%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT215^1 : 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 : n022.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 182.75s 27.21s
% Output : Refutation 182.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT215^1 : 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
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:11:36 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.51 ---- Original DTF file ---
% 0.30/0.51 thf(spec,logic,$$dhol).
% 0.30/0.51 %------------------------------------------------------------------------------
% 0.30/0.51 % File : DAT215^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.51 % Domain : Data Structures
% 0.30/0.51 % Problem : Splay tree analysis 270
% 0.30/0.51 % Version : [Bla16] axioms : Especial.
% 0.30/0.51 % English :
% 0.30/0.51
% 0.30/0.51 % Refs : [Nip14] Nipkow (2014), Amortized Complexity Verified
% 0.30/0.51 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.30/0.51 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.30/0.51 % Source : [Bla16]
% 0.30/0.51 % Names : splay_tree_analysis__270.p [Bla16]
% 0.30/0.51
% 0.30/0.51 % Status : Theorem
% 0.30/0.51 % Rating : 0.67 v9.1.0, 1.00 v9.0.0, 0.67 v8.2.0, 1.00 v8.1.0, 0.50 v7.5.0, 1.00 v7.1.0
% 0.30/0.51 % Syntax : Number of formulae : 359 ( 92 unt; 72 typ; 0 def)
% 0.30/0.51 % Number of atoms : 941 ( 286 equ; 0 cnn)
% 0.30/0.51 % Maximal formula atoms : 19 ( 3 avg)
% 0.30/0.51 % Number of connectives : 5834 ( 163 ~; 8 |; 81 &;4996 @)
% 0.30/0.51 % ( 0 <=>; 586 =>; 0 <=; 0 <~>)
% 0.30/0.51 % Maximal formula depth : 28 ( 10 avg)
% 0.30/0.51 % Number of types : 3 ( 2 usr)
% 0.30/0.51 % Number of type conns : 334 ( 334 >; 0 *; 0 +; 0 <<)
% 0.30/0.51 % Number of symbols : 73 ( 70 usr; 4 con; 0-6 aty)
% 0.30/0.51 % Number of variables : 1397 ( 19 ^;1278 !; 26 ?;1397 :)
% 0.30/0.51 % ( 74 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.51 % SPC : TH1_THM_EQU_NAR
% 0.30/0.51
% 0.30/0.51 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.51 % 2016-07-13 14:50:37.787
% 0.30/0.51 %------------------------------------------------------------------------------
% 0.30/0.51 %----Could-be-implicit typings (8)
% 0.30/0.51 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_2011811431op_s_t: $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.51 product_prod: $tType > $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_Tree_Otree,type,
% 0.30/0.51 tree: $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_List_Olist,type,
% 0.30/0.51 list: $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_Set_Oset,type,
% 0.30/0.51 set: $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_Nat_Onat,type,
% 0.30/0.51 nat: $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_t_itself,type,
% 0.30/0.51 itself: $tType > $tType ).
% 0.30/0.51
% 0.30/0.51 thf(ty_tf_a,type,
% 0.30/0.51 a: $tType ).
% 0.30/0.51
% 0.30/0.51 %----Explicit typings (64)
% 0.30/0.51 thf(sy_cl_HOL_Otype,type,
% 0.30/0.51 type:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.51 ord:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.51 order:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Ono__bot,type,
% 0.30/0.51 no_bot:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Ono__top,type,
% 0.30/0.51 no_top:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.51 linorder:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.51 preorder:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Owellorder,type,
% 0.30/0.51 wellorder:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Orderings_Odense__order,type,
% 0.30/0.51 dense_order:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.30/0.51 linordered_idom:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.30/0.51 linordered_semidom:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Divides_Osemiring__numeral__div,type,
% 0.30/0.51 semiring_numeral_div:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.30/0.51 ordere236663937imp_le:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.30/0.51 ordere223160158up_add:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.30/0.51 strict2144017051up_add:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.30/0.51 condit1037483654norder:
% 0.30/0.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.30/0.51 one_one:
% 0.30/0.51 !>[A: $tType] : A ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.30/0.51 plus_plus:
% 0.30/0.51 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_If,type,
% 0.30/0.51 if:
% 0.30/0.51 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Odistinct,type,
% 0.30/0.51 distinct:
% 0.30/0.51 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.51 ord_less:
% 0.30/0.51 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.51 ord_less_eq:
% 0.30/0.51 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.51 product_Pair:
% 0.30/0.51 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Product__Type_Ocurry,type,
% 0.30/0.51 product_curry:
% 0.30/0.51 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.30/0.51 produc2004651681e_prod:
% 0.30/0.51 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.30/0.51 product_rec_prod:
% 0.30/0.51 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Pure_Otype,type,
% 0.30/0.51 type2:
% 0.30/0.51 !>[A: $tType] : ( itself @ A ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Set_OCollect,type,
% 0.30/0.51 collect:
% 0.30/0.51 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat,type,
% 0.30/0.51 set_fo292404081st_nat:
% 0.30/0.51 !>[A: $tType] : ( ( nat > A > A ) > nat > nat > A > A ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel,type,
% 0.30/0.51 set_fo2092542664at_rel:
% 0.30/0.51 !>[A: $tType] : ( ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) > ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Odelete,type,
% 0.30/0.51 splay_delete:
% 0.30/0.51 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Oinsert,type,
% 0.30/0.51 splay_insert:
% 0.30/0.51 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Ois__root,type,
% 0.30/0.51 splay_is_root:
% 0.30/0.51 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Osplay,type,
% 0.30/0.51 splay_splay:
% 0.30/0.51 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Osplay__max,type,
% 0.30/0.51 splay_splay_max:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree_Osplay__rel,type,
% 0.30/0.51 splay_splay_rel:
% 0.30/0.51 !>[A: $tType] : ( ( product_prod @ A @ ( tree @ A ) ) > ( product_prod @ A @ ( tree @ A ) ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_859309299xt_s_t:
% 0.30/0.51 !>[A: $tType] : ( ( splay_2011811431op_s_t @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t__rel,type,
% 0.30/0.51 splay_1102316486_t_rel:
% 0.30/0.51 !>[A: $tType] : ( ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) > ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_ODelete,type,
% 0.30/0.51 splay_705249169Delete:
% 0.30/0.51 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OInsert,type,
% 0.30/0.51 splay_1105473951Insert:
% 0.30/0.51 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OSplay,type,
% 0.30/0.51 splay_2088287777_Splay:
% 0.30/0.51 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Ocase__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_549499974op_s_t:
% 0.30/0.51 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( A > B ) > ( splay_2011811431op_s_t @ A ) > B ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orec__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_2144473850op_s_t:
% 0.30/0.51 !>[A: $tType,C: $tType] : ( ( A > C ) > ( A > C ) > ( A > C ) > ( splay_2011811431op_s_t @ A ) > C ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orel__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_434753539op_s_t:
% 0.30/0.51 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Oset__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 0.30/0.51 splay_1816468620op_s_t:
% 0.30/0.51 !>[A: $tType] : ( ( splay_2011811431op_s_t @ A ) > ( set @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 0.30/0.51 splay_914434265_splay:
% 0.30/0.51 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max,type,
% 0.30/0.51 splay_878424299ay_max:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel,type,
% 0.30/0.51 splay_1816415694ax_rel:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Oinorder,type,
% 0.30/0.51 inorder:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( list @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 0.30/0.51 linorder_bst:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Olinorder__class_Obst__eq,type,
% 0.30/0.51 linorder_bst_eq:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Olinorder__class_Obst__eq__rel,type,
% 0.30/0.51 linorder_bst_eq_rel:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Olinorder__class_Obst__rel,type,
% 0.30/0.51 linorder_bst_rel:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Opreorder,type,
% 0.30/0.51 preorder2:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( list @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Otree_OLeaf,type,
% 0.30/0.51 leaf:
% 0.30/0.51 !>[A: $tType] : ( tree @ A ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Otree_ONode,type,
% 0.30/0.51 node:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Tree_Otree_Oset__tree,type,
% 0.30/0.51 set_tree:
% 0.30/0.51 !>[A: $tType] : ( ( tree @ A ) > ( set @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Wellfounded_Oaccp,type,
% 0.30/0.51 accp:
% 0.30/0.51 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Wellfounded_Olex__prod,type,
% 0.30/0.51 lex_prod:
% 0.30/0.51 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Wellfounded_Omeasure,type,
% 0.30/0.51 measure:
% 0.30/0.51 !>[A: $tType] : ( ( A > nat ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Wfrec_Osame__fst,type,
% 0.30/0.51 same_fst:
% 0.30/0.51 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_member,type,
% 0.30/0.51 member:
% 0.30/0.51 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.51
% 0.30/0.51 thf(sy_v_a____,type,
% 0.30/0.51 a2: tree @ a ).
% 0.30/0.51
% 0.30/0.51 thf(sy_v_f____,type,
% 0.30/0.51 f: splay_2011811431op_s_t @ a ).
% 0.30/0.51
% 0.30/0.51 %----Relevant facts (256)
% 0.30/0.51 thf(fact_0__C2_C,axiom,
% 0.30/0.51 linorder_bst @ a @ a2 ).
% 0.30/0.51
% 0.30/0.51 % "2"
% 0.30/0.51 thf(fact_1_bst__delete,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( linorder_bst @ A @ ( splay_delete @ A @ A2 @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_delete
% 0.30/0.51 thf(fact_2_bst__insert,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( linorder_bst @ A @ ( splay_insert @ A @ A2 @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_insert
% 0.30/0.51 thf(fact_3_bst__splay__max,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_splay_max
% 0.30/0.51 thf(fact_4_bst__eq__if__bst,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( linorder_bst_eq @ A @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq_if_bst
% 0.30/0.51 thf(fact_5_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,T2: tree @ A] :
% 0.30/0.51 ( ( splay_859309299xt_s_t @ A @ ( splay_705249169Delete @ A @ A2 ) @ T2 )
% 0.30/0.51 = ( splay_delete @ A @ A2 @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.simps(3)
% 0.30/0.51 thf(fact_6_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,T2: tree @ A] :
% 0.30/0.51 ( ( splay_859309299xt_s_t @ A @ ( splay_1105473951Insert @ A @ A2 ) @ T2 )
% 0.30/0.51 = ( splay_insert @ A @ A2 @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.simps(2)
% 0.30/0.51 thf(fact_7_bst__splay,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_splay
% 0.30/0.51 thf(fact_8_bst_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.simps(1)
% 0.30/0.51 thf(fact_9_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,T2: tree @ A] :
% 0.30/0.51 ( ( splay_859309299xt_s_t @ A @ ( splay_2088287777_Splay @ A @ A2 ) @ T2 )
% 0.30/0.51 = ( splay_splay @ A @ A2 @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.simps(1)
% 0.30/0.51 thf(fact_10_splay__max__eq__splay__ex,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ? [A3: A] :
% 0.30/0.51 ( ( splay_splay_max @ A @ T2 )
% 0.30/0.51 = ( splay_splay @ A @ A3 @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max_eq_splay_ex
% 0.30/0.51 thf(fact_11_distinct__preorder__if__bst,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( distinct @ A @ ( preorder2 @ A @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % distinct_preorder_if_bst
% 0.30/0.51 thf(fact_12_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,X3: A,Y3: A] :
% 0.30/0.51 ( ( ( splay_705249169Delete @ A @ X3 )
% 0.30/0.51 = ( splay_705249169Delete @ A @ Y3 ) )
% 0.30/0.51 = ( X3 = Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.inject(3)
% 0.30/0.51 thf(fact_13_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,X2: A,Y2: A] :
% 0.30/0.51 ( ( ( splay_1105473951Insert @ A @ X2 )
% 0.30/0.51 = ( splay_1105473951Insert @ A @ Y2 ) )
% 0.30/0.51 = ( X2 = Y2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.inject(2)
% 0.30/0.51 thf(fact_14_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,X1: A,Y1: A] :
% 0.30/0.51 ( ( ( splay_2088287777_Splay @ A @ X1 )
% 0.30/0.51 = ( splay_2088287777_Splay @ A @ Y1 ) )
% 0.30/0.51 = ( X1 = Y1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.inject(1)
% 0.30/0.51 thf(fact_15_splay__Leaf__iff,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,T2: tree @ A] :
% 0.30/0.51 ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 = ( T2
% 0.30/0.51 = ( leaf @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_Leaf_iff
% 0.30/0.51 thf(fact_16_splay__max__Leaf__iff,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( ( splay_splay_max @ A @ T2 )
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 = ( T2
% 0.30/0.51 = ( leaf @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max_Leaf_iff
% 0.30/0.51 thf(fact_17_splay_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A] :
% 0.30/0.51 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 0.30/0.51 = ( leaf @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(1)
% 0.30/0.51 thf(fact_18_splay__max_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 0.30/0.51 = ( leaf @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max.simps(1)
% 0.30/0.51 thf(fact_19_bst__eq_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ( linorder_bst_eq @ A @ ( leaf @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.simps(1)
% 0.30/0.51 thf(fact_20_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I5_J,axiom,
% 0.30/0.51 ! [A: $tType,X2: A,X3: A] :
% 0.30/0.51 ( ( splay_1105473951Insert @ A @ X2 )
% 0.30/0.51 != ( splay_705249169Delete @ A @ X3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.distinct(5)
% 0.30/0.51 thf(fact_21_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,X1: A,X3: A] :
% 0.30/0.51 ( ( splay_2088287777_Splay @ A @ X1 )
% 0.30/0.51 != ( splay_705249169Delete @ A @ X3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.distinct(3)
% 0.30/0.51 thf(fact_22_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,X1: A,X2: A] :
% 0.30/0.51 ( ( splay_2088287777_Splay @ A @ X1 )
% 0.30/0.51 != ( splay_1105473951Insert @ A @ X2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.distinct(1)
% 0.30/0.51 thf(fact_23_nxt_092_060_094sub_062s_092_060_094sub_062t_Oelims,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: splay_2011811431op_s_t @ A,Xa: tree @ A,Y: tree @ A] :
% 0.30/0.51 ( ( ( splay_859309299xt_s_t @ A @ X @ Xa )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_2088287777_Splay @ A @ A3 ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 != ( splay_splay @ A @ A3 @ Xa ) ) )
% 0.30/0.51 => ( ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_1105473951Insert @ A @ A3 ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 != ( splay_insert @ A @ A3 @ Xa ) ) )
% 0.30/0.51 => ~ ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_705249169Delete @ A @ A3 ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 != ( splay_delete @ A @ A3 @ Xa ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.elims
% 0.30/0.51 thf(fact_24_op_092_060_094sub_062s_092_060_094sub_062t_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType,P: ( splay_2011811431op_s_t @ A ) > $o,Op_s_t: splay_2011811431op_s_t @ A] :
% 0.30/0.51 ( ! [X4: A] : ( P @ ( splay_2088287777_Splay @ A @ X4 ) )
% 0.30/0.51 => ( ! [X4: A] : ( P @ ( splay_1105473951Insert @ A @ X4 ) )
% 0.30/0.51 => ( ! [X4: A] : ( P @ ( splay_705249169Delete @ A @ X4 ) )
% 0.30/0.51 => ( P @ Op_s_t ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.induct
% 0.30/0.51 thf(fact_25_nxt_092_060_094sub_062s_092_060_094sub_062t_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [P: ( splay_2011811431op_s_t @ A ) > ( tree @ A ) > $o,A0: splay_2011811431op_s_t @ A,A1: tree @ A] :
% 0.30/0.51 ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_2088287777_Splay @ A @ A3 ) @ X12 )
% 0.30/0.51 => ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_1105473951Insert @ A @ A3 ) @ X12 )
% 0.30/0.51 => ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_705249169Delete @ A @ A3 ) @ X12 )
% 0.30/0.51 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.induct
% 0.30/0.51 thf(fact_26_op_092_060_094sub_062s_092_060_094sub_062t_Oexhaust,axiom,
% 0.30/0.51 ! [A: $tType,Y: splay_2011811431op_s_t @ A] :
% 0.30/0.51 ( ! [X12: A] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( splay_2088287777_Splay @ A @ X12 ) )
% 0.30/0.51 => ( ! [X22: A] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( splay_1105473951Insert @ A @ X22 ) )
% 0.30/0.51 => ~ ! [X32: A] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( splay_705249169Delete @ A @ X32 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.exhaust
% 0.30/0.51 thf(fact_27_op_092_060_094sub_062s_092_060_094sub_062t_Oset__cases,axiom,
% 0.30/0.51 ! [A: $tType,E: A,A2: splay_2011811431op_s_t @ A] :
% 0.30/0.51 ( ( member @ A @ E @ ( splay_1816468620op_s_t @ A @ A2 ) )
% 0.30/0.51 => ( ( A2
% 0.30/0.51 != ( splay_2088287777_Splay @ A @ E ) )
% 0.30/0.51 => ( ( A2
% 0.30/0.51 != ( splay_1105473951Insert @ A @ E ) )
% 0.30/0.51 => ( A2
% 0.30/0.51 = ( splay_705249169Delete @ A @ E ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.set_cases
% 0.30/0.51 thf(fact_28_nxt_092_060_094sub_062s_092_060_094sub_062t_Opelims,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: splay_2011811431op_s_t @ A,Xa: tree @ A,Y: tree @ A] :
% 0.30/0.51 ( ( ( splay_859309299xt_s_t @ A @ X @ Xa )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ X @ Xa ) )
% 0.30/0.51 => ( ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_2088287777_Splay @ A @ A3 ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( splay_splay @ A @ A3 @ Xa ) )
% 0.30/0.51 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_2088287777_Splay @ A @ A3 ) @ Xa ) ) ) )
% 0.30/0.51 => ( ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_1105473951Insert @ A @ A3 ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( splay_insert @ A @ A3 @ Xa ) )
% 0.30/0.51 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_1105473951Insert @ A @ A3 ) @ Xa ) ) ) )
% 0.30/0.51 => ~ ! [A3: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( splay_705249169Delete @ A @ A3 ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( splay_delete @ A @ A3 @ Xa ) )
% 0.30/0.51 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_705249169Delete @ A @ A3 ) @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.pelims
% 0.30/0.51 thf(fact_29_nxt_092_060_094sub_062s_092_060_094sub_062t_Ocases,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A )] :
% 0.30/0.51 ( ! [A3: A,T3: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_2088287777_Splay @ A @ A3 ) @ T3 ) )
% 0.30/0.51 => ( ! [A3: A,T3: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_1105473951Insert @ A @ A3 ) @ T3 ) )
% 0.30/0.51 => ~ ! [A3: A,T3: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_705249169Delete @ A @ A3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nxt\<^sub>s\<^sub>t.cases
% 0.30/0.51 thf(fact_30_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cases,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,A2: splay_2011811431op_s_t @ A,B2: splay_2011811431op_s_t @ B] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ A2 @ B2 )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( A2
% 0.30/0.51 = ( splay_2088287777_Splay @ A @ X4 ) )
% 0.30/0.51 => ! [Y4: B] :
% 0.30/0.51 ( ( B2
% 0.30/0.51 = ( splay_2088287777_Splay @ B @ Y4 ) )
% 0.30/0.51 => ~ ( R @ X4 @ Y4 ) ) )
% 0.30/0.51 => ( ! [Xa2: A] :
% 0.30/0.51 ( ( A2
% 0.30/0.51 = ( splay_1105473951Insert @ A @ Xa2 ) )
% 0.30/0.51 => ! [Ya: B] :
% 0.30/0.51 ( ( B2
% 0.30/0.51 = ( splay_1105473951Insert @ B @ Ya ) )
% 0.30/0.51 => ~ ( R @ Xa2 @ Ya ) ) )
% 0.30/0.51 => ~ ! [Xb: A] :
% 0.30/0.51 ( ( A2
% 0.30/0.51 = ( splay_705249169Delete @ A @ Xb ) )
% 0.30/0.51 => ! [Yb: B] :
% 0.30/0.51 ( ( B2
% 0.30/0.51 = ( splay_705249169Delete @ B @ Yb ) )
% 0.30/0.51 => ~ ( R @ Xb @ Yb ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_cases
% 0.30/0.51 thf(fact_31_op_092_060_094sub_062s_092_060_094sub_062t_Orel__induct,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Q: ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 0.30/0.51 => ( ! [A12: A,B1: B] :
% 0.30/0.51 ( ( R @ A12 @ B1 )
% 0.30/0.51 => ( Q @ ( splay_2088287777_Splay @ A @ A12 ) @ ( splay_2088287777_Splay @ B @ B1 ) ) )
% 0.30/0.51 => ( ! [A22: A,B22: B] :
% 0.30/0.51 ( ( R @ A22 @ B22 )
% 0.30/0.51 => ( Q @ ( splay_1105473951Insert @ A @ A22 ) @ ( splay_1105473951Insert @ B @ B22 ) ) )
% 0.30/0.51 => ( ! [A32: A,B3: B] :
% 0.30/0.51 ( ( R @ A32 @ B3 )
% 0.30/0.51 => ( Q @ ( splay_705249169Delete @ A @ A32 ) @ ( splay_705249169Delete @ B @ B3 ) ) )
% 0.30/0.51 => ( Q @ X @ Y ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_induct
% 0.30/0.51 thf(fact_32_distinct__inorder__if__bst,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( distinct @ A @ ( inorder @ A @ T2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % distinct_inorder_if_bst
% 0.30/0.51 thf(fact_33_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I15_J,axiom,
% 0.30/0.51 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X3: A] :
% 0.30/0.51 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_705249169Delete @ A @ X3 ) )
% 0.30/0.51 = ( F3 @ X3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(15)
% 0.30/0.51 thf(fact_34_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I14_J,axiom,
% 0.30/0.51 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X2: A] :
% 0.30/0.51 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_1105473951Insert @ A @ X2 ) )
% 0.30/0.51 = ( F2 @ X2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(14)
% 0.30/0.51 thf(fact_35_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I13_J,axiom,
% 0.30/0.51 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X1: A] :
% 0.30/0.51 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_2088287777_Splay @ A @ X1 ) )
% 0.30/0.51 = ( F1 @ X1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(13)
% 0.30/0.51 thf(fact_36_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I12_J,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X3: A] :
% 0.30/0.51 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_705249169Delete @ A @ X3 ) )
% 0.30/0.51 = ( F3 @ X3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(12)
% 0.30/0.51 thf(fact_37_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I11_J,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X2: A] :
% 0.30/0.51 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_1105473951Insert @ A @ X2 ) )
% 0.30/0.51 = ( F2 @ X2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(11)
% 0.30/0.51 thf(fact_38_insert_Ocases,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: product_prod @ A @ ( tree @ A )] :
% 0.30/0.51 ~ ! [X4: A,T3: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ A @ ( tree @ A ) @ X4 @ T3 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % insert.cases
% 0.30/0.51 thf(fact_39_op_092_060_094sub_062s_092_060_094sub_062t_Orel__eq,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ A
% 0.30/0.51 @ ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.30/0.51 = ( ^ [Y5: splay_2011811431op_s_t @ A,Z: splay_2011811431op_s_t @ A] : ( Y5 = Z ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_eq
% 0.30/0.51 thf(fact_40_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cong,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,X: splay_2011811431op_s_t @ A,Ya2: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Xa: splay_2011811431op_s_t @ B,R: A > B > $o,Ra: A > B > $o] :
% 0.30/0.51 ( ( X = Ya2 )
% 0.30/0.51 => ( ( Y = Xa )
% 0.30/0.51 => ( ! [Z2: A,Yb: B] :
% 0.30/0.51 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ Ya2 ) )
% 0.30/0.51 => ( ( member @ B @ Yb @ ( splay_1816468620op_s_t @ B @ Xa ) )
% 0.30/0.51 => ( ( R @ Z2 @ Yb )
% 0.30/0.51 = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.51 => ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 0.30/0.51 = ( splay_434753539op_s_t @ A @ B @ Ra @ Ya2 @ Xa ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_cong
% 0.30/0.51 thf(fact_41_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl,axiom,
% 0.30/0.51 ! [B: $tType,Ra: B > B > $o,X: splay_2011811431op_s_t @ B] :
% 0.30/0.51 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 0.30/0.51 => ( splay_434753539op_s_t @ B @ B @ Ra @ X @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_refl
% 0.30/0.51 thf(fact_42_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono__strong,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Ra: A > B > $o] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 0.30/0.51 => ( ! [Z2: A,Yb: B] :
% 0.30/0.51 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ X ) )
% 0.30/0.51 => ( ( member @ B @ Yb @ ( splay_1816468620op_s_t @ B @ Y ) )
% 0.30/0.51 => ( ( R @ Z2 @ Yb )
% 0.30/0.51 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.51 => ( splay_434753539op_s_t @ A @ B @ Ra @ X @ Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_mono_strong
% 0.30/0.51 thf(fact_43_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl__strong,axiom,
% 0.30/0.51 ! [A: $tType,X: splay_2011811431op_s_t @ A,Ra: A > A > $o] :
% 0.30/0.51 ( ! [Z2: A] :
% 0.30/0.51 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ X ) )
% 0.30/0.51 => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.51 => ( splay_434753539op_s_t @ A @ A @ Ra @ X @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_refl_strong
% 0.30/0.51 thf(fact_44_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y1: B] :
% 0.30/0.51 ( ( R @ X1 @ Y1 )
% 0.30/0.51 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_2088287777_Splay @ B @ Y1 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_intros(1)
% 0.30/0.51 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.51 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.51 = ( P @ A2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A: $tType,A4: set @ A] :
% 0.30/0.51 ( ( collect @ A
% 0.30/0.51 @ ^ [X5: A] : ( member @ A @ X5 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_47_Collect__cong,axiom,
% 0.30/0.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.51 ( ! [X4: A] :
% 0.30/0.51 ( ( P @ X4 )
% 0.30/0.51 = ( Q @ X4 ) )
% 0.30/0.51 => ( ( collect @ A @ P )
% 0.30/0.51 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_48_ext,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.51 ( ! [X4: A] :
% 0.30/0.51 ( ( F @ X4 )
% 0.30/0.51 = ( G @ X4 ) )
% 0.30/0.51 => ( F = G ) ) ).
% 0.30/0.51
% 0.30/0.51 % ext
% 0.30/0.51 thf(fact_49_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y2: B] :
% 0.30/0.51 ( ( R @ X2 @ Y2 )
% 0.30/0.51 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_1105473951Insert @ B @ Y2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_intros(2)
% 0.30/0.51 thf(fact_50_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y3: B] :
% 0.30/0.51 ( ( R @ X3 @ Y3 )
% 0.30/0.51 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ X3 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_intros(3)
% 0.30/0.51 thf(fact_51_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y1: B] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_2088287777_Splay @ B @ Y1 ) )
% 0.30/0.51 = ( R @ X1 @ Y1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_inject(1)
% 0.30/0.51 thf(fact_52_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y2: B] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_1105473951Insert @ B @ Y2 ) )
% 0.30/0.51 = ( R @ X2 @ Y2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_inject(2)
% 0.30/0.51 thf(fact_53_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y3: B] :
% 0.30/0.51 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ X3 ) @ ( splay_705249169Delete @ B @ Y3 ) )
% 0.30/0.51 = ( R @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_inject(3)
% 0.30/0.51 thf(fact_54_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( splay_1816468620op_s_t @ A @ ( splay_2088287777_Splay @ A @ A2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.set_intros(1)
% 0.30/0.51 thf(fact_55_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,Aa: A] : ( member @ A @ Aa @ ( splay_1816468620op_s_t @ A @ ( splay_1105473951Insert @ A @ Aa ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.set_intros(2)
% 0.30/0.51 thf(fact_56_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,Ab: A] : ( member @ A @ Ab @ ( splay_1816468620op_s_t @ A @ ( splay_705249169Delete @ A @ Ab ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.set_intros(3)
% 0.30/0.51 thf(fact_57_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y2: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_1105473951Insert @ B @ Y2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(1)
% 0.30/0.51 thf(fact_58_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,Y2: A,X1: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ Y2 ) @ ( splay_2088287777_Splay @ B @ X1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(2)
% 0.30/0.51 thf(fact_59_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y3: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(3)
% 0.30/0.51 thf(fact_60_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I4_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,Y3: A,X1: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ Y3 ) @ ( splay_2088287777_Splay @ B @ X1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(4)
% 0.30/0.51 thf(fact_61_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I5_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y3: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(5)
% 0.30/0.51 thf(fact_62_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I6_J,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,R: A > B > $o,Y3: A,X2: B] :
% 0.30/0.51 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ Y3 ) @ ( splay_1105473951Insert @ B @ X2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_distinct(6)
% 0.30/0.51 thf(fact_63_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I10_J,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X1: A] :
% 0.30/0.51 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_2088287777_Splay @ A @ X1 ) )
% 0.30/0.51 = ( F1 @ X1 ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.simps(10)
% 0.30/0.51 thf(fact_64_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 0.30/0.51 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.51 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.51 = ( ( A2 = A5 )
% 0.30/0.51 & ( B2 = B4 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_65_prod_Oinject,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.30/0.51 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.30/0.51 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.30/0.51 = ( ( X1 = Y1 )
% 0.30/0.51 & ( X2 = Y2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod.inject
% 0.30/0.51 thf(fact_66_splay_Opsimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A] :
% 0.30/0.51 ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( leaf @ A ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 0.30/0.51 = ( leaf @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(1)
% 0.30/0.51 thf(fact_67_accp__induct__rule,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,A2: A,P: A > $o] :
% 0.30/0.51 ( ( accp @ A @ R2 @ A2 )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( accp @ A @ R2 @ X4 )
% 0.30/0.51 => ( ! [Y6: A] :
% 0.30/0.51 ( ( R2 @ Y6 @ X4 )
% 0.30/0.51 => ( P @ Y6 ) )
% 0.30/0.51 => ( P @ X4 ) ) )
% 0.30/0.51 => ( P @ A2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp_induct_rule
% 0.30/0.51 thf(fact_68_not__accp__down,axiom,
% 0.30/0.51 ! [A: $tType,R: A > A > $o,X: A] :
% 0.30/0.51 ( ~ ( accp @ A @ R @ X )
% 0.30/0.51 => ~ ! [Z2: A] :
% 0.30/0.51 ( ( R @ Z2 @ X )
% 0.30/0.51 => ( accp @ A @ R @ Z2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % not_accp_down
% 0.30/0.51 thf(fact_69_accp__downward,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,B2: A,A2: A] :
% 0.30/0.51 ( ( accp @ A @ R2 @ B2 )
% 0.30/0.51 => ( ( R2 @ A2 @ B2 )
% 0.30/0.51 => ( accp @ A @ R2 @ A2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp_downward
% 0.30/0.51 thf(fact_70_accp_Oinducts,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,X: A,P: A > $o] :
% 0.30/0.51 ( ( accp @ A @ R2 @ X )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ! [Y6: A] :
% 0.30/0.51 ( ( R2 @ Y6 @ X4 )
% 0.30/0.51 => ( accp @ A @ R2 @ Y6 ) )
% 0.30/0.51 => ( ! [Y6: A] :
% 0.30/0.51 ( ( R2 @ Y6 @ X4 )
% 0.30/0.51 => ( P @ Y6 ) )
% 0.30/0.51 => ( P @ X4 ) ) )
% 0.30/0.51 => ( P @ X ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp.inducts
% 0.30/0.51 thf(fact_71_accp__induct,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,A2: A,P: A > $o] :
% 0.30/0.51 ( ( accp @ A @ R2 @ A2 )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( accp @ A @ R2 @ X4 )
% 0.30/0.51 => ( ! [Y6: A] :
% 0.30/0.51 ( ( R2 @ Y6 @ X4 )
% 0.30/0.51 => ( P @ Y6 ) )
% 0.30/0.51 => ( P @ X4 ) ) )
% 0.30/0.51 => ( P @ A2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp_induct
% 0.30/0.51 thf(fact_72_accp_Ointros,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,X: A] :
% 0.30/0.51 ( ! [Y4: A] :
% 0.30/0.51 ( ( R2 @ Y4 @ X )
% 0.30/0.51 => ( accp @ A @ R2 @ Y4 ) )
% 0.30/0.51 => ( accp @ A @ R2 @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp.intros
% 0.30/0.51 thf(fact_73_surj__pair,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.30/0.51 ? [X4: A,Y4: B] :
% 0.30/0.51 ( P2
% 0.30/0.51 = ( product_Pair @ A @ B @ X4 @ Y4 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_74_prod__cases,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.30/0.51 ( ! [A3: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 0.30/0.51 => ( P @ P2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_75_Pair__inject,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 0.30/0.51 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.30/0.51 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 0.30/0.51 => ~ ( ( A2 = A5 )
% 0.30/0.51 => ( B2 != B4 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_76_prod__cases3,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.51 ~ ! [A3: A,B5: B,C2: C] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases3
% 0.30/0.51 thf(fact_77_prod__cases4,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.51 ~ ! [A3: A,B5: B,C2: C,D2: D] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases4
% 0.30/0.51 thf(fact_78_prod__cases5,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.30/0.51 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases5
% 0.30/0.51 thf(fact_79_prod__cases6,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) )] :
% 0.30/0.51 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F4 ) @ D2 @ ( product_Pair @ E2 @ F4 @ E3 @ F5 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases6
% 0.30/0.51 thf(fact_80_prod__cases7,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.30/0.51 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4,G3: G2] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F4 @ G2 ) @ E3 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases7
% 0.30/0.51 thf(fact_81_prod__induct3,axiom,
% 0.30/0.51 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.30/0.51 ( ! [A3: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct3
% 0.30/0.51 thf(fact_82_prod__induct4,axiom,
% 0.30/0.51 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.30/0.51 ( ! [A3: A,B5: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct4
% 0.30/0.51 thf(fact_83_prod__induct5,axiom,
% 0.30/0.51 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.30/0.51 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct5
% 0.30/0.51 thf(fact_84_prod__induct6,axiom,
% 0.30/0.51 ! [F4: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) )] :
% 0.30/0.51 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F4 ) @ D2 @ ( product_Pair @ E2 @ F4 @ E3 @ F5 ) ) ) ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct6
% 0.30/0.51 thf(fact_85_prod__induct7,axiom,
% 0.30/0.51 ! [G2: $tType,F4: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.30/0.51 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F4 @ G2 ) @ E3 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct7
% 0.30/0.51 thf(fact_86_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.30/0.51 ~ ! [A3: A,B5: B] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair @ A @ B @ A3 @ B5 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_87_old_Oprod_Oinducts,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.30/0.51 ( ! [A3: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 0.30/0.51 => ( P @ Prod ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inducts
% 0.30/0.51 thf(fact_88_accp_Ocases,axiom,
% 0.30/0.51 ! [A: $tType,R2: A > A > $o,A2: A] :
% 0.30/0.51 ( ( accp @ A @ R2 @ A2 )
% 0.30/0.51 => ! [Y6: A] :
% 0.30/0.51 ( ( R2 @ Y6 @ A2 )
% 0.30/0.51 => ( accp @ A @ R2 @ Y6 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp.cases
% 0.30/0.51 thf(fact_89_accp_Osimps,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( accp @ A )
% 0.30/0.51 = ( ^ [R3: A > A > $o,A6: A] :
% 0.30/0.51 ? [X5: A] :
% 0.30/0.51 ( ( A6 = X5 )
% 0.30/0.51 & ! [Y7: A] :
% 0.30/0.51 ( ( R3 @ Y7 @ X5 )
% 0.30/0.51 => ( accp @ A @ R3 @ Y7 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp.simps
% 0.30/0.51 thf(fact_90_old_Oprod_Orec,axiom,
% 0.30/0.51 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.30/0.51 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.51 = ( F1 @ A2 @ B2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.rec
% 0.30/0.51 thf(fact_91_in__lex__prod,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B,R2: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ B @ B )] :
% 0.30/0.51 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A5 @ B4 ) ) @ ( lex_prod @ A @ B @ R2 @ S ) )
% 0.30/0.51 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A5 ) @ R2 )
% 0.30/0.51 | ( ( A2 = A5 )
% 0.30/0.51 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B4 ) @ S ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % in_lex_prod
% 0.30/0.51 thf(fact_92_splay_Opsimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ L @ A2 @ R2 ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 = ( node @ A @ L @ A2 @ R2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(2)
% 0.30/0.51 thf(fact_93_internal__case__prod__conv,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.30/0.51 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.30/0.51 = ( C3 @ A2 @ B2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % internal_case_prod_conv
% 0.30/0.51 thf(fact_94_ssubst__Pair__rhs,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,R2: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 0.30/0.51 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S ) @ R )
% 0.30/0.51 => ( ( S2 = S )
% 0.30/0.51 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ssubst_Pair_rhs
% 0.30/0.51 thf(fact_95_curry__conv,axiom,
% 0.30/0.51 ! [A: $tType,C: $tType,B: $tType] :
% 0.30/0.51 ( ( product_curry @ B @ C @ A )
% 0.30/0.51 = ( ^ [F6: ( product_prod @ B @ C ) > A,A6: B,B6: C] : ( F6 @ ( product_Pair @ B @ C @ A6 @ B6 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % curry_conv
% 0.30/0.51 thf(fact_96_curryI,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.30/0.51 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.30/0.51 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % curryI
% 0.30/0.51 thf(fact_97_tree_Oinject,axiom,
% 0.30/0.51 ! [A: $tType,X21: tree @ A,X222: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 0.30/0.51 ( ( ( node @ A @ X21 @ X222 @ X23 )
% 0.30/0.51 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 0.30/0.51 = ( ( X21 = Y21 )
% 0.30/0.51 & ( X222 = Y22 )
% 0.30/0.51 & ( X23 = Y23 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.inject
% 0.30/0.51 thf(fact_98_t__splay__max_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.30/0.51 ( ( P @ ( leaf @ A ) )
% 0.30/0.51 => ( ! [L2: tree @ A,B5: A] : ( P @ ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 0.30/0.51 => ( ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.30/0.51 ( ( ( Rr
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( P @ Rr ) )
% 0.30/0.51 => ( P @ ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 0.30/0.51 => ( P @ A0 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.induct
% 0.30/0.51 thf(fact_99_t__splay__max_Ocases,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ! [L2: tree @ A,B5: A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.cases
% 0.30/0.51 thf(fact_100__092_060Phi_062_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.30/0.51 ( ( P @ ( leaf @ A ) )
% 0.30/0.51 => ( ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( P @ L2 )
% 0.30/0.51 => ( ( P @ R4 )
% 0.30/0.51 => ( P @ ( node @ A @ L2 @ A3 @ R4 ) ) ) )
% 0.30/0.51 => ( P @ A0 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % \<Phi>.induct
% 0.30/0.51 thf(fact_101__092_060Phi_062_Ocases,axiom,
% 0.30/0.51 ! [A: $tType,X: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( node @ A @ L2 @ A3 @ R4 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % \<Phi>.cases
% 0.30/0.51 thf(fact_102_bst__eq_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.30/0.51 ( ( P @ ( leaf @ A ) )
% 0.30/0.51 => ( ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( P @ L2 )
% 0.30/0.51 => ( ( P @ R4 )
% 0.30/0.51 => ( P @ ( node @ A @ L2 @ A3 @ R4 ) ) ) )
% 0.30/0.51 => ( P @ A0 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.induct
% 0.30/0.51 thf(fact_103_bst__eq_Ocases,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.cases
% 0.30/0.51 thf(fact_104_mirror_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 0.30/0.51 ( ( P @ ( leaf @ A ) )
% 0.30/0.51 => ( ! [L2: tree @ A,X4: A,R4: tree @ A] :
% 0.30/0.51 ( ( P @ R4 )
% 0.30/0.51 => ( ( P @ L2 )
% 0.30/0.51 => ( P @ ( node @ A @ L2 @ X4 @ R4 ) ) ) )
% 0.30/0.51 => ( P @ A0 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % mirror.induct
% 0.30/0.51 thf(fact_105_tree_Oexhaust,axiom,
% 0.30/0.51 ! [A: $tType,Y: tree @ A] :
% 0.30/0.51 ( ( Y
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ~ ! [X212: tree @ A,X223: A,X232: tree @ A] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( node @ A @ X212 @ X223 @ X232 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.exhaust
% 0.30/0.51 thf(fact_106_neq__Leaf__iff,axiom,
% 0.30/0.51 ! [A: $tType,T2: tree @ A] :
% 0.30/0.51 ( ( T2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 = ( ? [L3: tree @ A,A6: A,R3: tree @ A] :
% 0.30/0.51 ( T2
% 0.30/0.51 = ( node @ A @ L3 @ A6 @ R3 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % neq_Leaf_iff
% 0.30/0.51 thf(fact_107_tree_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 0.30/0.51 ( ( P @ ( leaf @ A ) )
% 0.30/0.51 => ( ! [X12: tree @ A,X22: A,X32: tree @ A] :
% 0.30/0.51 ( ( P @ X12 )
% 0.30/0.51 => ( ( P @ X32 )
% 0.30/0.51 => ( P @ ( node @ A @ X12 @ X22 @ X32 ) ) ) )
% 0.30/0.51 => ( P @ Tree ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.induct
% 0.30/0.51 thf(fact_108_tree_Odistinct_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,X21: tree @ A,X222: A,X23: tree @ A] :
% 0.30/0.51 ( ( leaf @ A )
% 0.30/0.51 != ( node @ A @ X21 @ X222 @ X23 ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.distinct(1)
% 0.30/0.51 thf(fact_109_splay_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( splay_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 = ( node @ A @ L @ A2 @ R2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(2)
% 0.30/0.51 thf(fact_110_curryE,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.30/0.51 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.30/0.51 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % curryE
% 0.30/0.51 thf(fact_111_curryD,axiom,
% 0.30/0.51 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 0.30/0.51 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 0.30/0.51 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % curryD
% 0.30/0.51 thf(fact_112_splay__not__Leaf,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( T2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ? [L2: tree @ A,X4: A,R4: tree @ A] :
% 0.30/0.51 ( ( splay_splay @ A @ A2 @ T2 )
% 0.30/0.51 = ( node @ A @ L2 @ X4 @ R4 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_not_Leaf
% 0.30/0.51 thf(fact_113_t__splay_Ocases,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: product_prod @ A @ ( tree @ A )] :
% 0.30/0.51 ( ! [A3: A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ A @ ( tree @ A ) @ A3 @ ( leaf @ A ) ) )
% 0.30/0.51 => ~ ! [A3: A,L2: tree @ A,B5: A,R4: tree @ A] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair @ A @ ( tree @ A ) @ A3 @ ( node @ A @ L2 @ B5 @ R4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay.cases
