max @ a @ rr ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_1_sp,axiom,
% 2.93/1.62 ( ( splay_splay_max @ a @ rr )
% 2.93/1.62 = ( node @ a @ l @ u @ r ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062l_H_Au_Ar_H_O_Asplay__max_Arr_A_061_A_092_060langle_062l_H_M_Au_M_Ar_H_092_060rangle_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.93/1.62 ~ ! [L: tree @ a,U: a,R: tree @ a] :
% 2.93/1.62 ( ( splay_splay_max @ a @ rr )
% 2.93/1.62 != ( node @ a @ L @ U @ R ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_3__092_060open_062rr_A_092_060noteq_062_A_092_060langle_062_092_060rangle_062_092_060close_062,axiom,
% 2.93/1.62 ( rr
% 2.93/1.62 != ( leaf @ a ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_4_add__left__cancel,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ A2 @ B )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ C ) )
% 2.93/1.62 = ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_5_add__right__cancel,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ B @ A2 )
% 2.93/1.62 = ( plus_plus @ A @ C @ A2 ) )
% 2.93/1.62 = ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_6_size__if__splay__max,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A,L2: tree @ A,U2: A,R2: tree @ A] :
% 2.93/1.62 ( ( ( splay_splay_max @ A @ T2 )
% 2.93/1.62 = ( node @ A @ L2 @ U2 @ R2 ) )
% 2.93/1.62 => ( ( size_size @ ( tree @ A ) @ T2 )
% 2.93/1.62 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ L2 ) @ ( size_size @ ( tree @ A ) @ R2 ) ) @ ( one_one @ nat ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_7_one__natural_Orsp,axiom,
% 2.93/1.62 ( ( one_one @ nat )
% 2.93/1.62 = ( one_one @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_8_size__ne__size__imp__ne,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( size @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A,Y: A] :
% 2.93/1.62 ( ( ( size_size @ A @ X )
% 2.93/1.62 != ( size_size @ A @ Y ) )
% 2.93/1.62 => ( X != Y ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_9_nat__add__left__cancel,axiom,
% 2.93/1.62 ! [K: nat,M: nat,N: nat] :
% 2.93/1.62 ( ( ( plus_plus @ nat @ K @ M )
% 2.93/1.62 = ( plus_plus @ nat @ K @ N ) )
% 2.93/1.62 = ( M = N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_10_nat__add__right__cancel,axiom,
% 2.93/1.62 ! [M: nat,K: nat,N: nat] :
% 2.93/1.62 ( ( ( plus_plus @ nat @ M @ K )
% 2.93/1.62 = ( plus_plus @ nat @ N @ K ) )
% 2.93/1.62 = ( M = N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_11_one__reorient,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( one @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A] :
% 2.93/1.62 ( ( ( one_one @ A )
% 2.93/1.62 = X )
% 2.93/1.62 = ( X
% 2.93/1.62 = ( one_one @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_12_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_13_is__num__normalize_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_14_linordered__field__class_Osign__simps_I28_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_15_splay__max__Leaf__iff,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A] :
% 2.93/1.62 ( ( ( splay_splay_max @ A @ T2 )
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 = ( T2
% 2.93/1.62 = ( leaf @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_16_splay__max_Osimps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [La: tree @ A,A2: A] :
% 2.93/1.62 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 2.93/1.62 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_17_splay__max_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 2.93/1.62 = ( leaf @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_18_splay__max__Leaf,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A,L2: tree @ A,A2: A,R2: tree @ A] :
% 2.93/1.62 ( ( ( splay_splay_max @ A @ T2 )
% 2.93/1.62 = ( node @ A @ L2 @ A2 @ R2 ) )
% 2.93/1.62 => ( R2
% 2.93/1.62 = ( leaf @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_19_size__splay__max,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A] :
% 2.93/1.62 ( ( size_size @ ( tree @ A ) @ ( splay_splay_max @ A @ T2 ) )
% 2.93/1.62 = ( size_size @ ( tree @ A ) @ T2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_20_add__right__imp__eq,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ B @ A2 )
% 2.93/1.62 = ( plus_plus @ A @ C @ A2 ) )
% 2.93/1.62 => ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_21_add__left__imp__eq,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ A2 @ B )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ C ) )
% 2.93/1.62 => ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_22_add_Oleft__commute,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_23_add_Ocommute,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( plus_plus @ A )
% 2.93/1.62 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_24_add_Oright__cancel,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( group_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ B @ A2 )
% 2.93/1.62 = ( plus_plus @ A @ C @ A2 ) )
% 2.93/1.62 = ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_25_add_Oleft__cancel,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( group_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ A2 @ B )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ C ) )
% 2.93/1.62 = ( B = C ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_26_add_Oassoc,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_27_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [I: A,J: A,K: A,L2: A] :
% 2.93/1.62 ( ( ( I = J )
% 2.93/1.62 & ( K = L2 ) )
% 2.93/1.62 => ( ( plus_plus @ A @ I @ K )
% 2.93/1.62 = ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_28_linordered__field__class_Osign__simps_I26_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_29_linordered__field__class_Osign__simps_I27_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( plus_plus @ A )
% 2.93/1.62 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_30__C3_Oprems_C_I2_J,axiom,
% 2.93/1.62 ( ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) )
% 2.93/1.62 != ( leaf @ a ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_31_tree_Oinject,axiom,
% 2.93/1.62 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 2.93/1.62 ( ( ( node @ A @ X21 @ X22 @ X23 )
% 2.93/1.62 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 2.93/1.62 = ( ( X21 = Y21 )
% 2.93/1.62 & ( X22 = Y22 )
% 2.93/1.62 & ( X23 = Y23 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_32_tree_Odistinct_I1_J,axiom,
% 2.93/1.62 ! [A: $tType,X21: tree @ A,X22: A,X23: tree @ A] :
% 2.93/1.62 ( ( leaf @ A )
% 2.93/1.62 != ( node @ A @ X21 @ X22 @ X23 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_33_tree_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 2.93/1.62 ( ( P @ ( leaf @ A ) )
% 2.93/1.62 => ( ! [X1: tree @ A,X2: A,X3: tree @ A] :
% 2.93/1.62 ( ( P @ X1 )
% 2.93/1.62 => ( ( P @ X3 )
% 2.93/1.62 => ( P @ ( node @ A @ X1 @ X2 @ X3 ) ) ) )
% 2.93/1.62 => ( P @ Tree ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_34_neq__Leaf__iff,axiom,
% 2.93/1.62 ! [A: $tType,T2: tree @ A] :
% 2.93/1.62 ( ( T2
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 = ( ? [L3: tree @ A,A3: A,R3: tree @ A] :
% 2.93/1.62 ( T2
% 2.93/1.62 = ( node @ A @ L3 @ A3 @ R3 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_35_tree_Oexhaust,axiom,
% 2.93/1.62 ! [A: $tType,Y: tree @ A] :
% 2.93/1.62 ( ( Y
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ~ ! [X212: tree @ A,X222: A,X232: tree @ A] :
% 2.93/1.62 ( Y
% 2.93/1.62 != ( node @ A @ X212 @ X222 @ X232 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_36_mirror_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.93/1.62 ( ( P @ ( leaf @ A ) )
% 2.93/1.62 => ( ! [L4: tree @ A,X4: A,R4: tree @ A] :
% 2.93/1.62 ( ( P @ R4 )
% 2.93/1.62 => ( ( P @ L4 )
% 2.93/1.62 => ( P @ ( node @ A @ L4 @ X4 @ R4 ) ) ) )
% 2.93/1.62 => ( P @ A0 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_37_bst__eq_Ocases,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 2.93/1.62 ( X
% 2.93/1.62 != ( node @ A @ L4 @ A4 @ R4 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_38_bst__eq_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.93/1.62 ( ( P @ ( leaf @ A ) )
% 2.93/1.62 => ( ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 2.93/1.62 ( ( P @ L4 )
% 2.93/1.62 => ( ( P @ R4 )
% 2.93/1.62 => ( P @ ( node @ A @ L4 @ A4 @ R4 ) ) ) )
% 2.93/1.62 => ( P @ A0 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_39__092_060Phi_062_Ocases,axiom,
% 2.93/1.62 ! [A: $tType,X: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 2.93/1.62 ( X
% 2.93/1.62 != ( node @ A @ L4 @ A4 @ R4 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_40__C3_Oprems_C_I1_J,axiom,
% 2.93/1.62 linorder_bst @ a @ ( node @ a @ l2 @ b @ ( node @ a @ rl @ c @ rr ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_41_t__splay__max_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.93/1.62 ( ( P @ ( leaf @ A ) )
% 2.93/1.62 => ( ! [L4: tree @ A,B3: A] : ( P @ ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 2.93/1.62 => ( ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.93/1.62 ( ( ( Rr
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( P @ Rr ) )
% 2.93/1.62 => ( P @ ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 2.93/1.62 => ( P @ A0 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_42_t__splay__max_Ocases,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ! [L4: tree @ A,B3: A] :
% 2.93/1.62 ( X
% 2.93/1.62 != ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.93/1.62 ( X
% 2.93/1.62 != ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_43__092_060Phi_062_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.93/1.62 ( ( P @ ( leaf @ A ) )
% 2.93/1.62 => ( ! [L4: tree @ A,A4: A,R4: tree @ A] :
% 2.93/1.62 ( ( P @ L4 )
% 2.93/1.62 => ( ( P @ R4 )
% 2.93/1.62 => ( P @ ( node @ A @ L4 @ A4 @ R4 ) ) ) )
% 2.93/1.62 => ( P @ A0 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_44_ext,axiom,
% 2.93/1.62 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 2.93/1.62 ( ! [X4: A] :
% 2.93/1.62 ( ( F @ X4 )
% 2.93/1.62 = ( G @ X4 ) )
% 2.93/1.62 => ( F = G ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_45_t__splay__max_Osimps_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [Rr2: tree @ A,L2: tree @ A,B: A,Rl2: tree @ A,C: A] :
% 2.93/1.62 ( ( ( Rr2
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Rr2
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_46_t__splay__max_Oelims,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: tree @ A,Y: nat] :
% 2.93/1.62 ( ( ( splay_878424299ay_max @ A @ X )
% 2.93/1.62 = Y )
% 2.93/1.62 => ( ( ( X
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 != ( one_one @ nat ) ) )
% 2.93/1.62 => ( ( ? [L4: tree @ A,B3: A] :
% 2.93/1.62 ( X
% 2.93/1.62 = ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 != ( one_one @ nat ) ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 = ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 2.93/1.62 => ~ ( ( ( Rr
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Rr
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_47_path__len_Osimps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType,L2: tree @ A,Uu: A,R2: tree @ A] :
% 2.93/1.62 ( ( path_len @ A @ ( node @ A @ L2 @ Uu @ R2 ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L2 ) @ ( size_size @ ( tree @ A ) @ L2 ) ) @ ( path_len @ A @ R2 ) ) @ ( size_size @ ( tree @ A ) @ R2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_48_t__splay__max_Osimps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [L2: tree @ A,B: A] :
% 2.93/1.62 ( ( splay_878424299ay_max @ A @ ( node @ A @ L2 @ B @ ( leaf @ A ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_49_size__if__splay,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,T2: tree @ A,L2: tree @ A,U2: A,R2: tree @ A] :
% 2.93/1.62 ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.93/1.62 = ( node @ A @ L2 @ U2 @ R2 ) )
% 2.93/1.62 => ( ( size_size @ ( tree @ A ) @ T2 )
% 2.93/1.62 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ L2 ) @ ( size_size @ ( tree @ A ) @ R2 ) ) @ ( one_one @ nat ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_50_size1__def,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( size1 @ A )
% 2.93/1.62 = ( ^ [T3: tree @ A] : ( plus_plus @ nat @ ( size_size @ ( tree @ A ) @ T3 ) @ ( one_one @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_51_dbl__inc__def,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( neg_numeral_dbl_inc @ A )
% 2.93/1.62 = ( ^ [X5: A] : ( plus_plus @ A @ ( plus_plus @ A @ X5 @ X5 ) @ ( one_one @ A ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_52_t__splay__max_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( splay_878424299ay_max @ A @ ( leaf @ A ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_53_splay__Leaf__iff,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,T2: tree @ A] :
% 2.93/1.62 ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 = ( T2
% 2.93/1.62 = ( leaf @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_54_size__splay,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,T2: tree @ A] :
% 2.93/1.62 ( ( size_size @ ( tree @ A ) @ ( splay_splay @ A @ A2 @ T2 ) )