% 0.30/0.51 thf(fact_114_splay__max__Leaf,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,L: tree @ A,A2: A,R2: tree @ A] :
% 0.30/0.51 ( ( ( splay_splay_max @ A @ T2 )
% 0.30/0.51 = ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 => ( R2
% 0.30/0.51 = ( leaf @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max_Leaf
% 0.30/0.51 thf(fact_115_splay__max_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [La: tree @ A,A2: A] :
% 0.30/0.51 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 0.30/0.51 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max.simps(2)
% 0.30/0.51 thf(fact_116_splay_Opsimps_I13_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,B2: A,La: tree @ A,Lb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( ord_less @ A @ B2 @ X )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B2 @ ( leaf @ A ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(13)
% 0.30/0.51 thf(fact_117_splay_Opsimps_I12_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,B2: A,La: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(12)
% 0.30/0.51 thf(fact_118_splay_Opsimps_I10_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,L: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) )
% 0.30/0.51 = ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(10)
% 0.30/0.51 thf(fact_119_splay_Opsimps_I7_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: A,B2: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(7)
% 0.30/0.51 thf(fact_120_splay_Opsimps_I5_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: A,A2: A,B2: A,Ra2: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ X @ A2 )
% 0.30/0.51 => ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(5)
% 0.30/0.51 thf(fact_121_splay_Osimps_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(3)
% 0.30/0.51 thf(fact_122_splay_Osimps_I9_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ Lb @ B2 @ La ) @ A2 @ Ra2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(9)
% 0.30/0.51 thf(fact_123_splay_Osimps_I13_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,B2: A,La: tree @ A,Lb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( ord_less @ A @ B2 @ X )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B2 @ ( leaf @ A ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(13)
% 0.30/0.51 thf(fact_124_splay_Osimps_I12_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,B2: A,La: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(12)
% 0.30/0.51 thf(fact_125_splay_Osimps_I10_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,X: A,L: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) )
% 0.30/0.51 = ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(10)
% 0.30/0.51 thf(fact_126_splay_Osimps_I7_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: A,B2: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ A2 @ X )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(7)
% 0.30/0.51 thf(fact_127_splay_Osimps_I5_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: A,A2: A,B2: A,Ra2: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ X @ A2 )
% 0.30/0.51 => ( ( ord_less @ A @ X @ B2 )
% 0.30/0.51 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(5)
% 0.30/0.51 thf(fact_128_splay_Osimps_I4_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 0.30/0.51 = ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.simps(4)
% 0.30/0.51 thf(fact_129_splay_Opsimps_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 0.30/0.51 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(3)
% 0.30/0.51 thf(fact_130_splay_Opsimps_I9_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 0.30/0.51 = ( node @ A @ ( node @ A @ Lb @ B2 @ La ) @ A2 @ Ra2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(9)
% 0.30/0.51 thf(fact_131_splay_Opsimps_I4_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) )
% 0.30/0.51 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 0.30/0.51 = ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay.psimps(4)
% 0.30/0.51 thf(fact_132_in__measure,axiom,
% 0.30/0.51 ! [A: $tType,X: A,Y: A,F: A > nat] :
% 0.30/0.51 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( measure @ A @ F ) )
% 0.30/0.51 = ( ord_less @ nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % in_measure
% 0.30/0.51 thf(fact_133_same__fstI,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,P: A > $o,X: A,Y8: B,Y: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 0.30/0.51 ( ( P @ X )
% 0.30/0.51 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y8 @ Y ) @ ( R @ X ) )
% 0.30/0.51 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y8 ) @ ( product_Pair @ A @ B @ X @ Y ) ) @ ( same_fst @ A @ B @ P @ R ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % same_fstI
% 0.30/0.51 thf(fact_134_splay__bstR,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A,L: tree @ A,E: A,R2: tree @ A,X: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.30/0.51 = ( node @ A @ L @ E @ R2 ) )
% 0.30/0.51 => ( ( member @ A @ X @ ( set_tree @ A @ R2 ) )
% 0.30/0.51 => ( ord_less @ A @ A2 @ X ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_bstR
% 0.30/0.51 thf(fact_135_splay__bstL,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A,L: tree @ A,E: A,R2: tree @ A,X: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.30/0.51 = ( node @ A @ L @ E @ R2 ) )
% 0.30/0.51 => ( ( member @ A @ X @ ( set_tree @ A @ L ) )
% 0.30/0.51 => ( ord_less @ A @ X @ A2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_bstL
% 0.30/0.51 thf(fact_136_set__splay,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,T2: tree @ A] :
% 0.30/0.51 ( ( set_tree @ A @ ( splay_splay @ A @ A2 @ T2 ) )
% 0.30/0.51 = ( set_tree @ A @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % set_splay
% 0.30/0.51 thf(fact_137_set__splay__max,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A] :
% 0.30/0.51 ( ( set_tree @ A @ ( splay_splay_max @ A @ T2 ) )
% 0.30/0.51 = ( set_tree @ A @ T2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % set_splay_max
% 0.30/0.51 thf(fact_138_tree_Oset__cases,axiom,
% 0.30/0.51 ! [A: $tType,E: A,A2: tree @ A] :
% 0.30/0.51 ( ( member @ A @ E @ ( set_tree @ A @ A2 ) )
% 0.30/0.51 => ( ! [Z1: tree @ A] :
% 0.30/0.51 ( ? [Z22: A,Z3: tree @ A] :
% 0.30/0.51 ( A2
% 0.30/0.51 = ( node @ A @ Z1 @ Z22 @ Z3 ) )
% 0.30/0.51 => ~ ( member @ A @ E @ ( set_tree @ A @ Z1 ) ) )
% 0.30/0.51 => ( ! [Z1: tree @ A,Z3: tree @ A] :
% 0.30/0.51 ( A2
% 0.30/0.51 != ( node @ A @ Z1 @ E @ Z3 ) )
% 0.30/0.51 => ~ ! [Z1: tree @ A,Z22: A,Z3: tree @ A] :
% 0.30/0.51 ( ( A2
% 0.30/0.51 = ( node @ A @ Z1 @ Z22 @ Z3 ) )
% 0.30/0.51 => ~ ( member @ A @ E @ ( set_tree @ A @ Z3 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.set_cases
% 0.30/0.51 thf(fact_139_tree_Oset__intros_I1_J,axiom,
% 0.30/0.51 ! [A: $tType,X: A,A1: tree @ A,A23: A,A33: tree @ A] :
% 0.30/0.51 ( ( member @ A @ X @ ( set_tree @ A @ A1 ) )
% 0.30/0.51 => ( member @ A @ X @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.set_intros(1)
% 0.30/0.51 thf(fact_140_tree_Oset__intros_I2_J,axiom,
% 0.30/0.51 ! [A: $tType,A23: A,A1: tree @ A,A33: tree @ A] : ( member @ A @ A23 @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.set_intros(2)
% 0.30/0.51 thf(fact_141_tree_Oset__intros_I3_J,axiom,
% 0.30/0.51 ! [A: $tType,Xa: A,A33: tree @ A,A1: tree @ A,A23: A] :
% 0.30/0.51 ( ( member @ A @ Xa @ ( set_tree @ A @ A33 ) )
% 0.30/0.51 => ( member @ A @ Xa @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % tree.set_intros(3)
% 0.30/0.51 thf(fact_142_splay__to__root,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A,T4: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 0.30/0.51 = T4 )
% 0.30/0.51 => ( ( member @ A @ A2 @ ( set_tree @ A @ T2 ) )
% 0.30/0.51 = ( ? [L3: tree @ A,R3: tree @ A] :
% 0.30/0.51 ( T4
% 0.30/0.51 = ( node @ A @ L3 @ A2 @ R3 ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_to_root
% 0.30/0.51 thf(fact_143_is__root__splay,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( ( splay_is_root @ A @ A2 @ ( splay_splay @ A @ A2 @ T2 ) )
% 0.30/0.51 = ( member @ A @ A2 @ ( set_tree @ A @ T2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % is_root_splay
% 0.30/0.51 thf(fact_144_ex__in__set__tree,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( T2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ? [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ T2 ) )
% 0.30/0.51 & ( ( splay_splay @ A @ X4 @ T2 )
% 0.30/0.51 = ( splay_splay @ A @ A2 @ T2 ) )
% 0.30/0.51 & ( ( splay_914434265_splay @ A @ X4 @ T2 )
% 0.30/0.51 = ( splay_914434265_splay @ A @ A2 @ T2 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ex_in_set_tree
% 0.30/0.51 thf(fact_145_bst_Oelims_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: $o] :
% 0.30/0.51 ( ( ( linorder_bst @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ~ Y )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( ~ ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X5 @ A3 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X5 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.elims(1)
% 0.30/0.51 thf(fact_146_bst_Oelims_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ X )
% 0.30/0.51 => ( ( X
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ~ ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X6 @ A3 ) )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X6 ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.elims(2)
% 0.30/0.51 thf(fact_147_bst_Oelims_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ~ ( linorder_bst @ A @ X )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X4 @ A3 ) )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X4 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.elims(3)
% 0.30/0.51 thf(fact_148_bst_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [L: tree @ A,A2: A,R2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 = ( ( linorder_bst @ A @ L )
% 0.30/0.51 & ( linorder_bst @ A @ R2 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L ) )
% 0.30/0.51 => ( ord_less @ A @ X5 @ A2 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R2 ) )
% 0.30/0.51 => ( ord_less @ A @ A2 @ X5 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.simps(2)
% 0.30/0.51 thf(fact_149_bst_Opelims_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( linorder_bst @ A @ X )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( leaf @ A ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ~ ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X6 @ A3 ) )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.pelims(2)
% 0.30/0.51 thf(fact_150_bst_Opelims_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: $o] :
% 0.30/0.51 ( ( ( linorder_bst @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( leaf @ A ) ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X5 @ A3 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X5 ) ) ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.pelims(1)
% 0.30/0.51 thf(fact_151_bst_Opelims_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ~ ( linorder_bst @ A @ X )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( linorder_bst @ A @ L2 )
% 0.30/0.51 & ( linorder_bst @ A @ R4 )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less @ A @ X4 @ A3 ) )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less @ A @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst.pelims(3)
% 0.30/0.51 thf(fact_152_t__splay__simps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(2)
% 0.30/0.51 thf(fact_153_t__splay__simps_I6_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,L: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(6)
% 0.30/0.51 thf(fact_154_bst__eq_Oelims_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: $o] :
% 0.30/0.51 ( ( ( linorder_bst_eq @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ~ Y )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( ~ ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X5 @ A3 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X5 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.elims(1)
% 0.30/0.51 thf(fact_155_t__splay__simps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(1)
% 0.30/0.51 thf(fact_156_t__splay__simps_I7_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,L: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(7)
% 0.30/0.51 thf(fact_157_t__splay__simps_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B2 @ R2 ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(3)
% 0.30/0.51 thf(fact_158_accp__subset__induct,axiom,
% 0.30/0.51 ! [A: $tType,D3: A > $o,R: A > A > $o,X: A,P: A > $o] :
% 0.30/0.51 ( ( ord_less_eq @ ( A > $o ) @ D3 @ ( accp @ A @ R ) )
% 0.30/0.51 => ( ! [X4: A,Z2: A] :
% 0.30/0.51 ( ( D3 @ X4 )
% 0.30/0.51 => ( ( R @ Z2 @ X4 )
% 0.30/0.51 => ( D3 @ Z2 ) ) )
% 0.30/0.51 => ( ( D3 @ X )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( D3 @ X4 )
% 0.30/0.51 => ( ! [Z4: A] :
% 0.30/0.51 ( ( R @ Z4 @ X4 )
% 0.30/0.51 => ( P @ Z4 ) )
% 0.30/0.51 => ( P @ X4 ) ) )
% 0.30/0.51 => ( P @ X ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp_subset_induct
% 0.30/0.51 thf(fact_159_accp__subset,axiom,
% 0.30/0.51 ! [A: $tType,R1: A > A > $o,R22: A > A > $o] :
% 0.30/0.51 ( ( ord_less_eq @ ( A > A > $o ) @ R1 @ R22 )
% 0.30/0.51 => ( ord_less_eq @ ( A > $o ) @ ( accp @ A @ R22 ) @ ( accp @ A @ R1 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % accp_subset
% 0.30/0.51 thf(fact_160_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono,axiom,
% 0.30/0.51 ! [B: $tType,A: $tType,R: A > B > $o,Ra: A > B > $o] :
% 0.30/0.51 ( ( ord_less_eq @ ( A > B > $o ) @ R @ Ra )
% 0.30/0.51 => ( ord_less_eq @ ( ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o ) @ ( splay_434753539op_s_t @ A @ B @ R ) @ ( splay_434753539op_s_t @ A @ B @ Ra ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % op\<^sub>s\<^sub>t.rel_mono
% 0.30/0.51 thf(fact_161_t__splay_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A] :
% 0.30/0.51 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay.simps(1)
% 0.30/0.51 thf(fact_162_bst__eq_Oelims_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ~ ( linorder_bst_eq @ A @ X )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X4 @ A3 ) )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X4 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.elims(3)
% 0.30/0.51 thf(fact_163_bst__eq_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [L: tree @ A,A2: A,R2: tree @ A] :
% 0.30/0.51 ( ( linorder_bst_eq @ A @ ( node @ A @ L @ A2 @ R2 ) )
% 0.30/0.51 = ( ( linorder_bst_eq @ A @ L )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R2 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X5 @ A2 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A2 @ X5 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.simps(2)
% 0.30/0.51 thf(fact_164_splay__max__eq__splay,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [T2: tree @ A,A2: A] :
% 0.30/0.51 ( ( linorder_bst @ A @ T2 )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ T2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X4 @ A2 ) )
% 0.30/0.51 => ( ( splay_splay_max @ A @ T2 )
% 0.30/0.51 = ( splay_splay @ A @ A2 @ T2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % splay_max_eq_splay
% 0.30/0.51 thf(fact_165_bst__eq_Oelims_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( linorder_bst_eq @ A @ X )
% 0.30/0.51 => ( ( X
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ~ ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X6 @ A3 ) )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X6 ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.elims(2)
% 0.30/0.51 thf(fact_166_bst__eq_Opelims_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ( linorder_bst_eq @ A @ X )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( leaf @ A ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ~ ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X6 @ A3 ) )
% 0.30/0.51 & ! [X6: A] :
% 0.30/0.51 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.pelims(2)
% 0.30/0.51 thf(fact_167_bst__eq_Opelims_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: $o] :
% 0.30/0.51 ( ( ( linorder_bst_eq @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( leaf @ A ) ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X5 @ A3 ) )
% 0.30/0.51 & ! [X5: A] :
% 0.30/0.51 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X5 ) ) ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.pelims(1)
% 0.30/0.51 thf(fact_168_bst__eq_Opelims_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A] :
% 0.30/0.51 ( ~ ( linorder_bst_eq @ A @ X )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 0.30/0.51 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 0.30/0.51 => ( ( linorder_bst_eq @ A @ L2 )
% 0.30/0.51 & ( linorder_bst_eq @ A @ R4 )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ X4 @ A3 ) )
% 0.30/0.51 & ! [X4: A] :
% 0.30/0.51 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 0.30/0.51 => ( ord_less_eq @ A @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % bst_eq.pelims(3)
% 0.30/0.51 thf(fact_169_less__numeral__extra_I4_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.30/0.51 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_numeral_extra(4)
% 0.30/0.51 thf(fact_170_t__splay__simps_I4_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ A2 @ C3 )
% 0.30/0.51 => ( ( ( Ll
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Ll
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(4)
% 0.30/0.51 thf(fact_171_t__splay__simps_I5_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ C3 @ A2 )
% 0.30/0.51 => ( ( ( Lr
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Lr
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(5)
% 0.30/0.51 thf(fact_172_t__splay__simps_I9_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,C3: A,Rr2: tree @ A,L: tree @ A,Rl2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( ord_less @ A @ C3 @ A2 )
% 0.30/0.51 => ( ( ( Rr2
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Rr2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(9)
% 0.30/0.51 thf(fact_173_t__splay__simps_I8_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [B2: A,A2: A,C3: A,Rl2: tree @ A,L: tree @ A,Rr2: tree @ A] :
% 0.30/0.51 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.51 => ( ( ord_less @ A @ A2 @ C3 )
% 0.30/0.51 => ( ( ( Rl2
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Rl2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_simps(8)
% 0.30/0.51 thf(fact_174_nat__add__left__cancel__less,axiom,
% 0.30/0.51 ! [K: nat,M: nat,N: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.30/0.51 = ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat_add_left_cancel_less
% 0.30/0.51 thf(fact_175_add__less__cancel__left,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.51 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.51 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_cancel_left
% 0.30/0.51 thf(fact_176_add__less__cancel__right,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.51 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.51 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_cancel_right
% 0.30/0.51 thf(fact_177_nat__neq__iff,axiom,
% 0.30/0.51 ! [M: nat,N: nat] :
% 0.30/0.51 ( ( M != N )
% 0.30/0.51 = ( ( ord_less @ nat @ M @ N )
% 0.30/0.51 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat_neq_iff
% 0.30/0.51 thf(fact_178_less__not__refl,axiom,
% 0.30/0.51 ! [N: nat] :
% 0.30/0.51 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.51
% 0.30/0.51 % less_not_refl
% 0.30/0.51 thf(fact_179_less__not__refl2,axiom,
% 0.30/0.51 ! [N: nat,M: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ N @ M )
% 0.30/0.51 => ( M != N ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_not_refl2
% 0.30/0.51 thf(fact_180_less__not__refl3,axiom,
% 0.30/0.51 ! [S: nat,T2: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ S @ T2 )
% 0.30/0.51 => ( S != T2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_not_refl3
% 0.30/0.51 thf(fact_181_measure__induct,axiom,
% 0.30/0.51 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.30/0.51 ( ! [X4: A] :
% 0.30/0.51 ( ! [Y6: A] :
% 0.30/0.51 ( ( ord_less @ nat @ ( F @ Y6 ) @ ( F @ X4 ) )
% 0.30/0.51 => ( P @ Y6 ) )
% 0.30/0.51 => ( P @ X4 ) )
% 0.30/0.51 => ( P @ A2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % measure_induct
% 0.30/0.51 thf(fact_182_less__irrefl__nat,axiom,
% 0.30/0.51 ! [N: nat] :
% 0.30/0.51 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.51
% 0.30/0.51 % less_irrefl_nat
% 0.30/0.51 thf(fact_183_nat__less__induct,axiom,
% 0.30/0.51 ! [P: nat > $o,N: nat] :
% 0.30/0.51 ( ! [N2: nat] :
% 0.30/0.51 ( ! [M2: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.51 => ( P @ M2 ) )
% 0.30/0.51 => ( P @ N2 ) )
% 0.30/0.51 => ( P @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat_less_induct
% 0.30/0.51 thf(fact_184_infinite__descent,axiom,
% 0.30/0.51 ! [P: nat > $o,N: nat] :
% 0.30/0.51 ( ! [N2: nat] :
% 0.30/0.51 ( ~ ( P @ N2 )
% 0.30/0.51 => ? [M2: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.51 & ~ ( P @ M2 ) ) )
% 0.30/0.51 => ( P @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % infinite_descent
% 0.30/0.51 thf(fact_185_linorder__neqE__nat,axiom,
% 0.30/0.51 ! [X: nat,Y: nat] :
% 0.30/0.51 ( ( X != Y )
% 0.30/0.51 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.30/0.51 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_neqE_nat
% 0.30/0.51 thf(fact_186_measure__induct__rule,axiom,
% 0.30/0.51 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.30/0.51 ( ! [X4: A] :
% 0.30/0.51 ( ! [Y6: A] :
% 0.30/0.51 ( ( ord_less @ nat @ ( F @ Y6 ) @ ( F @ X4 ) )
% 0.30/0.51 => ( P @ Y6 ) )
% 0.30/0.51 => ( P @ X4 ) )
% 0.30/0.51 => ( P @ A2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % measure_induct_rule
% 0.30/0.51 thf(fact_187_infinite__descent__measure,axiom,
% 0.30/0.51 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.30/0.51 ( ! [X4: A] :
% 0.30/0.51 ( ~ ( P @ X4 )
% 0.30/0.51 => ? [Y6: A] :
% 0.30/0.51 ( ( ord_less @ nat @ ( V @ Y6 ) @ ( V @ X4 ) )
% 0.30/0.51 & ~ ( P @ Y6 ) ) )
% 0.30/0.51 => ( P @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % infinite_descent_measure
% 0.30/0.51 thf(fact_188_less__mono__imp__le__mono,axiom,
% 0.30/0.51 ! [F: nat > nat,I: nat,J: nat] :
% 0.30/0.51 ( ! [I2: nat,J2: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ I2 @ J2 )
% 0.30/0.51 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.30/0.51 => ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.51 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_mono_imp_le_mono
% 0.30/0.51 thf(fact_189_le__neq__implies__less,axiom,
% 0.30/0.51 ! [M: nat,N: nat] :
% 0.30/0.51 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.51 => ( ( M != N )
% 0.30/0.51 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_neq_implies_less
% 0.30/0.51 thf(fact_190_less__or__eq__imp__le,axiom,
% 0.30/0.51 ! [M: nat,N: nat] :
% 0.30/0.51 ( ( ( ord_less @ nat @ M @ N )
% 0.30/0.51 | ( M = N ) )
% 0.30/0.51 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_or_eq_imp_le
% 0.30/0.51 thf(fact_191_le__eq__less__or__eq,axiom,
% 0.30/0.51 ( ( ord_less_eq @ nat )
% 0.30/0.51 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ M3 @ N3 )
% 0.30/0.51 | ( M3 = N3 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_eq_less_or_eq
% 0.30/0.51 thf(fact_192_less__imp__le__nat,axiom,
% 0.30/0.51 ! [M: nat,N: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ M @ N )
% 0.30/0.51 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_imp_le_nat
% 0.30/0.51 thf(fact_193_nat__less__le,axiom,
% 0.30/0.51 ( ( ord_less @ nat )
% 0.30/0.51 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.51 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 0.30/0.51 & ( M3 != N3 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat_less_le
% 0.30/0.51 thf(fact_194_add__less__imp__less__right,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.51 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.51 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_imp_less_right
% 0.30/0.51 thf(fact_195_add__less__imp__less__left,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.51 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.51 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_imp_less_left
% 0.30/0.51 thf(fact_196_add__strict__right__mono,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_strict_right_mono
% 0.30/0.51 thf(fact_197_add__strict__left__mono,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_strict_left_mono
% 0.30/0.51 thf(fact_198_add__strict__mono,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A,D4: A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ C3 @ D4 )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_strict_mono
% 0.30/0.51 thf(fact_199_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.51 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.51 & ( K = L ) )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_mono_thms_linordered_field(1)
% 0.30/0.51 thf(fact_200_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.51 ( ( ( I = J )
% 0.30/0.51 & ( ord_less @ A @ K @ L ) )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_mono_thms_linordered_field(2)
% 0.30/0.51 thf(fact_201_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.51 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.51 & ( ord_less @ A @ K @ L ) )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_mono_thms_linordered_field(5)
% 0.30/0.51 thf(fact_202_less__add__eq__less,axiom,
% 0.30/0.51 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ K @ L )
% 0.30/0.51 => ( ( ( plus_plus @ nat @ M @ L )
% 0.30/0.51 = ( plus_plus @ nat @ K @ N ) )
% 0.30/0.51 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_add_eq_less
% 0.30/0.51 thf(fact_203_trans__less__add2,axiom,
% 0.30/0.51 ! [I: nat,J: nat,M: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ I @ J )
% 0.30/0.51 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % trans_less_add2
% 0.30/0.51 thf(fact_204_trans__less__add1,axiom,
% 0.30/0.51 ! [I: nat,J: nat,M: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ I @ J )
% 0.30/0.51 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % trans_less_add1
% 0.30/0.51 thf(fact_205_add__less__mono1,axiom,
% 0.30/0.51 ! [I: nat,J: nat,K: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ I @ J )
% 0.30/0.51 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_mono1
% 0.30/0.51 thf(fact_206_not__add__less2,axiom,
% 0.30/0.51 ! [J: nat,I: nat] :
% 0.30/0.51 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.30/0.51
% 0.30/0.51 % not_add_less2
% 0.30/0.51 thf(fact_207_not__add__less1,axiom,
% 0.30/0.51 ! [I: nat,J: nat] :
% 0.30/0.51 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.30/0.51
% 0.30/0.51 % not_add_less1
% 0.30/0.51 thf(fact_208_add__less__mono,axiom,
% 0.30/0.51 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ I @ J )
% 0.30/0.51 => ( ( ord_less @ nat @ K @ L )
% 0.30/0.51 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_mono
% 0.30/0.51 thf(fact_209_add__lessD1,axiom,
% 0.30/0.51 ! [I: nat,J: nat,K: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.30/0.51 => ( ord_less @ nat @ I @ K ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_lessD1
% 0.30/0.51 thf(fact_210_mono__nat__linear__lb,axiom,
% 0.30/0.51 ! [F: nat > nat,M: nat,K: nat] :
% 0.30/0.51 ( ! [M4: nat,N2: nat] :
% 0.30/0.51 ( ( ord_less @ nat @ M4 @ N2 )
% 0.30/0.51 => ( ord_less @ nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.30/0.51 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % mono_nat_linear_lb
% 0.30/0.51 thf(fact_211_add__less__le__mono,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A,D4: A] :
% 0.30/0.51 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( ord_less_eq @ A @ C3 @ D4 )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_less_le_mono
% 0.30/0.51 thf(fact_212_add__le__less__mono,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A,B2: A,C3: A,D4: A] :
% 0.30/0.51 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.51 => ( ( ord_less @ A @ C3 @ D4 )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_le_less_mono
% 0.30/0.51 thf(fact_213_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.51 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.51 & ( ord_less_eq @ A @ K @ L ) )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_mono_thms_linordered_field(3)
% 0.30/0.51 thf(fact_214_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.51 ( ( ( ord_less_eq @ A @ I @ J )
% 0.30/0.51 & ( ord_less @ A @ K @ L ) )
% 0.30/0.51 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % add_mono_thms_linordered_field(4)
% 0.30/0.51 thf(fact_215_discrete,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( semiring_numeral_div @ A @ ( type2 @ A ) )
% 0.30/0.51 => ( ( ord_less @ A )
% 0.30/0.51 = ( ^ [A6: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A6 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % discrete
% 0.30/0.51 thf(fact_216_fold__atLeastAtMost__nat_Oinduct,axiom,
% 0.30/0.51 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A1: nat,A23: nat,A33: A] :
% 0.30/0.51 ( ! [F5: nat > A > A,A3: nat,B5: nat,Acc: A] :
% 0.30/0.51 ( ( ~ ( ord_less @ nat @ B5 @ A3 )
% 0.30/0.51 => ( P @ F5 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B5 @ ( F5 @ A3 @ Acc ) ) )
% 0.30/0.51 => ( P @ F5 @ A3 @ B5 @ Acc ) )
% 0.30/0.51 => ( P @ A0 @ A1 @ A23 @ A33 ) ) ).
% 0.30/0.51
% 0.30/0.51 % fold_atLeastAtMost_nat.induct
% 0.30/0.51 thf(fact_217_less__add__one,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % less_add_one
% 0.30/0.51 thf(fact_218_linorder__neqE__linordered__idom,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: A,Y: A] :
% 0.30/0.51 ( ( X != Y )
% 0.30/0.51 => ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.51 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_neqE_linordered_idom
% 0.30/0.51 thf(fact_219_ex__has__greatest__nat__lemma,axiom,
% 0.30/0.51 ! [A: $tType,P: A > $o,K: A,M: A > nat,N: nat] :
% 0.30/0.51 ( ( P @ K )
% 0.30/0.51 => ( ! [X4: A] :
% 0.30/0.51 ( ( P @ X4 )
% 0.30/0.51 => ? [Y6: A] :
% 0.30/0.51 ( ( P @ Y6 )
% 0.30/0.51 & ~ ( ord_less_eq @ nat @ ( M @ Y6 ) @ ( M @ X4 ) ) ) )
% 0.30/0.51 => ? [Y4: A] :
% 0.30/0.51 ( ( P @ Y4 )
% 0.30/0.51 & ~ ( ord_less @ nat @ ( M @ Y4 ) @ ( plus_plus @ nat @ ( M @ K ) @ N ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ex_has_greatest_nat_lemma
% 0.30/0.51 thf(fact_220_t__splay__max_Osimps_I3_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [Rr2: tree @ A,L: tree @ A,B2: A,Rl2: tree @ A,C3: A] :
% 0.30/0.51 ( ( ( Rr2
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Rr2
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.simps(3)
% 0.30/0.51 thf(fact_221_t__splay__max_Osimps_I1_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ( ( splay_878424299ay_max @ A @ ( leaf @ A ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.simps(1)
% 0.30/0.51 thf(fact_222_t__splay__max_Osimps_I2_J,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [L: tree @ A,B2: A] :
% 0.30/0.51 ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 0.30/0.51 = ( one_one @ nat ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.simps(2)
% 0.30/0.51 thf(fact_223_ex__has__greatest__nat,axiom,
% 0.30/0.51 ! [A: $tType,P: A > $o,K: A,M: A > nat,B2: nat] :
% 0.30/0.51 ( ( P @ K )
% 0.30/0.51 => ( ! [Y4: A] :
% 0.30/0.51 ( ( P @ Y4 )
% 0.30/0.51 => ( ord_less @ nat @ ( M @ Y4 ) @ B2 ) )
% 0.30/0.51 => ? [X4: A] :
% 0.30/0.51 ( ( P @ X4 )
% 0.30/0.51 & ! [Y6: A] :
% 0.30/0.51 ( ( P @ Y6 )
% 0.30/0.51 => ( ord_less_eq @ nat @ ( M @ Y6 ) @ ( M @ X4 ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ex_has_greatest_nat
% 0.30/0.51 thf(fact_224_t__splay__max_Oelims,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: nat] :
% 0.30/0.51 ( ( ( splay_878424299ay_max @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 != ( one_one @ nat ) ) )
% 0.30/0.51 => ( ( ? [L2: tree @ A,B5: A] :
% 0.30/0.51 ( X
% 0.30/0.51 = ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 != ( one_one @ nat ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 0.30/0.51 => ~ ( ( ( Rr
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Rr
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.elims
% 0.30/0.51 thf(fact_225_t__splay__max_Opelims,axiom,
% 0.30/0.51 ! [A: $tType] :
% 0.30/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.51 => ! [X: tree @ A,Y: nat] :
% 0.30/0.51 ( ( ( splay_878424299ay_max @ A @ X )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ X )
% 0.30/0.51 => ( ( ( X
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( one_one @ nat ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( leaf @ A ) ) ) )
% 0.30/0.51 => ( ! [L2: tree @ A,B5: A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 0.30/0.51 => ( ( Y
% 0.30/0.51 = ( one_one @ nat ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) ) ) )
% 0.30/0.51 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 0.30/0.51 ( ( X
% 0.30/0.51 = ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 0.30/0.51 => ( ( ( ( Rr
% 0.30/0.51 = ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( one_one @ nat ) ) )
% 0.30/0.51 & ( ( Rr
% 0.30/0.51 != ( leaf @ A ) )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) )
% 0.30/0.51 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % t_splay_max.pelims
% 0.30/0.51 thf(fact_226_fold__atLeastAtMost__nat_Opinduct,axiom,
% 0.30/0.51 ! [A: $tType,A0: nat > A > A,A1: nat,A23: nat,A33: A,P: ( nat > A > A ) > nat > nat > A > $o] :
% 0.30/0.51 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ A0 @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A1 @ ( product_Pair @ nat @ A @ A23 @ A33 ) ) ) )
% 0.30/0.51 => ( ! [F5: nat > A > A,A3: nat,B5: nat,Acc: A] :
% 0.30/0.51 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ F5 @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A3 @ ( product_Pair @ nat @ A @ B5 @ Acc ) ) ) )
% 0.30/0.51 => ( ( ~ ( ord_less @ nat @ B5 @ A3 )
% 0.30/0.51 => ( P @ F5 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B5 @ ( F5 @ A3 @ Acc ) ) )
% 0.30/0.51 => ( P @ F5 @ A3 @ B5 @ Acc ) ) )
% 0.30/0.51 => ( P @ A0 @ A1 @ A23 @ A33 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % fold_atLeastAtMost_nat.pinduct
% 0.30/0.51 thf(fact_227_fold__atLeastAtMost__nat_Opelims,axiom,
% 0.30/0.51 ! [A: $tType,X: nat > A > A,Xa: nat,Xb2: nat,Xc: A,Y: A] :
% 0.30/0.51 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb2 @ Xc )
% 0.30/0.51 = Y )
% 0.30/0.51 => ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ X @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ Xa @ ( product_Pair @ nat @ A @ Xb2 @ Xc ) ) ) )
% 0.30/0.51 => ~ ( ( ( ( ord_less @ nat @ Xb2 @ Xa )
% 0.30/0.51 => ( Y = Xc ) )
% 0.30/0.51 & ( ~ ( ord_less @ nat @ Xb2 @ Xa )
% 0.30/0.51 => ( Y
% 0.30/0.51 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb2 @ ( X @ Xa @ Xc ) ) ) ) )
% 0.30/0.52 => ~ ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ X @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ Xa @ ( product_Pair @ nat @ A @ Xb2 @ Xc ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % fold_atLeastAtMost_nat.pelims
% 0.30/0.52 thf(fact_228_fold__atLeastAtMost__nat_Opsimps,axiom,
% 0.30/0.52 ! [A: $tType,F: nat > A > A,A2: nat,B2: nat,Acc2: A] :
% 0.30/0.52 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ F @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A2 @ ( product_Pair @ nat @ A @ B2 @ Acc2 ) ) ) )
% 0.30/0.52 => ( ( ( ord_less @ nat @ B2 @ A2 )
% 0.30/0.52 => ( ( set_fo292404081st_nat @ A @ F @ A2 @ B2 @ Acc2 )
% 0.30/0.52 = Acc2 ) )
% 0.30/0.52 & ( ~ ( ord_less @ nat @ B2 @ A2 )
% 0.30/0.52 => ( ( set_fo292404081st_nat @ A @ F @ A2 @ B2 @ Acc2 )
% 0.30/0.52 = ( set_fo292404081st_nat @ A @ F @ ( plus_plus @ nat @ A2 @ ( one_one @ nat ) ) @ B2 @ ( F @ A2 @ Acc2 ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % fold_atLeastAtMost_nat.psimps
% 0.30/0.52 thf(fact_229_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.30/0.52 ! [A: $tType,X: nat > A > A,Xa: nat,Xb2: nat,Xc: A,Y: A] :
% 0.30/0.52 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb2 @ Xc )
% 0.30/0.52 = Y )
% 0.30/0.52 => ( ( ( ord_less @ nat @ Xb2 @ Xa )
% 0.30/0.52 => ( Y = Xc ) )
% 0.30/0.52 & ( ~ ( ord_less @ nat @ Xb2 @ Xa )
% 0.30/0.52 => ( Y
% 0.30/0.52 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb2 @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % fold_atLeastAtMost_nat.elims
% 0.30/0.52 thf(fact_230_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( set_fo292404081st_nat @ A )
% 0.30/0.52 = ( ^ [F6: nat > A > A,A6: nat,B6: nat,Acc3: A] : ( if @ A @ ( ord_less @ nat @ B6 @ A6 ) @ Acc3 @ ( set_fo292404081st_nat @ A @ F6 @ ( plus_plus @ nat @ A6 @ ( one_one @ nat ) ) @ B6 @ ( F6 @ A6 @ Acc3 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % fold_atLeastAtMost_nat.simps
% 0.30/0.52 thf(fact_231_complete__interval,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A,P: A > $o] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ( ( P @ A2 )
% 0.30/0.52 => ( ~ ( P @ B2 )
% 0.30/0.52 => ? [C2: A] :
% 0.30/0.52 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.52 & ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.52 & ! [X6: A] :
% 0.30/0.52 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.30/0.52 & ( ord_less @ A @ X6 @ C2 ) )
% 0.30/0.52 => ( P @ X6 ) )
% 0.30/0.52 & ! [D5: A] :
% 0.30/0.52 ( ! [X4: A] :
% 0.30/0.52 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 0.30/0.52 & ( ord_less @ A @ X4 @ D5 ) )
% 0.30/0.52 => ( P @ X4 ) )
% 0.30/0.52 => ( ord_less_eq @ A @ D5 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % complete_interval
% 0.30/0.52 thf(fact_232_order_Onot__eq__order__implies__strict,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A] :
% 0.30/0.52 ( ( A2 != B2 )
% 0.30/0.52 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.52 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.not_eq_order_implies_strict
% 0.30/0.52 thf(fact_233_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: $tType,B: $tType] :
% 0.30/0.52 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/0.52 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/0.52 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 0.30/0.52 ( ( A2
% 0.30/0.52 = ( F @ B2 ) )
% 0.30/0.52 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.52 => ( ! [X4: B,Y4: B] :
% 0.30/0.52 ( ( ord_less @ B @ X4 @ Y4 )
% 0.30/0.52 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.52 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_234_ord__less__eq__subst,axiom,
% 0.30/0.52 ! [A: $tType,B: $tType] :
% 0.30/0.52 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.30/0.52 & ( ord @ A @ ( type2 @ A ) ) )
% 0.30/0.52 => ! [A2: A,B2: A,F: A > B,C3: B] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ( ( ( F @ B2 )
% 0.30/0.52 = C3 )
% 0.30/0.52 => ( ! [X4: A,Y4: A] :
% 0.30/0.52 ( ( ord_less @ A @ X4 @ Y4 )
% 0.30/0.52 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.52 => ( ord_less @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_subst
% 0.30/0.52 thf(fact_235_order__less__subst1,axiom,
% 0.30/0.52 ! [A: $tType,B: $tType] :
% 0.30/0.52 ( ( ( order @ B @ ( type2 @ B ) )
% 0.30/0.52 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/0.52 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.30/0.52 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.52 => ( ! [X4: B,Y4: B] :
% 0.30/0.52 ( ( ord_less @ B @ X4 @ Y4 )
% 0.30/0.52 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.52 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_subst1
% 0.30/0.52 thf(fact_236_order__less__subst2,axiom,
% 0.30/0.52 ! [A: $tType,C: $tType] :
% 0.30/0.52 ( ( ( order @ C @ ( type2 @ C ) )
% 0.30/0.52 & ( order @ A @ ( type2 @ A ) ) )
% 0.30/0.52 => ! [A2: A,B2: A,F: A > C,C3: C] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ( ( ord_less @ C @ ( F @ B2 ) @ C3 )
% 0.30/0.52 => ( ! [X4: A,Y4: A] :
% 0.30/0.52 ( ( ord_less @ A @ X4 @ Y4 )
% 0.30/0.52 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.30/0.52 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_subst2
% 0.30/0.52 thf(fact_237_lt__ex,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A] :
% 0.30/0.52 ? [Y4: A] : ( ord_less @ A @ Y4 @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % lt_ex
% 0.30/0.52 thf(fact_238_gt__ex,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( no_top @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A] :
% 0.30/0.52 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 0.30/0.52
% 0.30/0.52 % gt_ex
% 0.30/0.52 thf(fact_239_neqE,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % neqE
% 0.30/0.52 thf(fact_240_neq__iff,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % neq_iff
% 0.30/0.52 thf(fact_241_order_Oasym,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_242_dense,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ? [Z2: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Z2 )
% 0.30/0.52 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dense
% 0.30/0.52 thf(fact_243_less__imp__neq,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_244_less__asym,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_asym
% 0.30/0.52 thf(fact_245_less__asym_H,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_asym'
% 0.30/0.52 thf(fact_246_less__trans,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A,Z5: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ( ( ord_less @ A @ Y @ Z5 )
% 0.30/0.52 => ( ord_less @ A @ X @ Z5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_trans
% 0.30/0.52 thf(fact_247_less__linear,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 | ( X = Y )
% 0.30/0.52 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_linear
% 0.30/0.52 thf(fact_248_less__irrefl,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A] :
% 0.30/0.52 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_irrefl
% 0.30/0.52 thf(fact_249_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( ord @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.52 ( ( A2 = B2 )
% 0.30/0.52 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.52 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_250_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( ord @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.52 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.52 => ( ( B2 = C3 )
% 0.30/0.52 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_251_dual__order_Oasym,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [B2: A,A2: A] :
% 0.30/0.52 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.52 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_252_less__imp__not__eq,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( order @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_not_eq
% 0.30/0.52 thf(fact_253_less__not__sym,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( preorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [X: A,Y: A] :
% 0.30/0.52 ( ( ord_less @ A @ X @ Y )
% 0.30/0.52 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_not_sym
% 0.30/0.52 thf(fact_254_less__induct,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [P: A > $o,A2: A] :
% 0.30/0.52 ( ! [X4: A] :
% 0.30/0.52 ( ! [Y6: A] :
% 0.30/0.52 ( ( ord_less @ A @ Y6 @ X4 )
% 0.30/0.52 => ( P @ Y6 ) )
% 0.30/0.52 => ( P @ X4 ) )
% 0.30/0.52 => ( P @ A2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_induct
% 0.30/0.52 thf(fact_255_antisym__conv3,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ! [Y: A,X: A] :
% 0.30/0.52 ( ~ ( ord_less @ A @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52
% 0.30/0.52 %----Subclasses (4)
% 0.30/0.52 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ( type @ A @ ( type2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ( order @ A @ ( type2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.30/0.52 ! [A: $tType] :
% 0.30/0.52 ( ( linorder @ A @ ( type2 @ A ) )
% 0.30/0.52 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 %----Type constructors (22)
% 0.30/0.52 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.52 ! [A7: $tType,A8: $tType] :
% 0.30/0.52 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.30/0.52 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.52 ! [A7: $tType,A8: $tType] :
% 0.30/0.52 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.30/0.52 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.52 ! [A7: $tType,A8: $tType] :
% 0.30/0.52 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.30/0.52 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.30/0.52 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.30/0.52 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.30/0.52 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.30/0.52 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div,axiom,
% 0.30/0.52 semiring_numeral_div @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.30/0.52 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.30/0.52 wellorder @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.30/0.52 preorder @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.52 linorder @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.30/0.52 no_top @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.30/0.52 order @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.30/0.52 ord @ nat @ ( type2 @ nat ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.30/0.52 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.30/0.52 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.30/0.52 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.30/0.52 preorder @ $o @ ( type2 @ $o ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.30/0.52 linorder @ $o @ ( type2 @ $o ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.30/0.52 order @ $o @ ( type2 @ $o ) ).