% 2.93/1.62 = ( size_size @ ( tree @ A ) @ T2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_55_size1__simps_I2_J,axiom,
% 2.93/1.62 ! [B4: $tType,L2: tree @ B4,X: B4,R2: tree @ B4] :
% 2.93/1.62 ( ( size1 @ B4 @ ( node @ B4 @ L2 @ X @ R2 ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( size1 @ B4 @ L2 ) @ ( size1 @ B4 @ R2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_56_size1__simps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( size1 @ A @ ( leaf @ A ) )
% 2.93/1.62 = ( one_one @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_57_bst__splay,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A,A2: A] :
% 2.93/1.62 ( ( linorder_bst @ A @ T2 )
% 2.93/1.62 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_58_splay__max__eq__splay__ex,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A] :
% 2.93/1.62 ( ( linorder_bst @ A @ T2 )
% 2.93/1.62 => ? [A4: A] :
% 2.93/1.62 ( ( splay_splay_max @ A @ T2 )
% 2.93/1.62 = ( splay_splay @ A @ A4 @ T2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_59_splay_Osimps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( splay_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.93/1.62 = ( node @ A @ L2 @ A2 @ R2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_60_splay_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 2.93/1.62 = ( leaf @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_61_bst_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_62_bst__splay__max,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A] :
% 2.93/1.62 ( ( linorder_bst @ A @ T2 )
% 2.93/1.62 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_63_splay__not__Leaf,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [T2: tree @ A,A2: A] :
% 2.93/1.62 ( ( T2
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ? [L4: tree @ A,X4: A,R4: tree @ A] :
% 2.93/1.62 ( ( splay_splay @ A @ A2 @ T2 )
% 2.93/1.62 = ( node @ A @ L4 @ X4 @ R4 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_64_path__len_Oelims,axiom,
% 2.93/1.62 ! [A: $tType,X: tree @ A,Y: nat] :
% 2.93/1.62 ( ( ( path_len @ A @ X )
% 2.93/1.62 = Y )
% 2.93/1.62 => ( ( ( X
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 != ( zero_zero @ nat ) ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,Uu2: A,R4: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 = ( node @ A @ L4 @ Uu2 @ R4 ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 != ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L4 ) @ ( size_size @ ( tree @ A ) @ L4 ) ) @ ( path_len @ A @ R4 ) ) @ ( size_size @ ( tree @ A ) @ R4 ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_65_A__simps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( splay_266122055elle_A @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.93/1.62 = ( one_one @ real ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_66_t__splay__max_Opelims,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: tree @ A,Y: nat] :
% 2.93/1.62 ( ( ( splay_878424299ay_max @ A @ X )
% 2.93/1.62 = Y )
% 2.93/1.62 => ( ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ X )
% 2.93/1.62 => ( ( ( X
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( Y
% 2.93/1.62 = ( one_one @ nat ) )
% 2.93/1.62 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( leaf @ A ) ) ) )
% 2.93/1.62 => ( ! [L4: tree @ A,B3: A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 = ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) )
% 2.93/1.62 => ( ( Y
% 2.93/1.62 = ( one_one @ nat ) )
% 2.93/1.62 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L4 @ B3 @ ( leaf @ A ) ) ) ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,B3: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 = ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 2.93/1.62 => ( ( ( ( Rr
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Rr
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( Y
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) )
% 2.93/1.62 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L4 @ B3 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_67_dbl__dec__simps_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 2.93/1.62 = ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_68_dbl__inc__simps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( neg_numeral_dbl_inc @ A @ ( zero_zero @ A ) )
% 2.93/1.62 = ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_69_t__splay__simps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,L2: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ A2 @ R2 ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_70_splay_Osimps_I13_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,X: A,B: A,La: tree @ A,Lb: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ X )
% 2.93/1.62 => ( ( ord_less @ A @ B @ X )
% 2.93/1.62 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B @ ( leaf @ A ) ) ) )
% 2.93/1.62 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B @ ( leaf @ A ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_71_natural_Osize_I3_J,axiom,
% 2.93/1.62 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_72_neq0__conv,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ( ( N
% 2.93/1.62 != ( zero_zero @ nat ) )
% 2.93/1.62 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_73_nat__add__left__cancel__less,axiom,
% 2.93/1.62 ! [K: nat,M: nat,N: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.93/1.62 = ( ord_less @ nat @ M @ N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_74_not__gr__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [N: A] :
% 2.93/1.62 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.93/1.62 = ( N
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_75_add_Oleft__neutral,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_76_add_Oright__neutral,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_77_double__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.93/1.62 = ( zero_zero @ A ) )
% 2.93/1.62 = ( A2
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_78_double__zero__sym,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ( zero_zero @ A )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.93/1.62 = ( A2
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_79_add__cancel__left__left,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ B @ A2 )
% 2.93/1.62 = A2 )
% 2.93/1.62 = ( B
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_80_add__cancel__left__right,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ A2 @ B )
% 2.93/1.62 = A2 )
% 2.93/1.62 = ( B
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_81_add__cancel__right__left,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( A2
% 2.93/1.62 = ( plus_plus @ A @ B @ A2 ) )
% 2.93/1.62 = ( B
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_82_add__cancel__right__right,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( A2
% 2.93/1.62 = ( plus_plus @ A @ A2 @ B ) )
% 2.93/1.62 = ( B
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_83_add__less__cancel__left,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [C: A,A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.93/1.62 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_84_add__less__cancel__right,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,C: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.93/1.62 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_85_add__gr__0,axiom,
% 2.93/1.62 ! [M: nat,N: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ M @ N ) )
% 2.93/1.62 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.93/1.62 | ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_86_add__is__0,axiom,
% 2.93/1.62 ! [M: nat,N: nat] :
% 2.93/1.62 ( ( ( plus_plus @ nat @ M @ N )
% 2.93/1.62 = ( zero_zero @ nat ) )
% 2.93/1.62 = ( ( M
% 2.93/1.62 = ( zero_zero @ nat ) )
% 2.93/1.62 & ( N
% 2.93/1.62 = ( zero_zero @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_87_Nat_Oadd__0__right,axiom,
% 2.93/1.62 ! [M: nat] :
% 2.93/1.62 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 2.93/1.62 = M ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_88_less__one,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.93/1.62 = ( N
% 2.93/1.62 = ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_89_add__less__same__cancel1,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 2.93/1.62 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_90_add__less__same__cancel2,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 2.93/1.62 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_91_less__add__same__cancel1,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 2.93/1.62 = ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_92_less__add__same__cancel2,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 2.93/1.62 = ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_93_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.93/1.62 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_94_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.93/1.62 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_95_t__splay__simps_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B @ R2 ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_96_t__splay__simps_I7_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,L2: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ B @ A2 )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_97_t__splay__simps_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,R2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ R2 ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_98_t__splay__simps_I6_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,L2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ B @ A2 )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( leaf @ A ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_99_t__splay__simps_I9_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A,Rr2: tree @ A,L2: tree @ A,Rl2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ B @ A2 )
% 2.93/1.62 => ( ( ord_less @ A @ C @ A2 )
% 2.93/1.62 => ( ( ( Rr2
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Rr2
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_100_t__splay__simps_I8_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,C: A,Rl2: tree @ A,L2: tree @ A,Rr2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ B @ A2 )
% 2.93/1.62 => ( ( ord_less @ A @ A2 @ C )
% 2.93/1.62 => ( ( ( Rl2
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Rl2
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L2 @ B @ ( node @ A @ Rl2 @ C @ Rr2 ) ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_101_t__splay__simps_I5_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( ord_less @ A @ C @ A2 )
% 2.93/1.62 => ( ( ( Lr
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Lr
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_102_t__splay__simps_I4_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( ord_less @ A @ A2 @ C )
% 2.93/1.62 => ( ( ( Ll
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 2.93/1.62 = ( one_one @ nat ) ) )
% 2.93/1.62 & ( ( Ll
% 2.93/1.62 != ( leaf @ A ) )
% 2.93/1.62 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C @ Lr ) @ B @ R2 ) )
% 2.93/1.62 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_103_size1__ge0,axiom,
% 2.93/1.62 ! [A: $tType,T2: tree @ A] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size1 @ A @ T2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_104_less__numeral__extra_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_105_gr0I,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ( ( N
% 2.93/1.62 != ( zero_zero @ nat ) )
% 2.93/1.62 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_106_not__gr0,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.93/1.62 = ( N
% 2.93/1.62 = ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_107_not__less0,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_108_less__zeroE,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_109_gr__implies__not0,axiom,
% 2.93/1.62 ! [M: nat,N: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ M @ N )
% 2.93/1.62 => ( N
% 2.93/1.62 != ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_110_zero__reorient,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( zero @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A] :
% 2.93/1.62 ( ( ( zero_zero @ A )
% 2.93/1.62 = X )
% 2.93/1.62 = ( X
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_111_infinite__descent0,axiom,
% 2.93/1.62 ! [P: nat > $o,N: nat] :
% 2.93/1.62 ( ( P @ ( zero_zero @ nat ) )
% 2.93/1.62 => ( ! [N2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.93/1.62 => ( ~ ( P @ N2 )
% 2.93/1.62 => ? [M2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ M2 @ N2 )
% 2.93/1.62 & ~ ( P @ M2 ) ) ) )
% 2.93/1.62 => ( P @ N ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_112_less__nat__zero__code,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_113_zero__natural_Orsp,axiom,
% 2.93/1.62 ( ( zero_zero @ nat )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_114_infinite__descent0__measure,axiom,
% 2.93/1.62 ! [A: $tType,V: A > nat,P: A > $o,X: A] :
% 2.93/1.62 ( ! [X4: A] :
% 2.93/1.62 ( ( ( V @ X4 )
% 2.93/1.62 = ( zero_zero @ nat ) )
% 2.93/1.62 => ( P @ X4 ) )
% 2.93/1.62 => ( ! [X4: A] :
% 2.93/1.62 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X4 ) )
% 2.93/1.62 => ( ~ ( P @ X4 )
% 2.93/1.62 => ? [Y2: A] :
% 2.93/1.62 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X4 ) )
% 2.93/1.62 & ~ ( P @ Y2 ) ) ) )
% 2.93/1.62 => ( P @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_115_linordered__field__no__lb,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X6: A] :
% 2.93/1.62 ? [Y3: A] : ( ord_less @ A @ Y3 @ X6 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_116_linordered__field__no__ub,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X6: A] :
% 2.93/1.62 ? [X1: A] : ( ord_less @ A @ X6 @ X1 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_117_gr__zeroI,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [N: A] :
% 2.93/1.62 ( ( N
% 2.93/1.62 != ( zero_zero @ A ) )
% 2.93/1.62 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_118_not__less__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [N: A] :
% 2.93/1.62 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_119_gr__implies__not__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [M: A,N: A] :
% 2.93/1.62 ( ( ord_less @ A @ M @ N )
% 2.93/1.62 => ( N
% 2.93/1.62 != ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_120_zero__less__iff__neq__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [N: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.93/1.62 = ( N
% 2.93/1.62 != ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_121_less__imp__add__positive,axiom,
% 2.93/1.62 ! [I: nat,J: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ I @ J )
% 2.93/1.62 => ? [K2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K2 )
% 2.93/1.62 & ( ( plus_plus @ nat @ I @ K2 )
% 2.93/1.62 = J ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_122_less__numeral__extra_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_123_less__numeral__extra_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_124_add__neg__neg,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.93/1.62 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_125_add__pos__pos,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 2.93/1.62 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_126_pos__add__strict,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( strict797366125id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 => ( ( ord_less @ A @ B @ C )
% 2.93/1.62 => ( ord_less @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_127_op_092_060_094sub_062s_092_060_094sub_062t_Osize__neq,axiom,
% 2.93/1.62 ! [A: $tType,X: splay_2011811431op_s_t @ A] :
% 2.93/1.62 ( ( size_size @ ( splay_2011811431op_s_t @ A ) @ X )
% 2.93/1.62 != ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_128_add__mono__thms__linordered__field_I5_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [I: A,J: A,K: A,L2: A] :
% 2.93/1.62 ( ( ( ord_less @ A @ I @ J )
% 2.93/1.62 & ( ord_less @ A @ K @ L2 ) )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_129_add__mono__thms__linordered__field_I2_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [I: A,J: A,K: A,L2: A] :
% 2.93/1.62 ( ( ( I = J )
% 2.93/1.62 & ( ord_less @ A @ K @ L2 ) )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_130_add__mono__thms__linordered__field_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [I: A,J: A,K: A,L2: A] :
% 2.93/1.62 ( ( ( ord_less @ A @ I @ J )
% 2.93/1.62 & ( K = L2 ) )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_131_add__strict__mono,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,D: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( ord_less @ A @ C @ D )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_132_add__strict__left__mono,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_133_add__strict__right__mono,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_134_add__less__imp__less__left,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [C: A,A2: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.93/1.62 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_135_add__less__imp__less__right,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,C: A,B: A] :
% 2.93/1.62 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.93/1.62 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_136_less__numeral__extra_I4_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_137_add__lessD1,axiom,
% 2.93/1.62 ! [I: nat,J: nat,K: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 2.93/1.62 => ( ord_less @ nat @ I @ K ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_138_add__less__mono,axiom,
% 2.93/1.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ I @ J )
% 2.93/1.62 => ( ( ord_less @ nat @ K @ L2 )
% 2.93/1.62 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_139_not__add__less1,axiom,
% 2.93/1.62 ! [I: nat,J: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_140_not__add__less2,axiom,
% 2.93/1.62 ! [J: nat,I: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_141_add__less__mono1,axiom,
% 2.93/1.62 ! [I: nat,J: nat,K: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ I @ J )
% 2.93/1.62 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_142_trans__less__add1,axiom,
% 2.93/1.62 ! [I: nat,J: nat,M: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ I @ J )
% 2.93/1.62 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_143_trans__less__add2,axiom,
% 2.93/1.62 ! [I: nat,J: nat,M: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ I @ J )
% 2.93/1.62 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_144_less__add__eq__less,axiom,
% 2.93/1.62 ! [K: nat,L2: nat,M: nat,N: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ K @ L2 )
% 2.93/1.62 => ( ( ( plus_plus @ nat @ M @ L2 )
% 2.93/1.62 = ( plus_plus @ nat @ K @ N ) )
% 2.93/1.62 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_145_comm__monoid__add__class_Oadd__0,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_146_add_Ocomm__neutral,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_147_add_Ogroup__left__neutral,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( group_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_148_add__eq__0__iff__both__eq__0,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A,Y: A] :
% 2.93/1.62 ( ( ( plus_plus @ A @ X @ Y )
% 2.93/1.62 = ( zero_zero @ A ) )
% 2.93/1.62 = ( ( X
% 2.93/1.62 = ( zero_zero @ A ) )
% 2.93/1.62 & ( Y
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_149_plus__nat_Oadd__0,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 2.93/1.62 = N ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_150_add__eq__self__zero,axiom,
% 2.93/1.62 ! [M: nat,N: nat] :
% 2.93/1.62 ( ( ( plus_plus @ nat @ M @ N )
% 2.93/1.62 = M )
% 2.93/1.62 => ( N
% 2.93/1.62 = ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_151_splay_Osimps_I9_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A,Lb: tree @ A,La: tree @ A,Ra: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ B @ A2 )
% 2.93/1.62 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B @ ( node @ A @ La @ A2 @ Ra ) ) )
% 2.93/1.62 = ( node @ A @ ( node @ A @ Lb @ B @ La ) @ A2 @ Ra ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_152_splay_Osimps_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,La: tree @ A,Ra: tree @ A,Rb: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra ) @ B @ Rb ) )
% 2.93/1.62 = ( node @ A @ La @ A2 @ ( node @ A @ Ra @ B @ Rb ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_153_size__0__iff__Leaf,axiom,
% 2.93/1.62 ! [A: $tType,T2: tree @ A] :
% 2.93/1.62 ( ( ( size_size @ ( tree @ A ) @ T2 )
% 2.93/1.62 = ( zero_zero @ nat ) )
% 2.93/1.62 = ( T2
% 2.93/1.62 = ( leaf @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_154_tree_Osize_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( size_size @ ( tree @ A ) @ ( leaf @ A ) )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_155_t__splay_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 2.93/1.62 = ( one_one @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_156_path__len_Osimps_I1_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( path_len @ A @ ( leaf @ A ) )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_157_splay_Osimps_I4_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,R2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ R2 ) )
% 2.93/1.62 = ( node @ A @ ( leaf @ A ) @ B @ R2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_158_splay_Osimps_I5_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A,A2: A,B: A,Ra: tree @ A,Rb: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ X @ A2 )
% 2.93/1.62 => ( ( ord_less @ A @ X @ B )
% 2.93/1.62 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra ) @ B @ Rb ) )
% 2.93/1.62 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra @ B @ Rb ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_159_splay_Osimps_I7_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A,B: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ X @ B )
% 2.93/1.62 => ( ( ord_less @ A @ A2 @ X )
% 2.93/1.62 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B @ Rb ) )
% 2.93/1.62 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ Rb ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_160_splay_Osimps_I10_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,X: A,L2: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ X )
% 2.93/1.62 => ( ( splay_splay @ A @ X @ ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) )
% 2.93/1.62 = ( node @ A @ L2 @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_161_splay_Osimps_I12_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,X: A,B: A,La: tree @ A,Rb: tree @ A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ X )
% 2.93/1.62 => ( ( ord_less @ A @ X @ B )
% 2.93/1.62 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B @ Rb ) ) )
% 2.93/1.62 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B @ Rb ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_162_path__len_Opelims,axiom,
% 2.93/1.62 ! [A: $tType,X: tree @ A,Y: nat] :
% 2.93/1.62 ( ( ( path_len @ A @ X )
% 2.93/1.62 = Y )
% 2.93/1.62 => ( ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ X )
% 2.93/1.62 => ( ( ( X
% 2.93/1.62 = ( leaf @ A ) )
% 2.93/1.62 => ( ( Y
% 2.93/1.62 = ( zero_zero @ nat ) )
% 2.93/1.62 => ~ ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ ( leaf @ A ) ) ) )
% 2.93/1.62 => ~ ! [L4: tree @ A,Uu2: A,R4: tree @ A] :
% 2.93/1.62 ( ( X
% 2.93/1.62 = ( node @ A @ L4 @ Uu2 @ R4 ) )
% 2.93/1.62 => ( ( Y
% 2.93/1.62 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( path_len @ A @ L4 ) @ ( size_size @ ( tree @ A ) @ L4 ) ) @ ( path_len @ A @ R4 ) ) @ ( size_size @ ( tree @ A ) @ R4 ) ) )
% 2.93/1.62 => ~ ( accp @ ( tree @ A ) @ ( path_len_rel @ A ) @ ( node @ A @ L4 @ Uu2 @ R4 ) ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_163_zero__less__two,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_164_less__add__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_165_zero__less__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( zero_less_one @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_166_not__one__less__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 2.93/1.62 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_167_bool_Osize_I4_J,axiom,
% 2.93/1.62 ( ( size_size @ $o @ $false )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_168_bool_Osize_I3_J,axiom,
% 2.93/1.62 ( ( size_size @ $o @ $true )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_169_nat__neq__iff,axiom,
% 2.93/1.62 ! [M: nat,N: nat] :
% 2.93/1.62 ( ( M != N )
% 2.93/1.62 = ( ( ord_less @ nat @ M @ N )
% 2.93/1.62 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_170_less__not__refl,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ N @ N ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_171_less__not__refl2,axiom,
% 2.93/1.62 ! [N: nat,M: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ N @ M )
% 2.93/1.62 => ( M != N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_172_less__not__refl3,axiom,
% 2.93/1.62 ! [S: nat,T2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ S @ T2 )
% 2.93/1.62 => ( S != T2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_173_measure__induct,axiom,
% 2.93/1.62 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.93/1.62 ( ! [X4: A] :
% 2.93/1.62 ( ! [Y2: A] :
% 2.93/1.62 ( ( ord_less @ nat @ ( F @ Y2 ) @ ( F @ X4 ) )
% 2.93/1.62 => ( P @ Y2 ) )
% 2.93/1.62 => ( P @ X4 ) )
% 2.93/1.62 => ( P @ A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_174_less__irrefl__nat,axiom,
% 2.93/1.62 ! [N: nat] :
% 2.93/1.62 ~ ( ord_less @ nat @ N @ N ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_175_nat__less__induct,axiom,
% 2.93/1.62 ! [P: nat > $o,N: nat] :
% 2.93/1.62 ( ! [N2: nat] :
% 2.93/1.62 ( ! [M2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ M2 @ N2 )
% 2.93/1.62 => ( P @ M2 ) )
% 2.93/1.62 => ( P @ N2 ) )
% 2.93/1.62 => ( P @ N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_176_infinite__descent,axiom,
% 2.93/1.62 ! [P: nat > $o,N: nat] :
% 2.93/1.62 ( ! [N2: nat] :
% 2.93/1.62 ( ~ ( P @ N2 )
% 2.93/1.62 => ? [M2: nat] :