% 0.30/0.52
% 0.30/0.52 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.30/0.52 ord @ $o @ ( type2 @ $o ) ).
% 0.30/0.52
% 0.30/0.52 %----Helper facts (3)
% 0.30/0.52 thf(help_If_3_1_T,axiom,
% 0.30/0.52 ! [P: $o] :
% 0.30/0.52 ( ( P = $true )
% 0.30/0.52 | ( P = $false ) ) ).
% 0.30/0.52
% 0.30/0.52 thf(help_If_2_1_T,axiom,
% 0.30/0.52 ! [A: $tType,X: A,Y: A] :
% 0.30/0.52 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.52 = Y ) ).
% 0.30/0.52
% 0.30/0.52 thf(help_If_1_1_T,axiom,
% 0.30/0.52 ! [A: $tType,X: A,Y: A] :
% 0.30/0.52 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.52 = X ) ).
% 0.30/0.52
% 0.30/0.52 %----Free types (1)
% 0.30/0.52 thf(tfree_0,hypothesis,
% 0.30/0.52 linorder @ a @ ( type2 @ a ) ).
% 0.30/0.52
% 0.30/0.52 %----Conjectures (1)
% 0.30/0.52 thf(conj_0,conjecture,
% 0.30/0.52 linorder_bst @ a @ ( splay_859309299xt_s_t @ a @ f @ a2 ) ).
% 0.30/0.52
% 0.30/0.52 %------------------------------------------------------------------------------
% 0.30/0.52 ------------------------
% 2.94/1.51 ---- Embedded in THF ---
% 2.94/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.94/1.51 %%% Generated on Tue Feb 24 06:11:37 EST 2026
% 2.94/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.94/1.51 %%% Logic specification used:
% 2.94/1.51 %%% thf(spec, logic, $$dhol).
% 2.94/1.51
% 2.94/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2DTF28704.p
% 2.94/1.51 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t, type, splay_2011811431op_s_t: ($tType > $tType)).
% 2.94/1.51 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.94/1.51 thf(ty_t_Tree_Otree, type, tree: ($tType > $tType)).
% 2.94/1.51 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.94/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.94/1.51 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.94/1.51 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.94/1.51 thf(ty_tf_a, type, a: $tType).
% 2.94/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Divides_Osemiring__numeral__div, type, semiring_numeral_div: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.94/1.51 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.94/1.51 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.94/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.94/1.51 thf(sy_c_List_Odistinct, type, distinct: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.94/1.51 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.94/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.94/1.51 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.94/1.51 thf(sy_c_Product__Type_Ocurry, type, product_curry: (!> [A:$tType,B:$tType,C:$tType]: (((((product_prod @ A) @ B) > C) > (A > (B > C)))))).
% 2.94/1.51 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.94/1.51 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.94/1.51 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.94/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.94/1.51 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat, type, set_fo292404081st_nat: (!> [A:$tType]: (((nat > (A > A)) > (nat > (nat > (A > A))))))).
% 2.94/1.51 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel, type, set_fo2092542664at_rel: (!> [A:$tType]: ((((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) > (((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) > $o))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Odelete, type, splay_delete: (!> [A:$tType]: ((A > ((tree @ A) > (tree @ A)))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Oinsert, type, splay_insert: (!> [A:$tType]: ((A > ((tree @ A) > (tree @ A)))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Ois__root, type, splay_is_root: (!> [A:$tType]: ((A > ((tree @ A) > $o))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Osplay, type, splay_splay: (!> [A:$tType]: ((A > ((tree @ A) > (tree @ A)))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Osplay__max, type, splay_splay_max: (!> [A:$tType]: (((tree @ A) > (tree @ A))))).
% 2.94/1.51 thf(sy_c_Splay__Tree_Osplay__rel, type, splay_splay_rel: (!> [A:$tType]: ((((product_prod @ A) @ (tree @ A)) > (((product_prod @ A) @ (tree @ A)) > $o))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t, type, splay_859309299xt_s_t: (!> [A:$tType]: (((splay_2011811431op_s_t @ A) > ((tree @ A) > (tree @ A)))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t__rel, type, splay_1102316486_t_rel: (!> [A:$tType]: ((((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) > (((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) > $o))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_ODelete, type, splay_705249169Delete: (!> [A:$tType]: ((A > (splay_2011811431op_s_t @ A))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OInsert, type, splay_1105473951Insert: (!> [A:$tType]: ((A > (splay_2011811431op_s_t @ A))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OSplay, type, splay_2088287777_Splay: (!> [A:$tType]: ((A > (splay_2011811431op_s_t @ A))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Ocase__op_092_060_094sub_062s_092_060_094sub_062t, type, splay_549499974op_s_t: (!> [A:$tType,B:$tType]: (((A > B) > ((A > B) > ((A > B) > ((splay_2011811431op_s_t @ A) > B))))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orec__op_092_060_094sub_062s_092_060_094sub_062t, type, splay_2144473850op_s_t: (!> [A:$tType,C:$tType]: (((A > C) > ((A > C) > ((A > C) > ((splay_2011811431op_s_t @ A) > C))))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orel__op_092_060_094sub_062s_092_060_094sub_062t, type, splay_434753539op_s_t: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((splay_2011811431op_s_t @ A) > ((splay_2011811431op_s_t @ B) > $o)))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Oset__op_092_060_094sub_062s_092_060_094sub_062t, type, splay_1816468620op_s_t: (!> [A:$tType]: (((splay_2011811431op_s_t @ A) > (set @ A))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay, type, splay_914434265_splay: (!> [A:$tType]: ((A > ((tree @ A) > nat))))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max, type, splay_878424299ay_max: (!> [A:$tType]: (((tree @ A) > nat)))).
% 2.94/1.51 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel, type, splay_1816415694ax_rel: (!> [A:$tType]: (((tree @ A) > ((tree @ A) > $o))))).
% 2.94/1.51 thf(sy_c_Tree_Oinorder, type, inorder: (!> [A:$tType]: (((tree @ A) > (list @ A))))).
% 2.94/1.51 thf(sy_c_Tree_Olinorder__class_Obst, type, linorder_bst: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.94/1.51 thf(sy_c_Tree_Olinorder__class_Obst__eq, type, linorder_bst_eq: (!> [A:$tType]: (((tree @ A) > $o)))).
% 2.94/1.51 thf(sy_c_Tree_Olinorder__class_Obst__eq__rel, type, linorder_bst_eq_rel: (!> [A:$tType]: (((tree @ A) > ((tree @ A) > $o))))).
% 2.94/1.51 thf(sy_c_Tree_Olinorder__class_Obst__rel, type, linorder_bst_rel: (!> [A:$tType]: (((tree @ A) > ((tree @ A) > $o))))).
% 2.94/1.51 thf(sy_c_Tree_Opreorder, type, preorder2: (!> [A:$tType]: (((tree @ A) > (list @ A))))).
% 2.94/1.51 thf(sy_c_Tree_Otree_OLeaf, type, leaf: (!> [A:$tType]: ((tree @ A)))).
% 2.94/1.51 thf(sy_c_Tree_Otree_ONode, type, node: (!> [A:$tType]: (((tree @ A) > (A > ((tree @ A) > (tree @ A))))))).
% 2.94/1.51 thf(sy_c_Tree_Otree_Oset__tree, type, set_tree: (!> [A:$tType]: (((tree @ A) > (set @ A))))).
% 2.94/1.51 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.94/1.51 thf(sy_c_Wellfounded_Olex__prod, type, lex_prod: (!> [A:$tType,B:$tType]: (((set @ ((product_prod @ A) @ A)) > ((set @ ((product_prod @ B) @ B)) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.94/1.51 thf(sy_c_Wellfounded_Omeasure, type, measure: (!> [A:$tType]: (((A > nat) > (set @ ((product_prod @ A) @ A)))))).
% 2.94/1.51 thf(sy_c_Wfrec_Osame__fst, type, same_fst: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > (set @ ((product_prod @ B) @ B))) > (set @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)))))))).
% 2.94/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.94/1.51 thf(sy_v_a____, type, a2: (tree @ a)).
% 2.94/1.51 thf(sy_v_f____, type, f: (splay_2011811431op_s_t @ a)).
% 2.94/1.51 thf(fact_0__C2_C, axiom, ((linorder_bst @ a) @ a2)).
% 2.94/1.51 thf(fact_1_bst__delete, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ (((splay_delete @ A) @ A2) @ T2))))))))).
% 2.94/1.51 thf(fact_2_bst__insert, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ (((splay_insert @ A) @ A2) @ T2))))))))).
% 2.94/1.51 thf(fact_3_bst__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ ((splay_splay_max @ A) @ T2))))))))).
% 2.94/1.51 thf(fact_4_bst__eq__if__bst, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => ((linorder_bst_eq @ A) @ T2)))))))).
% 2.94/1.51 thf(fact_5_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: (((((splay_859309299xt_s_t @ A) @ ((splay_705249169Delete @ A) @ A2)) @ T2) = (((splay_delete @ A) @ A2) @ T2)))))))).
% 2.94/1.51 thf(fact_6_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: (((((splay_859309299xt_s_t @ A) @ ((splay_1105473951Insert @ A) @ A2)) @ T2) = (((splay_insert @ A) @ A2) @ T2)))))))).
% 2.94/1.51 thf(fact_7_bst__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((linorder_bst @ A) @ (((splay_splay @ A) @ A2) @ T2))))))))).
% 2.94/1.51 thf(fact_8_bst_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_bst @ A) @ (leaf @ A)))))).
% 2.94/1.51 thf(fact_9_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: (((((splay_859309299xt_s_t @ A) @ ((splay_2088287777_Splay @ A) @ A2)) @ T2) = (((splay_splay @ A) @ A2) @ T2)))))))).
% 2.94/1.51 thf(fact_10_splay__max__eq__splay__ex, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => (? [A3:A]: ((((splay_splay_max @ A) @ T2) = (((splay_splay @ A) @ A3) @ T2))))))))))).
% 2.94/1.51 thf(fact_11_distinct__preorder__if__bst, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => ((distinct @ A) @ ((preorder2 @ A) @ T2))))))))).
% 2.94/1.51 thf(fact_12_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I3_J, axiom, (! [A:$tType,X3:A,Y3:A]: (((((splay_705249169Delete @ A) @ X3) = ((splay_705249169Delete @ A) @ Y3)) = (X3 = Y3))))).
% 2.94/1.51 thf(fact_13_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I2_J, axiom, (! [A:$tType,X2:A,Y2:A]: (((((splay_1105473951Insert @ A) @ X2) = ((splay_1105473951Insert @ A) @ Y2)) = (X2 = Y2))))).
% 2.94/1.51 thf(fact_14_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I1_J, axiom, (! [A:$tType,X1:A,Y1:A]: (((((splay_2088287777_Splay @ A) @ X1) = ((splay_2088287777_Splay @ A) @ Y1)) = (X1 = Y1))))).
% 2.94/1.51 thf(fact_15_splay__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: ((((((splay_splay @ A) @ A2) @ T2) = (leaf @ A)) = (T2 = (leaf @ A))))))))).
% 2.94/1.51 thf(fact_16_splay__max__Leaf__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: (((((splay_splay_max @ A) @ T2) = (leaf @ A)) = (T2 = (leaf @ A))))))))).
% 2.94/1.51 thf(fact_17_splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_splay @ A) @ A2) @ (leaf @ A)) = (leaf @ A)))))))).
% 2.94/1.51 thf(fact_18_splay__max_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((splay_splay_max @ A) @ (leaf @ A)) = (leaf @ A)))))).
% 2.94/1.51 thf(fact_19_bst__eq_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_bst_eq @ A) @ (leaf @ A)))))).
% 2.94/1.51 thf(fact_20_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I5_J, axiom, (! [A:$tType,X2:A,X3:A]: ((((splay_1105473951Insert @ A) @ X2) != ((splay_705249169Delete @ A) @ X3))))).
% 2.94/1.51 thf(fact_21_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I3_J, axiom, (! [A:$tType,X1:A,X3:A]: ((((splay_2088287777_Splay @ A) @ X1) != ((splay_705249169Delete @ A) @ X3))))).
% 2.94/1.51 thf(fact_22_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I1_J, axiom, (! [A:$tType,X1:A,X2:A]: ((((splay_2088287777_Splay @ A) @ X1) != ((splay_1105473951Insert @ A) @ X2))))).
% 2.94/1.51 thf(fact_23_nxt_092_060_094sub_062s_092_060_094sub_062t_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(splay_2011811431op_s_t @ A),Xa:(tree @ A),Y:(tree @ A)]: ((((((splay_859309299xt_s_t @ A) @ X) @ Xa) = Y) => ((! [A3:A]: (((X = ((splay_2088287777_Splay @ A) @ A3)) => (Y != (((splay_splay @ A) @ A3) @ Xa))))) => ((! [A3:A]: (((X = ((splay_1105473951Insert @ A) @ A3)) => (Y != (((splay_insert @ A) @ A3) @ Xa))))) => (~ ((! [A3:A]: (((X = ((splay_705249169Delete @ A) @ A3)) => (Y != (((splay_delete @ A) @ A3) @ Xa)))))))))))))))).
% 2.94/1.51 thf(fact_24_op_092_060_094sub_062s_092_060_094sub_062t_Oinduct, axiom, (! [A:$tType,P:((splay_2011811431op_s_t @ A) > $o),Op_s_t:(splay_2011811431op_s_t @ A)]: (((! [X4:A]: ((P @ ((splay_2088287777_Splay @ A) @ X4)))) => ((! [X4:A]: ((P @ ((splay_1105473951Insert @ A) @ X4)))) => ((! [X4:A]: ((P @ ((splay_705249169Delete @ A) @ X4)))) => (P @ Op_s_t))))))).
% 2.94/1.51 thf(fact_25_nxt_092_060_094sub_062s_092_060_094sub_062t_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((splay_2011811431op_s_t @ A) > ((tree @ A) > $o)),A0:(splay_2011811431op_s_t @ A),A1:(tree @ A)]: (((! [A3:A,X12:(tree @ A)]: (((P @ ((splay_2088287777_Splay @ A) @ A3)) @ X12))) => ((! [A3:A,X12:(tree @ A)]: (((P @ ((splay_1105473951Insert @ A) @ A3)) @ X12))) => ((! [A3:A,X12:(tree @ A)]: (((P @ ((splay_705249169Delete @ A) @ A3)) @ X12))) => ((P @ A0) @ A1)))))))))).
% 2.94/1.51 thf(fact_26_op_092_060_094sub_062s_092_060_094sub_062t_Oexhaust, axiom, (! [A:$tType,Y:(splay_2011811431op_s_t @ A)]: (((! [X12:A]: ((Y != ((splay_2088287777_Splay @ A) @ X12)))) => ((! [X22:A]: ((Y != ((splay_1105473951Insert @ A) @ X22)))) => (~ ((! [X32:A]: ((Y != ((splay_705249169Delete @ A) @ X32))))))))))).
% 2.94/1.51 thf(fact_27_op_092_060_094sub_062s_092_060_094sub_062t_Oset__cases, axiom, (! [A:$tType,E:A,A2:(splay_2011811431op_s_t @ A)]: (((((member @ A) @ E) @ ((splay_1816468620op_s_t @ A) @ A2)) => ((A2 != ((splay_2088287777_Splay @ A) @ E)) => ((A2 != ((splay_1105473951Insert @ A) @ E)) => (A2 = ((splay_705249169Delete @ A) @ E)))))))).
% 2.94/1.51 thf(fact_28_nxt_092_060_094sub_062s_092_060_094sub_062t_Opelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(splay_2011811431op_s_t @ A),Xa:(tree @ A),Y:(tree @ A)]: ((((((splay_859309299xt_s_t @ A) @ X) @ Xa) = Y) => ((((accp @ ((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A))) @ (splay_1102316486_t_rel @ A)) @ ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ X) @ Xa)) => ((! [A3:A]: (((X = ((splay_2088287777_Splay @ A) @ A3)) => ((Y = (((splay_splay @ A) @ A3) @ Xa)) => (~ ((((accp @ ((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A))) @ (splay_1102316486_t_rel @ A)) @ ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_2088287777_Splay @ A) @ A3)) @ Xa)))))))) => ((! [A3:A]: (((X = ((splay_1105473951Insert @ A) @ A3)) => ((Y = (((splay_insert @ A) @ A3) @ Xa)) => (~ ((((accp @ ((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A))) @ (splay_1102316486_t_rel @ A)) @ ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_1105473951Insert @ A) @ A3)) @ Xa)))))))) => (~ ((! [A3:A]: (((X = ((splay_705249169Delete @ A) @ A3)) => ((Y = (((splay_delete @ A) @ A3) @ Xa)) => (~ ((((accp @ ((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A))) @ (splay_1102316486_t_rel @ A)) @ ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_705249169Delete @ A) @ A3)) @ Xa)))))))))))))))))))).
% 2.94/1.51 thf(fact_29_nxt_092_060_094sub_062s_092_060_094sub_062t_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:((product_prod @ (splay_2011811431op_s_t @ A)) @ (tree @ A))]: (((! [A3:A,T3:(tree @ A)]: ((X != ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_2088287777_Splay @ A) @ A3)) @ T3)))) => ((! [A3:A,T3:(tree @ A)]: ((X != ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_1105473951Insert @ A) @ A3)) @ T3)))) => (~ ((! [A3:A,T3:(tree @ A)]: ((X != ((((product_Pair @ (splay_2011811431op_s_t @ A)) @ (tree @ A)) @ ((splay_705249169Delete @ A) @ A3)) @ T3)))))))))))))).
% 2.94/1.51 thf(fact_30_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(splay_2011811431op_s_t @ A),B2:(splay_2011811431op_s_t @ B)]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ A2) @ B2) => ((! [X4:A]: (((A2 = ((splay_2088287777_Splay @ A) @ X4)) => (! [Y4:B]: (((B2 = ((splay_2088287777_Splay @ B) @ Y4)) => (~ (((R @ X4) @ Y4))))))))) => ((! [Xa2:A]: (((A2 = ((splay_1105473951Insert @ A) @ Xa2)) => (! [Ya:B]: (((B2 = ((splay_1105473951Insert @ B) @ Ya)) => (~ (((R @ Xa2) @ Ya))))))))) => (~ ((! [Xb:A]: (((A2 = ((splay_705249169Delete @ A) @ Xb)) => (! [Yb:B]: (((B2 = ((splay_705249169Delete @ B) @ Yb)) => (~ (((R @ Xb) @ Yb))))))))))))))))).
% 2.94/1.51 thf(fact_31_op_092_060_094sub_062s_092_060_094sub_062t_Orel__induct, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X:(splay_2011811431op_s_t @ A),Y:(splay_2011811431op_s_t @ B),Q:((splay_2011811431op_s_t @ A) > ((splay_2011811431op_s_t @ B) > $o))]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ X) @ Y) => ((! [A12:A,B1:B]: ((((R @ A12) @ B1) => ((Q @ ((splay_2088287777_Splay @ A) @ A12)) @ ((splay_2088287777_Splay @ B) @ B1))))) => ((! [A22:A,B22:B]: ((((R @ A22) @ B22) => ((Q @ ((splay_1105473951Insert @ A) @ A22)) @ ((splay_1105473951Insert @ B) @ B22))))) => ((! [A32:A,B3:B]: ((((R @ A32) @ B3) => ((Q @ ((splay_705249169Delete @ A) @ A32)) @ ((splay_705249169Delete @ B) @ B3))))) => ((Q @ X) @ Y)))))))).
% 2.94/1.51 thf(fact_32_distinct__inorder__if__bst, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((linorder_bst @ A) @ T2) => ((distinct @ A) @ ((inorder @ A) @ T2))))))))).
% 2.94/1.51 thf(fact_33_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I15_J, axiom, (! [C:$tType,A:$tType,F1:(A > C),F2:(A > C),F3:(A > C),X3:A]: ((((((((splay_2144473850op_s_t @ A) @ C) @ F1) @ F2) @ F3) @ ((splay_705249169Delete @ A) @ X3)) = (F3 @ X3))))).
% 2.94/1.51 thf(fact_34_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I14_J, axiom, (! [C:$tType,A:$tType,F1:(A > C),F2:(A > C),F3:(A > C),X2:A]: ((((((((splay_2144473850op_s_t @ A) @ C) @ F1) @ F2) @ F3) @ ((splay_1105473951Insert @ A) @ X2)) = (F2 @ X2))))).
% 2.94/1.51 thf(fact_35_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I13_J, axiom, (! [C:$tType,A:$tType,F1:(A > C),F2:(A > C),F3:(A > C),X1:A]: ((((((((splay_2144473850op_s_t @ A) @ C) @ F1) @ F2) @ F3) @ ((splay_2088287777_Splay @ A) @ X1)) = (F1 @ X1))))).
% 2.94/1.51 thf(fact_36_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I12_J, axiom, (! [B:$tType,A:$tType,F1:(A > B),F2:(A > B),F3:(A > B),X3:A]: ((((((((splay_549499974op_s_t @ A) @ B) @ F1) @ F2) @ F3) @ ((splay_705249169Delete @ A) @ X3)) = (F3 @ X3))))).
% 2.94/1.51 thf(fact_37_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I11_J, axiom, (! [B:$tType,A:$tType,F1:(A > B),F2:(A > B),F3:(A > B),X2:A]: ((((((((splay_549499974op_s_t @ A) @ B) @ F1) @ F2) @ F3) @ ((splay_1105473951Insert @ A) @ X2)) = (F2 @ X2))))).
% 2.94/1.51 thf(fact_38_insert_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:((product_prod @ A) @ (tree @ A))]: ((~ ((! [X4:A,T3:(tree @ A)]: ((X != ((((product_Pair @ A) @ (tree @ A)) @ X4) @ T3)))))))))))).
% 2.94/1.51 thf(fact_39_op_092_060_094sub_062s_092_060_094sub_062t_Orel__eq, axiom, (! [A:$tType]: (((((splay_434753539op_s_t @ A) @ A) @ (^ [Y5:A,Z:A]: ((Y5 = Z)))) = (^ [Y5:(splay_2011811431op_s_t @ A),Z:(splay_2011811431op_s_t @ A)]: ((Y5 = Z))))))).
% 2.94/1.51 thf(fact_40_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cong, axiom, (! [A:$tType,B:$tType,X:(splay_2011811431op_s_t @ A),Ya2:(splay_2011811431op_s_t @ A),Y:(splay_2011811431op_s_t @ B),Xa:(splay_2011811431op_s_t @ B),R:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya2) => ((Y = Xa) => ((! [Z2:A,Yb:B]: (((((member @ A) @ Z2) @ ((splay_1816468620op_s_t @ A) @ Ya2)) => ((((member @ B) @ Yb) @ ((splay_1816468620op_s_t @ B) @ Xa)) => (((R @ Z2) @ Yb) = ((Ra @ Z2) @ Yb)))))) => ((((((splay_434753539op_s_t @ A) @ B) @ R) @ X) @ Y) = (((((splay_434753539op_s_t @ A) @ B) @ Ra) @ Ya2) @ Xa)))))))).
% 2.94/1.51 thf(fact_41_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(splay_2011811431op_s_t @ B)]: (((! [X4:B]: (((Ra @ X4) @ X4))) => (((((splay_434753539op_s_t @ B) @ B) @ Ra) @ X) @ X))))).
% 2.94/1.51 thf(fact_42_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X:(splay_2011811431op_s_t @ A),Y:(splay_2011811431op_s_t @ B),Ra:(A > (B > $o))]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ X) @ Y) => ((! [Z2:A,Yb:B]: (((((member @ A) @ Z2) @ ((splay_1816468620op_s_t @ A) @ X)) => ((((member @ B) @ Yb) @ ((splay_1816468620op_s_t @ B) @ Y)) => (((R @ Z2) @ Yb) => ((Ra @ Z2) @ Yb)))))) => (((((splay_434753539op_s_t @ A) @ B) @ Ra) @ X) @ Y)))))).
% 2.94/1.51 thf(fact_43_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl__strong, axiom, (! [A:$tType,X:(splay_2011811431op_s_t @ A),Ra:(A > (A > $o))]: (((! [Z2:A]: (((((member @ A) @ Z2) @ ((splay_1816468620op_s_t @ A) @ X)) => ((Ra @ Z2) @ Z2)))) => (((((splay_434753539op_s_t @ A) @ A) @ Ra) @ X) @ X))))).
% 2.94/1.51 thf(fact_44_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:A,Y1:B]: ((((R @ X1) @ Y1) => (((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_2088287777_Splay @ A) @ X1)) @ ((splay_2088287777_Splay @ B) @ Y1)))))).
% 2.94/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.94/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member @ A) @ X5) @ A4)))) = A4)))).
% 2.94/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.94/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.94/1.51 thf(fact_49_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X2:A,Y2:B]: ((((R @ X2) @ Y2) => (((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_1105473951Insert @ A) @ X2)) @ ((splay_1105473951Insert @ B) @ Y2)))))).
% 2.94/1.51 thf(fact_50_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I3_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X3:A,Y3:B]: ((((R @ X3) @ Y3) => (((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_705249169Delete @ A) @ X3)) @ ((splay_705249169Delete @ B) @ Y3)))))).
% 2.94/1.51 thf(fact_51_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:A,Y1:B]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_2088287777_Splay @ A) @ X1)) @ ((splay_2088287777_Splay @ B) @ Y1)) = ((R @ X1) @ Y1))))).
% 2.94/1.51 thf(fact_52_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X2:A,Y2:B]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_1105473951Insert @ A) @ X2)) @ ((splay_1105473951Insert @ B) @ Y2)) = ((R @ X2) @ Y2))))).
% 2.94/1.51 thf(fact_53_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I3_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X3:A,Y3:B]: (((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_705249169Delete @ A) @ X3)) @ ((splay_705249169Delete @ B) @ Y3)) = ((R @ X3) @ Y3))))).
% 2.94/1.51 thf(fact_54_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I1_J, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ ((splay_1816468620op_s_t @ A) @ ((splay_2088287777_Splay @ A) @ A2)))))).
% 2.94/1.51 thf(fact_55_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I2_J, axiom, (! [A:$tType,Aa:A]: ((((member @ A) @ Aa) @ ((splay_1816468620op_s_t @ A) @ ((splay_1105473951Insert @ A) @ Aa)))))).
% 2.94/1.51 thf(fact_56_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I3_J, axiom, (! [A:$tType,Ab:A]: ((((member @ A) @ Ab) @ ((splay_1816468620op_s_t @ A) @ ((splay_705249169Delete @ A) @ Ab)))))).
% 2.94/1.51 thf(fact_57_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:A,Y2:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_2088287777_Splay @ A) @ X1)) @ ((splay_1105473951Insert @ B) @ Y2))))))).
% 2.94/1.51 thf(fact_58_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y2:A,X1:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_1105473951Insert @ A) @ Y2)) @ ((splay_2088287777_Splay @ B) @ X1))))))).
% 2.94/1.51 thf(fact_59_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I3_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:A,Y3:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_2088287777_Splay @ A) @ X1)) @ ((splay_705249169Delete @ B) @ Y3))))))).
% 2.94/1.51 thf(fact_60_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I4_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y3:A,X1:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_705249169Delete @ A) @ Y3)) @ ((splay_2088287777_Splay @ B) @ X1))))))).
% 2.94/1.51 thf(fact_61_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I5_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X2:A,Y3:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_1105473951Insert @ A) @ X2)) @ ((splay_705249169Delete @ B) @ Y3))))))).
% 2.94/1.51 thf(fact_62_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I6_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y3:A,X2:B]: ((~ ((((((splay_434753539op_s_t @ A) @ B) @ R) @ ((splay_705249169Delete @ A) @ Y3)) @ ((splay_1105473951Insert @ B) @ X2))))))).
% 2.94/1.51 thf(fact_63_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I10_J, axiom, (! [B:$tType,A:$tType,F1:(A > B),F2:(A > B),F3:(A > B),X1:A]: ((((((((splay_549499974op_s_t @ A) @ B) @ F1) @ F2) @ F3) @ ((splay_2088287777_Splay @ A) @ X1)) = (F1 @ X1))))).
% 2.94/1.51 thf(fact_64_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B4)) = ((A2 = A5) & (B2 = B4)))))).
% 2.94/1.51 thf(fact_65_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 2.94/1.51 thf(fact_66_splay_Opsimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ A2) @ (leaf @ A))) => ((((splay_splay @ A) @ A2) @ (leaf @ A)) = (leaf @ A))))))))).
% 2.94/1.51 thf(fact_67_accp__induct__rule, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A,P:(A > $o)]: (((((accp @ A) @ R2) @ A2) => ((! [X4:A]: (((((accp @ A) @ R2) @ X4) => ((! [Y6:A]: ((((R2 @ Y6) @ X4) => (P @ Y6)))) => (P @ X4))))) => (P @ A2)))))).
% 2.94/1.51 thf(fact_68_not__accp__down, axiom, (! [A:$tType,R:(A > (A > $o)),X:A]: (((~ ((((accp @ A) @ R) @ X))) => (~ ((! [Z2:A]: ((((R @ Z2) @ X) => (((accp @ A) @ R) @ Z2)))))))))).
% 2.94/1.51 thf(fact_69_accp__downward, axiom, (! [A:$tType,R2:(A > (A > $o)),B2:A,A2:A]: (((((accp @ A) @ R2) @ B2) => (((R2 @ A2) @ B2) => (((accp @ A) @ R2) @ A2)))))).
% 2.94/1.51 thf(fact_70_accp_Oinducts, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A,P:(A > $o)]: (((((accp @ A) @ R2) @ X) => ((! [X4:A]: (((! [Y6:A]: ((((R2 @ Y6) @ X4) => (((accp @ A) @ R2) @ Y6)))) => ((! [Y6:A]: ((((R2 @ Y6) @ X4) => (P @ Y6)))) => (P @ X4))))) => (P @ X)))))).
% 2.94/1.51 thf(fact_71_accp__induct, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A,P:(A > $o)]: (((((accp @ A) @ R2) @ A2) => ((! [X4:A]: (((((accp @ A) @ R2) @ X4) => ((! [Y6:A]: ((((R2 @ Y6) @ X4) => (P @ Y6)))) => (P @ X4))))) => (P @ A2)))))).
% 2.94/1.51 thf(fact_72_accp_Ointros, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A]: (((! [Y4:A]: ((((R2 @ Y4) @ X) => (((accp @ A) @ R2) @ Y4)))) => (((accp @ A) @ R2) @ X))))).
% 2.94/1.51 thf(fact_73_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X4:A,Y4:B]: ((P2 = ((((product_Pair @ A) @ B) @ X4) @ Y4))))))).
% 2.94/1.51 thf(fact_74_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A3:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B5)))) => (P @ P2))))).
% 2.94/1.51 thf(fact_75_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B4)) => (~ (((A2 = A5) => (B2 != B4)))))))).
% 2.94/1.51 thf(fact_76_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A3:A,B5:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B5) @ C2)))))))))).
% 2.94/1.51 thf(fact_77_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.94/1.51 thf(fact_78_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E3:E2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3)))))))))))).
% 2.94/1.51 thf(fact_79_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4)))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E3:E2,F5:F4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F4)) @ D2) @ ((((product_Pair @ E2) @ F4) @ E3) @ F5))))))))))))).
% 2.94/1.51 thf(fact_80_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F4:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))))))]: ((~ ((! [A3:A,B5:B,C2:C,D2:D,E3:E2,F5:F4,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F4) @ G2)) @ E3) @ ((((product_Pair @ F4) @ G2) @ F5) @ G3)))))))))))))).
% 2.94/1.51 thf(fact_81_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A3:A,B5:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A3) @ ((((product_Pair @ B) @ C) @ B5) @ C2))))) => (P @ X))))).
% 2.94/1.51 thf(fact_82_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A3:A,B5:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B5) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X))))).
% 2.94/1.51 thf(fact_83_prod__induct5, axiom, (! [E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: (((! [A3:A,B5:B,C2:C,D2:D,E3:E2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3))))))) => (P @ X))))).
% 2.94/1.51 thf(fact_84_prod__induct6, axiom, (! [F4:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4)))))]: (((! [A3:A,B5:B,C2:C,D2:D,E3:E2,F5:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4)))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F4))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F4)) @ D2) @ ((((product_Pair @ E2) @ F4) @ E3) @ F5)))))))) => (P @ X))))).
% 2.94/1.51 thf(fact_85_prod__induct7, axiom, (! [G2:$tType,F4:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))))))]: (((! [A3:A,B5:B,C2:C,D2:D,E3:E2,F5:F4,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2)))))) @ A3) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))))) @ B5) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F4) @ G2)) @ E3) @ ((((product_Pair @ F4) @ G2) @ F5) @ G3))))))))) => (P @ X))))).
% 2.94/1.51 thf(fact_86_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A3:A,B5:B]: ((Y != ((((product_Pair @ A) @ B) @ A3) @ B5))))))))).
% 2.94/1.51 thf(fact_87_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A3:A,B5:B]: ((P @ ((((product_Pair @ A) @ B) @ A3) @ B5)))) => (P @ Prod))))).
% 2.94/1.51 thf(fact_88_accp_Ocases, axiom, (! [A:$tType,R2:(A > (A > $o)),A2:A]: (((((accp @ A) @ R2) @ A2) => (! [Y6:A]: ((((R2 @ Y6) @ A2) => (((accp @ A) @ R2) @ Y6)))))))).
% 2.94/1.51 thf(fact_89_accp_Osimps, axiom, (! [A:$tType]: (((accp @ A) = (^ [R3:(A > (A > $o)),A6:A]: ((? [X5:A]: (((A6 = X5) & (! [Y7:A]: ((((R3 @ Y7) @ X5) => (((accp @ A) @ R3) @ Y7))))))))))))).
% 2.94/1.51 thf(fact_90_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.94/1.51 thf(fact_91_in__lex__prod, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B4:B,R2:(set @ ((product_prod @ A) @ A)),S:(set @ ((product_prod @ B) @ B))]: (((((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ A5) @ B4))) @ ((((lex_prod @ A) @ B) @ R2) @ S)) = ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A5)) @ R2) | ((A2 = A5) & (((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ B2) @ B4)) @ S))))))).
% 2.94/1.51 thf(fact_92_splay_Opsimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L:(tree @ A),R2:(tree @ A)]: (((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ A2) @ ((((node @ A) @ L) @ A2) @ R2))) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ L) @ A2) @ R2)) = ((((node @ A) @ L) @ A2) @ R2))))))))).
% 2.94/1.51 thf(fact_93_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.94/1.51 thf(fact_94_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R2:A,S:B,R:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S)) @ R) => ((S2 = S) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S2)) @ R)))))).
% 2.94/1.51 thf(fact_95_curry__conv, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_curry @ B) @ C) @ A) = (^ [F6:(((product_prod @ B) @ C) > A),A6:B,B6:C]: ((F6 @ ((((product_Pair @ B) @ C) @ A6) @ B6)))))))).
% 2.94/1.51 thf(fact_96_curryI, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: (((F @ ((((product_Pair @ A) @ B) @ A2) @ B2)) => ((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2))))).
% 2.94/1.51 thf(fact_97_tree_Oinject, axiom, (! [A:$tType,X21:(tree @ A),X222:A,X23:(tree @ A),Y21:(tree @ A),Y22:A,Y23:(tree @ A)]: (((((((node @ A) @ X21) @ X222) @ X23) = ((((node @ A) @ Y21) @ Y22) @ Y23)) = ((X21 = Y21) & ((X222 = Y22) & (X23 = Y23))))))).
% 2.94/1.51 thf(fact_98_t__splay__max_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L2:(tree @ A),B5:A]: ((P @ ((((node @ A) @ L2) @ B5) @ (leaf @ A))))) => ((! [L2:(tree @ A),B5:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((((Rr != (leaf @ A)) => (P @ Rr)) => (P @ ((((node @ A) @ L2) @ B5) @ ((((node @ A) @ Rl) @ C2) @ Rr)))))) => (P @ A0)))))))))).
% 2.94/1.51 thf(fact_99_t__splay__max_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => ((! [L2:(tree @ A),B5:A]: ((X != ((((node @ A) @ L2) @ B5) @ (leaf @ A))))) => (~ ((! [L2:(tree @ A),B5:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: ((X != ((((node @ A) @ L2) @ B5) @ ((((node @ A) @ Rl) @ C2) @ Rr))))))))))))))).
% 2.94/1.51 thf(fact_100__092_060Phi_062_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((P @ L2) => ((P @ R4) => (P @ ((((node @ A) @ L2) @ A3) @ R4)))))) => (P @ A0)))))).
% 2.94/1.51 thf(fact_101__092_060Phi_062_Ocases, axiom, (! [A:$tType,X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: ((X != ((((node @ A) @ L2) @ A3) @ R4)))))))))).
% 2.94/1.51 thf(fact_102_bst__eq_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((P @ L2) => ((P @ R4) => (P @ ((((node @ A) @ L2) @ A3) @ R4)))))) => (P @ A0))))))))).
% 2.94/1.51 thf(fact_103_bst__eq_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((X != (leaf @ A)) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: ((X != ((((node @ A) @ L2) @ A3) @ R4))))))))))))).
% 2.94/1.51 thf(fact_104_mirror_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),A0:(tree @ A)]: (((P @ (leaf @ A)) => ((! [L2:(tree @ A),X4:A,R4:(tree @ A)]: (((P @ R4) => ((P @ L2) => (P @ ((((node @ A) @ L2) @ X4) @ R4)))))) => (P @ A0)))))).
% 2.94/1.51 thf(fact_105_tree_Oexhaust, axiom, (! [A:$tType,Y:(tree @ A)]: (((Y != (leaf @ A)) => (~ ((! [X212:(tree @ A),X223:A,X232:(tree @ A)]: ((Y != ((((node @ A) @ X212) @ X223) @ X232)))))))))).
% 2.94/1.51 thf(fact_106_neq__Leaf__iff, axiom, (! [A:$tType,T2:(tree @ A)]: (((T2 != (leaf @ A)) = (? [L3:(tree @ A),A6:A,R3:(tree @ A)]: ((T2 = ((((node @ A) @ L3) @ A6) @ R3)))))))).
% 2.94/1.51 thf(fact_107_tree_Oinduct, axiom, (! [A:$tType,P:((tree @ A) > $o),Tree:(tree @ A)]: (((P @ (leaf @ A)) => ((! [X12:(tree @ A),X22:A,X32:(tree @ A)]: (((P @ X12) => ((P @ X32) => (P @ ((((node @ A) @ X12) @ X22) @ X32)))))) => (P @ Tree)))))).
% 2.94/1.51 thf(fact_108_tree_Odistinct_I1_J, axiom, (! [A:$tType,X21:(tree @ A),X222:A,X23:(tree @ A)]: (((leaf @ A) != ((((node @ A) @ X21) @ X222) @ X23))))).
% 2.94/1.51 thf(fact_109_splay_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L:(tree @ A),R2:(tree @ A)]: (((((splay_splay @ A) @ A2) @ ((((node @ A) @ L) @ A2) @ R2)) = ((((node @ A) @ L) @ A2) @ R2)))))))).
% 2.94/1.51 thf(fact_110_curryE, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.94/1.51 thf(fact_111_curryD, axiom, (! [A:$tType,B:$tType,F:(((product_prod @ A) @ B) > $o),A2:A,B2:B]: ((((((((product_curry @ A) @ B) @ $o) @ F) @ A2) @ B2) => (F @ ((((product_Pair @ A) @ B) @ A2) @ B2)))))).
% 2.94/1.51 thf(fact_112_splay__not__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: (((T2 != (leaf @ A)) => (? [L2:(tree @ A),X4:A,R4:(tree @ A)]: (((((splay_splay @ A) @ A2) @ T2) = ((((node @ A) @ L2) @ X4) @ R4))))))))))).
% 2.94/1.51 thf(fact_113_t__splay_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:((product_prod @ A) @ (tree @ A))]: (((! [A3:A]: ((X != ((((product_Pair @ A) @ (tree @ A)) @ A3) @ (leaf @ A))))) => (~ ((! [A3:A,L2:(tree @ A),B5:A,R4:(tree @ A)]: ((X != ((((product_Pair @ A) @ (tree @ A)) @ A3) @ ((((node @ A) @ L2) @ B5) @ R4)))))))))))))).
% 2.94/1.51 thf(fact_114_splay__max__Leaf, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),L:(tree @ A),A2:A,R2:(tree @ A)]: (((((splay_splay_max @ A) @ T2) = ((((node @ A) @ L) @ A2) @ R2)) => (R2 = (leaf @ A))))))))).
% 2.94/1.51 thf(fact_115_splay__max_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [La:(tree @ A),A2:A]: ((((splay_splay_max @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) = ((((node @ A) @ La) @ A2) @ (leaf @ A))))))))).
% 2.94/1.51 thf(fact_116_splay_Opsimps_I13_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A,La:(tree @ A),Lb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ B2) @ X) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Lb) @ B2) @ (leaf @ A))))) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Lb) @ B2) @ (leaf @ A)))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Lb)) @ B2) @ (leaf @ A)))))))))))).
% 2.94/1.51 thf(fact_117_splay_Opsimps_I12_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ X) @ B2) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ Rb)))) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ Rb))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B2) @ Rb))))))))))).
% 2.94/1.51 thf(fact_118_splay_Opsimps_I10_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,L:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ X) @ ((((node @ A) @ L) @ A2) @ (leaf @ A)))) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ L) @ A2) @ (leaf @ A))) = ((((node @ A) @ L) @ A2) @ (leaf @ A))))))))))).
% 2.94/1.51 thf(fact_119_splay_Opsimps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,B2:A,A2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ B2) => ((((ord_less @ A) @ A2) @ X) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ X) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B2) @ Rb))) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B2) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ Rb)))))))))))).
% 2.94/1.51 thf(fact_120_splay_Opsimps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A,Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ A2) => ((((ord_less @ A) @ X) @ B2) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ X) @ ((((node @ A) @ ((((node @ A) @ (leaf @ A)) @ A2) @ Ra2)) @ B2) @ Rb))) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ (leaf @ A)) @ A2) @ Ra2)) @ B2) @ Rb)) = ((((node @ A) @ (leaf @ A)) @ A2) @ ((((node @ A) @ Ra2) @ B2) @ Rb)))))))))))).
% 2.94/1.51 thf(fact_121_splay_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,La:(tree @ A),Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Ra2)) @ B2) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Ra2) @ B2) @ Rb)))))))))).
% 2.94/1.51 thf(fact_122_splay_Osimps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,Lb:(tree @ A),La:(tree @ A),Ra2:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ Lb) @ B2) @ ((((node @ A) @ La) @ A2) @ Ra2))) = ((((node @ A) @ ((((node @ A) @ Lb) @ B2) @ La)) @ A2) @ Ra2))))))))).
% 2.94/1.51 thf(fact_123_splay_Osimps_I13_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A,La:(tree @ A),Lb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ B2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Lb) @ B2) @ (leaf @ A)))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Lb)) @ B2) @ (leaf @ A))))))))))).
% 2.94/1.51 thf(fact_124_splay_Osimps_I12_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((ord_less @ A) @ X) @ B2) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ Rb))) = ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B2) @ Rb)))))))))).
% 2.94/1.51 thf(fact_125_splay_Osimps_I10_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,X:A,L:(tree @ A)]: (((((ord_less @ A) @ A2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ L) @ A2) @ (leaf @ A))) = ((((node @ A) @ L) @ A2) @ (leaf @ A)))))))))).
% 2.94/1.51 thf(fact_126_splay_Osimps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,B2:A,A2:A,La:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ B2) => ((((ord_less @ A) @ A2) @ X) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ (leaf @ A))) @ B2) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ Rb))))))))))).
% 2.94/1.51 thf(fact_127_splay_Osimps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A,Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ X) @ A2) => ((((ord_less @ A) @ X) @ B2) => ((((splay_splay @ A) @ X) @ ((((node @ A) @ ((((node @ A) @ (leaf @ A)) @ A2) @ Ra2)) @ B2) @ Rb)) = ((((node @ A) @ (leaf @ A)) @ A2) @ ((((node @ A) @ Ra2) @ B2) @ Rb))))))))))).
% 2.94/1.51 thf(fact_128_splay_Osimps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ R2)) = ((((node @ A) @ (leaf @ A)) @ B2) @ R2))))))))).
% 2.94/1.51 thf(fact_129_splay_Opsimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,La:(tree @ A),Ra2:(tree @ A),Rb:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ A2) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Ra2)) @ B2) @ Rb))) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ La) @ A2) @ Ra2)) @ B2) @ Rb)) = ((((node @ A) @ La) @ A2) @ ((((node @ A) @ Ra2) @ B2) @ Rb))))))))))).
% 2.94/1.51 thf(fact_130_splay_Opsimps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,Lb:(tree @ A),La:(tree @ A),Ra2:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ A2) @ ((((node @ A) @ Lb) @ B2) @ ((((node @ A) @ La) @ A2) @ Ra2)))) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ Lb) @ B2) @ ((((node @ A) @ La) @ A2) @ Ra2))) = ((((node @ A) @ ((((node @ A) @ Lb) @ B2) @ La)) @ A2) @ Ra2)))))))))).
% 2.94/1.51 thf(fact_131_splay_Opsimps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((accp @ ((product_prod @ A) @ (tree @ A))) @ (splay_splay_rel @ A)) @ ((((product_Pair @ A) @ (tree @ A)) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ R2))) => ((((splay_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ R2)) = ((((node @ A) @ (leaf @ A)) @ B2) @ R2)))))))))).
% 2.94/1.51 thf(fact_132_in__measure, axiom, (! [A:$tType,X:A,Y:A,F:(A > nat)]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ ((measure @ A) @ F)) = (((ord_less @ nat) @ (F @ X)) @ (F @ Y)))))).
% 2.94/1.51 thf(fact_133_same__fstI, axiom, (! [B:$tType,A:$tType,P:(A > $o),X:A,Y8:B,Y:B,R:(A > (set @ ((product_prod @ B) @ B)))]: (((P @ X) => ((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ Y8) @ Y)) @ (R @ X)) => (((member @ ((product_prod @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B))) @ ((((product_Pair @ ((product_prod @ A) @ B)) @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y8)) @ ((((product_Pair @ A) @ B) @ X) @ Y))) @ ((((same_fst @ A) @ B) @ P) @ R))))))).
% 2.94/1.51 thf(fact_134_splay__bstR, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A,L:(tree @ A),E:A,R2:(tree @ A),X:A]: ((((linorder_bst @ A) @ T2) => (((((splay_splay @ A) @ A2) @ T2) = ((((node @ A) @ L) @ E) @ R2)) => ((((member @ A) @ X) @ ((set_tree @ A) @ R2)) => (((ord_less @ A) @ A2) @ X)))))))))).
% 2.94/1.51 thf(fact_135_splay__bstL, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A,L:(tree @ A),E:A,R2:(tree @ A),X:A]: ((((linorder_bst @ A) @ T2) => (((((splay_splay @ A) @ A2) @ T2) = ((((node @ A) @ L) @ E) @ R2)) => ((((member @ A) @ X) @ ((set_tree @ A) @ L)) => (((ord_less @ A) @ X) @ A2)))))))))).
% 2.94/1.51 thf(fact_136_set__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,T2:(tree @ A)]: ((((set_tree @ A) @ (((splay_splay @ A) @ A2) @ T2)) = ((set_tree @ A) @ T2)))))))).
% 2.94/1.51 thf(fact_137_set__splay__max, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A)]: ((((set_tree @ A) @ ((splay_splay_max @ A) @ T2)) = ((set_tree @ A) @ T2)))))))).
% 2.94/1.51 thf(fact_138_tree_Oset__cases, axiom, (! [A:$tType,E:A,A2:(tree @ A)]: (((((member @ A) @ E) @ ((set_tree @ A) @ A2)) => ((! [Z1:(tree @ A)]: (((? [Z22:A,Z3:(tree @ A)]: ((A2 = ((((node @ A) @ Z1) @ Z22) @ Z3)))) => (~ ((((member @ A) @ E) @ ((set_tree @ A) @ Z1))))))) => ((! [Z1:(tree @ A),Z3:(tree @ A)]: ((A2 != ((((node @ A) @ Z1) @ E) @ Z3)))) => (~ ((! [Z1:(tree @ A),Z22:A,Z3:(tree @ A)]: (((A2 = ((((node @ A) @ Z1) @ Z22) @ Z3)) => (~ ((((member @ A) @ E) @ ((set_tree @ A) @ Z3))))))))))))))).
% 2.94/1.51 thf(fact_139_tree_Oset__intros_I1_J, axiom, (! [A:$tType,X:A,A1:(tree @ A),A23:A,A33:(tree @ A)]: (((((member @ A) @ X) @ ((set_tree @ A) @ A1)) => (((member @ A) @ X) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A23) @ A33))))))).
% 2.94/1.51 thf(fact_140_tree_Oset__intros_I2_J, axiom, (! [A:$tType,A23:A,A1:(tree @ A),A33:(tree @ A)]: ((((member @ A) @ A23) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A23) @ A33)))))).
% 2.94/1.51 thf(fact_141_tree_Oset__intros_I3_J, axiom, (! [A:$tType,Xa:A,A33:(tree @ A),A1:(tree @ A),A23:A]: (((((member @ A) @ Xa) @ ((set_tree @ A) @ A33)) => (((member @ A) @ Xa) @ ((set_tree @ A) @ ((((node @ A) @ A1) @ A23) @ A33))))))).
% 2.94/1.51 thf(fact_142_splay__to__root, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A,T4:(tree @ A)]: ((((linorder_bst @ A) @ T2) => (((((splay_splay @ A) @ A2) @ T2) = T4) => ((((member @ A) @ A2) @ ((set_tree @ A) @ T2)) = (? [L3:(tree @ A),R3:(tree @ A)]: ((T4 = ((((node @ A) @ L3) @ A2) @ R3))))))))))))).
% 2.94/1.51 thf(fact_143_is__root__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((((splay_is_root @ A) @ A2) @ (((splay_splay @ A) @ A2) @ T2)) = (((member @ A) @ A2) @ ((set_tree @ A) @ T2)))))))))).
% 2.94/1.51 thf(fact_144_ex__in__set__tree, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: (((T2 != (leaf @ A)) => (((linorder_bst @ A) @ T2) => (? [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ T2)) & (((((splay_splay @ A) @ X4) @ T2) = (((splay_splay @ A) @ A2) @ T2)) & ((((splay_914434265_splay @ A) @ X4) @ T2) = (((splay_914434265_splay @ A) @ A2) @ T2)))))))))))))).
% 2.94/1.51 thf(fact_145_bst_Oelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:$o]: (((((linorder_bst @ A) @ X) = Y) => (((X = (leaf @ A)) => (~ (Y))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (Y = (~ ((((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X5) @ A3)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X5))))))))))))))))))))))).
% 2.94/1.51 thf(fact_146_bst_Oelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst @ A) @ X) => ((X != (leaf @ A)) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (~ ((((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X6) @ A3)))) & (! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X6)))))))))))))))))))))).
% 2.94/1.51 thf(fact_147_bst_Oelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst @ A) @ X))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X4) @ A3)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X4))))))))))))))))))).
% 2.94/1.51 thf(fact_148_bst_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L:(tree @ A),A2:A,R2:(tree @ A)]: ((((linorder_bst @ A) @ ((((node @ A) @ L) @ A2) @ R2)) = (((linorder_bst @ A) @ L) & (((linorder_bst @ A) @ R2) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L)) => (((ord_less @ A) @ X5) @ A2)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R2)) => (((ord_less @ A) @ A2) @ X5)))))))))))))).
% 2.94/1.51 thf(fact_149_bst_Opelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst @ A) @ X) => ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ X) => (((X = (leaf @ A)) => (~ ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ (leaf @ A))))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4)) => (~ ((((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X6) @ A3)))) & (! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X6)))))))))))))))))))))))).
% 2.94/1.51 thf(fact_150_bst_Opelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:$o]: (((((linorder_bst @ A) @ X) = Y) => ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ X) => (((X = (leaf @ A)) => (Y => (~ ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ (leaf @ A)))))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((Y = (((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X5) @ A3)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X5)))))))) => (~ ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4))))))))))))))))))).
% 2.94/1.51 thf(fact_151_bst_Opelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst @ A) @ X))) => ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ X) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((((accp @ (tree @ A)) @ (linorder_bst_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4)) => (((linorder_bst @ A) @ L2) & (((linorder_bst @ A) @ R4) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L2)) => (((ord_less @ A) @ X4) @ A3)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R4)) => (((ord_less @ A) @ A3) @ X4))))))))))))))))))))).
% 2.94/1.51 thf(fact_152_t__splay__simps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ (leaf @ A)) @ B2) @ R2)) = (one_one @ nat))))))))).
% 2.94/1.51 thf(fact_153_t__splay__simps_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,L:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ (leaf @ A))) = (one_one @ nat))))))))).
% 2.94/1.51 thf(fact_154_bst__eq_Oelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:$o]: (((((linorder_bst_eq @ A) @ X) = Y) => (((X = (leaf @ A)) => (~ (Y))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (Y = (~ ((((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X5) @ A3)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X5))))))))))))))))))))))).
% 2.94/1.51 thf(fact_155_t__splay__simps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,L:(tree @ A),R2:(tree @ A)]: (((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ A2) @ R2)) = (one_one @ nat)))))))).
% 2.94/1.51 thf(fact_156_t__splay__simps_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,L:(tree @ A),Rl2:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ A2) @ Rr2))) = (one_one @ nat))))))))).
% 2.94/1.51 thf(fact_157_t__splay__simps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ A2) @ Lr)) @ B2) @ R2)) = (one_one @ nat))))))))).
% 2.94/1.51 thf(fact_158_accp__subset__induct, axiom, (! [A:$tType,D3:(A > $o),R:(A > (A > $o)),X:A,P:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ D3) @ ((accp @ A) @ R)) => ((! [X4:A,Z2:A]: (((D3 @ X4) => (((R @ Z2) @ X4) => (D3 @ Z2))))) => ((D3 @ X) => ((! [X4:A]: (((D3 @ X4) => ((! [Z4:A]: ((((R @ Z4) @ X4) => (P @ Z4)))) => (P @ X4))))) => (P @ X)))))))).
% 2.94/1.51 thf(fact_159_accp__subset, axiom, (! [A:$tType,R1:(A > (A > $o)),R22:(A > (A > $o))]: (((((ord_less_eq @ (A > (A > $o))) @ R1) @ R22) => (((ord_less_eq @ (A > $o)) @ ((accp @ A) @ R22)) @ ((accp @ A) @ R1)))))).
% 2.94/1.51 thf(fact_160_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R) @ Ra) => (((ord_less_eq @ ((splay_2011811431op_s_t @ A) > ((splay_2011811431op_s_t @ B) > $o))) @ (((splay_434753539op_s_t @ A) @ B) @ R)) @ (((splay_434753539op_s_t @ A) @ B) @ Ra)))))).
% 2.94/1.51 thf(fact_161_t__splay_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((splay_914434265_splay @ A) @ A2) @ (leaf @ A)) = (one_one @ nat)))))))).
% 2.94/1.51 thf(fact_162_bst__eq_Oelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst_eq @ A) @ X))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X4) @ A3)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X4))))))))))))))))))).
% 2.94/1.51 thf(fact_163_bst__eq_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L:(tree @ A),A2:A,R2:(tree @ A)]: ((((linorder_bst_eq @ A) @ ((((node @ A) @ L) @ A2) @ R2)) = (((linorder_bst_eq @ A) @ L) & (((linorder_bst_eq @ A) @ R2) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L)) => (((ord_less_eq @ A) @ X5) @ A2)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R2)) => (((ord_less_eq @ A) @ A2) @ X5)))))))))))))).
% 2.94/1.51 thf(fact_164_splay__max__eq__splay, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:(tree @ A),A2:A]: ((((linorder_bst @ A) @ T2) => ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ T2)) => (((ord_less_eq @ A) @ X4) @ A2)))) => (((splay_splay_max @ A) @ T2) = (((splay_splay @ A) @ A2) @ T2)))))))))).
% 2.94/1.51 thf(fact_165_bst__eq_Oelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst_eq @ A) @ X) => ((X != (leaf @ A)) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => (~ ((((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X6) @ A3)))) & (! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X6)))))))))))))))))))))).
% 2.94/1.51 thf(fact_166_bst__eq_Opelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: ((((linorder_bst_eq @ A) @ X) => ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ X) => (((X = (leaf @ A)) => (~ ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ (leaf @ A))))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4)) => (~ ((((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X6) @ A3)))) & (! [X6:A]: (((((member @ A) @ X6) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X6)))))))))))))))))))))))).
% 2.94/1.51 thf(fact_167_bst__eq_Opelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:$o]: (((((linorder_bst_eq @ A) @ X) = Y) => ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ X) => (((X = (leaf @ A)) => (Y => (~ ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ (leaf @ A)))))) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((Y = (((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X5) @ A3)))) & (! [X5:A]: (((((member @ A) @ X5) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X5)))))))) => (~ ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4))))))))))))))))))).
% 2.94/1.51 thf(fact_168_bst__eq_Opelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A)]: (((~ (((linorder_bst_eq @ A) @ X))) => ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ X) => (~ ((! [L2:(tree @ A),A3:A,R4:(tree @ A)]: (((X = ((((node @ A) @ L2) @ A3) @ R4)) => ((((accp @ (tree @ A)) @ (linorder_bst_eq_rel @ A)) @ ((((node @ A) @ L2) @ A3) @ R4)) => (((linorder_bst_eq @ A) @ L2) & (((linorder_bst_eq @ A) @ R4) & ((! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ L2)) => (((ord_less_eq @ A) @ X4) @ A3)))) & (! [X4:A]: (((((member @ A) @ X4) @ ((set_tree @ A) @ R4)) => (((ord_less_eq @ A) @ A3) @ X4))))))))))))))))))))).
% 2.94/1.51 thf(fact_169_less__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.94/1.51 thf(fact_170_t__splay__simps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A,Ll:(tree @ A),Lr:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ A2) @ C3) => (((Ll = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B2) @ R2)) = (one_one @ nat))) & ((Ll != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B2) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Ll)) @ (one_one @ nat))))))))))))).
% 2.94/1.51 thf(fact_171_t__splay__simps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A,Lr:(tree @ A),Ll:(tree @ A),R2:(tree @ A)]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C3) @ A2) => (((Lr = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B2) @ R2)) = (one_one @ nat))) & ((Lr != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ ((((node @ A) @ Ll) @ C3) @ Lr)) @ B2) @ R2)) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Lr)) @ (one_one @ nat))))))))))))).
% 2.94/1.51 thf(fact_172_t__splay__simps_I9_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C3:A,Rr2:(tree @ A),L:(tree @ A),Rl2:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C3) @ A2) => (((Rr2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (one_one @ nat))) & ((Rr2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rr2)) @ (one_one @ nat))))))))))))).
% 2.94/1.51 thf(fact_173_t__splay__simps_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C3:A,Rl2:(tree @ A),L:(tree @ A),Rr2:(tree @ A)]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ A2) @ C3) => (((Rl2 = (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (one_one @ nat))) & ((Rl2 != (leaf @ A)) => ((((splay_914434265_splay @ A) @ A2) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (((plus_plus @ nat) @ (((splay_914434265_splay @ A) @ A2) @ Rl2)) @ (one_one @ nat))))))))))))).
% 2.94/1.51 thf(fact_174_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.94/1.51 thf(fact_175_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.94/1.51 thf(fact_176_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.94/1.51 thf(fact_177_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.94/1.51 thf(fact_178_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.94/1.51 thf(fact_179_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.94/1.51 thf(fact_180_less__not__refl3, axiom, (! [S:nat,T2:nat]: (((((ord_less @ nat) @ S) @ T2) => (S != T2))))).
% 2.94/1.51 thf(fact_181_measure__induct, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y6:A]: (((((ord_less @ nat) @ (F @ Y6)) @ (F @ X4)) => (P @ Y6)))) => (P @ X4)))) => (P @ A2))))).
% 2.94/1.51 thf(fact_182_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.94/1.51 thf(fact_183_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.94/1.51 thf(fact_184_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.94/1.51 thf(fact_185_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 2.94/1.51 thf(fact_186_measure__induct__rule, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y6:A]: (((((ord_less @ nat) @ (F @ Y6)) @ (F @ X4)) => (P @ Y6)))) => (P @ X4)))) => (P @ A2))))).
% 2.94/1.51 thf(fact_187_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X:A]: (((! [X4:A]: (((~ ((P @ X4))) => (? [Y6:A]: (((((ord_less @ nat) @ (V @ Y6)) @ (V @ X4)) & (~ ((P @ Y6))))))))) => (P @ X))))).
% 2.94/1.51 thf(fact_188_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (((ord_less @ nat) @ (F @ I2)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 2.94/1.51 thf(fact_189_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.94/1.51 thf(fact_190_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.94/1.51 thf(fact_191_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less @ nat) @ M3) @ N3) | (M3 = N3)))))).
% 2.94/1.51 thf(fact_192_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.94/1.51 thf(fact_193_nat__less__le, axiom, ((ord_less @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less_eq @ nat) @ M3) @ N3) & (M3 != N3)))))).
% 2.94/1.51 thf(fact_194_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.94/1.51 thf(fact_195_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.94/1.51 thf(fact_196_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 2.94/1.51 thf(fact_197_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2))))))))).
% 2.94/1.51 thf(fact_198_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A,D4:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C3) @ D4) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D4)))))))))).
% 2.94/1.51 thf(fact_199_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.94/1.51 thf(fact_200_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.94/1.51 thf(fact_201_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.94/1.51 thf(fact_202_less__add__eq__less, axiom, (! [K:nat,L:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K) @ L) => (((((plus_plus @ nat) @ M) @ L) = (((plus_plus @ nat) @ K) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 2.94/1.51 thf(fact_203_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.94/1.51 thf(fact_204_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.94/1.51 thf(fact_205_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)))))).
% 2.94/1.51 thf(fact_206_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.94/1.51 thf(fact_207_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.94/1.51 thf(fact_208_add__less__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K) @ L) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.94/1.51 thf(fact_209_add__lessD1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K) => (((ord_less @ nat) @ I) @ K))))).
% 2.94/1.51 thf(fact_210_mono__nat__linear__lb, axiom, (! [F:(nat > nat),M:nat,K:nat]: (((! [M4:nat,N2:nat]: (((((ord_less @ nat) @ M4) @ N2) => (((ord_less @ nat) @ (F @ M4)) @ (F @ N2))))) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (F @ M)) @ K)) @ (F @ (((plus_plus @ nat) @ M) @ K))))))).
% 2.94/1.51 thf(fact_211_add__less__le__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A,D4:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C3) @ D4) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D4)))))))))).
% 2.94/1.51 thf(fact_212_add__le__less__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A,D4:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ C3) @ D4) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D4)))))))))).
% 2.94/1.51 thf(fact_213_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.94/1.51 thf(fact_214_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.94/1.51 thf(fact_215_discrete, axiom, (! [A:$tType]: ((((semiring_numeral_div @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [A6:A]: (((ord_less_eq @ A) @ (((plus_plus @ A) @ A6) @ (one_one @ A)))))))))).
% 2.94/1.51 thf(fact_216_fold__atLeastAtMost__nat_Oinduct, axiom, (! [A:$tType,P:((nat > (A > A)) > (nat > (nat > (A > $o)))),A0:(nat > (A > A)),A1:nat,A23:nat,A33:A]: (((! [F5:(nat > (A > A)),A3:nat,B5:nat,Acc:A]: ((((~ ((((ord_less @ nat) @ B5) @ A3))) => ((((P @ F5) @ (((plus_plus @ nat) @ A3) @ (one_one @ nat))) @ B5) @ ((F5 @ A3) @ Acc))) => ((((P @ F5) @ A3) @ B5) @ Acc)))) => ((((P @ A0) @ A1) @ A23) @ A33))))).
% 2.94/1.51 thf(fact_217_less__add__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 2.94/1.51 thf(fact_218_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.94/1.51 thf(fact_219_ex__has__greatest__nat__lemma, axiom, (! [A:$tType,P:(A > $o),K:A,M:(A > nat),N:nat]: (((P @ K) => ((! [X4:A]: (((P @ X4) => (? [Y6:A]: (((P @ Y6) & (~ ((((ord_less_eq @ nat) @ (M @ Y6)) @ (M @ X4)))))))))) => (? [Y4:A]: (((P @ Y4) & (~ ((((ord_less @ nat) @ (M @ Y4)) @ (((plus_plus @ nat) @ (M @ K)) @ N)))))))))))).
% 2.94/1.51 thf(fact_220_t__splay__max_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Rr2:(tree @ A),L:(tree @ A),B2:A,Rl2:(tree @ A),C3:A]: ((((Rr2 = (leaf @ A)) => (((splay_878424299ay_max @ A) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (one_one @ nat))) & ((Rr2 != (leaf @ A)) => (((splay_878424299ay_max @ A) @ ((((node @ A) @ L) @ B2) @ ((((node @ A) @ Rl2) @ C3) @ Rr2))) = (((plus_plus @ nat) @ ((splay_878424299ay_max @ A) @ Rr2)) @ (one_one @ nat))))))))))).
% 2.94/1.51 thf(fact_221_t__splay__max_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((splay_878424299ay_max @ A) @ (leaf @ A)) = (one_one @ nat)))))).
% 2.94/1.51 thf(fact_222_t__splay__max_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L:(tree @ A),B2:A]: ((((splay_878424299ay_max @ A) @ ((((node @ A) @ L) @ B2) @ (leaf @ A))) = (one_one @ nat)))))))).
% 2.94/1.51 thf(fact_223_ex__has__greatest__nat, axiom, (! [A:$tType,P:(A > $o),K:A,M:(A > nat),B2:nat]: (((P @ K) => ((! [Y4:A]: (((P @ Y4) => (((ord_less @ nat) @ (M @ Y4)) @ B2)))) => (? [X4:A]: (((P @ X4) & (! [Y6:A]: (((P @ Y6) => (((ord_less_eq @ nat) @ (M @ Y6)) @ (M @ X4))))))))))))).
% 2.94/1.51 thf(fact_224_t__splay__max_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:nat]: (((((splay_878424299ay_max @ A) @ X) = Y) => (((X = (leaf @ A)) => (Y != (one_one @ nat))) => (((? [L2:(tree @ A),B5:A]: ((X = ((((node @ A) @ L2) @ B5) @ (leaf @ A))))) => (Y != (one_one @ nat))) => (~ ((! [L2:(tree @ A),B5:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: (((X = ((((node @ A) @ L2) @ B5) @ ((((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))))))))))))))))))))).
% 2.94/1.51 thf(fact_225_t__splay__max_Opelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(tree @ A),Y:nat]: (((((splay_878424299ay_max @ A) @ X) = Y) => ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ X) => (((X = (leaf @ A)) => ((Y = (one_one @ nat)) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ (leaf @ A)))))) => ((! [L2:(tree @ A),B5:A]: (((X = ((((node @ A) @ L2) @ B5) @ (leaf @ A))) => ((Y = (one_one @ nat)) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ ((((node @ A) @ L2) @ B5) @ (leaf @ A))))))))) => (~ ((! [L2:(tree @ A),B5:A,Rl:(tree @ A),C2:A,Rr:(tree @ A)]: (((X = ((((node @ A) @ L2) @ B5) @ ((((node @ A) @ Rl) @ C2) @ Rr))) => ((((Rr = (leaf @ A)) => (Y = (one_one @ nat))) & ((Rr != (leaf @ A)) => (Y = (((plus_plus @ nat) @ ((splay_878424299ay_max @ A) @ Rr)) @ (one_one @ nat))))) => (~ ((((accp @ (tree @ A)) @ (splay_1816415694ax_rel @ A)) @ ((((node @ A) @ L2) @ B5) @ ((((node @ A) @ Rl) @ C2) @ Rr))))))))))))))))))))).
% 2.94/1.51 thf(fact_226_fold__atLeastAtMost__nat_Opinduct, axiom, (! [A:$tType,A0:(nat > (A > A)),A1:nat,A23:nat,A33:A,P:((nat > (A > A)) > (nat > (nat > (A > $o))))]: (((((accp @ ((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A)))) @ (set_fo2092542664at_rel @ A)) @ ((((product_Pair @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) @ A0) @ ((((product_Pair @ nat) @ ((product_prod @ nat) @ A)) @ A1) @ ((((product_Pair @ nat) @ A) @ A23) @ A33)))) => ((! [F5:(nat > (A > A)),A3:nat,B5:nat,Acc:A]: (((((accp @ ((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A)))) @ (set_fo2092542664at_rel @ A)) @ ((((product_Pair @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) @ F5) @ ((((product_Pair @ nat) @ ((product_prod @ nat) @ A)) @ A3) @ ((((product_Pair @ nat) @ A) @ B5) @ Acc)))) => (((~ ((((ord_less @ nat) @ B5) @ A3))) => ((((P @ F5) @ (((plus_plus @ nat) @ A3) @ (one_one @ nat))) @ B5) @ ((F5 @ A3) @ Acc))) => ((((P @ F5) @ A3) @ B5) @ Acc))))) => ((((P @ A0) @ A1) @ A23) @ A33)))))).
% 2.94/1.51 thf(fact_227_fold__atLeastAtMost__nat_Opelims, axiom, (! [A:$tType,X:(nat > (A > A)),Xa:nat,Xb2:nat,Xc:A,Y:A]: ((((((((set_fo292404081st_nat @ A) @ X) @ Xa) @ Xb2) @ Xc) = Y) => ((((accp @ ((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A)))) @ (set_fo2092542664at_rel @ A)) @ ((((product_Pair @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) @ X) @ ((((product_Pair @ nat) @ ((product_prod @ nat) @ A)) @ Xa) @ ((((product_Pair @ nat) @ A) @ Xb2) @ Xc)))) => (~ (((((((ord_less @ nat) @ Xb2) @ Xa) => (Y = Xc)) & ((~ ((((ord_less @ nat) @ Xb2) @ Xa))) => (Y = (((((set_fo292404081st_nat @ A) @ X) @ (((plus_plus @ nat) @ Xa) @ (one_one @ nat))) @ Xb2) @ ((X @ Xa) @ Xc))))) => (~ ((((accp @ ((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A)))) @ (set_fo2092542664at_rel @ A)) @ ((((product_Pair @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) @ X) @ ((((product_Pair @ nat) @ ((product_prod @ nat) @ A)) @ Xa) @ ((((product_Pair @ nat) @ A) @ Xb2) @ Xc)))))))))))))).
% 2.94/1.51 thf(fact_228_fold__atLeastAtMost__nat_Opsimps, axiom, (! [A:$tType,F:(nat > (A > A)),A2:nat,B2:nat,Acc2:A]: (((((accp @ ((product_prod @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A)))) @ (set_fo2092542664at_rel @ A)) @ ((((product_Pair @ (nat > (A > A))) @ ((product_prod @ nat) @ ((product_prod @ nat) @ A))) @ F) @ ((((product_Pair @ nat) @ ((product_prod @ nat) @ A)) @ A2) @ ((((product_Pair @ nat) @ A) @ B2) @ Acc2)))) => (((((ord_less @ nat) @ B2) @ A2) => ((((((set_fo292404081st_nat @ A) @ F) @ A2) @ B2) @ Acc2) = Acc2)) & ((~ ((((ord_less @ nat) @ B2) @ A2))) => ((((((set_fo292404081st_nat @ A) @ F) @ A2) @ B2) @ Acc2) = (((((set_fo292404081st_nat @ A) @ F) @ (((plus_plus @ nat) @ A2) @ (one_one @ nat))) @ B2) @ ((F @ A2) @ Acc2))))))))).
% 2.94/1.51 thf(fact_229_fold__atLeastAtMost__nat_Oelims, axiom, (! [A:$tType,X:(nat > (A > A)),Xa:nat,Xb2:nat,Xc:A,Y:A]: ((((((((set_fo292404081st_nat @ A) @ X) @ Xa) @ Xb2) @ Xc) = Y) => (((((ord_less @ nat) @ Xb2) @ Xa) => (Y = Xc)) & ((~ ((((ord_less @ nat) @ Xb2) @ Xa))) => (Y = (((((set_fo292404081st_nat @ A) @ X) @ (((plus_plus @ nat) @ Xa) @ (one_one @ nat))) @ Xb2) @ ((X @ Xa) @ Xc))))))))).
% 2.94/1.51 thf(fact_230_fold__atLeastAtMost__nat_Osimps, axiom, (! [A:$tType]: (((set_fo292404081st_nat @ A) = (^ [F6:(nat > (A > A)),A6:nat,B6:nat,Acc3:A]: (((((if @ A) @ (((ord_less @ nat) @ B6) @ A6)) @ Acc3) @ (((((set_fo292404081st_nat @ A) @ F6) @ (((plus_plus @ nat) @ A6) @ (one_one @ nat))) @ B6) @ ((F6 @ A6) @ Acc3))))))))).