% 2.93/1.62 ( ( ord_less @ nat @ M2 @ N2 )
% 2.93/1.62 & ~ ( P @ M2 ) ) )
% 2.93/1.62 => ( P @ N ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_177_linorder__neqE__nat,axiom,
% 2.93/1.62 ! [X: nat,Y: nat] :
% 2.93/1.62 ( ( X != Y )
% 2.93/1.62 => ( ~ ( ord_less @ nat @ X @ Y )
% 2.93/1.62 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_178_measure__induct__rule,axiom,
% 2.93/1.62 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.93/1.62 ( ! [X4: A] :
% 2.93/1.62 ( ! [Y2: A] :
% 2.93/1.62 ( ( ord_less @ nat @ ( F @ Y2 ) @ ( F @ X4 ) )
% 2.93/1.62 => ( P @ Y2 ) )
% 2.93/1.62 => ( P @ X4 ) )
% 2.93/1.62 => ( P @ A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_179_infinite__descent__measure,axiom,
% 2.93/1.62 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 2.93/1.62 ( ! [X4: A] :
% 2.93/1.62 ( ~ ( P @ X4 )
% 2.93/1.62 => ? [Y2: A] :
% 2.93/1.62 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X4 ) )
% 2.93/1.62 & ~ ( P @ Y2 ) ) )
% 2.93/1.62 => ( P @ X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_180_linorder__neqE__linordered__idom,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A,Y: A] :
% 2.93/1.62 ( ( X != Y )
% 2.93/1.62 => ( ~ ( ord_less @ A @ X @ Y )
% 2.93/1.62 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_181_prod_Osize__neq,axiom,
% 2.93/1.62 ! [A: $tType,B4: $tType,X: product_prod @ A @ B4] :
% 2.93/1.62 ( ( size_size @ ( product_prod @ A @ B4 ) @ X )
% 2.93/1.62 != ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_182_sum_Osize__neq,axiom,
% 2.93/1.62 ! [A: $tType,B4: $tType,X: sum_sum @ A @ B4] :
% 2.93/1.62 ( ( size_size @ ( sum_sum @ A @ B4 ) @ X )
% 2.93/1.62 != ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_183_size__bool,axiom,
% 2.93/1.62 ( ( size_size @ $o )
% 2.93/1.62 = ( ^ [B2: $o] : ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_184_zero__neq__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( zero_zero @ A )
% 2.93/1.62 != ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_185_natural_Osize_I1_J,axiom,
% 2.93/1.62 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_186_fold__atLeastAtMost__nat_Oinduct,axiom,
% 2.93/1.62 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A1: nat,A22: nat,A32: A] :
% 2.93/1.62 ( ! [F2: nat > A > A,A4: nat,B3: nat,Acc: A] :
% 2.93/1.62 ( ( ~ ( ord_less @ nat @ B3 @ A4 )
% 2.93/1.62 => ( P @ F2 @ ( plus_plus @ nat @ A4 @ ( one_one @ nat ) ) @ B3 @ ( F2 @ A4 @ Acc ) ) )
% 2.93/1.62 => ( P @ F2 @ A4 @ B3 @ Acc ) )
% 2.93/1.62 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_187_natural_Osimps_I4_J,axiom,
% 2.93/1.62 ! [T: $tType,F1: T,F22: code_natural > T] :
% 2.93/1.62 ( ( code_case_natural @ T @ F1 @ F22 @ ( zero_zero @ code_natural ) )
% 2.93/1.62 = F1 ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_188_bool_Osize_I1_J,axiom,
% 2.93/1.62 ( ( size_bool @ $true )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_189_bool_Osize_I2_J,axiom,
% 2.93/1.62 ( ( size_bool @ $false )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_190_size__bool__def,axiom,
% 2.93/1.62 ( size_bool
% 2.93/1.62 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_191_ind__euclid,axiom,
% 2.93/1.62 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 2.93/1.62 ( ! [A4: nat,B3: nat] :
% 2.93/1.62 ( ( P @ A4 @ B3 )
% 2.93/1.62 = ( P @ B3 @ A4 ) )
% 2.93/1.62 => ( ! [A4: nat] : ( P @ A4 @ ( zero_zero @ nat ) )
% 2.93/1.62 => ( ! [A4: nat,B3: nat] :
% 2.93/1.62 ( ( P @ A4 @ B3 )
% 2.93/1.62 => ( P @ A4 @ ( plus_plus @ nat @ A4 @ B3 ) ) )
% 2.93/1.62 => ( P @ A2 @ B ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_192_size__bool__overloaded__def,axiom,
% 2.93/1.62 ( ( size_size @ $o )
% 2.93/1.62 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_193_add__0__iff,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A] :
% 2.93/1.62 ( ( B
% 2.93/1.62 = ( plus_plus @ A @ B @ A2 ) )
% 2.93/1.62 = ( A2
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_194_semiring__normalization__rules_I5_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_195_semiring__normalization__rules_I20_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,D: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) )
% 2.93/1.62 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_196_semiring__normalization__rules_I21_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_197_semiring__normalization__rules_I22_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,C: A,D: A] :
% 2.93/1.62 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 2.93/1.62 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A2 @ D ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_198_semiring__normalization__rules_I23_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A] :
% 2.93/1.62 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.93/1.62 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_199_semiring__normalization__rules_I24_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( plus_plus @ A )
% 2.93/1.62 = ( ^ [A3: A,C3: A] : ( plus_plus @ A @ C3 @ A3 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_200_semiring__normalization__rules_I25_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,C: A,D: A] :
% 2.93/1.62 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ C @ D ) )
% 2.93/1.62 = ( plus_plus @ A @ ( plus_plus @ A @ A2 @ C ) @ D ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_201_semiring__normalization__rules_I6_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.93/1.62 = A2 ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_202_natural_Osimps_I6_J,axiom,
% 2.93/1.62 ! [T: $tType,F1: T,F22: code_natural > T > T] :
% 2.93/1.62 ( ( code_rec_natural @ T @ F1 @ F22 @ ( zero_zero @ code_natural ) )
% 2.93/1.62 = F1 ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_203_fold__atLeastAtMost__nat_Osimps,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( set_fo292404081st_nat @ A )
% 2.93/1.62 = ( ^ [F3: nat > A > A,A3: nat,B2: nat,Acc2: A] : ( if @ A @ ( ord_less @ nat @ B2 @ A3 ) @ Acc2 @ ( set_fo292404081st_nat @ A @ F3 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B2 @ ( F3 @ A3 @ Acc2 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_204_fold__atLeastAtMost__nat_Oelims,axiom,
% 2.93/1.62 ! [A: $tType,X: nat > A > A,Xa: nat,Xb: nat,Xc: A,Y: A] :
% 2.93/1.62 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb @ Xc )
% 2.93/1.62 = Y )
% 2.93/1.62 => ( ( ( ord_less @ nat @ Xb @ Xa )
% 2.93/1.62 => ( Y = Xc ) )
% 2.93/1.62 & ( ~ ( ord_less @ nat @ Xb @ Xa )
% 2.93/1.62 => ( Y
% 2.93/1.62 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_205_ln__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ln @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ( ln_ln @ A @ ( one_one @ A ) )
% 2.93/1.62 = ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_206_tree_Osize__gen_I1_J,axiom,
% 2.93/1.62 ! [A: $tType,X: A > nat] :
% 2.93/1.62 ( ( size_tree @ A @ X @ ( leaf @ A ) )
% 2.93/1.62 = ( zero_zero @ nat ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_207_ln__less__zero__iff,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( zero_zero @ real ) )
% 2.93/1.62 = ( ord_less @ real @ X @ ( one_one @ real ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_208_ln__gt__zero__iff,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 2.93/1.62 = ( ord_less @ real @ ( one_one @ real ) @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_209_ln__eq__zero__iff,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ( ln_ln @ real @ X )
% 2.93/1.62 = ( zero_zero @ real ) )
% 2.93/1.62 = ( X
% 2.93/1.62 = ( one_one @ real ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_210_ln__gt__zero__imp__gt__one,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ord_less @ real @ ( one_one @ real ) @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_211_ln__less__zero,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ X @ ( one_one @ real ) )
% 2.93/1.62 => ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( zero_zero @ real ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_212_ln__gt__zero,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ord_less @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_213_powr__zero__eq__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ln @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A] :
% 2.93/1.62 ( ( ( X
% 2.93/1.62 = ( zero_zero @ A ) )
% 2.93/1.62 => ( ( powr @ A @ X @ ( zero_zero @ A ) )
% 2.93/1.62 = ( zero_zero @ A ) ) )
% 2.93/1.62 & ( ( X
% 2.93/1.62 != ( zero_zero @ A ) )
% 2.93/1.62 => ( ( powr @ A @ X @ ( zero_zero @ A ) )
% 2.93/1.62 = ( one_one @ A ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_214_powr__one__eq__one,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ln @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( powr @ A @ ( one_one @ A ) @ A2 )
% 2.93/1.62 = ( one_one @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_215_powr__gt__zero,axiom,
% 2.93/1.62 ! [X: real,A2: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ ( powr @ real @ X @ A2 ) )
% 2.93/1.62 = ( X
% 2.93/1.62 != ( zero_zero @ real ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_216_powr__less__cancel__iff,axiom,
% 2.93/1.62 ! [X: real,A2: real,B: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 2.93/1.62 = ( ord_less @ real @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_217_powr__0,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ln @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [Z: A] :
% 2.93/1.62 ( ( powr @ A @ ( zero_zero @ A ) @ Z )
% 2.93/1.62 = ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_218_powr__eq__0__iff,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ln @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [W: A,Z: A] :
% 2.93/1.62 ( ( ( powr @ A @ W @ Z )
% 2.93/1.62 = ( zero_zero @ A ) )
% 2.93/1.62 = ( W
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_219_ln__inj__iff,axiom,
% 2.93/1.62 ! [X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 2.93/1.62 => ( ( ( ln_ln @ real @ X )
% 2.93/1.62 = ( ln_ln @ real @ Y ) )
% 2.93/1.62 = ( X = Y ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_220_ln__less__cancel__iff,axiom,
% 2.93/1.62 ! [X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 2.93/1.62 => ( ( ord_less @ real @ ( ln_ln @ real @ X ) @ ( ln_ln @ real @ Y ) )
% 2.93/1.62 = ( ord_less @ real @ X @ Y ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_221_ln__less__self,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ord_less @ real @ ( ln_ln @ real @ X ) @ X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_222_powr__less__mono2__neg,axiom,
% 2.93/1.62 ! [A2: real,X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ X @ Y )
% 2.93/1.62 => ( ord_less @ real @ ( powr @ real @ Y @ A2 ) @ ( powr @ real @ X @ A2 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_223_powr__less__cancel,axiom,
% 2.93/1.62 ! [X: real,A2: real,B: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 2.93/1.62 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ord_less @ real @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_224_powr__less__mono,axiom,
% 2.93/1.62 ! [A2: real,B: real,X: real] :
% 2.93/1.62 ( ( ord_less @ real @ A2 @ B )
% 2.93/1.62 => ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_225_powr__inj,axiom,
% 2.93/1.62 ! [A2: real,X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 2.93/1.62 => ( ( A2
% 2.93/1.62 != ( one_one @ real ) )
% 2.93/1.62 => ( ( ( powr @ real @ A2 @ X )
% 2.93/1.62 = ( powr @ real @ A2 @ Y ) )
% 2.93/1.62 = ( X = Y ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_226_real__lbound__gt__zero,axiom,
% 2.93/1.62 ! [D1: real,D2: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ D1 )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ D2 )
% 2.93/1.62 => ? [E: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ E )
% 2.93/1.62 & ( ord_less @ real @ E @ D1 )
% 2.93/1.62 & ( ord_less @ real @ E @ D2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_227_ln__ge__zero__iff,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( ln_ln @ real @ X ) )
% 2.93/1.62 = ( ord_less_eq @ real @ ( one_one @ real ) @ X ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_228_le__zero__eq,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [N: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.93/1.62 = ( N
% 2.93/1.62 = ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_229_add__le__cancel__left,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [C: A,A2: A,B: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.93/1.62 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_230_add__le__cancel__right,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,C: A,B: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.93/1.62 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_231_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.93/1.62 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_232_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.93/1.62 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_233_le__add__same__cancel2,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 2.93/1.62 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_234_le__add__same__cancel1,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 2.93/1.62 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_235_add__le__same__cancel2,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 2.93/1.62 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_236_add__le__same__cancel1,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [B: A,A2: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 2.93/1.62 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_237_ln__le__cancel__iff,axiom,
% 2.93/1.62 ! [X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Y )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( ln_ln @ real @ X ) @ ( ln_ln @ real @ Y ) )
% 2.93/1.62 = ( ord_less_eq @ real @ X @ Y ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_238_powr__one__gt__zero__iff,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ( powr @ real @ X @ ( one_one @ real ) )
% 2.93/1.62 = X )
% 2.93/1.62 = ( ord_less_eq @ real @ ( zero_zero @ real ) @ X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_239_powr__one,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( powr @ real @ X @ ( one_one @ real ) )
% 2.93/1.62 = X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_240_powr__le__cancel__iff,axiom,
% 2.93/1.62 ! [X: real,A2: real,B: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) )
% 2.93/1.62 = ( ord_less_eq @ real @ A2 @ B ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_241_ln__bound,axiom,
% 2.93/1.62 ! [X: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ord_less_eq @ real @ ( ln_ln @ real @ X ) @ X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_242_powr__mono,axiom,
% 2.93/1.62 ! [A2: real,B: real,X: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ A2 @ B )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ X @ B ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_243_powr__mono2,axiom,
% 2.93/1.62 ! [A2: real,X: real,Y: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less_eq @ real @ X @ Y )
% 2.93/1.62 => ( ord_less_eq @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ Y @ A2 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_244_powr__mono2_H,axiom,
% 2.93/1.62 ! [A2: real,X: real,Y: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 2.93/1.62 => ( ( ord_less @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less_eq @ real @ X @ Y )
% 2.93/1.62 => ( ord_less_eq @ real @ ( powr @ real @ Y @ A2 ) @ ( powr @ real @ X @ A2 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_245_powr__ge__pzero,axiom,
% 2.93/1.62 ! [X: real,Y: real] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( powr @ real @ X @ Y ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_246_powr__less__mono2,axiom,
% 2.93/1.62 ! [A2: real,X: real,Y: real] :
% 2.93/1.62 ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ X )
% 2.93/1.62 => ( ( ord_less @ real @ X @ Y )
% 2.93/1.62 => ( ord_less @ real @ ( powr @ real @ X @ A2 ) @ ( powr @ real @ Y @ A2 ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_247_ge__one__powr__ge__zero,axiom,
% 2.93/1.62 ! [X: real,A2: real] :
% 2.93/1.62 ( ( ord_less_eq @ real @ ( one_one @ real ) @ X )
% 2.93/1.62 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 2.93/1.62 => ( ord_less_eq @ real @ ( one_one @ real ) @ ( powr @ real @ X @ A2 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_248_less__eq__real__def,axiom,
% 2.93/1.62 ( ( ord_less_eq @ real )
% 2.93/1.62 = ( ^ [X5: real,Y4: real] :
% 2.93/1.62 ( ( ord_less @ real @ X5 @ Y4 )
% 2.93/1.62 | ( X5 = Y4 ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_249_zero__le,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_250_le__numeral__extra_I3_J,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_251_add__less__le__mono,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,D: A] :
% 2.93/1.62 ( ( ord_less @ A @ A2 @ B )
% 2.93/1.62 => ( ( ord_less_eq @ A @ C @ D )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(fact_252_add__le__less__mono,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.93/1.62 => ! [A2: A,B: A,C: A,D: A] :
% 2.93/1.62 ( ( ord_less_eq @ A @ A2 @ B )
% 2.93/1.62 => ( ( ord_less @ A @ C @ D )
% 2.93/1.62 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.93/1.62 ! [A: $tType] :
% 2.93/1.62 ( ( linorder @ A @ ( type2 @ A ) )
% 2.93/1.62 => ( type @ A @ ( type2 @ A ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.93/1.62 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.93/1.62 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.93/1.62 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.93/1.62 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.93/1.62 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 2.93/1.62 strict797366125id_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.93/1.62 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.93/1.62 linord1659791738miring @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.93/1.62 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 2.93/1.62 ordere216010020id_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.93/1.62 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.93/1.62 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.93/1.62 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.93/1.62 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.93/1.62 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.93/1.62 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.93/1.62 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 2.93/1.62 zero_less_one @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.93/1.62 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.93/1.62 linorder @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.93/1.62 monoid_add @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.93/1.62 zero @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.93/1.62 one @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.93/1.62 size @ nat @ ( type2 @ nat ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_HOL_Obool___Orderings_Olinorder_1,axiom,
% 2.93/1.62 linorder @ $o @ ( type2 @ $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_HOL_Obool___Nat_Osize_2,axiom,
% 2.93/1.62 size @ $o @ ( type2 @ $o ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_3,axiom,
% 2.93/1.62 semiri456707255roduct @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4,axiom,
% 2.93/1.62 ordere516151231imp_le @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_5,axiom,
% 2.93/1.62 strict2144017051up_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_6,axiom,
% 2.93/1.62 ordere223160158up_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_7,axiom,
% 2.93/1.62 ordere236663937imp_le @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add_8,axiom,
% 2.93/1.62 strict797366125id_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_9,axiom,
% 2.93/1.62 linord1659791738miring @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_10,axiom,
% 2.93/1.62 ordere779506340up_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_11,axiom,
% 2.93/1.62 ordere216010020id_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 2.93/1.62 linord219039673up_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_12,axiom,
% 2.93/1.62 cancel1352612707id_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_13,axiom,
% 2.93/1.62 cancel_semigroup_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_14,axiom,
% 2.93/1.62 linordered_semidom @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_15,axiom,
% 2.93/1.62 ab_semigroup_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 2.93/1.62 linordered_field @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_16,axiom,
% 2.93/1.62 comm_monoid_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 2.93/1.62 linordered_idom @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1_17,axiom,
% 2.93/1.62 comm_semiring_1 @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Osemigroup__add_18,axiom,
% 2.93/1.62 semigroup_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Ozero__less__one_19,axiom,
% 2.93/1.62 zero_less_one @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_20,axiom,
% 2.93/1.62 zero_neq_one @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Orderings_Olinorder_21,axiom,
% 2.93/1.62 linorder @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Transcendental_Oln,axiom,
% 2.93/1.62 ln @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Omonoid__add_22,axiom,
% 2.93/1.62 monoid_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 2.93/1.62 group_add @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 2.93/1.62 neg_numeral @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Ozero_23,axiom,
% 2.93/1.62 zero @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Real_Oreal___Groups_Oone_24,axiom,
% 2.93/1.62 one @ real @ ( type2 @ real ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Tree_Otree___Nat_Osize_25,axiom,
% 2.93/1.62 ! [A5: $tType] : ( size @ ( tree @ A5 ) @ ( type2 @ ( tree @ A5 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Sum__Type_Osum___Nat_Osize_26,axiom,
% 2.93/1.62 ! [A5: $tType,A6: $tType] : ( size @ ( sum_sum @ A5 @ A6 ) @ ( type2 @ ( sum_sum @ A5 @ A6 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Product__Type_Oprod___Nat_Osize_27,axiom,
% 2.93/1.62 ! [A5: $tType,A6: $tType] : ( size @ ( product_prod @ A5 @ A6 ) @ ( type2 @ ( product_prod @ A5 @ A6 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__monoid__add__imp__le_28,axiom,
% 2.93/1.62 ordere516151231imp_le @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__ab__semigroup__add_29,axiom,
% 2.93/1.62 strict2144017051up_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__cancel__ab__semigroup__add_30,axiom,
% 2.93/1.62 ordere223160158up_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add__imp__le_31,axiom,
% 2.93/1.62 ordere236663937imp_le @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ostrict__ordered__comm__monoid__add_32,axiom,
% 2.93/1.62 strict797366125id_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__ab__semigroup__add_33,axiom,
% 2.93/1.62 ordere779506340up_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oordered__comm__monoid__add_34,axiom,
% 2.93/1.62 ordere216010020id_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__comm__monoid__add_35,axiom,
% 2.93/1.62 cancel1352612707id_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ocancel__semigroup__add_36,axiom,
% 2.93/1.62 cancel_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oab__semigroup__add_37,axiom,
% 2.93/1.62 ab_semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ocomm__monoid__add_38,axiom,
% 2.93/1.62 comm_monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Rings_Ocomm__semiring__1_39,axiom,
% 2.93/1.62 comm_semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Osemigroup__add_40,axiom,
% 2.93/1.62 semigroup_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_41,axiom,
% 2.93/1.62 zero_neq_one @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Orderings_Olinorder_42,axiom,
% 2.93/1.62 linorder @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Omonoid__add_43,axiom,
% 2.93/1.62 monoid_add @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_44,axiom,
% 2.93/1.62 zero @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Groups_Oone_45,axiom,
% 2.93/1.62 one @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Code__Numeral_Onatural___Nat_Osize_46,axiom,
% 2.93/1.62 size @ code_natural @ ( type2 @ code_natural ) ).
% 2.93/1.62
% 2.93/1.62 thf(tcon_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t___Nat_Osize_47,axiom,
% 2.93/1.62 ! [A5: $tType] : ( size @ ( splay_2011811431op_s_t @ A5 ) @ ( type2 @ ( splay_2011811431op_s_t @ A5 ) ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(help_If_3_1_T,axiom,
% 2.93/1.62 ! [P: $o] :
% 2.93/1.62 ( ( P = $true )
% 2.93/1.62 | ( P = $false ) ) ).
% 2.93/1.62
% 2.93/1.62 thf(help_If_2_1_T,axiom,
% 2.93/1.62 ! [A: $tType,X: A,Y: A] :
% 2.93/1.62 ( ( if @ A @ $false @ X @ Y )
% 2.93/1.62 = Y ) ).
% 2.93/1.62
% 2.93/1.62 thf(help_If_1_1_T,axiom,
% 2.93/1.62 ! [A: $tType,X: A,Y: A] :
% 2.93/1.62 ( ( if @ A @ $true @ X @ Y )
% 2.93/1.62 = X ) ).
% 2.93/1.62
% 2.93/1.62 thf(tfree_0,hypothesis,
% 2.93/1.62 linorder @ a @ ( type2 @ a ) ).
% 2.93/1.62
% 2.93/1.62 thf(conj_0,conjecture,
% 2.93/1.62 ( ( size_size @ ( tree @ a ) @ rr )
% 2.93/1.62 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( tree @ a ) @ l ) @ ( size_size @ ( tree @ a ) @ r ) ) @ ( one_one @ nat ) ) ) ).
% 2.93/1.62 ------------------------
% 2.93/1.65 % (30513)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/18Mi)
% 2.93/1.65 % (30511)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_30178 for (2999ds/2Mi)
% 2.93/1.65 % (30511)Instruction limit reached!
% 2.93/1.65 % (30511)------------------------------
% 2.93/1.65 % (30511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (30511)Termination reason: Unknown
% 2.93/1.65 % (30511)Termination phase: shuffling
% 2.93/1.65
% 2.93/1.65 % (30511)Memory used [KB]: 1407
% 2.93/1.65 % (30511)Time elapsed: 0.002 s
% 2.93/1.65 % (30511)Instructions burned: 2 (million)
% 2.93/1.65 % (30511)------------------------------
% 2.93/1.65 % (30511)------------------------------
% 2.93/1.66 % (30513)Instruction limit reached!