% 2.94/1.51 thf(fact_231_complete__interval, axiom, (! [A:$tType]: ((((condit1037483654norder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B2) => ((P @ A2) => ((~ ((P @ B2))) => (? [C2:A]: (((((ord_less_eq @ A) @ A2) @ C2) & ((((ord_less_eq @ A) @ C2) @ B2) & ((! [X6:A]: ((((((ord_less_eq @ A) @ A2) @ X6) & (((ord_less @ A) @ X6) @ C2)) => (P @ X6)))) & (! [D5:A]: (((! [X4:A]: ((((((ord_less_eq @ A) @ A2) @ X4) & (((ord_less @ A) @ X4) @ D5)) => (P @ X4)))) => (((ord_less_eq @ A) @ D5) @ C2)))))))))))))))))).
% 2.94/1.51 thf(fact_232_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 != B2) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 2.94/1.51 thf(fact_233_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C3:B]: (((A2 = (F @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.94/1.51 thf(fact_234_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C3:B]: (((((ord_less @ A) @ A2) @ B2) => (((F @ B2) = C3) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ B) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ B) @ (F @ A2)) @ C3)))))))))).
% 2.94/1.51 thf(fact_235_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C3:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X4:B,Y4:B]: (((((ord_less @ B) @ X4) @ Y4) => (((ord_less @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C3))))))))))).
% 2.94/1.51 thf(fact_236_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C) @ (F @ B2)) @ C3) => ((! [X4:A,Y4:A]: (((((ord_less @ A) @ X4) @ Y4) => (((ord_less @ C) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less @ C) @ (F @ A2)) @ C3)))))))))).
% 2.94/1.51 thf(fact_237_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X))))))))).
% 2.94/1.51 thf(fact_238_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X12:A]: ((((ord_less @ A) @ X) @ X12))))))))).
% 2.94/1.51 thf(fact_239_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.94/1.51 thf(fact_240_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.94/1.51 thf(fact_241_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.94/1.51 thf(fact_242_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z2:A]: (((((ord_less @ A) @ X) @ Z2) & (((ord_less @ A) @ Z2) @ Y))))))))))).
% 2.94/1.51 thf(fact_243_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.94/1.51 thf(fact_244_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.94/1.51 thf(fact_245_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.94/1.51 thf(fact_246_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z5:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z5) => (((ord_less @ A) @ X) @ Z5))))))))).
% 2.94/1.51 thf(fact_247_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.94/1.51 thf(fact_248_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.94/1.51 thf(fact_249_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.94/1.51 thf(fact_250_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 2.94/1.51 thf(fact_251_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 2.94/1.51 thf(fact_252_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.94/1.51 thf(fact_253_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.94/1.51 thf(fact_254_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X4:A]: (((! [Y6:A]: (((((ord_less @ A) @ Y6) @ X4) => (P @ Y6)))) => (P @ X4)))) => (P @ A2)))))))).
% 2.94/1.51 thf(fact_255_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 2.94/1.51 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((type @ A) @ (type2 @ A)))))).
% 2.94/1.51 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord @ A) @ (type2 @ A)))))).
% 2.94/1.51 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((order @ A) @ (type2 @ A)))))).
% 2.94/1.51 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((preorder @ A) @ (type2 @ A)))))).
% 2.94/1.51 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.94/1.51 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.94/1.51 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.94/1.51 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, ((condit1037483654norder @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, ((ordere223160158up_add @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div, axiom, ((semiring_numeral_div @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.94/1.51 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.94/1.51 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.94/1.51 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.94/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.94/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder_8, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.94/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.94/1.51 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.94/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.94/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.94/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.94/1.51 thf(tfree_0, hypothesis, ((linorder @ a) @ (type2 @ a))).
% 2.94/1.51 thf(conj_0, conjecture, ((linorder_bst @ a) @ (((splay_859309299xt_s_t @ a) @ f) @ a2))).
% 2.94/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2DTF28704.p
% 2.94/1.51 ------------------------
% 2.94/1.55 ---- Cleaned THF ---
% 2.94/1.55 thf(ty_t_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_2011811431op_s_t: $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_Product__Type_Oprod,type,
% 2.94/1.55 product_prod: $tType > $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_Tree_Otree,type,
% 2.94/1.55 tree: $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_List_Olist,type,
% 2.94/1.55 list: $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_Set_Oset,type,
% 2.94/1.55 set: $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_Nat_Onat,type,
% 2.94/1.55 nat: $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_t_itself,type,
% 2.94/1.55 itself: $tType > $tType ).
% 2.94/1.55
% 2.94/1.55 thf(ty_tf_a,type,
% 2.94/1.55 a: $tType ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_HOL_Otype,type,
% 2.94/1.55 type:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.94/1.55 ord:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.94/1.55 order:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Ono__bot,type,
% 2.94/1.55 no_bot:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Ono__top,type,
% 2.94/1.55 no_top:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.94/1.55 linorder:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 2.94/1.55 preorder:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Owellorder,type,
% 2.94/1.55 wellorder:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Orderings_Odense__order,type,
% 2.94/1.55 dense_order:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.94/1.55 linordered_idom:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.94/1.55 linordered_semidom:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Divides_Osemiring__numeral__div,type,
% 2.94/1.55 semiring_numeral_div:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.94/1.55 ordere236663937imp_le:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.94/1.55 ordere223160158up_add:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.94/1.55 strict2144017051up_add:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 2.94/1.55 condit1037483654norder:
% 2.94/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.94/1.55 one_one:
% 2.94/1.55 !>[A: $tType] : A ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.94/1.55 plus_plus:
% 2.94/1.55 !>[A: $tType] : ( A > A > A ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_If,type,
% 2.94/1.55 if:
% 2.94/1.55 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_List_Odistinct,type,
% 2.94/1.55 distinct:
% 2.94/1.55 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.94/1.55 ord_less:
% 2.94/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.94/1.55 ord_less_eq:
% 2.94/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Product__Type_OPair,type,
% 2.94/1.55 product_Pair:
% 2.94/1.55 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Product__Type_Ocurry,type,
% 2.94/1.55 product_curry:
% 2.94/1.55 !>[A: $tType,B: $tType,C: $tType] : ( ( ( product_prod @ A @ B ) > C ) > A > B > C ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.94/1.55 produc2004651681e_prod:
% 2.94/1.55 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.94/1.55 product_rec_prod:
% 2.94/1.55 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Pure_Otype,type,
% 2.94/1.55 type2:
% 2.94/1.55 !>[A: $tType] : ( itself @ A ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Set_OCollect,type,
% 2.94/1.55 collect:
% 2.94/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat,type,
% 2.94/1.55 set_fo292404081st_nat:
% 2.94/1.55 !>[A: $tType] : ( ( nat > A > A ) > nat > nat > A > A ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel,type,
% 2.94/1.55 set_fo2092542664at_rel:
% 2.94/1.55 !>[A: $tType] : ( ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) > ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Odelete,type,
% 2.94/1.55 splay_delete:
% 2.94/1.55 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Oinsert,type,
% 2.94/1.55 splay_insert:
% 2.94/1.55 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Ois__root,type,
% 2.94/1.55 splay_is_root:
% 2.94/1.55 !>[A: $tType] : ( A > ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Osplay,type,
% 2.94/1.55 splay_splay:
% 2.94/1.55 !>[A: $tType] : ( A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Osplay__max,type,
% 2.94/1.55 splay_splay_max:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree_Osplay__rel,type,
% 2.94/1.55 splay_splay_rel:
% 2.94/1.55 !>[A: $tType] : ( ( product_prod @ A @ ( tree @ A ) ) > ( product_prod @ A @ ( tree @ A ) ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_859309299xt_s_t:
% 2.94/1.55 !>[A: $tType] : ( ( splay_2011811431op_s_t @ A ) > ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Onxt_092_060_094sub_062s_092_060_094sub_062t__rel,type,
% 2.94/1.55 splay_1102316486_t_rel:
% 2.94/1.55 !>[A: $tType] : ( ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) > ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_ODelete,type,
% 2.94/1.55 splay_705249169Delete:
% 2.94/1.55 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OInsert,type,
% 2.94/1.55 splay_1105473951Insert:
% 2.94/1.55 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_OSplay,type,
% 2.94/1.55 splay_2088287777_Splay:
% 2.94/1.55 !>[A: $tType] : ( A > ( splay_2011811431op_s_t @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Ocase__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_549499974op_s_t:
% 2.94/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( A > B ) > ( splay_2011811431op_s_t @ A ) > B ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orec__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_2144473850op_s_t:
% 2.94/1.55 !>[A: $tType,C: $tType] : ( ( A > C ) > ( A > C ) > ( A > C ) > ( splay_2011811431op_s_t @ A ) > C ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Orel__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_434753539op_s_t:
% 2.94/1.55 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Oop_092_060_094sub_062s_092_060_094sub_062t_Oset__op_092_060_094sub_062s_092_060_094sub_062t,type,
% 2.94/1.55 splay_1816468620op_s_t:
% 2.94/1.55 !>[A: $tType] : ( ( splay_2011811431op_s_t @ A ) > ( set @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay,type,
% 2.94/1.55 splay_914434265_splay:
% 2.94/1.55 !>[A: $tType] : ( A > ( tree @ A ) > nat ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max,type,
% 2.94/1.55 splay_878424299ay_max:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > nat ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Splay__Tree__Analysis__Base_Ot__splay__max__rel,type,
% 2.94/1.55 splay_1816415694ax_rel:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Oinorder,type,
% 2.94/1.55 inorder:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( list @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Olinorder__class_Obst,type,
% 2.94/1.55 linorder_bst:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Olinorder__class_Obst__eq,type,
% 2.94/1.55 linorder_bst_eq:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Olinorder__class_Obst__eq__rel,type,
% 2.94/1.55 linorder_bst_eq_rel:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Olinorder__class_Obst__rel,type,
% 2.94/1.55 linorder_bst_rel:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( tree @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Opreorder,type,
% 2.94/1.55 preorder2:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( list @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Otree_OLeaf,type,
% 2.94/1.55 leaf:
% 2.94/1.55 !>[A: $tType] : ( tree @ A ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Otree_ONode,type,
% 2.94/1.55 node:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > A > ( tree @ A ) > ( tree @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Tree_Otree_Oset__tree,type,
% 2.94/1.55 set_tree:
% 2.94/1.55 !>[A: $tType] : ( ( tree @ A ) > ( set @ A ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Wellfounded_Oaccp,type,
% 2.94/1.55 accp:
% 2.94/1.55 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Wellfounded_Olex__prod,type,
% 2.94/1.55 lex_prod:
% 2.94/1.55 !>[A: $tType,B: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ B @ B ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Wellfounded_Omeasure,type,
% 2.94/1.55 measure:
% 2.94/1.55 !>[A: $tType] : ( ( A > nat ) > ( set @ ( product_prod @ A @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_Wfrec_Osame__fst,type,
% 2.94/1.55 same_fst:
% 2.94/1.55 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > ( set @ ( product_prod @ B @ B ) ) ) > ( set @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_c_member,type,
% 2.94/1.55 member:
% 2.94/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.94/1.55
% 2.94/1.55 thf(sy_v_a____,type,
% 2.94/1.55 a2: tree @ a ).
% 2.94/1.55
% 2.94/1.55 thf(sy_v_f____,type,
% 2.94/1.55 f: splay_2011811431op_s_t @ a ).
% 2.94/1.55
% 2.94/1.55 thf(fact_0__C2_C,axiom,
% 2.94/1.55 linorder_bst @ a @ a2 ).
% 2.94/1.55
% 2.94/1.55 thf(fact_1_bst__delete,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( linorder_bst @ A @ ( splay_delete @ A @ A2 @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_2_bst__insert,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( linorder_bst @ A @ ( splay_insert @ A @ A2 @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_3_bst__splay__max,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( linorder_bst @ A @ ( splay_splay_max @ A @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_4_bst__eq__if__bst,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( linorder_bst_eq @ A @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_5_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,T2: tree @ A] :
% 2.94/1.55 ( ( splay_859309299xt_s_t @ A @ ( splay_705249169Delete @ A @ A2 ) @ T2 )
% 2.94/1.55 = ( splay_delete @ A @ A2 @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_6_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,T2: tree @ A] :
% 2.94/1.55 ( ( splay_859309299xt_s_t @ A @ ( splay_1105473951Insert @ A @ A2 ) @ T2 )
% 2.94/1.55 = ( splay_insert @ A @ A2 @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_7_bst__splay,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( linorder_bst @ A @ ( splay_splay @ A @ A2 @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_8_bst_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ( linorder_bst @ A @ ( leaf @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_9_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,T2: tree @ A] :
% 2.94/1.55 ( ( splay_859309299xt_s_t @ A @ ( splay_2088287777_Splay @ A @ A2 ) @ T2 )
% 2.94/1.55 = ( splay_splay @ A @ A2 @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_10_splay__max__eq__splay__ex,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ? [A3: A] :
% 2.94/1.55 ( ( splay_splay_max @ A @ T2 )
% 2.94/1.55 = ( splay_splay @ A @ A3 @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_11_distinct__preorder__if__bst,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( distinct @ A @ ( preorder2 @ A @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_12_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,X3: A,Y3: A] :
% 2.94/1.55 ( ( ( splay_705249169Delete @ A @ X3 )
% 2.94/1.55 = ( splay_705249169Delete @ A @ Y3 ) )
% 2.94/1.55 = ( X3 = Y3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_13_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,X2: A,Y2: A] :
% 2.94/1.55 ( ( ( splay_1105473951Insert @ A @ X2 )
% 2.94/1.55 = ( splay_1105473951Insert @ A @ Y2 ) )
% 2.94/1.55 = ( X2 = Y2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_14_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,X1: A,Y1: A] :
% 2.94/1.55 ( ( ( splay_2088287777_Splay @ A @ X1 )
% 2.94/1.55 = ( splay_2088287777_Splay @ A @ Y1 ) )
% 2.94/1.55 = ( X1 = Y1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_15_splay__Leaf__iff,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,T2: tree @ A] :
% 2.94/1.55 ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 = ( T2
% 2.94/1.55 = ( leaf @ A ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_16_splay__max__Leaf__iff,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( ( splay_splay_max @ A @ T2 )
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 = ( T2
% 2.94/1.55 = ( leaf @ A ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_17_splay_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A] :
% 2.94/1.55 ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 2.94/1.55 = ( leaf @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_18_splay__max_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ( ( splay_splay_max @ A @ ( leaf @ A ) )
% 2.94/1.55 = ( leaf @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_19_bst__eq_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ( linorder_bst_eq @ A @ ( leaf @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_20_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I5_J,axiom,
% 2.94/1.55 ! [A: $tType,X2: A,X3: A] :
% 2.94/1.55 ( ( splay_1105473951Insert @ A @ X2 )
% 2.94/1.55 != ( splay_705249169Delete @ A @ X3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_21_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,X1: A,X3: A] :
% 2.94/1.55 ( ( splay_2088287777_Splay @ A @ X1 )
% 2.94/1.55 != ( splay_705249169Delete @ A @ X3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_22_op_092_060_094sub_062s_092_060_094sub_062t_Odistinct_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,X1: A,X2: A] :
% 2.94/1.55 ( ( splay_2088287777_Splay @ A @ X1 )
% 2.94/1.55 != ( splay_1105473951Insert @ A @ X2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_23_nxt_092_060_094sub_062s_092_060_094sub_062t_Oelims,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: splay_2011811431op_s_t @ A,Xa: tree @ A,Y: tree @ A] :
% 2.94/1.55 ( ( ( splay_859309299xt_s_t @ A @ X @ Xa )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_2088287777_Splay @ A @ A3 ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 != ( splay_splay @ A @ A3 @ Xa ) ) )
% 2.94/1.55 => ( ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_1105473951Insert @ A @ A3 ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 != ( splay_insert @ A @ A3 @ Xa ) ) )
% 2.94/1.55 => ~ ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_705249169Delete @ A @ A3 ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 != ( splay_delete @ A @ A3 @ Xa ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_24_op_092_060_094sub_062s_092_060_094sub_062t_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType,P: ( splay_2011811431op_s_t @ A ) > $o,Op_s_t: splay_2011811431op_s_t @ A] :
% 2.94/1.55 ( ! [X4: A] : ( P @ ( splay_2088287777_Splay @ A @ X4 ) )
% 2.94/1.55 => ( ! [X4: A] : ( P @ ( splay_1105473951Insert @ A @ X4 ) )
% 2.94/1.55 => ( ! [X4: A] : ( P @ ( splay_705249169Delete @ A @ X4 ) )
% 2.94/1.55 => ( P @ Op_s_t ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_25_nxt_092_060_094sub_062s_092_060_094sub_062t_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [P: ( splay_2011811431op_s_t @ A ) > ( tree @ A ) > $o,A0: splay_2011811431op_s_t @ A,A1: tree @ A] :
% 2.94/1.55 ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_2088287777_Splay @ A @ A3 ) @ X12 )
% 2.94/1.55 => ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_1105473951Insert @ A @ A3 ) @ X12 )
% 2.94/1.55 => ( ! [A3: A,X12: tree @ A] : ( P @ ( splay_705249169Delete @ A @ A3 ) @ X12 )
% 2.94/1.55 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_26_op_092_060_094sub_062s_092_060_094sub_062t_Oexhaust,axiom,
% 2.94/1.55 ! [A: $tType,Y: splay_2011811431op_s_t @ A] :
% 2.94/1.55 ( ! [X12: A] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( splay_2088287777_Splay @ A @ X12 ) )
% 2.94/1.55 => ( ! [X22: A] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( splay_1105473951Insert @ A @ X22 ) )
% 2.94/1.55 => ~ ! [X32: A] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( splay_705249169Delete @ A @ X32 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_27_op_092_060_094sub_062s_092_060_094sub_062t_Oset__cases,axiom,
% 2.94/1.55 ! [A: $tType,E: A,A2: splay_2011811431op_s_t @ A] :
% 2.94/1.55 ( ( member @ A @ E @ ( splay_1816468620op_s_t @ A @ A2 ) )
% 2.94/1.55 => ( ( A2
% 2.94/1.55 != ( splay_2088287777_Splay @ A @ E ) )
% 2.94/1.55 => ( ( A2
% 2.94/1.55 != ( splay_1105473951Insert @ A @ E ) )
% 2.94/1.55 => ( A2
% 2.94/1.55 = ( splay_705249169Delete @ A @ E ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_28_nxt_092_060_094sub_062s_092_060_094sub_062t_Opelims,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: splay_2011811431op_s_t @ A,Xa: tree @ A,Y: tree @ A] :
% 2.94/1.55 ( ( ( splay_859309299xt_s_t @ A @ X @ Xa )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ X @ Xa ) )
% 2.94/1.55 => ( ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_2088287777_Splay @ A @ A3 ) )
% 2.94/1.55 => ( ( Y
% 2.94/1.55 = ( splay_splay @ A @ A3 @ Xa ) )
% 2.94/1.55 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_2088287777_Splay @ A @ A3 ) @ Xa ) ) ) )
% 2.94/1.55 => ( ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_1105473951Insert @ A @ A3 ) )
% 2.94/1.55 => ( ( Y
% 2.94/1.55 = ( splay_insert @ A @ A3 @ Xa ) )
% 2.94/1.55 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_1105473951Insert @ A @ A3 ) @ Xa ) ) ) )
% 2.94/1.55 => ~ ! [A3: A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( splay_705249169Delete @ A @ A3 ) )
% 2.94/1.55 => ( ( Y
% 2.94/1.55 = ( splay_delete @ A @ A3 @ Xa ) )
% 2.94/1.55 => ~ ( accp @ ( product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) ) @ ( splay_1102316486_t_rel @ A ) @ ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_705249169Delete @ A @ A3 ) @ Xa ) ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_29_nxt_092_060_094sub_062s_092_060_094sub_062t_Ocases,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: product_prod @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A )] :
% 2.94/1.55 ( ! [A3: A,T3: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_2088287777_Splay @ A @ A3 ) @ T3 ) )
% 2.94/1.55 => ( ! [A3: A,T3: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_1105473951Insert @ A @ A3 ) @ T3 ) )
% 2.94/1.55 => ~ ! [A3: A,T3: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ ( splay_2011811431op_s_t @ A ) @ ( tree @ A ) @ ( splay_705249169Delete @ A @ A3 ) @ T3 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_30_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cases,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,A2: splay_2011811431op_s_t @ A,B2: splay_2011811431op_s_t @ B] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ A2 @ B2 )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ( A2
% 2.94/1.55 = ( splay_2088287777_Splay @ A @ X4 ) )
% 2.94/1.55 => ! [Y4: B] :
% 2.94/1.55 ( ( B2
% 2.94/1.55 = ( splay_2088287777_Splay @ B @ Y4 ) )
% 2.94/1.55 => ~ ( R @ X4 @ Y4 ) ) )
% 2.94/1.55 => ( ! [Xa2: A] :
% 2.94/1.55 ( ( A2
% 2.94/1.55 = ( splay_1105473951Insert @ A @ Xa2 ) )
% 2.94/1.55 => ! [Ya: B] :
% 2.94/1.55 ( ( B2
% 2.94/1.55 = ( splay_1105473951Insert @ B @ Ya ) )
% 2.94/1.55 => ~ ( R @ Xa2 @ Ya ) ) )
% 2.94/1.55 => ~ ! [Xb: A] :
% 2.94/1.55 ( ( A2
% 2.94/1.55 = ( splay_705249169Delete @ A @ Xb ) )
% 2.94/1.55 => ! [Yb: B] :
% 2.94/1.55 ( ( B2
% 2.94/1.55 = ( splay_705249169Delete @ B @ Yb ) )
% 2.94/1.55 => ~ ( R @ Xb @ Yb ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_31_op_092_060_094sub_062s_092_060_094sub_062t_Orel__induct,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Q: ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 2.94/1.55 => ( ! [A12: A,B1: B] :
% 2.94/1.55 ( ( R @ A12 @ B1 )
% 2.94/1.55 => ( Q @ ( splay_2088287777_Splay @ A @ A12 ) @ ( splay_2088287777_Splay @ B @ B1 ) ) )
% 2.94/1.55 => ( ! [A22: A,B22: B] :
% 2.94/1.55 ( ( R @ A22 @ B22 )
% 2.94/1.55 => ( Q @ ( splay_1105473951Insert @ A @ A22 ) @ ( splay_1105473951Insert @ B @ B22 ) ) )
% 2.94/1.55 => ( ! [A32: A,B3: B] :
% 2.94/1.55 ( ( R @ A32 @ B3 )
% 2.94/1.55 => ( Q @ ( splay_705249169Delete @ A @ A32 ) @ ( splay_705249169Delete @ B @ B3 ) ) )
% 2.94/1.55 => ( Q @ X @ Y ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_32_distinct__inorder__if__bst,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( distinct @ A @ ( inorder @ A @ T2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_33_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I15_J,axiom,
% 2.94/1.55 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X3: A] :
% 2.94/1.55 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_705249169Delete @ A @ X3 ) )
% 2.94/1.55 = ( F3 @ X3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_34_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I14_J,axiom,
% 2.94/1.55 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X2: A] :
% 2.94/1.55 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_1105473951Insert @ A @ X2 ) )
% 2.94/1.55 = ( F2 @ X2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_35_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I13_J,axiom,
% 2.94/1.55 ! [C: $tType,A: $tType,F1: A > C,F2: A > C,F3: A > C,X1: A] :
% 2.94/1.55 ( ( splay_2144473850op_s_t @ A @ C @ F1 @ F2 @ F3 @ ( splay_2088287777_Splay @ A @ X1 ) )
% 2.94/1.55 = ( F1 @ X1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_36_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I12_J,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X3: A] :
% 2.94/1.55 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_705249169Delete @ A @ X3 ) )
% 2.94/1.55 = ( F3 @ X3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_37_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I11_J,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X2: A] :
% 2.94/1.55 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_1105473951Insert @ A @ X2 ) )
% 2.94/1.55 = ( F2 @ X2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_38_insert_Ocases,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: product_prod @ A @ ( tree @ A )] :
% 2.94/1.55 ~ ! [X4: A,T3: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ A @ ( tree @ A ) @ X4 @ T3 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_39_op_092_060_094sub_062s_092_060_094sub_062t_Orel__eq,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ A
% 2.94/1.55 @ ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.94/1.55 = ( ^ [Y5: splay_2011811431op_s_t @ A,Z: splay_2011811431op_s_t @ A] : ( Y5 = Z ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_40_op_092_060_094sub_062s_092_060_094sub_062t_Orel__cong,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,X: splay_2011811431op_s_t @ A,Ya2: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Xa: splay_2011811431op_s_t @ B,R: A > B > $o,Ra: A > B > $o] :
% 2.94/1.55 ( ( X = Ya2 )
% 2.94/1.55 => ( ( Y = Xa )
% 2.94/1.55 => ( ! [Z2: A,Yb: B] :
% 2.94/1.55 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ Ya2 ) )
% 2.94/1.55 => ( ( member @ B @ Yb @ ( splay_1816468620op_s_t @ B @ Xa ) )
% 2.94/1.55 => ( ( R @ Z2 @ Yb )
% 2.94/1.55 = ( Ra @ Z2 @ Yb ) ) ) )
% 2.94/1.55 => ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 2.94/1.55 = ( splay_434753539op_s_t @ A @ B @ Ra @ Ya2 @ Xa ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_41_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl,axiom,
% 2.94/1.55 ! [B: $tType,Ra: B > B > $o,X: splay_2011811431op_s_t @ B] :
% 2.94/1.55 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 2.94/1.55 => ( splay_434753539op_s_t @ B @ B @ Ra @ X @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_42_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono__strong,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X: splay_2011811431op_s_t @ A,Y: splay_2011811431op_s_t @ B,Ra: A > B > $o] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ X @ Y )
% 2.94/1.55 => ( ! [Z2: A,Yb: B] :
% 2.94/1.55 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ X ) )
% 2.94/1.55 => ( ( member @ B @ Yb @ ( splay_1816468620op_s_t @ B @ Y ) )
% 2.94/1.55 => ( ( R @ Z2 @ Yb )
% 2.94/1.55 => ( Ra @ Z2 @ Yb ) ) ) )
% 2.94/1.55 => ( splay_434753539op_s_t @ A @ B @ Ra @ X @ Y ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_43_op_092_060_094sub_062s_092_060_094sub_062t_Orel__refl__strong,axiom,
% 2.94/1.55 ! [A: $tType,X: splay_2011811431op_s_t @ A,Ra: A > A > $o] :
% 2.94/1.55 ( ! [Z2: A] :
% 2.94/1.55 ( ( member @ A @ Z2 @ ( splay_1816468620op_s_t @ A @ X ) )
% 2.94/1.55 => ( Ra @ Z2 @ Z2 ) )
% 2.94/1.55 => ( splay_434753539op_s_t @ A @ A @ Ra @ X @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_44_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y1: B] :
% 2.94/1.55 ( ( R @ X1 @ Y1 )
% 2.94/1.55 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_2088287777_Splay @ B @ Y1 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 2.94/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 2.94/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.94/1.55 = ( P @ A2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 2.94/1.55 ! [A: $tType,A4: set @ A] :
% 2.94/1.55 ( ( collect @ A
% 2.94/1.55 @ ^ [X5: A] : ( member @ A @ X5 @ A4 ) )
% 2.94/1.55 = A4 ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_47_Collect__cong,axiom,
% 2.94/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.94/1.55 ( ! [X4: A] :
% 2.94/1.55 ( ( P @ X4 )
% 2.94/1.55 = ( Q @ X4 ) )
% 2.94/1.55 => ( ( collect @ A @ P )
% 2.94/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_48_ext,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.94/1.55 ( ! [X4: A] :
% 2.94/1.55 ( ( F @ X4 )
% 2.94/1.55 = ( G @ X4 ) )
% 2.94/1.55 => ( F = G ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_49_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y2: B] :
% 2.94/1.55 ( ( R @ X2 @ Y2 )
% 2.94/1.55 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_1105473951Insert @ B @ Y2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_50_op_092_060_094sub_062s_092_060_094sub_062t_Orel__intros_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y3: B] :
% 2.94/1.55 ( ( R @ X3 @ Y3 )
% 2.94/1.55 => ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ X3 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_51_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y1: B] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_2088287777_Splay @ B @ Y1 ) )
% 2.94/1.55 = ( R @ X1 @ Y1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_52_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y2: B] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_1105473951Insert @ B @ Y2 ) )
% 2.94/1.55 = ( R @ X2 @ Y2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_53_op_092_060_094sub_062s_092_060_094sub_062t_Orel__inject_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y3: B] :
% 2.94/1.55 ( ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ X3 ) @ ( splay_705249169Delete @ B @ Y3 ) )
% 2.94/1.55 = ( R @ X3 @ Y3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_54_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( splay_1816468620op_s_t @ A @ ( splay_2088287777_Splay @ A @ A2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_55_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,Aa: A] : ( member @ A @ Aa @ ( splay_1816468620op_s_t @ A @ ( splay_1105473951Insert @ A @ Aa ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_56_op_092_060_094sub_062s_092_060_094sub_062t_Oset__intros_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,Ab: A] : ( member @ A @ Ab @ ( splay_1816468620op_s_t @ A @ ( splay_705249169Delete @ A @ Ab ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_57_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y2: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_1105473951Insert @ B @ Y2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_58_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,Y2: A,X1: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ Y2 ) @ ( splay_2088287777_Splay @ B @ X1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_59_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X1: A,Y3: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_2088287777_Splay @ A @ X1 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_60_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I4_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,Y3: A,X1: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ Y3 ) @ ( splay_2088287777_Splay @ B @ X1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_61_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I5_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,X2: A,Y3: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_1105473951Insert @ A @ X2 ) @ ( splay_705249169Delete @ B @ Y3 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_62_op_092_060_094sub_062s_092_060_094sub_062t_Orel__distinct_I6_J,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,R: A > B > $o,Y3: A,X2: B] :
% 2.94/1.55 ~ ( splay_434753539op_s_t @ A @ B @ R @ ( splay_705249169Delete @ A @ Y3 ) @ ( splay_1105473951Insert @ B @ X2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_63_op_092_060_094sub_062s_092_060_094sub_062t_Osimps_I10_J,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,F1: A > B,F2: A > B,F3: A > B,X1: A] :
% 2.94/1.55 ( ( splay_549499974op_s_t @ A @ B @ F1 @ F2 @ F3 @ ( splay_2088287777_Splay @ A @ X1 ) )
% 2.94/1.55 = ( F1 @ X1 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_64_old_Oprod_Oinject,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 2.94/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.94/1.55 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 2.94/1.55 = ( ( A2 = A5 )
% 2.94/1.55 & ( B2 = B4 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_65_prod_Oinject,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 2.94/1.55 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 2.94/1.55 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.94/1.55 = ( ( X1 = Y1 )
% 2.94/1.55 & ( X2 = Y2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_66_splay_Opsimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A] :
% 2.94/1.55 ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( leaf @ A ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( leaf @ A ) )
% 2.94/1.55 = ( leaf @ A ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_67_accp__induct__rule,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,A2: A,P: A > $o] :
% 2.94/1.55 ( ( accp @ A @ R2 @ A2 )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ( accp @ A @ R2 @ X4 )
% 2.94/1.55 => ( ! [Y6: A] :
% 2.94/1.55 ( ( R2 @ Y6 @ X4 )
% 2.94/1.55 => ( P @ Y6 ) )
% 2.94/1.55 => ( P @ X4 ) ) )
% 2.94/1.55 => ( P @ A2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_68_not__accp__down,axiom,
% 2.94/1.55 ! [A: $tType,R: A > A > $o,X: A] :
% 2.94/1.55 ( ~ ( accp @ A @ R @ X )
% 2.94/1.55 => ~ ! [Z2: A] :
% 2.94/1.55 ( ( R @ Z2 @ X )
% 2.94/1.55 => ( accp @ A @ R @ Z2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_69_accp__downward,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,B2: A,A2: A] :
% 2.94/1.55 ( ( accp @ A @ R2 @ B2 )
% 2.94/1.55 => ( ( R2 @ A2 @ B2 )
% 2.94/1.55 => ( accp @ A @ R2 @ A2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_70_accp_Oinducts,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,X: A,P: A > $o] :
% 2.94/1.55 ( ( accp @ A @ R2 @ X )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ! [Y6: A] :
% 2.94/1.55 ( ( R2 @ Y6 @ X4 )
% 2.94/1.55 => ( accp @ A @ R2 @ Y6 ) )
% 2.94/1.55 => ( ! [Y6: A] :
% 2.94/1.55 ( ( R2 @ Y6 @ X4 )
% 2.94/1.55 => ( P @ Y6 ) )
% 2.94/1.55 => ( P @ X4 ) ) )
% 2.94/1.55 => ( P @ X ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_71_accp__induct,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,A2: A,P: A > $o] :
% 2.94/1.55 ( ( accp @ A @ R2 @ A2 )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ( accp @ A @ R2 @ X4 )
% 2.94/1.55 => ( ! [Y6: A] :
% 2.94/1.55 ( ( R2 @ Y6 @ X4 )
% 2.94/1.55 => ( P @ Y6 ) )
% 2.94/1.55 => ( P @ X4 ) ) )
% 2.94/1.55 => ( P @ A2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_72_accp_Ointros,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,X: A] :
% 2.94/1.55 ( ! [Y4: A] :
% 2.94/1.55 ( ( R2 @ Y4 @ X )
% 2.94/1.55 => ( accp @ A @ R2 @ Y4 ) )
% 2.94/1.55 => ( accp @ A @ R2 @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_73_surj__pair,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.94/1.55 ? [X4: A,Y4: B] :
% 2.94/1.55 ( P2
% 2.94/1.55 = ( product_Pair @ A @ B @ X4 @ Y4 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_74_prod__cases,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.94/1.55 ( ! [A3: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 2.94/1.55 => ( P @ P2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_75_Pair__inject,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B] :
% 2.94/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.94/1.55 = ( product_Pair @ A @ B @ A5 @ B4 ) )
% 2.94/1.55 => ~ ( ( A2 = A5 )
% 2.94/1.55 => ( B2 != B4 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_76_prod__cases3,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.94/1.55 ~ ! [A3: A,B5: B,C2: C] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_77_prod__cases4,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.94/1.55 ~ ! [A3: A,B5: B,C2: C,D2: D] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_78_prod__cases5,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.94/1.55 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_79_prod__cases6,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) )] :
% 2.94/1.55 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F4 ) @ D2 @ ( product_Pair @ E2 @ F4 @ E3 @ F5 ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_80_prod__cases7,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 2.94/1.55 ~ ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4,G3: G2] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F4 @ G2 ) @ E3 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_81_prod__induct3,axiom,
% 2.94/1.55 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.94/1.55 ( ! [A3: A,B5: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A3 @ ( product_Pair @ B @ C @ B5 @ C2 ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_82_prod__induct4,axiom,
% 2.94/1.55 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.94/1.55 ( ! [A3: A,B5: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B5 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_83_prod__induct5,axiom,
% 2.94/1.55 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.94/1.55 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_84_prod__induct6,axiom,
% 2.94/1.55 ! [F4: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) )] :
% 2.94/1.55 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F4 ) @ D2 @ ( product_Pair @ E2 @ F4 @ E3 @ F5 ) ) ) ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_85_prod__induct7,axiom,
% 2.94/1.55 ! [G2: $tType,F4: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 2.94/1.55 ( ! [A3: A,B5: B,C2: C,D2: D,E3: E2,F5: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A3 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) ) @ B5 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F4 @ G2 ) @ E3 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_86_old_Oprod_Oexhaust,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.94/1.55 ~ ! [A3: A,B5: B] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( product_Pair @ A @ B @ A3 @ B5 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_87_old_Oprod_Oinducts,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.94/1.55 ( ! [A3: A,B5: B] : ( P @ ( product_Pair @ A @ B @ A3 @ B5 ) )
% 2.94/1.55 => ( P @ Prod ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_88_accp_Ocases,axiom,
% 2.94/1.55 ! [A: $tType,R2: A > A > $o,A2: A] :
% 2.94/1.55 ( ( accp @ A @ R2 @ A2 )
% 2.94/1.55 => ! [Y6: A] :
% 2.94/1.55 ( ( R2 @ Y6 @ A2 )
% 2.94/1.55 => ( accp @ A @ R2 @ Y6 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_89_accp_Osimps,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( accp @ A )
% 2.94/1.55 = ( ^ [R3: A > A > $o,A6: A] :
% 2.94/1.55 ? [X5: A] :
% 2.94/1.55 ( ( A6 = X5 )
% 2.94/1.55 & ! [Y7: A] :
% 2.94/1.55 ( ( R3 @ Y7 @ X5 )
% 2.94/1.55 => ( accp @ A @ R3 @ Y7 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_90_old_Oprod_Orec,axiom,
% 2.94/1.55 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.94/1.55 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.94/1.55 = ( F1 @ A2 @ B2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_91_in__lex__prod,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B4: B,R2: set @ ( product_prod @ A @ A ),S: set @ ( product_prod @ B @ B )] :
% 2.94/1.55 ( ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ A5 @ B4 ) ) @ ( lex_prod @ A @ B @ R2 @ S ) )
% 2.94/1.55 = ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A5 ) @ R2 )
% 2.94/1.55 | ( ( A2 = A5 )
% 2.94/1.55 & ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ B2 @ B4 ) @ S ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_92_splay_Opsimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ L @ A2 @ R2 ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 = ( node @ A @ L @ A2 @ R2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_93_internal__case__prod__conv,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.94/1.55 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.94/1.55 = ( C3 @ A2 @ B2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_94_ssubst__Pair__rhs,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,R2: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 2.94/1.55 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S ) @ R )
% 2.94/1.55 => ( ( S2 = S )
% 2.94/1.55 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_95_curry__conv,axiom,
% 2.94/1.55 ! [A: $tType,C: $tType,B: $tType] :
% 2.94/1.55 ( ( product_curry @ B @ C @ A )
% 2.94/1.55 = ( ^ [F6: ( product_prod @ B @ C ) > A,A6: B,B6: C] : ( F6 @ ( product_Pair @ B @ C @ A6 @ B6 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_96_curryI,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.94/1.55 ( ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.94/1.55 => ( product_curry @ A @ B @ $o @ F @ A2 @ B2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_97_tree_Oinject,axiom,
% 2.94/1.55 ! [A: $tType,X21: tree @ A,X222: A,X23: tree @ A,Y21: tree @ A,Y22: A,Y23: tree @ A] :
% 2.94/1.55 ( ( ( node @ A @ X21 @ X222 @ X23 )
% 2.94/1.55 = ( node @ A @ Y21 @ Y22 @ Y23 ) )
% 2.94/1.55 = ( ( X21 = Y21 )
% 2.94/1.55 & ( X222 = Y22 )
% 2.94/1.55 & ( X23 = Y23 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_98_t__splay__max_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.94/1.55 ( ( P @ ( leaf @ A ) )
% 2.94/1.55 => ( ! [L2: tree @ A,B5: A] : ( P @ ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 2.94/1.55 => ( ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.94/1.55 ( ( ( Rr
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( P @ Rr ) )
% 2.94/1.55 => ( P @ ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) )
% 2.94/1.55 => ( P @ A0 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_99_t__splay__max_Ocases,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ! [L2: tree @ A,B5: A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_100__092_060Phi_062_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.94/1.55 ( ( P @ ( leaf @ A ) )
% 2.94/1.55 => ( ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( P @ L2 )
% 2.94/1.55 => ( ( P @ R4 )
% 2.94/1.55 => ( P @ ( node @ A @ L2 @ A3 @ R4 ) ) ) )
% 2.94/1.55 => ( P @ A0 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_101__092_060Phi_062_Ocases,axiom,
% 2.94/1.55 ! [A: $tType,X: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( node @ A @ L2 @ A3 @ R4 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_102_bst__eq_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.94/1.55 ( ( P @ ( leaf @ A ) )
% 2.94/1.55 => ( ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( P @ L2 )
% 2.94/1.55 => ( ( P @ R4 )
% 2.94/1.55 => ( P @ ( node @ A @ L2 @ A3 @ R4 ) ) ) )
% 2.94/1.55 => ( P @ A0 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_103_bst__eq_Ocases,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_104_mirror_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType,P: ( tree @ A ) > $o,A0: tree @ A] :
% 2.94/1.55 ( ( P @ ( leaf @ A ) )
% 2.94/1.55 => ( ! [L2: tree @ A,X4: A,R4: tree @ A] :
% 2.94/1.55 ( ( P @ R4 )
% 2.94/1.55 => ( ( P @ L2 )
% 2.94/1.55 => ( P @ ( node @ A @ L2 @ X4 @ R4 ) ) ) )
% 2.94/1.55 => ( P @ A0 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_105_tree_Oexhaust,axiom,
% 2.94/1.55 ! [A: $tType,Y: tree @ A] :
% 2.94/1.55 ( ( Y
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ~ ! [X212: tree @ A,X223: A,X232: tree @ A] :
% 2.94/1.55 ( Y
% 2.94/1.55 != ( node @ A @ X212 @ X223 @ X232 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_106_neq__Leaf__iff,axiom,
% 2.94/1.55 ! [A: $tType,T2: tree @ A] :
% 2.94/1.55 ( ( T2
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 = ( ? [L3: tree @ A,A6: A,R3: tree @ A] :
% 2.94/1.55 ( T2
% 2.94/1.55 = ( node @ A @ L3 @ A6 @ R3 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_107_tree_Oinduct,axiom,
% 2.94/1.55 ! [A: $tType,P: ( tree @ A ) > $o,Tree: tree @ A] :
% 2.94/1.55 ( ( P @ ( leaf @ A ) )
% 2.94/1.55 => ( ! [X12: tree @ A,X22: A,X32: tree @ A] :
% 2.94/1.55 ( ( P @ X12 )
% 2.94/1.55 => ( ( P @ X32 )
% 2.94/1.55 => ( P @ ( node @ A @ X12 @ X22 @ X32 ) ) ) )
% 2.94/1.55 => ( P @ Tree ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_108_tree_Odistinct_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,X21: tree @ A,X222: A,X23: tree @ A] :
% 2.94/1.55 ( ( leaf @ A )
% 2.94/1.55 != ( node @ A @ X21 @ X222 @ X23 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_109_splay_Osimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( splay_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 = ( node @ A @ L @ A2 @ R2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_110_curryE,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.94/1.55 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.94/1.55 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_111_curryD,axiom,
% 2.94/1.55 ! [A: $tType,B: $tType,F: ( product_prod @ A @ B ) > $o,A2: A,B2: B] :
% 2.94/1.55 ( ( product_curry @ A @ B @ $o @ F @ A2 @ B2 )
% 2.94/1.55 => ( F @ ( product_Pair @ A @ B @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_112_splay__not__Leaf,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( T2
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ? [L2: tree @ A,X4: A,R4: tree @ A] :
% 2.94/1.55 ( ( splay_splay @ A @ A2 @ T2 )
% 2.94/1.55 = ( node @ A @ L2 @ X4 @ R4 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_113_t__splay_Ocases,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: product_prod @ A @ ( tree @ A )] :
% 2.94/1.55 ( ! [A3: A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ A @ ( tree @ A ) @ A3 @ ( leaf @ A ) ) )
% 2.94/1.55 => ~ ! [A3: A,L2: tree @ A,B5: A,R4: tree @ A] :
% 2.94/1.55 ( X
% 2.94/1.55 != ( product_Pair @ A @ ( tree @ A ) @ A3 @ ( node @ A @ L2 @ B5 @ R4 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_114_splay__max__Leaf,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,L: tree @ A,A2: A,R2: tree @ A] :
% 2.94/1.55 ( ( ( splay_splay_max @ A @ T2 )
% 2.94/1.55 = ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 => ( R2
% 2.94/1.55 = ( leaf @ A ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_115_splay__max_Osimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [La: tree @ A,A2: A] :
% 2.94/1.55 ( ( splay_splay_max @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) )
% 2.94/1.55 = ( node @ A @ La @ A2 @ ( leaf @ A ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_116_splay_Opsimps_I13_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,B2: A,La: tree @ A,Lb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( ord_less @ A @ B2 @ X )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B2 @ ( leaf @ A ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_117_splay_Opsimps_I12_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,B2: A,La: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_118_splay_Opsimps_I10_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,L: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) )
% 2.94/1.55 = ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_119_splay_Opsimps_I7_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: A,B2: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_120_splay_Opsimps_I5_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: A,A2: A,B2: A,Ra2: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ X @ A2 )
% 2.94/1.55 => ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_121_splay_Osimps_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_122_splay_Osimps_I9_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ Lb @ B2 @ La ) @ A2 @ Ra2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_123_splay_Osimps_I13_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,B2: A,La: tree @ A,Lb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( ord_less @ A @ B2 @ X )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ Lb @ B2 @ ( leaf @ A ) ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ La @ A2 @ Lb ) @ B2 @ ( leaf @ A ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_124_splay_Osimps_I12_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,B2: A,La: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_125_splay_Osimps_I10_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,X: A,L: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ L @ A2 @ ( leaf @ A ) ) )
% 2.94/1.55 = ( node @ A @ L @ A2 @ ( leaf @ A ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_126_splay_Osimps_I7_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: A,B2: A,A2: A,La: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( ord_less @ A @ A2 @ X )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ La @ A2 @ ( leaf @ A ) ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ La @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ Rb ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_127_splay_Osimps_I5_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: A,A2: A,B2: A,Ra2: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ X @ A2 )
% 2.94/1.55 => ( ( ord_less @ A @ X @ B2 )
% 2.94/1.55 => ( ( splay_splay @ A @ X @ ( node @ A @ ( node @ A @ ( leaf @ A ) @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ ( leaf @ A ) @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_128_splay_Osimps_I4_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 2.94/1.55 = ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_129_splay_Opsimps_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,La: tree @ A,Ra2: tree @ A,Rb: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( node @ A @ La @ A2 @ Ra2 ) @ B2 @ Rb ) )
% 2.94/1.55 = ( node @ A @ La @ A2 @ ( node @ A @ Ra2 @ B2 @ Rb ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_130_splay_Opsimps_I9_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,Lb: tree @ A,La: tree @ A,Ra2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ Lb @ B2 @ ( node @ A @ La @ A2 @ Ra2 ) ) )
% 2.94/1.55 = ( node @ A @ ( node @ A @ Lb @ B2 @ La ) @ A2 @ Ra2 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_131_splay_Opsimps_I4_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( accp @ ( product_prod @ A @ ( tree @ A ) ) @ ( splay_splay_rel @ A ) @ ( product_Pair @ A @ ( tree @ A ) @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) )
% 2.94/1.55 => ( ( splay_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 2.94/1.55 = ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_132_in__measure,axiom,
% 2.94/1.55 ! [A: $tType,X: A,Y: A,F: A > nat] :
% 2.94/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ ( measure @ A @ F ) )
% 2.94/1.55 = ( ord_less @ nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_133_same__fstI,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,P: A > $o,X: A,Y8: B,Y: B,R: A > ( set @ ( product_prod @ B @ B ) )] :
% 2.94/1.55 ( ( P @ X )
% 2.94/1.55 => ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ Y8 @ Y ) @ ( R @ X ) )
% 2.94/1.55 => ( member @ ( product_prod @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) ) @ ( product_Pair @ ( product_prod @ A @ B ) @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y8 ) @ ( product_Pair @ A @ B @ X @ Y ) ) @ ( same_fst @ A @ B @ P @ R ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_134_splay__bstR,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A,L: tree @ A,E: A,R2: tree @ A,X: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.94/1.55 = ( node @ A @ L @ E @ R2 ) )
% 2.94/1.55 => ( ( member @ A @ X @ ( set_tree @ A @ R2 ) )
% 2.94/1.55 => ( ord_less @ A @ A2 @ X ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_135_splay__bstL,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A,L: tree @ A,E: A,R2: tree @ A,X: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.94/1.55 = ( node @ A @ L @ E @ R2 ) )
% 2.94/1.55 => ( ( member @ A @ X @ ( set_tree @ A @ L ) )
% 2.94/1.55 => ( ord_less @ A @ X @ A2 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_136_set__splay,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,T2: tree @ A] :
% 2.94/1.55 ( ( set_tree @ A @ ( splay_splay @ A @ A2 @ T2 ) )
% 2.94/1.55 = ( set_tree @ A @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_137_set__splay__max,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A] :
% 2.94/1.55 ( ( set_tree @ A @ ( splay_splay_max @ A @ T2 ) )
% 2.94/1.55 = ( set_tree @ A @ T2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_138_tree_Oset__cases,axiom,
% 2.94/1.55 ! [A: $tType,E: A,A2: tree @ A] :
% 2.94/1.55 ( ( member @ A @ E @ ( set_tree @ A @ A2 ) )
% 2.94/1.55 => ( ! [Z1: tree @ A] :
% 2.94/1.55 ( ? [Z22: A,Z3: tree @ A] :
% 2.94/1.55 ( A2
% 2.94/1.55 = ( node @ A @ Z1 @ Z22 @ Z3 ) )
% 2.94/1.55 => ~ ( member @ A @ E @ ( set_tree @ A @ Z1 ) ) )
% 2.94/1.55 => ( ! [Z1: tree @ A,Z3: tree @ A] :
% 2.94/1.55 ( A2
% 2.94/1.55 != ( node @ A @ Z1 @ E @ Z3 ) )
% 2.94/1.55 => ~ ! [Z1: tree @ A,Z22: A,Z3: tree @ A] :
% 2.94/1.55 ( ( A2
% 2.94/1.55 = ( node @ A @ Z1 @ Z22 @ Z3 ) )
% 2.94/1.55 => ~ ( member @ A @ E @ ( set_tree @ A @ Z3 ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_139_tree_Oset__intros_I1_J,axiom,
% 2.94/1.55 ! [A: $tType,X: A,A1: tree @ A,A23: A,A33: tree @ A] :
% 2.94/1.55 ( ( member @ A @ X @ ( set_tree @ A @ A1 ) )
% 2.94/1.55 => ( member @ A @ X @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_140_tree_Oset__intros_I2_J,axiom,
% 2.94/1.55 ! [A: $tType,A23: A,A1: tree @ A,A33: tree @ A] : ( member @ A @ A23 @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_141_tree_Oset__intros_I3_J,axiom,
% 2.94/1.55 ! [A: $tType,Xa: A,A33: tree @ A,A1: tree @ A,A23: A] :
% 2.94/1.55 ( ( member @ A @ Xa @ ( set_tree @ A @ A33 ) )
% 2.94/1.55 => ( member @ A @ Xa @ ( set_tree @ A @ ( node @ A @ A1 @ A23 @ A33 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_142_splay__to__root,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A,T4: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( ( ( splay_splay @ A @ A2 @ T2 )
% 2.94/1.55 = T4 )
% 2.94/1.55 => ( ( member @ A @ A2 @ ( set_tree @ A @ T2 ) )
% 2.94/1.55 = ( ? [L3: tree @ A,R3: tree @ A] :
% 2.94/1.55 ( T4
% 2.94/1.55 = ( node @ A @ L3 @ A2 @ R3 ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_143_is__root__splay,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( ( splay_is_root @ A @ A2 @ ( splay_splay @ A @ A2 @ T2 ) )
% 2.94/1.55 = ( member @ A @ A2 @ ( set_tree @ A @ T2 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_144_ex__in__set__tree,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( T2
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ? [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ T2 ) )
% 2.94/1.55 & ( ( splay_splay @ A @ X4 @ T2 )
% 2.94/1.55 = ( splay_splay @ A @ A2 @ T2 ) )
% 2.94/1.55 & ( ( splay_914434265_splay @ A @ X4 @ T2 )
% 2.94/1.55 = ( splay_914434265_splay @ A @ A2 @ T2 ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_145_bst_Oelims_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A,Y: $o] :
% 2.94/1.55 ( ( ( linorder_bst @ A @ X )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ~ Y )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 = ( ~ ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X5 @ A3 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X5 ) ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_146_bst_Oelims_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ X )
% 2.94/1.55 => ( ( X
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ~ ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X6 @ A3 ) )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X6 ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_147_bst_Oelims_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ~ ( linorder_bst @ A @ X )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X4 @ A3 ) )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X4 ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_148_bst_Osimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [L: tree @ A,A2: A,R2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 = ( ( linorder_bst @ A @ L )
% 2.94/1.55 & ( linorder_bst @ A @ R2 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L ) )
% 2.94/1.55 => ( ord_less @ A @ X5 @ A2 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R2 ) )
% 2.94/1.55 => ( ord_less @ A @ A2 @ X5 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_149_bst_Opelims_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( linorder_bst @ A @ X )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( leaf @ A ) ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ~ ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X6 @ A3 ) )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X6 ) ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_150_bst_Opelims_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A,Y: $o] :
% 2.94/1.55 ( ( ( linorder_bst @ A @ X )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( leaf @ A ) ) ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( Y
% 2.94/1.55 = ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X5 @ A3 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X5 ) ) ) )
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_151_bst_Opelims_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ~ ( linorder_bst @ A @ X )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ X )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( linorder_bst @ A @ L2 )
% 2.94/1.55 & ( linorder_bst @ A @ R4 )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less @ A @ X4 @ A3 ) )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less @ A @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_152_t__splay__simps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( leaf @ A ) @ B2 @ R2 ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_153_t__splay__simps_I6_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,L: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_154_bst__eq_Oelims_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A,Y: $o] :
% 2.94/1.55 ( ( ( linorder_bst_eq @ A @ X )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ~ Y )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 = ( ~ ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X5 @ A3 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X5 ) ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_155_t__splay__simps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,L: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_156_t__splay__simps_I7_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,L: tree @ A,Rl2: tree @ A,Rr2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ A2 @ Rr2 ) ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_157_t__splay__simps_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ A2 @ Lr ) @ B2 @ R2 ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_158_accp__subset__induct,axiom,
% 2.94/1.55 ! [A: $tType,D3: A > $o,R: A > A > $o,X: A,P: A > $o] :
% 2.94/1.55 ( ( ord_less_eq @ ( A > $o ) @ D3 @ ( accp @ A @ R ) )
% 2.94/1.55 => ( ! [X4: A,Z2: A] :
% 2.94/1.55 ( ( D3 @ X4 )
% 2.94/1.55 => ( ( R @ Z2 @ X4 )
% 2.94/1.55 => ( D3 @ Z2 ) ) )
% 2.94/1.55 => ( ( D3 @ X )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ( D3 @ X4 )
% 2.94/1.55 => ( ! [Z4: A] :
% 2.94/1.55 ( ( R @ Z4 @ X4 )
% 2.94/1.55 => ( P @ Z4 ) )
% 2.94/1.55 => ( P @ X4 ) ) )
% 2.94/1.55 => ( P @ X ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_159_accp__subset,axiom,
% 2.94/1.55 ! [A: $tType,R1: A > A > $o,R22: A > A > $o] :
% 2.94/1.55 ( ( ord_less_eq @ ( A > A > $o ) @ R1 @ R22 )
% 2.94/1.55 => ( ord_less_eq @ ( A > $o ) @ ( accp @ A @ R22 ) @ ( accp @ A @ R1 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_160_op_092_060_094sub_062s_092_060_094sub_062t_Orel__mono,axiom,
% 2.94/1.55 ! [B: $tType,A: $tType,R: A > B > $o,Ra: A > B > $o] :
% 2.94/1.55 ( ( ord_less_eq @ ( A > B > $o ) @ R @ Ra )
% 2.94/1.55 => ( ord_less_eq @ ( ( splay_2011811431op_s_t @ A ) > ( splay_2011811431op_s_t @ B ) > $o ) @ ( splay_434753539op_s_t @ A @ B @ R ) @ ( splay_434753539op_s_t @ A @ B @ Ra ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_161_t__splay_Osimps_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A] :
% 2.94/1.55 ( ( splay_914434265_splay @ A @ A2 @ ( leaf @ A ) )
% 2.94/1.55 = ( one_one @ nat ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_162_bst__eq_Oelims_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ~ ( linorder_bst_eq @ A @ X )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X4 @ A3 ) )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X4 ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_163_bst__eq_Osimps_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [L: tree @ A,A2: A,R2: tree @ A] :
% 2.94/1.55 ( ( linorder_bst_eq @ A @ ( node @ A @ L @ A2 @ R2 ) )
% 2.94/1.55 = ( ( linorder_bst_eq @ A @ L )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R2 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X5 @ A2 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A2 @ X5 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_164_splay__max__eq__splay,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [T2: tree @ A,A2: A] :
% 2.94/1.55 ( ( linorder_bst @ A @ T2 )
% 2.94/1.55 => ( ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ T2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X4 @ A2 ) )
% 2.94/1.55 => ( ( splay_splay_max @ A @ T2 )
% 2.94/1.55 = ( splay_splay @ A @ A2 @ T2 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_165_bst__eq_Oelims_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( linorder_bst_eq @ A @ X )
% 2.94/1.55 => ( ( X
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ~ ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X6 @ A3 ) )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X6 ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_166_bst__eq_Opelims_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ( linorder_bst_eq @ A @ X )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( leaf @ A ) ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ~ ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X6 @ A3 ) )
% 2.94/1.55 & ! [X6: A] :
% 2.94/1.55 ( ( member @ A @ X6 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X6 ) ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_167_bst__eq_Opelims_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A,Y: $o] :
% 2.94/1.55 ( ( ( linorder_bst_eq @ A @ X )
% 2.94/1.55 = Y )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 2.94/1.55 => ( ( ( X
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( Y
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( leaf @ A ) ) ) )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( Y
% 2.94/1.55 = ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X5 @ A3 ) )
% 2.94/1.55 & ! [X5: A] :
% 2.94/1.55 ( ( member @ A @ X5 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X5 ) ) ) )
% 2.94/1.55 => ~ ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_168_bst__eq_Opelims_I3_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [X: tree @ A] :
% 2.94/1.55 ( ~ ( linorder_bst_eq @ A @ X )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ X )
% 2.94/1.55 => ~ ! [L2: tree @ A,A3: A,R4: tree @ A] :
% 2.94/1.55 ( ( X
% 2.94/1.55 = ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( accp @ ( tree @ A ) @ ( linorder_bst_eq_rel @ A ) @ ( node @ A @ L2 @ A3 @ R4 ) )
% 2.94/1.55 => ( ( linorder_bst_eq @ A @ L2 )
% 2.94/1.55 & ( linorder_bst_eq @ A @ R4 )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ L2 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ X4 @ A3 ) )
% 2.94/1.55 & ! [X4: A] :
% 2.94/1.55 ( ( member @ A @ X4 @ ( set_tree @ A @ R4 ) )
% 2.94/1.55 => ( ord_less_eq @ A @ A3 @ X4 ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_169_less__numeral__extra_I4_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.94/1.55 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_170_t__splay__simps_I4_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,C3: A,Ll: tree @ A,Lr: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( ord_less @ A @ A2 @ C3 )
% 2.94/1.55 => ( ( ( Ll
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 2.94/1.55 = ( one_one @ nat ) ) )
% 2.94/1.55 & ( ( Ll
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 2.94/1.55 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Ll ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_171_t__splay__simps_I5_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,C3: A,Lr: tree @ A,Ll: tree @ A,R2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( ord_less @ A @ C3 @ A2 )
% 2.94/1.55 => ( ( ( Lr
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 2.94/1.55 = ( one_one @ nat ) ) )
% 2.94/1.55 & ( ( Lr
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ ( node @ A @ Ll @ C3 @ Lr ) @ B2 @ R2 ) )
% 2.94/1.55 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Lr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_172_t__splay__simps_I9_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,C3: A,Rr2: tree @ A,L: tree @ A,Rl2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( ord_less @ A @ C3 @ A2 )
% 2.94/1.55 => ( ( ( Rr2
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.55 = ( one_one @ nat ) ) )
% 2.94/1.55 & ( ( Rr2
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.55 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_173_t__splay__simps_I8_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [B2: A,A2: A,C3: A,Rl2: tree @ A,L: tree @ A,Rr2: tree @ A] :
% 2.94/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.55 => ( ( ord_less @ A @ A2 @ C3 )
% 2.94/1.55 => ( ( ( Rl2
% 2.94/1.55 = ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.55 = ( one_one @ nat ) ) )
% 2.94/1.55 & ( ( Rl2
% 2.94/1.55 != ( leaf @ A ) )
% 2.94/1.55 => ( ( splay_914434265_splay @ A @ A2 @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.55 = ( plus_plus @ nat @ ( splay_914434265_splay @ A @ A2 @ Rl2 ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_174_nat__add__left__cancel__less,axiom,
% 2.94/1.55 ! [K: nat,M: nat,N: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.94/1.55 = ( ord_less @ nat @ M @ N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_175_add__less__cancel__left,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [C3: A,A2: A,B2: A] :
% 2.94/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 2.94/1.55 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_176_add__less__cancel__right,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,C3: A,B2: A] :
% 2.94/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 2.94/1.55 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_177_nat__neq__iff,axiom,
% 2.94/1.55 ! [M: nat,N: nat] :
% 2.94/1.55 ( ( M != N )
% 2.94/1.55 = ( ( ord_less @ nat @ M @ N )
% 2.94/1.55 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_178_less__not__refl,axiom,
% 2.94/1.55 ! [N: nat] :
% 2.94/1.55 ~ ( ord_less @ nat @ N @ N ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_179_less__not__refl2,axiom,
% 2.94/1.55 ! [N: nat,M: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ N @ M )
% 2.94/1.55 => ( M != N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_180_less__not__refl3,axiom,
% 2.94/1.55 ! [S: nat,T2: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ S @ T2 )
% 2.94/1.55 => ( S != T2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_181_measure__induct,axiom,
% 2.94/1.55 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.94/1.55 ( ! [X4: A] :
% 2.94/1.55 ( ! [Y6: A] :
% 2.94/1.55 ( ( ord_less @ nat @ ( F @ Y6 ) @ ( F @ X4 ) )
% 2.94/1.55 => ( P @ Y6 ) )
% 2.94/1.55 => ( P @ X4 ) )
% 2.94/1.55 => ( P @ A2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_182_less__irrefl__nat,axiom,
% 2.94/1.55 ! [N: nat] :
% 2.94/1.55 ~ ( ord_less @ nat @ N @ N ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_183_nat__less__induct,axiom,
% 2.94/1.55 ! [P: nat > $o,N: nat] :
% 2.94/1.55 ( ! [N2: nat] :
% 2.94/1.55 ( ! [M2: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ M2 @ N2 )
% 2.94/1.55 => ( P @ M2 ) )
% 2.94/1.55 => ( P @ N2 ) )
% 2.94/1.55 => ( P @ N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_184_infinite__descent,axiom,
% 2.94/1.55 ! [P: nat > $o,N: nat] :
% 2.94/1.55 ( ! [N2: nat] :
% 2.94/1.55 ( ~ ( P @ N2 )
% 2.94/1.55 => ? [M2: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ M2 @ N2 )
% 2.94/1.55 & ~ ( P @ M2 ) ) )
% 2.94/1.55 => ( P @ N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_185_linorder__neqE__nat,axiom,
% 2.94/1.55 ! [X: nat,Y: nat] :
% 2.94/1.55 ( ( X != Y )
% 2.94/1.55 => ( ~ ( ord_less @ nat @ X @ Y )
% 2.94/1.55 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_186_measure__induct__rule,axiom,
% 2.94/1.55 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.94/1.55 ( ! [X4: A] :
% 2.94/1.55 ( ! [Y6: A] :
% 2.94/1.55 ( ( ord_less @ nat @ ( F @ Y6 ) @ ( F @ X4 ) )
% 2.94/1.55 => ( P @ Y6 ) )
% 2.94/1.55 => ( P @ X4 ) )
% 2.94/1.55 => ( P @ A2 ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_187_infinite__descent__measure,axiom,
% 2.94/1.55 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 2.94/1.55 ( ! [X4: A] :
% 2.94/1.55 ( ~ ( P @ X4 )
% 2.94/1.55 => ? [Y6: A] :
% 2.94/1.55 ( ( ord_less @ nat @ ( V @ Y6 ) @ ( V @ X4 ) )
% 2.94/1.55 & ~ ( P @ Y6 ) ) )
% 2.94/1.55 => ( P @ X ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_188_less__mono__imp__le__mono,axiom,
% 2.94/1.55 ! [F: nat > nat,I: nat,J: nat] :
% 2.94/1.55 ( ! [I2: nat,J2: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ I2 @ J2 )
% 2.94/1.55 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 2.94/1.55 => ( ( ord_less_eq @ nat @ I @ J )
% 2.94/1.55 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_189_le__neq__implies__less,axiom,
% 2.94/1.55 ! [M: nat,N: nat] :
% 2.94/1.55 ( ( ord_less_eq @ nat @ M @ N )
% 2.94/1.55 => ( ( M != N )
% 2.94/1.55 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_190_less__or__eq__imp__le,axiom,
% 2.94/1.55 ! [M: nat,N: nat] :
% 2.94/1.55 ( ( ( ord_less @ nat @ M @ N )
% 2.94/1.55 | ( M = N ) )
% 2.94/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_191_le__eq__less__or__eq,axiom,
% 2.94/1.55 ( ( ord_less_eq @ nat )
% 2.94/1.55 = ( ^ [M3: nat,N3: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ M3 @ N3 )
% 2.94/1.55 | ( M3 = N3 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_192_less__imp__le__nat,axiom,
% 2.94/1.55 ! [M: nat,N: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ M @ N )
% 2.94/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_193_nat__less__le,axiom,
% 2.94/1.55 ( ( ord_less @ nat )
% 2.94/1.55 = ( ^ [M3: nat,N3: nat] :
% 2.94/1.55 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 2.94/1.55 & ( M3 != N3 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_194_add__less__imp__less__right,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,C3: A,B2: A] :
% 2.94/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 2.94/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_195_add__less__imp__less__left,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [C3: A,A2: A,B2: A] :
% 2.94/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 2.94/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_196_add__strict__right__mono,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,C3: A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_197_add__strict__left__mono,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,C3: A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_198_add__strict__mono,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [A2: A,B2: A,C3: A,D4: A] :
% 2.94/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.55 => ( ( ord_less @ A @ C3 @ D4 )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_199_add__mono__thms__linordered__field_I1_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [I: A,J: A,K: A,L: A] :
% 2.94/1.55 ( ( ( ord_less @ A @ I @ J )
% 2.94/1.55 & ( K = L ) )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_200_add__mono__thms__linordered__field_I2_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [I: A,J: A,K: A,L: A] :
% 2.94/1.55 ( ( ( I = J )
% 2.94/1.55 & ( ord_less @ A @ K @ L ) )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_201_add__mono__thms__linordered__field_I5_J,axiom,
% 2.94/1.55 ! [A: $tType] :
% 2.94/1.55 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.55 => ! [I: A,J: A,K: A,L: A] :
% 2.94/1.55 ( ( ( ord_less @ A @ I @ J )
% 2.94/1.55 & ( ord_less @ A @ K @ L ) )
% 2.94/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_202_less__add__eq__less,axiom,
% 2.94/1.55 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ K @ L )
% 2.94/1.55 => ( ( ( plus_plus @ nat @ M @ L )
% 2.94/1.55 = ( plus_plus @ nat @ K @ N ) )
% 2.94/1.55 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_203_trans__less__add2,axiom,
% 2.94/1.55 ! [I: nat,J: nat,M: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ I @ J )
% 2.94/1.55 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_204_trans__less__add1,axiom,
% 2.94/1.55 ! [I: nat,J: nat,M: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ I @ J )
% 2.94/1.55 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_205_add__less__mono1,axiom,
% 2.94/1.55 ! [I: nat,J: nat,K: nat] :
% 2.94/1.55 ( ( ord_less @ nat @ I @ J )
% 2.94/1.55 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.94/1.55
% 2.94/1.55 thf(fact_206_not__add__less2,axiom,
% 2.94/1.56 ! [J: nat,I: nat] :
% 2.94/1.56 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_207_not__add__less1,axiom,
% 2.94/1.56 ! [I: nat,J: nat] :
% 2.94/1.56 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_208_add__less__mono,axiom,
% 2.94/1.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.94/1.56 ( ( ord_less @ nat @ I @ J )
% 2.94/1.56 => ( ( ord_less @ nat @ K @ L )
% 2.94/1.56 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_209_add__lessD1,axiom,
% 2.94/1.56 ! [I: nat,J: nat,K: nat] :
% 2.94/1.56 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 2.94/1.56 => ( ord_less @ nat @ I @ K ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_210_mono__nat__linear__lb,axiom,
% 2.94/1.56 ! [F: nat > nat,M: nat,K: nat] :
% 2.94/1.56 ( ! [M4: nat,N2: nat] :
% 2.94/1.56 ( ( ord_less @ nat @ M4 @ N2 )
% 2.94/1.56 => ( ord_less @ nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 2.94/1.56 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_211_add__less__le__mono,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A,C3: A,D4: A] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( ord_less_eq @ A @ C3 @ D4 )
% 2.94/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_212_add__le__less__mono,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A,C3: A,D4: A] :
% 2.94/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( ord_less @ A @ C3 @ D4 )
% 2.94/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D4 ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_213_add__mono__thms__linordered__field_I3_J,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [I: A,J: A,K: A,L: A] :
% 2.94/1.56 ( ( ( ord_less @ A @ I @ J )
% 2.94/1.56 & ( ord_less_eq @ A @ K @ L ) )
% 2.94/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_214_add__mono__thms__linordered__field_I4_J,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [I: A,J: A,K: A,L: A] :
% 2.94/1.56 ( ( ( ord_less_eq @ A @ I @ J )
% 2.94/1.56 & ( ord_less @ A @ K @ L ) )
% 2.94/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_215_discrete,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( semiring_numeral_div @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( ( ord_less @ A )
% 2.94/1.56 = ( ^ [A6: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A6 @ ( one_one @ A ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_216_fold__atLeastAtMost__nat_Oinduct,axiom,
% 2.94/1.56 ! [A: $tType,P: ( nat > A > A ) > nat > nat > A > $o,A0: nat > A > A,A1: nat,A23: nat,A33: A] :
% 2.94/1.56 ( ! [F5: nat > A > A,A3: nat,B5: nat,Acc: A] :
% 2.94/1.56 ( ( ~ ( ord_less @ nat @ B5 @ A3 )
% 2.94/1.56 => ( P @ F5 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B5 @ ( F5 @ A3 @ Acc ) ) )
% 2.94/1.56 => ( P @ F5 @ A3 @ B5 @ Acc ) )
% 2.94/1.56 => ( P @ A0 @ A1 @ A23 @ A33 ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_217_less__add__one,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_218_linorder__neqE__linordered__idom,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( X != Y )
% 2.94/1.56 => ( ~ ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_219_ex__has__greatest__nat__lemma,axiom,
% 2.94/1.56 ! [A: $tType,P: A > $o,K: A,M: A > nat,N: nat] :
% 2.94/1.56 ( ( P @ K )
% 2.94/1.56 => ( ! [X4: A] :
% 2.94/1.56 ( ( P @ X4 )
% 2.94/1.56 => ? [Y6: A] :
% 2.94/1.56 ( ( P @ Y6 )
% 2.94/1.56 & ~ ( ord_less_eq @ nat @ ( M @ Y6 ) @ ( M @ X4 ) ) ) )
% 2.94/1.56 => ? [Y4: A] :
% 2.94/1.56 ( ( P @ Y4 )
% 2.94/1.56 & ~ ( ord_less @ nat @ ( M @ Y4 ) @ ( plus_plus @ nat @ ( M @ K ) @ N ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_220_t__splay__max_Osimps_I3_J,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [Rr2: tree @ A,L: tree @ A,B2: A,Rl2: tree @ A,C3: A] :
% 2.94/1.56 ( ( ( Rr2
% 2.94/1.56 = ( leaf @ A ) )
% 2.94/1.56 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.56 = ( one_one @ nat ) ) )
% 2.94/1.56 & ( ( Rr2
% 2.94/1.56 != ( leaf @ A ) )
% 2.94/1.56 => ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( node @ A @ Rl2 @ C3 @ Rr2 ) ) )
% 2.94/1.56 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr2 ) @ ( one_one @ nat ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_221_t__splay__max_Osimps_I1_J,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( ( splay_878424299ay_max @ A @ ( leaf @ A ) )
% 2.94/1.56 = ( one_one @ nat ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_222_t__splay__max_Osimps_I2_J,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [L: tree @ A,B2: A] :
% 2.94/1.56 ( ( splay_878424299ay_max @ A @ ( node @ A @ L @ B2 @ ( leaf @ A ) ) )
% 2.94/1.56 = ( one_one @ nat ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_223_ex__has__greatest__nat,axiom,
% 2.94/1.56 ! [A: $tType,P: A > $o,K: A,M: A > nat,B2: nat] :
% 2.94/1.56 ( ( P @ K )
% 2.94/1.56 => ( ! [Y4: A] :
% 2.94/1.56 ( ( P @ Y4 )
% 2.94/1.56 => ( ord_less @ nat @ ( M @ Y4 ) @ B2 ) )
% 2.94/1.56 => ? [X4: A] :
% 2.94/1.56 ( ( P @ X4 )
% 2.94/1.56 & ! [Y6: A] :
% 2.94/1.56 ( ( P @ Y6 )
% 2.94/1.56 => ( ord_less_eq @ nat @ ( M @ Y6 ) @ ( M @ X4 ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_224_t__splay__max_Oelims,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: tree @ A,Y: nat] :
% 2.94/1.56 ( ( ( splay_878424299ay_max @ A @ X )
% 2.94/1.56 = Y )
% 2.94/1.56 => ( ( ( X
% 2.94/1.56 = ( leaf @ A ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 != ( one_one @ nat ) ) )
% 2.94/1.56 => ( ( ? [L2: tree @ A,B5: A] :
% 2.94/1.56 ( X
% 2.94/1.56 = ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 != ( one_one @ nat ) ) )
% 2.94/1.56 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.94/1.56 ( ( X
% 2.94/1.56 = ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 2.94/1.56 => ~ ( ( ( Rr
% 2.94/1.56 = ( leaf @ A ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( one_one @ nat ) ) )
% 2.94/1.56 & ( ( Rr
% 2.94/1.56 != ( leaf @ A ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_225_t__splay__max_Opelims,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: tree @ A,Y: nat] :
% 2.94/1.56 ( ( ( splay_878424299ay_max @ A @ X )
% 2.94/1.56 = Y )
% 2.94/1.56 => ( ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ X )
% 2.94/1.56 => ( ( ( X
% 2.94/1.56 = ( leaf @ A ) )
% 2.94/1.56 => ( ( Y
% 2.94/1.56 = ( one_one @ nat ) )
% 2.94/1.56 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( leaf @ A ) ) ) )
% 2.94/1.56 => ( ! [L2: tree @ A,B5: A] :
% 2.94/1.56 ( ( X
% 2.94/1.56 = ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) )
% 2.94/1.56 => ( ( Y
% 2.94/1.56 = ( one_one @ nat ) )
% 2.94/1.56 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L2 @ B5 @ ( leaf @ A ) ) ) ) )
% 2.94/1.56 => ~ ! [L2: tree @ A,B5: A,Rl: tree @ A,C2: A,Rr: tree @ A] :
% 2.94/1.56 ( ( X
% 2.94/1.56 = ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) )
% 2.94/1.56 => ( ( ( ( Rr
% 2.94/1.56 = ( leaf @ A ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( one_one @ nat ) ) )
% 2.94/1.56 & ( ( Rr
% 2.94/1.56 != ( leaf @ A ) )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( plus_plus @ nat @ ( splay_878424299ay_max @ A @ Rr ) @ ( one_one @ nat ) ) ) ) )
% 2.94/1.56 => ~ ( accp @ ( tree @ A ) @ ( splay_1816415694ax_rel @ A ) @ ( node @ A @ L2 @ B5 @ ( node @ A @ Rl @ C2 @ Rr ) ) ) ) ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_226_fold__atLeastAtMost__nat_Opinduct,axiom,
% 2.94/1.56 ! [A: $tType,A0: nat > A > A,A1: nat,A23: nat,A33: A,P: ( nat > A > A ) > nat > nat > A > $o] :
% 2.94/1.56 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ A0 @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A1 @ ( product_Pair @ nat @ A @ A23 @ A33 ) ) ) )
% 2.94/1.56 => ( ! [F5: nat > A > A,A3: nat,B5: nat,Acc: A] :
% 2.94/1.56 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ F5 @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A3 @ ( product_Pair @ nat @ A @ B5 @ Acc ) ) ) )
% 2.94/1.56 => ( ( ~ ( ord_less @ nat @ B5 @ A3 )
% 2.94/1.56 => ( P @ F5 @ ( plus_plus @ nat @ A3 @ ( one_one @ nat ) ) @ B5 @ ( F5 @ A3 @ Acc ) ) )
% 2.94/1.56 => ( P @ F5 @ A3 @ B5 @ Acc ) ) )
% 2.94/1.56 => ( P @ A0 @ A1 @ A23 @ A33 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_227_fold__atLeastAtMost__nat_Opelims,axiom,
% 2.94/1.56 ! [A: $tType,X: nat > A > A,Xa: nat,Xb2: nat,Xc: A,Y: A] :
% 2.94/1.56 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb2 @ Xc )
% 2.94/1.56 = Y )
% 2.94/1.56 => ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ X @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ Xa @ ( product_Pair @ nat @ A @ Xb2 @ Xc ) ) ) )
% 2.94/1.56 => ~ ( ( ( ( ord_less @ nat @ Xb2 @ Xa )
% 2.94/1.56 => ( Y = Xc ) )
% 2.94/1.56 & ( ~ ( ord_less @ nat @ Xb2 @ Xa )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb2 @ ( X @ Xa @ Xc ) ) ) ) )
% 2.94/1.56 => ~ ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ X @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ Xa @ ( product_Pair @ nat @ A @ Xb2 @ Xc ) ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_228_fold__atLeastAtMost__nat_Opsimps,axiom,
% 2.94/1.56 ! [A: $tType,F: nat > A > A,A2: nat,B2: nat,Acc2: A] :
% 2.94/1.56 ( ( accp @ ( product_prod @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) ) @ ( set_fo2092542664at_rel @ A ) @ ( product_Pair @ ( nat > A > A ) @ ( product_prod @ nat @ ( product_prod @ nat @ A ) ) @ F @ ( product_Pair @ nat @ ( product_prod @ nat @ A ) @ A2 @ ( product_Pair @ nat @ A @ B2 @ Acc2 ) ) ) )
% 2.94/1.56 => ( ( ( ord_less @ nat @ B2 @ A2 )
% 2.94/1.56 => ( ( set_fo292404081st_nat @ A @ F @ A2 @ B2 @ Acc2 )
% 2.94/1.56 = Acc2 ) )
% 2.94/1.56 & ( ~ ( ord_less @ nat @ B2 @ A2 )
% 2.94/1.56 => ( ( set_fo292404081st_nat @ A @ F @ A2 @ B2 @ Acc2 )
% 2.94/1.56 = ( set_fo292404081st_nat @ A @ F @ ( plus_plus @ nat @ A2 @ ( one_one @ nat ) ) @ B2 @ ( F @ A2 @ Acc2 ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_229_fold__atLeastAtMost__nat_Oelims,axiom,
% 2.94/1.56 ! [A: $tType,X: nat > A > A,Xa: nat,Xb2: nat,Xc: A,Y: A] :
% 2.94/1.56 ( ( ( set_fo292404081st_nat @ A @ X @ Xa @ Xb2 @ Xc )
% 2.94/1.56 = Y )
% 2.94/1.56 => ( ( ( ord_less @ nat @ Xb2 @ Xa )
% 2.94/1.56 => ( Y = Xc ) )
% 2.94/1.56 & ( ~ ( ord_less @ nat @ Xb2 @ Xa )
% 2.94/1.56 => ( Y
% 2.94/1.56 = ( set_fo292404081st_nat @ A @ X @ ( plus_plus @ nat @ Xa @ ( one_one @ nat ) ) @ Xb2 @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_230_fold__atLeastAtMost__nat_Osimps,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( set_fo292404081st_nat @ A )
% 2.94/1.56 = ( ^ [F6: nat > A > A,A6: nat,B6: nat,Acc3: A] : ( if @ A @ ( ord_less @ nat @ B6 @ A6 ) @ Acc3 @ ( set_fo292404081st_nat @ A @ F6 @ ( plus_plus @ nat @ A6 @ ( one_one @ nat ) ) @ B6 @ ( F6 @ A6 @ Acc3 ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_231_complete__interval,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A,P: A > $o] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( P @ A2 )
% 2.94/1.56 => ( ~ ( P @ B2 )
% 2.94/1.56 => ? [C2: A] :
% 2.94/1.56 ( ( ord_less_eq @ A @ A2 @ C2 )
% 2.94/1.56 & ( ord_less_eq @ A @ C2 @ B2 )
% 2.94/1.56 & ! [X6: A] :
% 2.94/1.56 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 2.94/1.56 & ( ord_less @ A @ X6 @ C2 ) )
% 2.94/1.56 => ( P @ X6 ) )
% 2.94/1.56 & ! [D5: A] :
% 2.94/1.56 ( ! [X4: A] :
% 2.94/1.56 ( ( ( ord_less_eq @ A @ A2 @ X4 )
% 2.94/1.56 & ( ord_less @ A @ X4 @ D5 ) )
% 2.94/1.56 => ( P @ X4 ) )
% 2.94/1.56 => ( ord_less_eq @ A @ D5 @ C2 ) ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_232_order_Onot__eq__order__implies__strict,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A] :
% 2.94/1.56 ( ( A2 != B2 )
% 2.94/1.56 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.94/1.56 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_233_ord__eq__less__subst,axiom,
% 2.94/1.56 ! [A: $tType,B: $tType] :
% 2.94/1.56 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.94/1.56 & ( ord @ A @ ( type2 @ A ) ) )
% 2.94/1.56 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 2.94/1.56 ( ( A2
% 2.94/1.56 = ( F @ B2 ) )
% 2.94/1.56 => ( ( ord_less @ B @ B2 @ C3 )
% 2.94/1.56 => ( ! [X4: B,Y4: B] :
% 2.94/1.56 ( ( ord_less @ B @ X4 @ Y4 )
% 2.94/1.56 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.94/1.56 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_234_ord__less__eq__subst,axiom,
% 2.94/1.56 ! [A: $tType,B: $tType] :
% 2.94/1.56 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.94/1.56 & ( ord @ A @ ( type2 @ A ) ) )
% 2.94/1.56 => ! [A2: A,B2: A,F: A > B,C3: B] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( ( F @ B2 )
% 2.94/1.56 = C3 )
% 2.94/1.56 => ( ! [X4: A,Y4: A] :
% 2.94/1.56 ( ( ord_less @ A @ X4 @ Y4 )
% 2.94/1.56 => ( ord_less @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.94/1.56 => ( ord_less @ B @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_235_order__less__subst1,axiom,
% 2.94/1.56 ! [A: $tType,B: $tType] :
% 2.94/1.56 ( ( ( order @ B @ ( type2 @ B ) )
% 2.94/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 2.94/1.56 => ! [A2: A,F: B > A,B2: B,C3: B] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 2.94/1.56 => ( ( ord_less @ B @ B2 @ C3 )
% 2.94/1.56 => ( ! [X4: B,Y4: B] :
% 2.94/1.56 ( ( ord_less @ B @ X4 @ Y4 )
% 2.94/1.56 => ( ord_less @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.94/1.56 => ( ord_less @ A @ A2 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_236_order__less__subst2,axiom,
% 2.94/1.56 ! [A: $tType,C: $tType] :
% 2.94/1.56 ( ( ( order @ C @ ( type2 @ C ) )
% 2.94/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 2.94/1.56 => ! [A2: A,B2: A,F: A > C,C3: C] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( ord_less @ C @ ( F @ B2 ) @ C3 )
% 2.94/1.56 => ( ! [X4: A,Y4: A] :
% 2.94/1.56 ( ( ord_less @ A @ X4 @ Y4 )
% 2.94/1.56 => ( ord_less @ C @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 2.94/1.56 => ( ord_less @ C @ ( F @ A2 ) @ C3 ) ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_237_lt__ex,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A] :
% 2.94/1.56 ? [Y4: A] : ( ord_less @ A @ Y4 @ X ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_238_gt__ex,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( no_top @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A] :
% 2.94/1.56 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_239_neqE,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( X != Y )
% 2.94/1.56 => ( ~ ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_240_neq__iff,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( X != Y )
% 2.94/1.56 = ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_241_order_Oasym,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_242_dense,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ? [Z2: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Z2 )
% 2.94/1.56 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_243_less__imp__neq,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ( X != Y ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_244_less__asym,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_245_less__asym_H,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_246_less__trans,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A,Z5: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ( ( ord_less @ A @ Y @ Z5 )
% 2.94/1.56 => ( ord_less @ A @ X @ Z5 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_247_less__linear,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 | ( X = Y )
% 2.94/1.56 | ( ord_less @ A @ Y @ X ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_248_less__irrefl,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A] :
% 2.94/1.56 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_249_ord__eq__less__trans,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A,C3: A] :
% 2.94/1.56 ( ( A2 = B2 )
% 2.94/1.56 => ( ( ord_less @ A @ B2 @ C3 )
% 2.94/1.56 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_250_ord__less__eq__trans,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [A2: A,B2: A,C3: A] :
% 2.94/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 2.94/1.56 => ( ( B2 = C3 )
% 2.94/1.56 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_251_dual__order_Oasym,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [B2: A,A2: A] :
% 2.94/1.56 ( ( ord_less @ A @ B2 @ A2 )
% 2.94/1.56 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_252_less__imp__not__eq,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ( X != Y ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_253_less__not__sym,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [X: A,Y: A] :
% 2.94/1.56 ( ( ord_less @ A @ X @ Y )
% 2.94/1.56 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_254_less__induct,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [P: A > $o,A2: A] :
% 2.94/1.56 ( ! [X4: A] :
% 2.94/1.56 ( ! [Y6: A] :
% 2.94/1.56 ( ( ord_less @ A @ Y6 @ X4 )
% 2.94/1.56 => ( P @ Y6 ) )
% 2.94/1.56 => ( P @ X4 ) )
% 2.94/1.56 => ( P @ A2 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(fact_255_antisym__conv3,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ! [Y: A,X: A] :
% 2.94/1.56 ( ~ ( ord_less @ A @ Y @ X )
% 2.94/1.56 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.94/1.56 = ( X = Y ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( type @ A @ ( type2 @ A ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( order @ A @ ( type2 @ A ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.94/1.56 ! [A: $tType] :
% 2.94/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.94/1.56 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.94/1.56 ! [A7: $tType,A8: $tType] :
% 2.94/1.56 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 2.94/1.56 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.94/1.56 ! [A7: $tType,A8: $tType] :
% 2.94/1.56 ( ( order @ A8 @ ( type2 @ A8 ) )
% 2.94/1.56 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 2.94/1.56 ! [A7: $tType,A8: $tType] :
% 2.94/1.56 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 2.94/1.56 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 2.94/1.56 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.94/1.56 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.94/1.56 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.94/1.56 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div,axiom,
% 2.94/1.56 semiring_numeral_div @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.94/1.56 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.94/1.56 wellorder @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.94/1.56 preorder @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.94/1.56 linorder @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.94/1.56 no_top @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.94/1.56 order @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.94/1.56 ord @ nat @ ( type2 @ nat ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 2.94/1.56 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.94/1.56 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.94/1.56 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.94/1.56 preorder @ $o @ ( type2 @ $o ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 2.94/1.56 linorder @ $o @ ( type2 @ $o ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.94/1.56 order @ $o @ ( type2 @ $o ) ).