% 2.93/1.66 % (30513)------------------------------
% 2.93/1.66 % (30513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30513)Termination reason: Unknown
% 2.93/1.66 % (30513)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30513)Memory used [KB]: 1663
% 2.93/1.66 % (30513)Time elapsed: 0.008 s
% 2.93/1.66 % (30513)Instructions burned: 18 (million)
% 2.93/1.66 % (30513)------------------------------
% 2.93/1.66 % (30513)------------------------------
% 2.93/1.66 % (30507)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/183Mi)
% 2.93/1.66 % (30508)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_30178 for (2999ds/4Mi)
% 2.93/1.66 % (30509)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_30178 for (2999ds/27Mi)
% 2.93/1.66 % (30510)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/2Mi)
% 2.93/1.66 % (30512)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_30178 for (2999ds/275Mi)
% 2.93/1.66 % (30510)Instruction limit reached!
% 2.93/1.66 % (30510)------------------------------
% 2.93/1.66 % (30510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30510)Termination reason: Unknown
% 2.93/1.66 % (30510)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30510)Memory used [KB]: 1407
% 2.93/1.66 % (30510)Time elapsed: 0.004 s
% 2.93/1.66 % (30510)Instructions burned: 3 (million)
% 2.93/1.66 % (30510)------------------------------
% 2.93/1.66 % (30510)------------------------------
% 2.93/1.66 % (30508)Instruction limit reached!
% 2.93/1.66 % (30508)------------------------------
% 2.93/1.66 % (30508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30508)Termination reason: Unknown
% 2.93/1.66 % (30508)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30508)Memory used [KB]: 1407
% 2.93/1.66 % (30508)Time elapsed: 0.005 s
% 2.93/1.66 % (30508)Instructions burned: 5 (million)
% 2.93/1.66 % (30508)------------------------------
% 2.93/1.66 % (30508)------------------------------
% 2.93/1.66 % (30514)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/3Mi)
% 2.93/1.66 % (30514)Instruction limit reached!
% 2.93/1.66 % (30514)------------------------------
% 2.93/1.66 % (30514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (30514)Termination reason: Unknown
% 2.93/1.66 % (30514)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (30514)Memory used [KB]: 1407
% 2.93/1.66 % (30514)Time elapsed: 0.003 s
% 2.93/1.66 % (30514)Instructions burned: 4 (million)
% 2.93/1.66 % (30514)------------------------------
% 2.93/1.66 % (30514)------------------------------
% 2.93/1.67 % (30515)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_30178 for (2999ds/37Mi)
% 2.93/1.67 % (30518)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_30178 for (2999ds/1041Mi)
% 2.93/1.68 % (30509)Instruction limit reached!
% 2.93/1.68 % (30509)------------------------------
% 2.93/1.68 % (30509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30509)Termination reason: Unknown
% 2.93/1.68 % (30509)Termination phase: Property scanning
% 2.93/1.68
% 2.93/1.68 % (30509)Memory used [KB]: 1791
% 2.93/1.68 % (30509)Time elapsed: 0.019 s
% 2.93/1.68 % (30509)Instructions burned: 28 (million)
% 2.93/1.68 % (30509)------------------------------
% 2.93/1.68 % (30509)------------------------------
% 2.93/1.68 % (30516)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_30178 for (2999ds/15Mi)
% 2.93/1.68 % (30515)Instruction limit reached!
% 2.93/1.68 % (30515)------------------------------
% 2.93/1.68 % (30515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30515)Termination reason: Unknown
% 2.93/1.68 % (30515)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (30515)Memory used [KB]: 2046
% 2.93/1.68 % (30515)Time elapsed: 0.012 s
% 2.93/1.68 % (30515)Instructions burned: 37 (million)
% 2.93/1.68 % (30515)------------------------------
% 2.93/1.68 % (30515)------------------------------
% 2.93/1.68 % (30517)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_30178 for (2999ds/3Mi)
% 2.93/1.68 % (30517)Instruction limit reached!
% 2.93/1.68 % (30517)------------------------------
% 2.93/1.68 % (30517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30517)Termination reason: Unknown
% 2.93/1.68 % (30517)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (30517)Memory used [KB]: 1407
% 2.93/1.68 % (30517)Time elapsed: 0.004 s
% 2.93/1.68 % (30517)Instructions burned: 3 (million)
% 2.93/1.68 % (30517)------------------------------
% 2.93/1.68 % (30517)------------------------------
% 2.93/1.68 % (30516)Instruction limit reached!
% 2.93/1.68 % (30516)------------------------------
% 2.93/1.68 % (30516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.68 % (30516)Termination reason: Unknown
% 2.93/1.68 % (30516)Termination phase: shuffling
% 2.93/1.68
% 2.93/1.68 % (30516)Memory used [KB]: 1663
% 2.93/1.68 % (30516)Time elapsed: 0.008 s
% 2.93/1.68 % (30516)Instructions burned: 15 (million)
% 2.93/1.68 % (30516)------------------------------
% 2.93/1.68 % (30516)------------------------------
% 2.93/1.69 % (30520)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/16Mi)
% 2.93/1.69 % (30519)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/7Mi)
% 2.93/1.69 % (30520)Instruction limit reached!
% 2.93/1.69 % (30520)------------------------------
% 2.93/1.69 % (30520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.69 % (30520)Termination reason: Unknown
% 2.93/1.69 % (30520)Termination phase: shuffling
% 2.93/1.69
% 2.93/1.69 % (30520)Memory used [KB]: 1663
% 2.93/1.69 % (30520)Time elapsed: 0.007 s
% 2.93/1.69 % (30520)Instructions burned: 18 (million)
% 2.93/1.69 % (30520)------------------------------
% 2.93/1.69 % (30520)------------------------------
% 2.93/1.69 % (30512)Refutation not found, incomplete strategy
% 2.93/1.69 % (30512)------------------------------
% 2.93/1.69 % (30512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.69 % (30512)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.69
% 2.93/1.69
% 2.93/1.69 % (30512)Memory used [KB]: 6652
% 2.93/1.69 % (30512)Time elapsed: 0.037 s
% 2.93/1.69 % (30512)Instructions burned: 61 (million)
% 2.93/1.69 % (30512)------------------------------
% 2.93/1.69 % (30512)------------------------------
% 2.93/1.69 % (30522)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_30178 for (2999ds/3Mi)
% 2.93/1.70 % (30522)Instruction limit reached!
% 2.93/1.70 % (30522)------------------------------
% 2.93/1.70 % (30522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.70 % (30522)Termination reason: Unknown
% 2.93/1.70 % (30522)Termination phase: shuffling
% 2.93/1.70
% 2.93/1.70 % (30522)Memory used [KB]: 1407
% 2.93/1.70 % (30522)Time elapsed: 0.002 s
% 2.93/1.70 % (30522)Instructions burned: 3 (million)
% 2.93/1.70 % (30522)------------------------------
% 2.93/1.70 % (30522)------------------------------
% 2.97/1.70 % (30519)Instruction limit reached!
% 2.97/1.70 % (30519)------------------------------
% 2.97/1.70 % (30519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.70 % (30519)Termination reason: Unknown
% 2.97/1.70 % (30519)Termination phase: shuffling
% 2.97/1.70
% 2.97/1.70 % (30519)Memory used [KB]: 1535
% 2.97/1.70 % (30519)Time elapsed: 0.007 s
% 2.97/1.70 % (30519)Instructions burned: 8 (million)
% 2.97/1.70 % (30519)------------------------------
% 2.97/1.70 % (30519)------------------------------
% 2.97/1.70 % (30521)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_30178 for (2999ds/3Mi)
% 2.97/1.70 % (30521)Instruction limit reached!
% 2.97/1.70 % (30521)------------------------------
% 2.97/1.70 % (30521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.70 % (30521)Termination reason: Unknown
% 2.97/1.70 % (30521)Termination phase: shuffling
% 2.97/1.70
% 2.97/1.70 % (30521)Memory used [KB]: 1407
% 2.97/1.70 % (30521)Time elapsed: 0.004 s
% 2.97/1.70 % (30521)Instructions burned: 3 (million)
% 2.97/1.70 % (30521)------------------------------
% 2.97/1.70 % (30521)------------------------------
% 2.97/1.70 % (30523)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/7Mi)
% 2.97/1.71 % (30525)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/4Mi)
% 2.97/1.71 % (30523)Instruction limit reached!
% 2.97/1.71 % (30523)------------------------------
% 2.97/1.71 % (30523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (30523)Termination reason: Unknown
% 2.97/1.71 % (30523)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (30523)Memory used [KB]: 1407
% 2.97/1.71 % (30523)Time elapsed: 0.004 s
% 2.97/1.71 % (30523)Instructions burned: 8 (million)
% 2.97/1.71 % (30523)------------------------------
% 2.97/1.71 % (30523)------------------------------
% 2.97/1.71 % (30525)Instruction limit reached!
% 2.97/1.71 % (30525)------------------------------
% 2.97/1.71 % (30525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (30525)Termination reason: Unknown
% 2.97/1.71 % (30525)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (30525)Memory used [KB]: 1407
% 2.97/1.71 % (30525)Time elapsed: 0.003 s
% 2.97/1.71 % (30525)Instructions burned: 4 (million)
% 2.97/1.71 % (30525)------------------------------
% 2.97/1.71 % (30525)------------------------------
% 2.97/1.71 % (30524)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/3Mi)
% 2.97/1.71 % (30524)Instruction limit reached!
% 2.97/1.71 % (30524)------------------------------
% 2.97/1.71 % (30524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (30524)Termination reason: Unknown
% 2.97/1.71 % (30524)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (30524)Memory used [KB]: 1407
% 2.97/1.71 % (30524)Time elapsed: 0.003 s
% 2.97/1.71 % (30524)Instructions burned: 5 (million)
% 2.97/1.71 % (30524)------------------------------
% 2.97/1.71 % (30524)------------------------------
% 2.97/1.72 % (30528)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/6Mi)
% 2.97/1.72 % (30526)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/18Mi)
% 2.97/1.72 % (30529)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/902Mi)
% 2.97/1.72 % (30528)Instruction limit reached!
% 2.97/1.72 % (30528)------------------------------
% 2.97/1.72 % (30528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.72 % (30528)Termination reason: Unknown
% 2.97/1.72 % (30528)Termination phase: shuffling
% 2.97/1.72
% 2.97/1.72 % (30528)Memory used [KB]: 1407
% 2.97/1.72 % (30528)Time elapsed: 0.003 s
% 2.97/1.72 % (30528)Instructions burned: 6 (million)
% 2.97/1.72 % (30528)------------------------------
% 2.97/1.72 % (30528)------------------------------
% 2.97/1.72 % (30527)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/710Mi)
% 2.97/1.72 % (30530)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/21Mi)
% 2.97/1.73 % (30531)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/5Mi)
% 2.97/1.73 % (30526)Instruction limit reached!
% 2.97/1.73 % (30526)------------------------------
% 2.97/1.73 % (30526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (30526)Termination reason: Unknown
% 2.97/1.73 % (30526)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (30526)Memory used [KB]: 1663
% 2.97/1.73 % (30526)Time elapsed: 0.013 s
% 2.97/1.73 % (30526)Instructions burned: 18 (million)
% 2.97/1.73 % (30526)------------------------------
% 2.97/1.73 % (30526)------------------------------
% 2.97/1.73 % (30507)Instruction limit reached!
% 2.97/1.73 % (30507)------------------------------
% 2.97/1.73 % (30507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (30507)Termination reason: Unknown
% 2.97/1.73 % (30507)Termination phase: Saturation
% 2.97/1.73
% 2.97/1.73 % (30507)Memory used [KB]: 7036
% 2.97/1.73 % (30507)Time elapsed: 0.071 s
% 2.97/1.73 % (30507)Instructions burned: 185 (million)
% 2.97/1.73 % (30507)------------------------------
% 2.97/1.73 % (30507)------------------------------
% 2.97/1.73 % (30530)Instruction limit reached!
% 2.97/1.73 % (30530)------------------------------
% 2.97/1.73 % (30530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (30530)Termination reason: Unknown
% 2.97/1.73 % (30530)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (30530)Memory used [KB]: 1791
% 2.97/1.73 % (30530)Time elapsed: 0.010 s
% 2.97/1.73 % (30530)Instructions burned: 23 (million)
% 2.97/1.73 % (30530)------------------------------
% 2.97/1.73 % (30530)------------------------------
% 2.97/1.73 % (30531)Instruction limit reached!
% 2.97/1.73 % (30531)------------------------------
% 2.97/1.73 % (30531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (30531)Termination reason: Unknown
% 2.97/1.73 % (30531)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (30531)Memory used [KB]: 1407
% 2.97/1.73 % (30531)Time elapsed: 0.003 s
% 2.97/1.73 % (30531)Instructions burned: 7 (million)
% 2.97/1.73 % (30531)------------------------------
% 2.97/1.73 % (30531)------------------------------
% 2.97/1.74 % (30534)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/779Mi)
% 2.97/1.74 % (30533)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/377Mi)
% 2.97/1.74 % (30535)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/19Mi)
% 2.97/1.74 % (30535)Instruction limit reached!
% 2.97/1.74 % (30535)------------------------------
% 2.97/1.74 % (30535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.74 % (30535)Termination reason: Unknown
% 2.97/1.74 % (30535)Termination phase: shuffling
% 2.97/1.74
% 2.97/1.74 % (30535)Memory used [KB]: 1791
% 2.97/1.74 % (30535)Time elapsed: 0.007 s
% 2.97/1.74 % (30535)Instructions burned: 21 (million)
% 2.97/1.74 % (30535)------------------------------
% 2.97/1.74 % (30535)------------------------------
% 2.97/1.74 % (30532)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30178 for (2999ds/6Mi)
% 2.97/1.75 % (30532)Instruction limit reached!
% 2.97/1.75 % (30532)------------------------------
% 2.97/1.75 % (30532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.75 % (30532)Termination reason: Unknown
% 2.97/1.75 % (30532)Termination phase: shuffling
% 2.97/1.75
% 2.97/1.75 % (30532)Memory used [KB]: 1407
% 2.97/1.75 % (30532)Time elapsed: 0.005 s
% 2.97/1.75 % (30532)Instructions burned: 6 (million)
% 2.97/1.75 % (30532)------------------------------
% 2.97/1.75 % (30532)------------------------------
% 2.97/1.75 % (30536)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30178 for (2998ds/879Mi)
% 2.97/1.76 % (30537)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30178 for (2998ds/17Mi)
% 2.97/1.77 % (30529)First to succeed.
% 2.97/1.77 % (30537)Instruction limit reached!
% 2.97/1.77 % (30537)------------------------------
% 2.97/1.77 % (30537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.77 % (30537)Termination reason: Unknown
% 2.97/1.77 % (30537)Termination phase: shuffling
% 2.97/1.77
% 2.97/1.77 % (30537)Memory used [KB]: 1663
% 2.97/1.77 % (30537)Time elapsed: 0.008 s
% 2.97/1.77 % (30537)Instructions burned: 18 (million)
% 2.97/1.77 % (30537)------------------------------
% 2.97/1.77 % (30537)------------------------------
% 2.97/1.77 % (30529)Refutation found. Thanks to Tanya!
% 2.97/1.77 % SZS status Theorem for DTF2THF_30178
% 2.97/1.77 % SZS output start Proof for DTF2THF_30178
% 2.97/1.77 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.97/1.77 thf(type_def_7, type, code_natural: $tType).
% 2.97/1.77 thf(type_def_8, type, nat: $tType).
% 2.97/1.77 thf(type_def_9, type, tree: ($tType) > $tType).
% 2.97/1.77 thf(type_def_10, type, real: $tType).
% 2.97/1.77 thf(type_def_11, type, a: $tType).
% 2.97/1.77 thf(type_def_12, type, splay_2011811431op_s_t: ($tType) > $tType).
% 2.97/1.77 thf(type_def_13, type, product_prod: ($tType * $tType) > $tType).
% 2.97/1.77 thf(type_def_14, type, sum_sum: ($tType * $tType) > $tType).
% 2.97/1.77 thf(func_def_0, type, splay_2011811431op_s_t: ($tType) > $tType).
% 2.97/1.77 thf(func_def_1, type, code_natural: $tType).
% 2.97/1.77 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 2.97/1.77 thf(func_def_3, type, sum_sum: ($tType * $tType) > $tType).
% 2.97/1.77 thf(func_def_4, type, tree: ($tType) > $tType).
% 2.97/1.77 thf(func_def_5, type, real: $tType).
% 2.97/1.77 thf(func_def_6, type, nat: $tType).
% 2.97/1.77 thf(func_def_7, type, itself: ($tType) > $tType).
% 2.97/1.77 thf(func_def_8, type, a: $tType).
% 2.97/1.77 thf(func_def_9, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_10, type, size: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_11, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_12, type, zero: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_14, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_15, type, monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_16, type, ln: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_17, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_18, type, zero_neq_one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_19, type, zero_less_one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_20, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_21, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_22, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_23, type, comm_monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_24, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_25, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_26, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_27, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_28, type, cancel1352612707id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_29, type, linord219039673up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_30, type, ordere216010020id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_31, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_32, type, linord1659791738miring: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_33, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_34, type, strict797366125id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_35, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_36, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_37, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_38, type, ordere516151231imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_39, type, semiri456707255roduct: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.77 thf(func_def_40, type, code_case_natural: !>[X0: $tType]:(X0 > (code_natural > X0) > code_natural > X0)).
% 2.97/1.77 thf(func_def_41, type, code_rec_natural: !>[X0: $tType]:(X0 > (code_natural > X0 > X0) > code_natural > X0)).
% 2.97/1.77 thf(func_def_42, type, code_size_natural: code_natural > nat).
% 2.97/1.77 thf(func_def_43, type, one_one: !>[X0: $tType]:(X0)).
% 2.97/1.77 thf(func_def_44, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.97/1.77 thf(func_def_45, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.97/1.77 thf(func_def_46, type, size_bool: $o > nat).
% 2.97/1.77 thf(func_def_47, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.97/1.77 thf(func_def_48, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 2.97/1.77 thf(func_def_49, type, neg_numeral_dbl_dec: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.77 thf(func_def_50, type, neg_numeral_dbl_inc: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.77 thf(func_def_51, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.97/1.77 thf(func_def_52, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.97/1.77 thf(func_def_53, type, product_rec_bool: !>[X0: $tType]:(X0 > X0 > $o > X0)).
% 2.97/1.77 thf(func_def_54, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.97/1.77 thf(func_def_55, type, set_fo292404081st_nat: !>[X0: $tType]:((nat > X0 > X0) > nat > nat > X0 > X0)).
% 2.97/1.77 thf(func_def_56, type, splay_splay: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_57, type, splay_splay_max: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_58, type, splay_914434265_splay: !>[X0: $tType]:(X0 > tree @ X0 > nat)).
% 2.97/1.77 thf(func_def_59, type, splay_878424299ay_max: !>[X0: $tType]:(tree @ X0 > nat)).
% 2.97/1.77 thf(func_def_60, type, splay_1816415694ax_rel: !>[X0: $tType]:(tree @ X0 > tree @ X0 > $o)).
% 2.97/1.77 thf(func_def_61, type, splay_266122055elle_A: !>[X0: $tType]:(X0 > tree @ X0 > real)).
% 2.97/1.77 thf(func_def_62, type, ln_ln: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.77 thf(func_def_63, type, powr: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.97/1.77 thf(func_def_64, type, linorder_bst: !>[X0: $tType]:(tree @ X0 > $o)).
% 2.97/1.77 thf(func_def_65, type, path_len: !>[X0: $tType]:(tree @ X0 > nat)).
% 2.97/1.77 thf(func_def_66, type, path_len_rel: !>[X0: $tType]:(tree @ X0 > tree @ X0 > $o)).
% 2.97/1.77 thf(func_def_67, type, size1: !>[X0: $tType]:(tree @ X0 > nat)).
% 2.97/1.77 thf(func_def_68, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 2.97/1.77 thf(func_def_69, type, node: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_70, type, size_tree: !>[X0: $tType]:((X0 > nat) > tree @ X0 > nat)).
% 2.97/1.77 thf(func_def_71, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 2.97/1.77 thf(func_def_72, type, b: a).
% 2.97/1.77 thf(func_def_73, type, c: a).
% 2.97/1.77 thf(func_def_74, type, l: tree @ a).
% 2.97/1.77 thf(func_def_75, type, l2: tree @ a).
% 2.97/1.77 thf(func_def_76, type, r: tree @ a).
% 2.97/1.77 thf(func_def_77, type, rl: tree @ a).
% 2.97/1.77 thf(func_def_78, type, rr: tree @ a).
% 2.97/1.77 thf(func_def_79, type, u: a).
% 2.97/1.77 thf(func_def_90, type, sP0: !>[X0: $tType]:(tree @ X0 > nat > $o)).
% 2.97/1.77 thf(func_def_91, type, sP1: !>[X0: $tType]:(tree @ X0 > nat > $o)).
% 2.97/1.77 thf(func_def_92, type, sP2: !>[X0: $tType]:(tree @ X0 > nat > $o)).
% 2.97/1.77 thf(func_def_93, type, sP3: !>[X0: $tType]:(tree @ X0 > nat > $o)).
% 2.97/1.77 thf(func_def_94, type, sK4: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_95, type, sK5: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_96, type, sK6: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_97, type, sK7: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_98, type, sK8: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_99, type, sK9: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_100, type, sK10: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_101, type, sK11: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.77 thf(func_def_102, type, sK12: (nat > $o) > nat).
% 2.97/1.77 thf(func_def_103, type, sK13: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_104, type, sK14: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_105, type, sK15: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_106, type, sK16: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_107, type, sK17: !>[X0: $tType]:(tree @ X0 > nat > X0)).
% 2.97/1.77 thf(func_def_108, type, sK18: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_109, type, sK19: !>[X0: $tType]:(tree @ X0 > nat > X0)).
% 2.97/1.77 thf(func_def_110, type, sK20: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_111, type, sK21: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_112, type, sK22: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_113, type, sK23: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_114, type, sK24: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_115, type, sK25: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_116, type, sK26: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_117, type, sK27: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_118, type, sK28: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_119, type, sK29: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_120, type, sK30: (nat > $o) > nat).
% 2.97/1.77 thf(func_def_121, type, sK31: (nat > $o) > nat).
% 2.97/1.77 thf(func_def_122, type, sK32: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_123, type, sK33: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_124, type, sK34: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_125, type, sK35: tree @ a).
% 2.97/1.77 thf(func_def_126, type, sK36: a).
% 2.97/1.77 thf(func_def_127, type, sK37: tree @ a).