% 2.94/1.56
% 2.94/1.56 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.94/1.56 ord @ $o @ ( type2 @ $o ) ).
% 2.94/1.56
% 2.94/1.56 thf(help_If_3_1_T,axiom,
% 2.94/1.56 ! [P: $o] :
% 2.94/1.56 ( ( P = $true )
% 2.94/1.56 | ( P = $false ) ) ).
% 2.94/1.56
% 2.94/1.56 thf(help_If_2_1_T,axiom,
% 2.94/1.56 ! [A: $tType,X: A,Y: A] :
% 2.94/1.56 ( ( if @ A @ $false @ X @ Y )
% 2.94/1.56 = Y ) ).
% 2.94/1.56
% 2.94/1.56 thf(help_If_1_1_T,axiom,
% 2.94/1.56 ! [A: $tType,X: A,Y: A] :
% 2.94/1.56 ( ( if @ A @ $true @ X @ Y )
% 2.94/1.56 = X ) ).
% 2.94/1.56
% 2.94/1.56 thf(tfree_0,hypothesis,
% 2.94/1.56 linorder @ a @ ( type2 @ a ) ).
% 2.94/1.56
% 2.94/1.56 thf(conj_0,conjecture,
% 2.94/1.56 linorder_bst @ a @ ( splay_859309299xt_s_t @ a @ f @ a2 ) ).
% 2.94/1.56 ------------------------
% 2.94/1.59 % (29045)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_28704 for (2999ds/275Mi)
% 2.94/1.59 % (29040)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/183Mi)
% 2.94/1.59 % (29046)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/18Mi)
% 2.99/1.60 % (29041)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_28704 for (2999ds/4Mi)
% 2.99/1.60 % (29043)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/2Mi)
% 2.99/1.60 % (29044)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_28704 for (2999ds/2Mi)
% 2.99/1.60 % (29042)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_28704 for (2999ds/27Mi)
% 2.99/1.60 % (29043)Instruction limit reached!
% 2.99/1.60 % (29043)------------------------------
% 2.99/1.60 % (29043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.60 % (29043)Termination reason: Unknown
% 2.99/1.60 % (29043)Termination phase: shuffling
% 2.99/1.60
% 2.99/1.60 % (29043)Memory used [KB]: 1535
% 2.99/1.60 % (29043)Time elapsed: 0.004 s
% 2.99/1.60 % (29043)Instructions burned: 3 (million)
% 2.99/1.60 % (29043)------------------------------
% 2.99/1.60 % (29043)------------------------------
% 2.99/1.60 % (29044)Instruction limit reached!
% 2.99/1.60 % (29044)------------------------------
% 2.99/1.60 % (29044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.60 % (29044)Termination reason: Unknown
% 2.99/1.60 % (29044)Termination phase: shuffling
% 2.99/1.60
% 2.99/1.60 % (29044)Memory used [KB]: 1535
% 2.99/1.60 % (29044)Time elapsed: 0.004 s
% 2.99/1.60 % (29044)Instructions burned: 3 (million)
% 2.99/1.60 % (29044)------------------------------
% 2.99/1.60 % (29044)------------------------------
% 2.99/1.60 % (29046)Instruction limit reached!
% 2.99/1.60 % (29046)------------------------------
% 2.99/1.60 % (29046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.60 % (29046)Termination reason: Unknown
% 2.99/1.60 % (29046)Termination phase: shuffling
% 2.99/1.60
% 2.99/1.60 % (29046)Memory used [KB]: 1918
% 2.99/1.60 % (29046)Time elapsed: 0.010 s
% 2.99/1.60 % (29046)Instructions burned: 19 (million)
% 2.99/1.60 % (29046)------------------------------
% 2.99/1.60 % (29046)------------------------------
% 2.99/1.60 % (29041)Instruction limit reached!
% 2.99/1.60 % (29041)------------------------------
% 2.99/1.60 % (29041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.60 % (29041)Termination reason: Unknown
% 2.99/1.60 % (29041)Termination phase: shuffling
% 2.99/1.60
% 2.99/1.60 % (29041)Memory used [KB]: 1535
% 2.99/1.60 % (29041)Time elapsed: 0.005 s
% 2.99/1.60 % (29041)Instructions burned: 5 (million)
% 2.99/1.60 % (29041)------------------------------
% 2.99/1.60 % (29041)------------------------------
% 2.99/1.62 % (29048)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_28704 for (2999ds/37Mi)
% 2.99/1.62 % (29042)Instruction limit reached!
% 2.99/1.62 % (29042)------------------------------
% 2.99/1.62 % (29042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.62 % (29042)Termination reason: Unknown
% 2.99/1.62 % (29042)Termination phase: shuffling
% 2.99/1.62
% 2.99/1.62 % (29042)Memory used [KB]: 2174
% 2.99/1.62 % (29042)Time elapsed: 0.019 s
% 2.99/1.62 % (29042)Instructions burned: 28 (million)
% 2.99/1.62 % (29042)------------------------------
% 2.99/1.62 % (29042)------------------------------
% 2.99/1.62 % (29045)Refutation not found, incomplete strategy
% 2.99/1.62 % (29045)------------------------------
% 2.99/1.62 % (29045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.62 % (29045)Termination reason: Refutation not found, incomplete strategy
% 2.99/1.62
% 2.99/1.62
% 2.99/1.62 % (29045)Memory used [KB]: 7036
% 2.99/1.62 % (29045)Time elapsed: 0.028 s
% 2.99/1.62 % (29045)Instructions burned: 87 (million)
% 2.99/1.62 % (29045)------------------------------
% 2.99/1.62 % (29045)------------------------------
% 2.99/1.62 % (29047)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/3Mi)
% 2.99/1.62 % (29049)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_28704 for (2999ds/15Mi)
% 2.99/1.62 % (29050)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_28704 for (2999ds/3Mi)
% 2.99/1.62 % (29047)Instruction limit reached!
% 2.99/1.62 % (29047)------------------------------
% 2.99/1.62 % (29047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.62 % (29047)Termination reason: Unknown
% 2.99/1.62 % (29047)Termination phase: shuffling
% 2.99/1.62
% 2.99/1.62 % (29047)Memory used [KB]: 1535
% 2.99/1.62 % (29047)Time elapsed: 0.004 s
% 2.99/1.62 % (29047)Instructions burned: 3 (million)
% 2.99/1.62 % (29047)------------------------------
% 2.99/1.62 % (29047)------------------------------
% 2.99/1.62 % (29050)Instruction limit reached!
% 2.99/1.62 % (29050)------------------------------
% 2.99/1.62 % (29050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.62 % (29050)Termination reason: Unknown
% 2.99/1.62 % (29050)Termination phase: shuffling
% 2.99/1.62
% 2.99/1.62 % (29050)Memory used [KB]: 1535
% 2.99/1.62 % (29050)Time elapsed: 0.004 s
% 2.99/1.62 % (29050)Instructions burned: 3 (million)
% 2.99/1.62 % (29050)------------------------------
% 2.99/1.62 % (29050)------------------------------
% 2.99/1.63 % (29048)Instruction limit reached!
% 2.99/1.63 % (29048)------------------------------
% 2.99/1.63 % (29048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.63 % (29048)Termination reason: Unknown
% 2.99/1.63 % (29048)Termination phase: shuffling
% 2.99/1.63
% 2.99/1.63 % (29048)Memory used [KB]: 2174
% 2.99/1.63 % (29048)Time elapsed: 0.014 s
% 2.99/1.63 % (29048)Instructions burned: 37 (million)
% 2.99/1.63 % (29048)------------------------------
% 2.99/1.63 % (29048)------------------------------
% 2.99/1.63 % (29052)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/7Mi)
% 2.99/1.63 % (29049)Instruction limit reached!
% 2.99/1.63 % (29049)------------------------------
% 2.99/1.63 % (29049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.63 % (29049)Termination reason: Unknown
% 2.99/1.63 % (29049)Termination phase: shuffling
% 2.99/1.63
% 2.99/1.63 % (29049)Memory used [KB]: 1918
% 2.99/1.63 % (29049)Time elapsed: 0.012 s
% 2.99/1.63 % (29049)Instructions burned: 16 (million)
% 2.99/1.63 % (29049)------------------------------
% 2.99/1.63 % (29049)------------------------------
% 2.99/1.63 % (29052)Instruction limit reached!
% 2.99/1.63 % (29052)------------------------------
% 2.99/1.63 % (29052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.63 % (29052)Termination reason: Unknown
% 2.99/1.63 % (29052)Termination phase: shuffling
% 2.99/1.63
% 2.99/1.63 % (29052)Memory used [KB]: 1663
% 2.99/1.63 % (29052)Time elapsed: 0.004 s
% 2.99/1.63 % (29052)Instructions burned: 9 (million)
% 2.99/1.63 % (29052)------------------------------
% 2.99/1.63 % (29052)------------------------------
% 2.99/1.64 % (29051)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_28704 for (2999ds/1041Mi)
% 2.99/1.64 % (29055)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_28704 for (2999ds/3Mi)
% 2.99/1.64 % (29053)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/16Mi)
% 2.99/1.64 % (29054)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_28704 for (2999ds/3Mi)
% 2.99/1.64 % (29055)Instruction limit reached!
% 2.99/1.64 % (29055)------------------------------
% 2.99/1.64 % (29055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.64 % (29055)Termination reason: Unknown
% 2.99/1.64 % (29055)Termination phase: shuffling
% 2.99/1.64
% 2.99/1.64 % (29055)Memory used [KB]: 1535
% 2.99/1.64 % (29055)Time elapsed: 0.003 s
% 2.99/1.64 % (29055)Instructions burned: 4 (million)
% 2.99/1.64 % (29055)------------------------------
% 2.99/1.64 % (29055)------------------------------
% 2.99/1.64 % (29057)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/3Mi)
% 2.99/1.64 % (29054)Instruction limit reached!
% 2.99/1.64 % (29054)------------------------------
% 2.99/1.64 % (29054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.64 % (29054)Termination reason: Unknown
% 2.99/1.64 % (29054)Termination phase: shuffling
% 2.99/1.64
% 2.99/1.64 % (29054)Memory used [KB]: 1535
% 2.99/1.64 % (29054)Time elapsed: 0.004 s
% 2.99/1.64 % (29054)Instructions burned: 4 (million)
% 2.99/1.64 % (29054)------------------------------
% 2.99/1.64 % (29054)------------------------------
% 2.99/1.64 % (29057)Instruction limit reached!
% 2.99/1.64 % (29057)------------------------------
% 2.99/1.64 % (29057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.64 % (29057)Termination reason: Unknown
% 2.99/1.64 % (29057)Termination phase: shuffling
% 2.99/1.64
% 2.99/1.64 % (29057)Memory used [KB]: 1535
% 2.99/1.64 % (29057)Time elapsed: 0.002 s
% 2.99/1.64 % (29057)Instructions burned: 3 (million)
% 2.99/1.64 % (29057)------------------------------
% 2.99/1.64 % (29057)------------------------------
% 2.99/1.65 % (29056)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/7Mi)
% 2.99/1.65 % (29053)Instruction limit reached!
% 2.99/1.65 % (29053)------------------------------
% 2.99/1.65 % (29053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (29053)Termination reason: Unknown
% 2.99/1.65 % (29053)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (29053)Memory used [KB]: 1918
% 2.99/1.65 % (29053)Time elapsed: 0.012 s
% 2.99/1.65 % (29053)Instructions burned: 16 (million)
% 2.99/1.65 % (29053)------------------------------
% 2.99/1.65 % (29053)------------------------------
% 2.99/1.65 % (29058)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/4Mi)
% 2.99/1.65 % (29040)Instruction limit reached!
% 2.99/1.65 % (29040)------------------------------
% 2.99/1.65 % (29040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (29040)Termination reason: Unknown
% 2.99/1.65 % (29040)Termination phase: Saturation
% 2.99/1.65
% 2.99/1.65 % (29040)Memory used [KB]: 7675
% 2.99/1.65 % (29040)Time elapsed: 0.059 s
% 2.99/1.65 % (29040)Instructions burned: 184 (million)
% 2.99/1.65 % (29040)------------------------------
% 2.99/1.65 % (29040)------------------------------
% 2.99/1.65 % (29056)Instruction limit reached!
% 2.99/1.65 % (29056)------------------------------
% 2.99/1.65 % (29056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (29056)Termination reason: Unknown
% 2.99/1.65 % (29056)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (29056)Memory used [KB]: 1535
% 2.99/1.65 % (29056)Time elapsed: 0.006 s
% 2.99/1.65 % (29056)Instructions burned: 7 (million)
% 2.99/1.65 % (29056)------------------------------
% 2.99/1.65 % (29056)------------------------------
% 2.99/1.65 % (29058)Instruction limit reached!
% 2.99/1.65 % (29058)------------------------------
% 2.99/1.65 % (29058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (29058)Termination reason: Unknown
% 2.99/1.65 % (29058)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (29058)Memory used [KB]: 1535
% 2.99/1.65 % (29058)Time elapsed: 0.003 s
% 2.99/1.65 % (29058)Instructions burned: 6 (million)
% 2.99/1.65 % (29058)------------------------------
% 2.99/1.65 % (29058)------------------------------
% 2.99/1.65 % (29060)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/710Mi)
% 2.99/1.66 % (29059)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/18Mi)
% 2.99/1.66 % (29062)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_28704 for (2999ds/902Mi)
% 2.99/1.66 % (29064)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/5Mi)
% 2.99/1.66 % (29064)Instruction limit reached!
% 2.99/1.66 % (29064)------------------------------
% 2.99/1.66 % (29064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (29064)Termination reason: Unknown
% 2.99/1.66 % (29064)Termination phase: shuffling
% 2.99/1.66
% 2.99/1.66 % (29064)Memory used [KB]: 1663
% 2.99/1.66 % (29064)Time elapsed: 0.003 s
% 2.99/1.66 % (29064)Instructions burned: 8 (million)
% 2.99/1.66 % (29064)------------------------------
% 2.99/1.66 % (29064)------------------------------
% 2.99/1.67 % (29059)Instruction limit reached!
% 2.99/1.67 % (29059)------------------------------
% 2.99/1.67 % (29059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (29059)Termination reason: Unknown
% 2.99/1.67 % (29059)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (29059)Memory used [KB]: 1918
% 2.99/1.67 % (29059)Time elapsed: 0.010 s
% 2.99/1.67 % (29059)Instructions burned: 18 (million)
% 2.99/1.67 % (29059)------------------------------
% 2.99/1.67 % (29059)------------------------------
% 2.99/1.67 % (29061)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/6Mi)
% 2.99/1.67 % (29063)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_28704 for (2999ds/21Mi)
% 2.99/1.67 % (29061)Instruction limit reached!
% 2.99/1.67 % (29061)------------------------------
% 2.99/1.67 % (29061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (29061)Termination reason: Unknown
% 2.99/1.67 % (29061)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (29061)Memory used [KB]: 1535
% 2.99/1.67 % (29061)Time elapsed: 0.006 s
% 2.99/1.67 % (29061)Instructions burned: 6 (million)
% 2.99/1.67 % (29061)------------------------------
% 2.99/1.67 % (29061)------------------------------
% 2.99/1.67 % (29065)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_28704 for (2999ds/6Mi)
% 2.99/1.68 % (29065)Instruction limit reached!
% 2.99/1.68 % (29065)------------------------------
% 2.99/1.68 % (29065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (29065)Termination reason: Unknown
% 2.99/1.68 % (29065)Termination phase: shuffling
% 2.99/1.68
% 2.99/1.68 % (29065)Memory used [KB]: 1663
% 2.99/1.68 % (29065)Time elapsed: 0.003 s
% 2.99/1.68 % (29065)Instructions burned: 7 (million)
% 2.99/1.68 % (29065)------------------------------
% 2.99/1.68 % (29065)------------------------------
% 2.99/1.68 % (29066)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28704 for (2999ds/377Mi)
% 2.99/1.68 % (29063)Instruction limit reached!
% 2.99/1.68 % (29063)------------------------------
% 2.99/1.68 % (29063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (29063)Termination reason: Unknown
% 2.99/1.68 % (29063)Termination phase: shuffling
% 2.99/1.68
% 2.99/1.68 % (29063)Memory used [KB]: 1918
% 2.99/1.68 % (29063)Time elapsed: 0.014 s
% 2.99/1.68 % (29063)Instructions burned: 22 (million)
% 2.99/1.68 % (29063)------------------------------
% 2.99/1.68 % (29063)------------------------------
% 2.99/1.68 % (29068)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_28704 for (2998ds/19Mi)
% 2.99/1.69 % (29067)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_28704 for (2998ds/779Mi)
% 2.99/1.69 % (29068)Instruction limit reached!
% 2.99/1.69 % (29068)------------------------------
% 2.99/1.69 % (29068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.69 % (29068)Termination reason: Unknown
% 2.99/1.69 % (29068)Termination phase: shuffling
% 2.99/1.69
% 2.99/1.69 % (29068)Memory used [KB]: 1791
% 2.99/1.69 % (29068)Time elapsed: 0.007 s
% 2.99/1.69 % (29068)Instructions burned: 21 (million)
% 2.99/1.69 % (29068)------------------------------
% 2.99/1.69 % (29068)------------------------------
% 2.99/1.69 % (29069)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28704 for (2998ds/879Mi)
% 2.99/1.70 % (29070)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28704 for (2998ds/17Mi)
% 2.99/1.71 % (29070)Instruction limit reached!
% 2.99/1.71 % (29070)------------------------------
% 2.99/1.71 % (29070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.71 % (29070)Termination reason: Unknown
% 2.99/1.71 % (29070)Termination phase: shuffling
% 2.99/1.71
% 2.99/1.71 % (29070)Memory used [KB]: 1918
% 2.99/1.71 % (29070)Time elapsed: 0.007 s
% 2.99/1.71 % (29070)Instructions burned: 18 (million)
% 2.99/1.71 % (29070)------------------------------
% 2.99/1.71 % (29070)------------------------------
% 2.99/1.72 % (29071)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28704 for (2998ds/3Mi)
% 2.99/1.72 % (29071)Instruction limit reached!
% 2.99/1.72 % (29071)------------------------------
% 2.99/1.72 % (29071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.72 % (29071)Termination reason: Unknown
% 2.99/1.72 % (29071)Termination phase: shuffling
% 2.99/1.72
% 2.99/1.72 % (29071)Memory used [KB]: 1535
% 2.99/1.72 % (29071)Time elapsed: 0.003 s
% 2.99/1.72 % (29071)Instructions burned: 5 (million)
% 2.99/1.72 % (29071)------------------------------
% 2.99/1.72 % (29071)------------------------------
% 2.99/1.73 % (29072)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28704 for (2998ds/30Mi)
% 2.99/1.74 % (29072)Instruction limit reached!
% 2.99/1.74 % (29072)------------------------------
% 2.99/1.74 % (29072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.74 % (29072)Termination reason: Unknown
% 2.99/1.74 % (29072)Termination phase: shuffling
% 2.99/1.74
% 2.99/1.74 % (29072)Memory used [KB]: 2174
% 2.99/1.74 % (29072)Time elapsed: 0.011 s
% 2.99/1.74 % (29072)Instructions burned: 30 (million)
% 2.99/1.74 % (29072)------------------------------
% 2.99/1.74 % (29072)------------------------------
% 2.99/1.75 % (29073)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28704 for (2998ds/127Mi)
% 2.99/1.78 % (29073)Instruction limit reached!
% 2.99/1.78 % (29073)------------------------------
% 2.99/1.78 % (29073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.78 % (29073)Termination reason: Unknown
% 2.99/1.78 % (29073)Termination phase: Property scanning
% 2.99/1.78
% 2.99/1.78 % (29073)Memory used [KB]: 3070
% 2.99/1.78 % (29073)Time elapsed: 0.039 s
% 2.99/1.78 % (29073)Instructions burned: 129 (million)
% 2.99/1.78 % (29073)------------------------------
% 2.99/1.78 % (29073)------------------------------
% 2.99/1.79 % (29074)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28704 for (2997ds/100Mi)
% 2.99/1.80 % (29066)Instruction limit reached!
% 2.99/1.80 % (29066)------------------------------
% 2.99/1.80 % (29066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.80 % (29066)Termination reason: Unknown
% 2.99/1.80 % (29066)Termination phase: Saturation
% 2.99/1.80
% 2.99/1.80 % (29066)Memory used [KB]: 8827
% 2.99/1.80 % (29066)Time elapsed: 0.125 s
% 2.99/1.80 % (29066)Instructions burned: 377 (million)
% 2.99/1.80 % (29066)------------------------------
% 2.99/1.80 % (29066)------------------------------
% 2.99/1.81 % (29075)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_28704 for (2997ds/3Mi)
% 2.99/1.81 % (29075)Instruction limit reached!
% 2.99/1.81 % (29075)------------------------------
% 2.99/1.81 % (29075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.81 % (29075)Termination reason: Unknown
% 2.99/1.81 % (29075)Termination phase: shuffling
% 2.99/1.81
% 2.99/1.81 % (29075)Memory used [KB]: 1535
% 2.99/1.81 % (29075)Time elapsed: 0.002 s
% 2.99/1.81 % (29075)Instructions burned: 4 (million)
% 2.99/1.81 % (29075)------------------------------
% 2.99/1.81 % (29075)------------------------------
% 2.99/1.82 % (29074)Instruction limit reached!
% 2.99/1.82 % (29074)------------------------------
% 2.99/1.82 % (29074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.82 % (29074)Termination reason: Unknown
% 2.99/1.82 % (29074)Termination phase: Preprocessing 3
% 2.99/1.82
% 2.99/1.82 % (29074)Memory used [KB]: 2814
% 2.99/1.82 % (29074)Time elapsed: 0.029 s
% 2.99/1.82 % (29074)Instructions burned: 102 (million)
% 2.99/1.82 % (29074)------------------------------
% 2.99/1.82 % (29074)------------------------------
% 2.99/1.82 % (29076)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_28704 for (2997ds/20Mi)
% 2.99/1.83 % (29077)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_28704 for (2997ds/86Mi)
% 2.99/1.83 % (29076)Instruction limit reached!
% 2.99/1.83 % (29076)------------------------------
% 2.99/1.83 % (29076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.83 % (29076)Termination reason: Unknown
% 2.99/1.83 % (29076)Termination phase: shuffling
% 2.99/1.83
% 2.99/1.83 % (29076)Memory used [KB]: 1918
% 2.99/1.83 % (29076)Time elapsed: 0.009 s
% 2.99/1.83 % (29076)Instructions burned: 20 (million)
% 2.99/1.83 % (29076)------------------------------
% 2.99/1.83 % (29076)------------------------------
% 2.99/1.84 % (29078)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_28704 for (2997ds/107Mi)
% 2.99/1.86 % (29077)Instruction limit reached!
% 2.99/1.86 % (29077)------------------------------
% 2.99/1.86 % (29077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.86 % (29077)Termination reason: Unknown
% 2.99/1.86 % (29077)Termination phase: Property scanning
% 2.99/1.86
% 2.99/1.86 % (29077)Memory used [KB]: 3070
% 2.99/1.86 % (29077)Time elapsed: 0.028 s
% 2.99/1.86 % (29077)Instructions burned: 88 (million)
% 2.99/1.86 % (29077)------------------------------
% 2.99/1.86 % (29077)------------------------------
% 2.99/1.87 % (29079)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/39Mi)
% 2.99/1.87 % (29060)Instruction limit reached!
% 2.99/1.87 % (29060)------------------------------
% 2.99/1.87 % (29060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.87 % (29060)Termination reason: Unknown
% 2.99/1.87 % (29060)Termination phase: Saturation
% 2.99/1.87
% 2.99/1.87 % (29060)Memory used [KB]: 8443
% 2.99/1.87 % (29060)Time elapsed: 0.220 s
% 2.99/1.87 % (29060)Instructions burned: 711 (million)
% 2.99/1.87 % (29060)------------------------------
% 2.99/1.87 % (29060)------------------------------
% 2.99/1.88 % (29078)Instruction limit reached!
% 2.99/1.88 % (29078)------------------------------
% 2.99/1.88 % (29078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.88 % (29078)Termination reason: Unknown
% 2.99/1.88 % (29078)Termination phase: Property scanning
% 2.99/1.88
% 2.99/1.88 % (29078)Memory used [KB]: 2942
% 2.99/1.88 % (29078)Time elapsed: 0.037 s
% 2.99/1.88 % (29078)Instructions burned: 109 (million)
% 2.99/1.88 % (29078)------------------------------
% 2.99/1.88 % (29078)------------------------------
% 2.99/1.88 % (29079)Instruction limit reached!
% 2.99/1.88 % (29079)------------------------------
% 2.99/1.88 % (29079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.88 % (29079)Termination reason: Unknown
% 2.99/1.88 % (29079)Termination phase: shuffling
% 2.99/1.88
% 2.99/1.88 % (29079)Memory used [KB]: 2302
% 2.99/1.88 % (29079)Time elapsed: 0.012 s
% 2.99/1.88 % (29079)Instructions burned: 39 (million)
% 2.99/1.88 % (29079)------------------------------
% 2.99/1.88 % (29079)------------------------------
% 2.99/1.88 % (29080)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/448Mi)
% 2.99/1.89 % (29081)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/46Mi)
% 2.99/1.89 % (29082)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/98Mi)
% 2.99/1.90 % (29081)Instruction limit reached!
% 2.99/1.90 % (29081)------------------------------
% 2.99/1.90 % (29081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.90 % (29081)Termination reason: Unknown
% 2.99/1.90 % (29081)Termination phase: Property scanning
% 2.99/1.90
% 2.99/1.90 % (29081)Memory used [KB]: 2174
% 2.99/1.90 % (29081)Time elapsed: 0.018 s
% 2.99/1.90 % (29081)Instructions burned: 48 (million)
% 2.99/1.90 % (29081)------------------------------
% 2.99/1.90 % (29081)------------------------------
% 2.99/1.91 % (29083)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/507Mi)
% 2.99/1.91 % (29082)Instruction limit reached!
% 2.99/1.91 % (29082)------------------------------
% 2.99/1.91 % (29082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.91 % (29082)Termination reason: Unknown
% 2.99/1.91 % (29082)Termination phase: Preprocessing 1
% 2.99/1.91
% 2.99/1.91 % (29082)Memory used [KB]: 2814
% 2.99/1.91 % (29082)Time elapsed: 0.027 s
% 2.99/1.91 % (29082)Instructions burned: 98 (million)
% 2.99/1.91 % (29082)------------------------------
% 2.99/1.91 % (29082)------------------------------
% 2.99/1.92 % (29084)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/149Mi)
% 2.99/1.93 % (29062)Instruction limit reached!
% 2.99/1.93 % (29062)------------------------------
% 2.99/1.93 % (29062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.93 % (29062)Termination reason: Unknown
% 2.99/1.93 % (29062)Termination phase: Saturation
% 2.99/1.93
% 2.99/1.93 % (29062)Memory used [KB]: 9338
% 2.99/1.93 % (29062)Time elapsed: 0.267 s
% 2.99/1.93 % (29062)Instructions burned: 902 (million)
% 2.99/1.93 % (29062)------------------------------
% 2.99/1.93 % (29062)------------------------------
% 2.99/1.94 % (29085)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/39Mi)
% 2.99/1.95 % (29069)Refutation not found, non-redundant clauses discarded% (29069)------------------------------
% 2.99/1.95 % (29069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.95 % (29069)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.99/1.95
% 2.99/1.95 % (29069)Memory used [KB]: 8443
% 2.99/1.95 % (29069)Time elapsed: 0.274 s
% 2.99/1.95 % (29069)Instructions burned: 817 (million)
% 2.99/1.95 % (29069)------------------------------
% 2.99/1.95 % (29069)------------------------------
% 2.99/1.95 % (29085)Instruction limit reached!
% 2.99/1.95 % (29085)------------------------------
% 2.99/1.95 % (29085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.95 % (29085)Termination reason: Unknown
% 2.99/1.95 % (29085)Termination phase: Property scanning
% 2.99/1.95
% 2.99/1.95 % (29085)Memory used [KB]: 2174
% 2.99/1.95 % (29085)Time elapsed: 0.014 s
% 2.99/1.95 % (29085)Instructions burned: 41 (million)
% 2.99/1.95 % (29085)------------------------------
% 2.99/1.95 % (29085)------------------------------
% 2.99/1.96 % (29086)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/6Mi)
% 2.99/1.96 % (29067)Instruction limit reached!
% 2.99/1.96 % (29067)------------------------------
% 2.99/1.96 % (29067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.96 % (29067)Termination reason: Unknown
% 2.99/1.96 % (29067)Termination phase: Saturation
% 2.99/1.96
% 2.99/1.96 % (29067)Memory used [KB]: 9466
% 2.99/1.96 % (29067)Time elapsed: 0.270 s
% 2.99/1.96 % (29067)Instructions burned: 780 (million)
% 2.99/1.96 % (29067)------------------------------
% 2.99/1.96 % (29067)------------------------------
% 2.99/1.96 % (29086)Instruction limit reached!
% 2.99/1.96 % (29086)------------------------------
% 2.99/1.96 % (29086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.96 % (29086)Termination reason: Unknown
% 2.99/1.96 % (29086)Termination phase: shuffling
% 2.99/1.96
% 2.99/1.96 % (29086)Memory used [KB]: 1663
% 2.99/1.96 % (29086)Time elapsed: 0.003 s
% 2.99/1.96 % (29086)Instructions burned: 7 (million)
% 2.99/1.96 % (29086)------------------------------
% 2.99/1.96 % (29086)------------------------------
% 2.99/1.96 % (29087)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/1087Mi)
% 2.99/1.97 % (29084)Instruction limit reached!
% 2.99/1.97 % (29084)------------------------------
% 2.99/1.97 % (29084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.97 % (29084)Termination reason: Unknown
% 2.99/1.97 % (29084)Termination phase: Property scanning
% 2.99/1.97
% 2.99/1.97 % (29084)Memory used [KB]: 2942
% 2.99/1.97 % (29084)Time elapsed: 0.044 s
% 2.99/1.97 % (29084)Instructions burned: 151 (million)
% 2.99/1.97 % (29084)------------------------------
% 2.99/1.97 % (29084)------------------------------
% 2.99/1.97 % (29089)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/44Mi)
% 2.99/1.97 % (29088)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_28704 for (2996ds/47Mi)
% 2.99/1.98 % (29090)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/432Mi)
% 2.99/1.98 % (29089)Instruction limit reached!
% 2.99/1.98 % (29089)------------------------------
% 2.99/1.98 % (29089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.98 % (29089)Termination reason: Unknown
% 2.99/1.98 % (29089)Termination phase: shuffling
% 2.99/1.98
% 2.99/1.98 % (29089)Memory used [KB]: 2302
% 2.99/1.98 % (29089)Time elapsed: 0.013 s
% 2.99/1.98 % (29089)Instructions burned: 44 (million)
% 2.99/1.98 % (29089)------------------------------
% 2.99/1.98 % (29089)------------------------------
% 2.99/1.98 % (29088)Instruction limit reached!