% 2.97/1.77 thf(func_def_128, type, sK38: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_129, type, sK39: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_130, type, sK40: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_131, type, sK41: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_132, type, sK42: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_133, type, sK43: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_134, type, sK44: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_135, type, sK45: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_136, type, sK46: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_137, type, sK47: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_138, type, sK48: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_139, type, sK49: !>[X0: $tType]:(tree @ X0 > nat > X0)).
% 2.97/1.77 thf(func_def_140, type, sK50: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_141, type, sK51: real > real > real).
% 2.97/1.77 thf(func_def_142, type, sK52: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_143, type, sK53: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_144, type, sK54: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_145, type, sK55: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_146, type, sK56: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_147, type, sK57: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_148, type, sK58: (nat > nat > $o) > nat).
% 2.97/1.77 thf(func_def_149, type, sK59: (nat > nat > $o) > nat).
% 2.97/1.77 thf(func_def_150, type, sK60: (nat > nat > $o) > nat).
% 2.97/1.77 thf(func_def_151, type, sK61: (nat > nat > $o) > nat).
% 2.97/1.77 thf(func_def_152, type, sK62: (nat > nat > $o) > nat).
% 2.97/1.77 thf(func_def_153, type, sK63: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.97/1.77 thf(func_def_154, type, sK64: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_155, type, sK65: !>[X0: $tType]:(tree @ X0 > nat > X0)).
% 2.97/1.77 thf(func_def_156, type, sK66: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_157, type, sK67: !>[X0: $tType]:(tree @ X0 > nat > X0)).
% 2.97/1.77 thf(func_def_158, type, sK68: !>[X0: $tType]:(tree @ X0 > nat > tree @ X0)).
% 2.97/1.77 thf(func_def_159, type, sK69: !>[X0: $tType]:(nat > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_160, type, sK70: !>[X0: $tType]:(nat > tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_161, type, sK71: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_162, type, sK72: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_163, type, sK73: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_164, type, sK74: !>[X0: $tType]:(X0 > X0)).
% 2.97/1.77 thf(func_def_165, type, sK75: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.97/1.77 thf(func_def_166, type, sK76: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat > X0 > X0)).
% 2.97/1.77 thf(func_def_167, type, sK77: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat)).
% 2.97/1.77 thf(func_def_168, type, sK78: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > nat)).
% 2.97/1.77 thf(func_def_169, type, sK79: !>[X0: $tType]:(((nat > X0 > X0) > nat > nat > X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_170, type, sK80: !>[X0: $tType]:(tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_171, type, sK81: !>[X0: $tType]:(nat > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_172, type, sK82: !>[X0: $tType]:(nat > tree @ X0 > X0)).
% 2.97/1.77 thf(func_def_173, type, sK83: !>[X0: $tType]:(nat > tree @ X0 > tree @ X0)).
% 2.97/1.77 thf(func_def_174, type, sK84: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.97/1.77 thf(func_def_175, type, sK85: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.97/1.77 thf(func_def_176, type, sK86: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.97/1.77 thf(func_def_177, type, sK87: nat > nat > nat).
% 2.97/1.77 thf(func_def_178, type, sK88: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_179, type, sK89: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 2.97/1.77 thf(func_def_180, type, sK90: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 2.97/1.77 thf(func_def_182, type, ph92: !>[X0: $tType]:(X0)).
% 2.97/1.77 thf(f2018,plain,(
% 2.97/1.77 $false),
% 2.97/1.77 inference(trivial_inequality_removal,[status(thm)],[f2017])).
% 2.97/1.77 thf(f2017,plain,(
% 2.97/1.77 ((size_size @ tree @ a @ rr) != (size_size @ tree @ a @ rr))),
% 2.97/1.77 inference(equality_resolution,[status(thm)],[f1963])).
% 2.97/1.77 thf(f1963,plain,(
% 2.97/1.77 ( ! [X0 : tree @ a] : (((splay_splay_max @ a @ rr) != (splay_splay_max @ a @ X0)) | ((size_size @ tree @ a @ rr) != (size_size @ tree @ a @ X0))) )),
% 2.97/1.77 inference(superposition,[status(thm)],[f1885,f1617])).
% 2.97/1.77 thf(f1617,plain,(
% 2.97/1.77 ((splay_splay_max @ a @ rr) = (node @ a @ l @ u @ r))),
% 2.97/1.77 inference(cnf_transformation,[status(thm)],[f2])).
% 2.97/1.77 thf(f2,axiom,(
% 2.97/1.77 ((splay_splay_max @ a @ rr) = (node @ a @ l @ u @ r))),
% 2.97/1.77 file('/export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2THF_30178.p',fact_1_sp)).
% 2.97/1.77 thf(f1885,plain,(
% 2.97/1.77 ( ! [X0 : tree @ a,X1 : a] : (((splay_splay_max @ a @ X0) != (node @ a @ l @ X1 @ r)) | ((size_size @ tree @ a @ rr) != (size_size @ tree @ a @ X0))) )),
% 2.97/1.77 inference(trivial_inequality_removal,[status(thm)],[f1884])).
% 2.97/1.77 thf(f1884,plain,(
% 2.97/1.77 ( ! [X0 : tree @ a,X1 : a] : (((size_size @ tree @ a @ rr) != (size_size @ tree @ a @ X0)) | ($true != $true) | ((splay_splay_max @ a @ X0) != (node @ a @ l @ X1 @ r))) )),
% 2.97/1.77 inference(forward_demodulation,[status(thm)],[f1874,f1565])).
% 2.97/1.77 thf(f1565,plain,(
% 2.97/1.77 ((linorder @ a @ type2 @ a) = $true)),
% 2.97/1.77 inference(cnf_transformation,[status(thm)],[f686])).
% 2.97/1.77 thf(f686,plain,(
% 2.97/1.77 ((linorder @ a @ type2 @ a) = $true)),
% 2.97/1.77 inference(fool_elimination,[status(thm)],[f685])).
% 2.97/1.77 thf(f685,plain,(
% 2.97/1.77 (linorder @ a @ type2 @ a)),
% 2.97/1.77 inference(rectify,[status(thm)],[f335])).
% 2.97/1.77 thf(f335,axiom,(
% 2.97/1.77 (linorder @ a @ type2 @ a)),
% 2.97/1.77 file('/export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2THF_30178.p',tfree_0)).
% 2.97/1.77 thf(f1874,plain,(
% 2.97/1.77 ( ! [X0 : tree @ a,X1 : a] : (((linorder @ a @ type2 @ a) != $true) | ((size_size @ tree @ a @ rr) != (size_size @ tree @ a @ X0)) | ((splay_splay_max @ a @ X0) != (node @ a @ l @ X1 @ r))) )),
% 2.97/1.77 inference(superposition,[status(thm)],[f1399,f1632])).
% 2.97/1.77 thf(f1632,plain,(
% 2.97/1.77 ( ! [X0 : $tType,X2 : tree @ X0,X3 : X0,X1 : tree @ X0,X4 : tree @ X0] : (((plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ X0 @ X2) @ (size_size @ tree @ X0 @ X4)) @ one_one @ nat) = (size_size @ tree @ X0 @ X1)) | ((linorder @ X0 @ type2 @ X0) != $true) | ((splay_splay_max @ X0 @ X1) != (node @ X0 @ X2 @ X3 @ X4))) )),
% 2.97/1.77 inference(cnf_transformation,[status(thm)],[f1114])).
% 2.97/1.77 thf(f1114,plain,(
% 2.97/1.77 ! [X0 : $tType] : (! [X1 : tree @ X0,X2 : tree @ X0,X3 : X0,X4 : tree @ X0] : (((splay_splay_max @ X0 @ X1) != (node @ X0 @ X2 @ X3 @ X4)) | ((plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ X0 @ X2) @ (size_size @ tree @ X0 @ X4)) @ one_one @ nat) = (size_size @ tree @ X0 @ X1))) | ((linorder @ X0 @ type2 @ X0) != $true))),
% 2.97/1.77 inference(ennf_transformation,[status(thm)],[f816])).
% 2.97/1.77 thf(f816,plain,(
% 2.97/1.77 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $true) => ! [X1 : tree @ X0,X2 : tree @ X0,X3 : X0,X4 : tree @ X0] : (((splay_splay_max @ X0 @ X1) = (node @ X0 @ X2 @ X3 @ X4)) => ((plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ X0 @ X2) @ (size_size @ tree @ X0 @ X4)) @ one_one @ nat) = (size_size @ tree @ X0 @ X1))))),
% 2.97/1.77 inference(fool_elimination,[status(thm)],[f815])).
% 2.97/1.77 thf(f815,plain,(
% 2.97/1.77 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : tree @ X0,X2 : tree @ X0,X3 : X0,X4 : tree @ X0] : (((splay_splay_max @ X0 @ X1) = (node @ X0 @ X2 @ X3 @ X4)) => ((plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ X0 @ X2) @ (size_size @ tree @ X0 @ X4)) @ one_one @ nat) = (size_size @ tree @ X0 @ X1))))),
% 2.97/1.77 inference(rectify,[status(thm)],[f7])).
% 2.97/1.77 thf(f7,axiom,(
% 2.97/1.77 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X8 : tree @ X0,X9 : tree @ X0,X10 : X0,X11 : tree @ X0] : (((splay_splay_max @ X0 @ X8) = (node @ X0 @ X9 @ X10 @ X11)) => ((size_size @ tree @ X0 @ X8) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ X0 @ X9) @ (size_size @ tree @ X0 @ X11)) @ one_one @ nat))))),
% 2.97/1.77 file('/export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2THF_30178.p',fact_6_size__if__splay__max)).
% 2.97/1.77 thf(f1399,plain,(
% 2.97/1.77 ((size_size @ tree @ a @ rr) != (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ a @ l) @ (size_size @ tree @ a @ r)) @ one_one @ nat))),
% 2.97/1.77 inference(cnf_transformation,[status(thm)],[f979])).
% 2.97/1.77 thf(f979,plain,(
% 2.97/1.77 ((size_size @ tree @ a @ rr) != (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ a @ l) @ (size_size @ tree @ a @ r)) @ one_one @ nat))),
% 2.97/1.77 inference(flattening,[status(thm)],[f337])).
% 2.97/1.77 thf(f337,negated_conjecture,(
% 2.97/1.77 ~((size_size @ tree @ a @ rr) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ a @ l) @ (size_size @ tree @ a @ r)) @ one_one @ nat))),
% 2.97/1.77 inference(negated_conjecture,[status(cth)],[f336])).
% 2.97/1.77 thf(f336,conjecture,(
% 2.97/1.77 ((size_size @ tree @ a @ rr) = (plus_plus @ nat @ (plus_plus @ nat @ (size_size @ tree @ a @ l) @ (size_size @ tree @ a @ r)) @ one_one @ nat))),
% 2.97/1.77 file('/export/starexec/sandbox/tmp/tmp.zbsVZtOUsU/DTF2THF_30178.p',conj_0)).
% 2.97/1.77 % SZS output end Proof for DTF2THF_30178
% 2.97/1.77 % (30529)------------------------------
% 2.97/1.77 % (30529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.77 % (30529)Termination reason: Refutation
% 2.97/1.77
% 2.97/1.77 % (30529)Memory used [KB]: 7036
% 2.97/1.77 % (30529)Time elapsed: 0.051 s
% 2.97/1.77 % (30529)Instructions burned: 149 (million)
% 2.97/1.77 % (30529)------------------------------
% 2.97/1.77 % (30529)------------------------------
% 2.97/1.77 % (30506)Success in time 0.133 s
%------------------------------------------------------------------------------