% 2.99/1.98 % (29088)------------------------------
% 2.99/1.98 % (29088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.98 % (29088)Termination reason: Unknown
% 2.99/1.98 % (29088)Termination phase: Property scanning
% 2.99/1.98
% 2.99/1.98 % (29088)Memory used [KB]: 2174
% 2.99/1.98 % (29088)Time elapsed: 0.018 s
% 2.99/1.98 % (29088)Instructions burned: 48 (million)
% 2.99/1.98 % (29088)------------------------------
% 2.99/1.98 % (29088)------------------------------
% 2.99/1.99 % (29091)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/62Mi)
% 2.99/1.99 % (29092)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/31Mi)
% 2.99/2.00 % (29051)Instruction limit reached!
% 2.99/2.00 % (29051)------------------------------
% 2.99/2.00 % (29051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/2.00 % (29051)Termination reason: Unknown
% 2.99/2.00 % (29051)Termination phase: Saturation
% 2.99/2.00
% 2.99/2.00 % (29051)Memory used [KB]: 10234
% 2.99/2.00 % (29051)Time elapsed: 0.368 s
% 2.99/2.00 % (29051)Instructions burned: 1041 (million)
% 2.99/2.00 % (29051)------------------------------
% 2.99/2.00 % (29051)------------------------------
% 2.99/2.01 % (29092)Instruction limit reached!
% 2.99/2.01 % (29092)------------------------------
% 2.99/2.01 % (29092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/2.01 % (29092)Termination reason: Unknown
% 2.99/2.01 % (29092)Termination phase: shuffling
% 2.99/2.01
% 2.99/2.01 % (29092)Memory used [KB]: 2174
% 2.99/2.01 % (29092)Time elapsed: 0.013 s
% 2.99/2.01 % (29092)Instructions burned: 31 (million)
% 2.99/2.01 % (29092)------------------------------
% 2.99/2.01 % (29092)------------------------------
% 2.99/2.01 % (29091)Instruction limit reached!
% 2.99/2.01 % (29091)------------------------------
% 2.99/2.01 % (29091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/2.01 % (29091)Termination reason: Unknown
% 2.99/2.01 % (29091)Termination phase: Property scanning
% 2.99/2.01
% 2.99/2.01 % (29091)Memory used [KB]: 2558
% 2.99/2.01 % (29091)Time elapsed: 0.019 s
% 2.99/2.01 % (29091)Instructions burned: 65 (million)
% 2.99/2.01 % (29091)------------------------------
% 2.99/2.01 % (29091)------------------------------
% 2.99/2.01 % (29080)Instruction limit reached!
% 2.99/2.01 % (29080)------------------------------
% 2.99/2.01 % (29080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/2.01 % (29080)Termination reason: Unknown
% 2.99/2.01 % (29080)Termination phase: Saturation
% 2.99/2.01
% 2.99/2.01 % (29080)Memory used [KB]: 8955
% 2.99/2.01 % (29080)Time elapsed: 0.131 s
% 2.99/2.01 % (29080)Instructions burned: 450 (million)
% 2.99/2.01 % (29080)------------------------------
% 2.99/2.01 % (29080)------------------------------
% 5.98/2.02 % (29094)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/453Mi)
% 5.98/2.02 % (29095)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/71Mi)
% 5.98/2.02 % (29096)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/83Mi)
% 5.98/2.02 % (29093)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/96Mi)
% 5.98/2.04 % (29095)Instruction limit reached!
% 5.98/2.04 % (29095)------------------------------
% 5.98/2.04 % (29095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.04 % (29095)Termination reason: Unknown
% 5.98/2.04 % (29095)Termination phase: Preprocessing 3
% 5.98/2.04
% 5.98/2.04 % (29095)Memory used [KB]: 2686
% 5.98/2.04 % (29095)Time elapsed: 0.025 s
% 5.98/2.04 % (29095)Instructions burned: 74 (million)
% 5.98/2.04 % (29095)------------------------------
% 5.98/2.04 % (29095)------------------------------
% 5.98/2.05 % (29096)Instruction limit reached!
% 5.98/2.05 % (29096)------------------------------
% 5.98/2.05 % (29096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.05 % (29096)Termination reason: Unknown
% 5.98/2.05 % (29096)Termination phase: Saturation
% 5.98/2.05
% 5.98/2.05 % (29096)Memory used [KB]: 6908
% 5.98/2.05 % (29096)Time elapsed: 0.028 s
% 5.98/2.05 % (29096)Instructions burned: 85 (million)
% 5.98/2.05 % (29096)------------------------------
% 5.98/2.05 % (29096)------------------------------
% 5.98/2.05 % (29097)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/11Mi)
% 5.98/2.05 % (29097)Instruction limit reached!
% 5.98/2.05 % (29097)------------------------------
% 5.98/2.05 % (29097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.05 % (29097)Termination reason: Unknown
% 5.98/2.05 % (29097)Termination phase: shuffling
% 5.98/2.05
% 5.98/2.05 % (29097)Memory used [KB]: 1663
% 5.98/2.05 % (29097)Time elapsed: 0.004 s
% 5.98/2.05 % (29097)Instructions burned: 11 (million)
% 5.98/2.05 % (29097)------------------------------
% 5.98/2.05 % (29097)------------------------------
% 5.98/2.06 % (29098)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/41Mi)
% 5.98/2.06 % (29099)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/6Mi)
% 5.98/2.06 % (29099)Instruction limit reached!
% 5.98/2.06 % (29099)------------------------------
% 5.98/2.06 % (29099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.06 % (29099)Termination reason: Unknown
% 5.98/2.06 % (29099)Termination phase: shuffling
% 5.98/2.06
% 5.98/2.06 % (29099)Memory used [KB]: 1535
% 5.98/2.06 % (29099)Time elapsed: 0.003 s
% 5.98/2.06 % (29099)Instructions burned: 7 (million)
% 5.98/2.06 % (29099)------------------------------
% 5.98/2.06 % (29099)------------------------------
% 5.98/2.07 % (29098)Instruction limit reached!
% 5.98/2.07 % (29098)------------------------------
% 5.98/2.07 % (29098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.07 % (29098)Termination reason: Unknown
% 5.98/2.07 % (29098)Termination phase: shuffling
% 5.98/2.07
% 5.98/2.07 % (29098)Memory used [KB]: 2302
% 5.98/2.07 % (29098)Time elapsed: 0.013 s
% 5.98/2.07 % (29098)Instructions burned: 44 (million)
% 5.98/2.07 % (29098)------------------------------
% 5.98/2.07 % (29098)------------------------------
% 5.98/2.07 % (29100)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_28704 for (2995ds/150Mi)
% 5.98/2.08 % (29093)Instruction limit reached!
% 5.98/2.08 % (29093)------------------------------
% 5.98/2.08 % (29093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.08 % (29093)Termination reason: Unknown
% 5.98/2.08 % (29093)Termination phase: Property scanning
% 5.98/2.08
% 5.98/2.08 % (29093)Memory used [KB]: 2942
% 5.98/2.08 % (29093)Time elapsed: 0.057 s
% 5.98/2.08 % (29093)Instructions burned: 96 (million)
% 5.98/2.08 % (29093)------------------------------
% 5.98/2.08 % (29093)------------------------------
% 5.98/2.08 % (29083)Instruction limit reached!
% 5.98/2.08 % (29083)------------------------------
% 5.98/2.08 % (29083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.08 % (29083)Termination reason: Unknown
% 5.98/2.08 % (29083)Termination phase: Saturation
% 5.98/2.08
% 5.98/2.08 % (29083)Memory used [KB]: 9083
% 5.98/2.08 % (29083)Time elapsed: 0.165 s
% 5.98/2.08 % (29083)Instructions burned: 509 (million)
% 5.98/2.08 % (29083)------------------------------
% 5.98/2.08 % (29083)------------------------------
% 5.98/2.08 % (29101)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/343Mi)
% 5.98/2.09 % (29103)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/253Mi)
% 5.98/2.09 % (29102)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/109Mi)
% 5.98/2.11 % (29090)Instruction limit reached!
% 5.98/2.11 % (29090)------------------------------
% 5.98/2.11 % (29090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.11 % (29090)Termination reason: Unknown
% 5.98/2.11 % (29090)Termination phase: Saturation
% 5.98/2.11
% 5.98/2.11 % (29090)Memory used [KB]: 4605
% 5.98/2.11 % (29090)Time elapsed: 0.132 s
% 5.98/2.11 % (29090)Instructions burned: 435 (million)
% 5.98/2.11 % (29090)------------------------------
% 5.98/2.11 % (29090)------------------------------
% 6.44/2.12 % (29100)Instruction limit reached!
% 6.44/2.12 % (29100)------------------------------
% 6.44/2.12 % (29100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.12 % (29100)Termination reason: Unknown
% 6.44/2.12 % (29100)Termination phase: Property scanning
% 6.44/2.12
% 6.44/2.12 % (29100)Memory used [KB]: 3198
% 6.44/2.12 % (29100)Time elapsed: 0.044 s
% 6.44/2.12 % (29100)Instructions burned: 151 (million)
% 6.44/2.12 % (29100)------------------------------
% 6.44/2.12 % (29100)------------------------------
% 6.44/2.12 % (29104)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/140Mi)
% 6.44/2.13 % (29105)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/614Mi)
% 6.44/2.14 % (29102)Instruction limit reached!
% 6.44/2.14 % (29102)------------------------------
% 6.44/2.14 % (29102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (29102)Termination reason: Unknown
% 6.44/2.14 % (29102)Termination phase: Property scanning
% 6.44/2.14
% 6.44/2.14 % (29102)Memory used [KB]: 2942
% 6.44/2.14 % (29102)Time elapsed: 0.044 s
% 6.44/2.14 % (29102)Instructions burned: 109 (million)
% 6.44/2.14 % (29102)------------------------------
% 6.44/2.14 % (29102)------------------------------
% 6.44/2.15 % (29106)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/202Mi)
% 6.44/2.15 % (29094)Instruction limit reached!
% 6.44/2.15 % (29094)------------------------------
% 6.44/2.15 % (29094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.15 % (29094)Termination reason: Unknown
% 6.44/2.15 % (29094)Termination phase: Saturation
% 6.44/2.15
% 6.44/2.15 % (29094)Memory used [KB]: 8571
% 6.44/2.15 % (29094)Time elapsed: 0.136 s
% 6.44/2.15 % (29094)Instructions burned: 456 (million)
% 6.44/2.15 % (29094)------------------------------
% 6.44/2.15 % (29094)------------------------------
% 6.44/2.16 % (29107)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_28704 for (2994ds/339Mi)
% 6.44/2.16 % (29104)Instruction limit reached!
% 6.44/2.16 % (29104)------------------------------
% 6.44/2.16 % (29104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.16 % (29104)Termination reason: Unknown
% 6.44/2.16 % (29104)Termination phase: Saturation
% 6.44/2.16
% 6.44/2.16 % (29104)Memory used [KB]: 7419
% 6.44/2.16 % (29104)Time elapsed: 0.068 s
% 6.44/2.16 % (29104)Instructions burned: 142 (million)
% 6.44/2.16 % (29104)------------------------------
% 6.44/2.16 % (29104)------------------------------
% 6.44/2.16 % (29103)Instruction limit reached!
% 6.44/2.16 % (29103)------------------------------
% 6.44/2.16 % (29103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.16 % (29103)Termination reason: Unknown
% 6.44/2.16 % (29103)Termination phase: Saturation
% 6.44/2.16
% 6.44/2.16 % (29103)Memory used [KB]: 8187
% 6.44/2.16 % (29103)Time elapsed: 0.079 s
% 6.44/2.16 % (29103)Instructions burned: 254 (million)
% 6.44/2.16 % (29103)------------------------------
% 6.44/2.16 % (29103)------------------------------
% 6.44/2.17 % (29108)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_28704 for (2993ds/283Mi)
% 6.44/2.17 % (29109)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_28704 for (2993ds/134Mi)
% 6.44/2.18 % (29106)Refutation not found, incomplete strategy
% 6.44/2.18 % (29106)------------------------------
% 6.44/2.18 % (29106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (29106)Termination reason: Refutation not found, incomplete strategy
% 6.44/2.18
% 6.44/2.18
% 6.44/2.18 % (29106)Memory used [KB]: 7036
% 6.44/2.18 % (29106)Time elapsed: 0.033 s
% 6.44/2.18 % (29106)Instructions burned: 95 (million)
% 6.44/2.18 % (29106)------------------------------
% 6.44/2.18 % (29106)------------------------------
% 6.44/2.19 % (29101)Instruction limit reached!
% 6.44/2.19 % (29101)------------------------------
% 6.44/2.19 % (29101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.19 % (29101)Termination reason: Unknown
% 6.44/2.19 % (29101)Termination phase: Saturation
% 6.44/2.19
% 6.44/2.19 % (29101)Memory used [KB]: 8443
% 6.44/2.19 % (29101)Time elapsed: 0.131 s
% 6.44/2.19 % (29101)Instructions burned: 345 (million)
% 6.44/2.19 % (29101)------------------------------
% 6.44/2.19 % (29101)------------------------------
% 6.44/2.19 % (29110)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_28704 for (2993ds/298Mi)
% 7.07/2.20 % (29111)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_28704 for (2993ds/192Mi)
% 7.07/2.21 % (29109)Instruction limit reached!
% 7.07/2.21 % (29109)------------------------------
% 7.07/2.21 % (29109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.21 % (29109)Termination reason: Unknown
% 7.07/2.21 % (29109)Termination phase: Property scanning
% 7.07/2.21
% 7.07/2.21 % (29109)Memory used [KB]: 3070
% 7.07/2.21 % (29109)Time elapsed: 0.041 s
% 7.07/2.21 % (29109)Instructions burned: 137 (million)
% 7.07/2.21 % (29109)------------------------------
% 7.07/2.21 % (29109)------------------------------
% 7.07/2.22 % (29112)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_28704 for (2993ds/258Mi)
% 7.07/2.25 % (29108)Instruction limit reached!
% 7.07/2.25 % (29108)------------------------------
% 7.07/2.25 % (29108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.25 % (29108)Termination reason: Unknown
% 7.07/2.25 % (29108)Termination phase: Saturation
% 7.07/2.25
% 7.07/2.25 % (29108)Memory used [KB]: 7803
% 7.07/2.25 % (29108)Time elapsed: 0.085 s
% 7.07/2.25 % (29108)Instructions burned: 283 (million)
% 7.07/2.25 % (29108)------------------------------
% 7.07/2.25 % (29108)------------------------------
% 7.07/2.26 % (29111)Instruction limit reached!
% 7.07/2.26 % (29111)------------------------------
% 7.07/2.26 % (29111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.26 % (29111)Termination reason: Unknown
% 7.07/2.26 % (29111)Termination phase: Saturation
% 7.07/2.26
% 7.07/2.26 % (29111)Memory used [KB]: 3837
% 7.07/2.26 % (29111)Time elapsed: 0.059 s
% 7.07/2.26 % (29111)Instructions burned: 195 (million)
% 7.07/2.26 % (29111)------------------------------
% 7.07/2.26 % (29111)------------------------------
% 7.07/2.26 % (29107)Instruction limit reached!
% 7.07/2.26 % (29107)------------------------------
% 7.07/2.26 % (29107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.26 % (29107)Termination reason: Unknown
% 7.07/2.26 % (29107)Termination phase: Saturation
% 7.07/2.26
% 7.07/2.26 % (29107)Memory used [KB]: 8059
% 7.07/2.26 % (29107)Time elapsed: 0.099 s
% 7.07/2.26 % (29107)Instructions burned: 340 (million)
% 7.07/2.26 % (29107)------------------------------
% 7.07/2.26 % (29107)------------------------------
% 7.07/2.26 % (29113)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/90Mi)
% 7.07/2.27 % (29114)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/231Mi)
% 7.07/2.27 % (29115)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/458Mi)
% 7.07/2.28 % (29110)Instruction limit reached!
% 7.07/2.28 % (29110)------------------------------
% 7.07/2.28 % (29110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.28 % (29110)Termination reason: Unknown
% 7.07/2.28 % (29110)Termination phase: Saturation
% 7.07/2.28
% 7.07/2.28 % (29110)Memory used [KB]: 7931
% 7.07/2.28 % (29110)Time elapsed: 0.090 s
% 7.07/2.28 % (29110)Instructions burned: 299 (million)
% 7.07/2.28 % (29110)------------------------------
% 7.07/2.28 % (29110)------------------------------
% 7.07/2.29 % (29116)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/31Mi)
% 7.07/2.29 % (29113)Instruction limit reached!
% 7.07/2.29 % (29113)------------------------------
% 7.07/2.29 % (29113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.29 % (29113)Termination reason: Unknown
% 7.07/2.29 % (29113)Termination phase: Property scanning
% 7.07/2.29
% 7.07/2.29 % (29113)Memory used [KB]: 2942
% 7.07/2.29 % (29113)Time elapsed: 0.029 s
% 7.07/2.29 % (29113)Instructions burned: 91 (million)
% 7.07/2.29 % (29113)------------------------------
% 7.07/2.29 % (29113)------------------------------
% 7.07/2.30 % (29087)Instruction limit reached!
% 7.07/2.30 % (29087)------------------------------
% 7.07/2.30 % (29087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.07/2.30 % (29087)Termination reason: Unknown
% 7.07/2.30 % (29087)Termination phase: Saturation
% 7.07/2.30
% 7.07/2.30 % (29087)Memory used [KB]: 9210
% 7.07/2.30 % (29087)Time elapsed: 0.338 s
% 7.07/2.30 % (29087)Instructions burned: 1088 (million)
% 7.07/2.30 % (29087)------------------------------
% 7.07/2.30 % (29087)------------------------------
% 7.29/2.30 % (29112)Instruction limit reached!
% 7.29/2.30 % (29112)------------------------------
% 7.29/2.30 % (29112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.30 % (29112)Termination reason: Unknown
% 7.29/2.30 % (29112)Termination phase: Saturation
% 7.29/2.30
% 7.29/2.30 % (29112)Memory used [KB]: 3709
% 7.29/2.30 % (29112)Time elapsed: 0.076 s
% 7.29/2.30 % (29112)Instructions burned: 260 (million)
% 7.29/2.30 % (29112)------------------------------
% 7.29/2.30 % (29112)------------------------------
% 7.29/2.30 % (29116)Instruction limit reached!
% 7.29/2.30 % (29116)------------------------------
% 7.29/2.30 % (29116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.30 % (29116)Termination reason: Unknown
% 7.29/2.30 % (29116)Termination phase: shuffling
% 7.29/2.30
% 7.29/2.30 % (29116)Memory used [KB]: 2174
% 7.29/2.30 % (29116)Time elapsed: 0.013 s
% 7.29/2.30 % (29116)Instructions burned: 31 (million)
% 7.29/2.30 % (29116)------------------------------
% 7.29/2.30 % (29116)------------------------------
% 7.29/2.30 % (29117)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/297Mi)
% 7.29/2.31 % (29118)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/987Mi)
% 7.29/2.31 % (29119)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/182Mi)
% 7.29/2.31 % (29120)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/182Mi)
% 7.29/2.32 % (29105)Instruction limit reached!
% 7.29/2.32 % (29105)------------------------------
% 7.29/2.32 % (29105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.32 % (29105)Termination reason: Unknown
% 7.29/2.32 % (29105)Termination phase: Saturation
% 7.29/2.32
% 7.29/2.32 % (29105)Memory used [KB]: 9338
% 7.29/2.32 % (29105)Time elapsed: 0.215 s
% 7.29/2.32 % (29105)Instructions burned: 615 (million)
% 7.29/2.32 % (29105)------------------------------
% 7.29/2.32 % (29105)------------------------------
% 7.29/2.33 % (29114)Instruction limit reached!
% 7.29/2.33 % (29114)------------------------------
% 7.29/2.33 % (29114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.33 % (29114)Termination reason: Unknown
% 7.29/2.33 % (29114)Termination phase: Saturation
% 7.29/2.33
% 7.29/2.33 % (29114)Memory used [KB]: 7291
% 7.29/2.33 % (29114)Time elapsed: 0.063 s
% 7.29/2.33 % (29114)Instructions burned: 234 (million)
% 7.29/2.33 % (29114)------------------------------
% 7.29/2.33 % (29114)------------------------------
% 7.29/2.33 % (29121)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/154Mi)
% 7.29/2.34 % (29122)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_28704 for (2992ds/79Mi)
% 7.29/2.36 % (29119)Instruction limit reached!
% 7.29/2.36 % (29119)------------------------------
% 7.29/2.36 % (29119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.36 % (29119)Termination reason: Unknown
% 7.29/2.36 % (29119)Termination phase: Saturation
% 7.29/2.36
% 7.29/2.36 % (29119)Memory used [KB]: 7547
% 7.29/2.36 % (29119)Time elapsed: 0.052 s
% 7.29/2.36 % (29119)Instructions burned: 182 (million)
% 7.29/2.36 % (29119)------------------------------
% 7.29/2.36 % (29119)------------------------------
% 7.29/2.36 % (29122)Instruction limit reached!
% 7.29/2.36 % (29122)------------------------------
% 7.29/2.36 % (29122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.36 % (29122)Termination reason: Unknown
% 7.29/2.36 % (29122)Termination phase: Preprocessing 3
% 7.29/2.36
% 7.29/2.36 % (29122)Memory used [KB]: 2814
% 7.29/2.36 % (29122)Time elapsed: 0.026 s
% 7.29/2.36 % (29122)Instructions burned: 81 (million)
% 7.29/2.36 % (29122)------------------------------
% 7.29/2.36 % (29122)------------------------------
% 7.29/2.37 % (29120)Instruction limit reached!
% 7.29/2.37 % (29120)------------------------------
% 7.29/2.37 % (29120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.37 % (29120)Termination reason: Unknown
% 7.29/2.37 % (29120)Termination phase: Saturation
% 7.29/2.37
% 7.29/2.37 % (29120)Memory used [KB]: 7675
% 7.29/2.37 % (29120)Time elapsed: 0.059 s
% 7.29/2.37 % (29120)Instructions burned: 182 (million)
% 7.29/2.37 % (29120)------------------------------
% 7.29/2.37 % (29120)------------------------------
% 7.29/2.37 % (29123)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/216Mi)
% 7.29/2.37 % (29121)Instruction limit reached!
% 7.29/2.37 % (29121)------------------------------
% 7.29/2.37 % (29121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.37 % (29121)Termination reason: Unknown
% 7.29/2.37 % (29121)Termination phase: Saturation
% 7.29/2.37
% 7.29/2.37 % (29121)Memory used [KB]: 2942
% 7.29/2.37 % (29121)Time elapsed: 0.043 s
% 7.29/2.37 % (29121)Instructions burned: 156 (million)
% 7.29/2.37 % (29121)------------------------------
% 7.29/2.37 % (29121)------------------------------
% 7.29/2.37 % (29124)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/114Mi)
% 7.29/2.38 % (29125)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/922Mi)
% 7.29/2.38 % (29126)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/182Mi)
% 7.29/2.39 % (29117)Instruction limit reached!
% 7.29/2.39 % (29117)------------------------------
% 7.29/2.39 % (29117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.29/2.39 % (29117)Termination reason: Unknown
% 7.29/2.39 % (29117)Termination phase: Saturation
% 7.29/2.39
% 7.29/2.39 % (29117)Memory used [KB]: 7675
% 7.29/2.39 % (29117)Time elapsed: 0.088 s
% 7.29/2.39 % (29117)Instructions burned: 300 (million)
% 7.29/2.39 % (29117)------------------------------
% 7.29/2.39 % (29117)------------------------------
% 8.32/2.40 % (29127)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/164Mi)
% 8.32/2.41 % (29124)Instruction limit reached!
% 8.32/2.41 % (29124)------------------------------
% 8.32/2.41 % (29124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.41 % (29124)Termination reason: Unknown
% 8.32/2.41 % (29124)Termination phase: Equality resolution with deletion
% 8.32/2.41
% 8.32/2.41 % (29124)Memory used [KB]: 2942
% 8.32/2.41 % (29124)Time elapsed: 0.035 s
% 8.32/2.41 % (29124)Instructions burned: 114 (million)
% 8.32/2.41 % (29124)------------------------------
% 8.32/2.41 % (29124)------------------------------
% 8.32/2.41 % (29115)Instruction limit reached!
% 8.32/2.41 % (29115)------------------------------
% 8.32/2.41 % (29115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.41 % (29115)Termination reason: Unknown
% 8.32/2.41 % (29115)Termination phase: Saturation
% 8.32/2.41
% 8.32/2.41 % (29115)Memory used [KB]: 8699
% 8.32/2.41 % (29115)Time elapsed: 0.141 s
% 8.32/2.41 % (29115)Instructions burned: 460 (million)
% 8.32/2.41 % (29115)------------------------------
% 8.32/2.41 % (29115)------------------------------
% 8.32/2.41 % (29128)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/50Mi)
% 8.32/2.42 % (29129)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/368Mi)
% 8.32/2.43 % (29126)Instruction limit reached!
% 8.32/2.43 % (29126)------------------------------
% 8.32/2.43 % (29126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.43 % (29126)Termination reason: Unknown
% 8.32/2.43 % (29123)Instruction limit reached!
% 8.32/2.43 % (29123)------------------------------
% 8.32/2.43 % (29123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.43 % (29126)Termination phase: Saturation
% 8.32/2.43
% 8.32/2.43 % (29123)Termination reason: Unknown
% 8.32/2.43 % (29126)Memory used [KB]: 7291
% 8.32/2.43 % (29123)Termination phase: Saturation
% 8.32/2.43
% 8.32/2.43 % (29126)Time elapsed: 0.050 s
% 8.32/2.43 % (29126)Instructions burned: 184 (million)
% 8.32/2.43 % (29123)Memory used [KB]: 7547
% 8.32/2.43 % (29126)------------------------------
% 8.32/2.43 % (29126)------------------------------
% 8.32/2.43 % (29123)Time elapsed: 0.060 s
% 8.32/2.43 % (29123)Instructions burned: 216 (million)
% 8.32/2.43 % (29123)------------------------------
% 8.32/2.43 % (29123)------------------------------
% 8.32/2.43 % (29128)Instruction limit reached!
% 8.32/2.43 % (29128)------------------------------
% 8.32/2.43 % (29128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.43 % (29128)Termination reason: Unknown
% 8.32/2.43 % (29128)Termination phase: shuffling
% 8.32/2.43
% 8.32/2.43 % (29128)Memory used [KB]: 2430
% 8.32/2.43 % (29128)Time elapsed: 0.015 s
% 8.32/2.43 % (29128)Instructions burned: 51 (million)
% 8.32/2.43 % (29128)------------------------------
% 8.32/2.43 % (29128)------------------------------
% 8.32/2.44 % (29130)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/1021Mi)
% 8.32/2.44 % (29131)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/267Mi)
% 8.32/2.44 % (29132)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/204Mi)
% 8.32/2.44 % (29127)Instruction limit reached!
% 8.32/2.44 % (29127)------------------------------
% 8.32/2.44 % (29127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.44 % (29127)Termination reason: Unknown
% 8.32/2.44 % (29127)Termination phase: Saturation
% 8.32/2.44
% 8.32/2.44 % (29127)Memory used [KB]: 2814
% 8.32/2.44 % (29127)Time elapsed: 0.047 s
% 8.32/2.44 % (29127)Instructions burned: 166 (million)
% 8.32/2.44 % (29127)------------------------------
% 8.32/2.44 % (29127)------------------------------
% 8.32/2.45 % (29133)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/26Mi)
% 8.32/2.46 % (29133)Instruction limit reached!
% 8.32/2.46 % (29133)------------------------------
% 8.32/2.46 % (29133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.46 % (29133)Termination reason: Unknown
% 8.32/2.46 % (29133)Termination phase: shuffling
% 8.32/2.46
% 8.32/2.46 % (29133)Memory used [KB]: 2046
% 8.32/2.46 % (29133)Time elapsed: 0.009 s
% 8.32/2.46 % (29133)Instructions burned: 28 (million)
% 8.32/2.46 % (29133)------------------------------
% 8.32/2.46 % (29133)------------------------------
% 8.32/2.47 % (29134)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_28704 for (2991ds/53Mi)
% 8.32/2.49 % (29134)Instruction limit reached!
% 8.32/2.49 % (29134)------------------------------
% 8.32/2.49 % (29134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.49 % (29134)Termination reason: Unknown
% 8.32/2.49 % (29134)Termination phase: shuffling
% 8.32/2.49
% 8.32/2.49 % (29134)Memory used [KB]: 2430
% 8.32/2.49 % (29134)Time elapsed: 0.016 s
% 8.32/2.49 % (29134)Instructions burned: 54 (million)
% 8.32/2.49 % (29134)------------------------------
% 8.32/2.49 % (29134)------------------------------
% 8.32/2.50 % (29135)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_28704 for (2990ds/4436Mi)
% 8.77/2.50 % (29132)Instruction limit reached!
% 8.77/2.50 % (29132)------------------------------
% 8.77/2.50 % (29132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.50 % (29132)Termination reason: Unknown
% 8.77/2.50 % (29132)Termination phase: Saturation
% 8.77/2.50
% 8.77/2.50 % (29132)Memory used [KB]: 7675
% 8.77/2.50 % (29132)Time elapsed: 0.062 s
% 8.77/2.50 % (29132)Instructions burned: 204 (million)
% 8.77/2.50 % (29132)------------------------------
% 8.77/2.50 % (29132)------------------------------
% 8.77/2.51 % (29136)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_28704 for (2990ds/1539Mi)
% 8.77/2.52 % (29131)Instruction limit reached!
% 8.77/2.52 % (29131)------------------------------
% 8.77/2.52 % (29131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.52 % (29131)Termination reason: Unknown
% 8.77/2.52 % (29131)Termination phase: Saturation
% 8.77/2.52
% 8.77/2.52 % (29131)Memory used [KB]: 7803
% 8.77/2.52 % (29131)Time elapsed: 0.080 s
% 8.77/2.52 % (29131)Instructions burned: 269 (million)
% 8.77/2.52 % (29131)------------------------------
% 8.77/2.52 % (29131)------------------------------
% 8.77/2.53 % (29137)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_28704 for (2990ds/408Mi)
% 8.77/2.53 % (29129)Instruction limit reached!
% 8.77/2.53 % (29129)------------------------------
% 8.77/2.53 % (29129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.53 % (29129)Termination reason: Unknown
% 8.77/2.53 % (29129)Termination phase: Saturation
% 8.77/2.53
% 8.77/2.53 % (29129)Memory used [KB]: 8699
% 8.77/2.53 % (29129)Time elapsed: 0.115 s
% 8.77/2.53 % (29129)Instructions burned: 370 (million)
% 8.77/2.53 % (29129)------------------------------
% 8.77/2.53 % (29129)------------------------------
% 8.77/2.54 % (29138)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_28704 for (2990ds/5205Mi)
% 9.05/2.61 % (29118)Instruction limit reached!
% 9.05/2.61 % (29118)------------------------------
% 9.05/2.61 % (29118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.61 % (29118)Termination reason: Unknown
% 9.05/2.61 % (29118)Termination phase: Saturation
% 9.05/2.61
% 9.05/2.61 % (29118)Memory used [KB]: 9850
% 9.05/2.61 % (29118)Time elapsed: 0.301 s
% 9.05/2.61 % (29118)Instructions burned: 987 (million)
% 9.05/2.61 % (29118)------------------------------
% 9.05/2.61 % (29118)------------------------------
% 9.05/2.62 % (29139)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_28704 for (2989ds/1913Mi)
% 9.05/2.65 % (29137)Instruction limit reached!
% 9.05/2.65 % (29137)------------------------------
% 9.05/2.65 % (29137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.65 % (29137)Termination reason: Unknown
% 9.05/2.65 % (29137)Termination phase: Saturation
% 9.05/2.65
% 9.05/2.65 % (29137)Memory used [KB]: 9338
% 9.05/2.65 % (29137)Time elapsed: 0.123 s
% 9.05/2.65 % (29137)Instructions burned: 408 (million)
% 9.05/2.65 % (29137)------------------------------
% 9.05/2.65 % (29137)------------------------------
% 9.05/2.66 % (29140)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_28704 for (2989ds/4350Mi)
% 9.05/2.67 % (29125)Instruction limit reached!
% 9.05/2.67 % (29125)------------------------------
% 9.05/2.67 % (29125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.67 % (29125)Termination reason: Unknown
% 9.05/2.67 % (29125)Termination phase: Saturation
% 9.05/2.67
% 9.05/2.67 % (29125)Memory used [KB]: 8571
% 9.05/2.67 % (29125)Time elapsed: 0.293 s
% 9.05/2.67 % (29125)Instructions burned: 924 (million)
% 9.05/2.67 % (29125)------------------------------
% 9.05/2.67 % (29125)------------------------------
% 9.05/2.68 % (29141)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_28704 for (2988ds/68Mi)
% 9.80/2.70 % (29141)Instruction limit reached!
% 9.80/2.70 % (29141)------------------------------
% 9.80/2.70 % (29141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.70 % (29141)Termination reason: Unknown
% 9.80/2.70 % (29141)Termination phase: Preprocessing 3
% 9.80/2.70
% 9.80/2.70 % (29141)Memory used [KB]: 2430
% 9.80/2.70 % (29141)Time elapsed: 0.023 s
% 9.80/2.70 % (29141)Instructions burned: 71 (million)
% 9.80/2.70 % (29141)------------------------------
% 9.80/2.70 % (29141)------------------------------
% 9.80/2.71 % (29142)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_28704 for (2988ds/358Mi)
% 9.80/2.75 % (29130)Instruction limit reached!
% 9.80/2.75 % (29130)------------------------------
% 9.80/2.75 % (29130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.75 % (29130)Termination reason: Unknown
% 9.80/2.75 % (29130)Termination phase: Saturation
% 9.80/2.75
% 9.80/2.75 % (29130)Memory used [KB]: 9338
% 9.80/2.75 % (29130)Time elapsed: 0.314 s
% 9.80/2.75 % (29130)Instructions burned: 1023 (million)
% 9.80/2.75 % (29130)------------------------------
% 9.80/2.75 % (29130)------------------------------
% 9.80/2.76 % (29143)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28704 for (2988ds/31Mi)
% 9.80/2.77 % (29143)Instruction limit reached!
% 9.80/2.77 % (29143)------------------------------
% 9.80/2.77 % (29143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.77 % (29143)Termination reason: Unknown
% 9.80/2.77 % (29143)Termination phase: shuffling
% 9.80/2.77
% 9.80/2.77 % (29143)Memory used [KB]: 2174
% 9.80/2.77 % (29143)Time elapsed: 0.012 s
% 9.80/2.77 % (29143)Instructions burned: 31 (million)
% 9.80/2.77 % (29143)------------------------------
% 9.80/2.77 % (29143)------------------------------
% 9.80/2.78 % (29144)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_28704 for (2987ds/279Mi)
% 10.17/2.82 % (29142)Instruction limit reached!
% 10.17/2.82 % (29142)------------------------------
% 10.17/2.82 % (29142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/2.82 % (29142)Termination reason: Unknown
% 10.17/2.82 % (29142)Termination phase: Saturation
% 10.17/2.82
% 10.17/2.82 % (29142)Memory used [KB]: 7803
% 10.17/2.82 % (29142)Time elapsed: 0.114 s
% 10.17/2.82 % (29142)Instructions burned: 361 (million)
% 10.17/2.82 % (29142)------------------------------
% 10.17/2.82 % (29142)------------------------------
% 10.17/2.83 % (29145)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_28704 for (2987ds/258Mi)
% 10.17/2.86 % (29144)Instruction limit reached!
% 10.17/2.86 % (29144)------------------------------
% 10.17/2.86 % (29144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/2.86 % (29144)Termination reason: Unknown
% 10.17/2.86 % (29144)Termination phase: Saturation
% 10.17/2.86
% 10.17/2.86 % (29144)Memory used [KB]: 7675
% 10.17/2.86 % (29144)Time elapsed: 0.079 s
% 10.17/2.86 % (29144)Instructions burned: 280 (million)
% 10.17/2.86 % (29144)------------------------------
% 10.17/2.86 % (29144)------------------------------
% 10.17/2.87 % (29146)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_28704 for (2986ds/26Mi)
% 10.17/2.88 % (29146)Instruction limit reached!
% 10.17/2.88 % (29146)------------------------------
% 10.17/2.88 % (29146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/2.88 % (29146)Termination reason: Unknown
% 10.17/2.88 % (29146)Termination phase: shuffling
% 10.17/2.88
% 10.17/2.88 % (29146)Memory used [KB]: 2046
% 10.17/2.88 % (29146)Time elapsed: 0.009 s
% 10.17/2.88 % (29146)Instructions burned: 27 (million)
% 10.17/2.88 % (29146)------------------------------
% 10.17/2.88 % (29146)------------------------------
% 10.17/2.89 % (29147)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_28704 for (2986ds/995Mi)
% 10.40/2.91 % (29145)Instruction limit reached!
% 10.40/2.91 % (29145)------------------------------
% 10.40/2.91 % (29145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.91 % (29145)Termination reason: Unknown
% 10.40/2.91 % (29145)Termination phase: Saturation
% 10.40/2.91
% 10.40/2.91 % (29145)Memory used [KB]: 8059
% 10.40/2.91 % (29145)Time elapsed: 0.078 s
% 10.40/2.91 % (29145)Instructions burned: 260 (million)
% 10.40/2.91 % (29145)------------------------------
% 10.40/2.91 % (29145)------------------------------
% 10.40/2.92 % (29148)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_28704 for (2986ds/373Mi)
% 10.40/2.98 % (29136)Instruction limit reached!
% 10.40/2.98 % (29136)------------------------------
% 10.40/2.98 % (29136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.98 % (29136)Termination reason: Unknown
% 10.40/2.98 % (29136)Termination phase: Saturation
% 10.40/2.98
% 10.40/2.98 % (29136)Memory used [KB]: 11257
% 10.40/2.98 % (29136)Time elapsed: 0.477 s
% 10.40/2.98 % (29136)Instructions burned: 1540 (million)
% 10.40/2.98 % (29136)------------------------------
% 10.40/2.98 % (29136)------------------------------
% 10.40/2.99 % (29149)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_28704 for (2985ds/253Mi)
% 12.97/3.03 % (29148)Instruction limit reached!
% 12.97/3.03 % (29148)------------------------------
% 12.97/3.03 % (29148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.03 % (29148)Termination reason: Unknown
% 12.97/3.03 % (29148)Termination phase: Saturation
% 12.97/3.03
% 12.97/3.03 % (29148)Memory used [KB]: 8571
% 12.97/3.03 % (29148)Time elapsed: 0.116 s
% 12.97/3.03 % (29148)Instructions burned: 373 (million)
% 12.97/3.03 % (29148)------------------------------
% 12.97/3.03 % (29148)------------------------------
% 12.97/3.04 % (29150)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_28704 for (2985ds/832Mi)
% 13.61/3.13 % (29149)Instruction limit reached!
% 13.61/3.13 % (29149)------------------------------
% 13.61/3.13 % (29149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.61/3.13 % (29149)Termination reason: Unknown
% 13.61/3.13 % (29149)Termination phase: Saturation
% 13.61/3.13
% 13.61/3.13 % (29149)Memory used [KB]: 7803
% 13.61/3.13 % (29149)Time elapsed: 0.135 s
% 13.61/3.13 % (29149)Instructions burned: 254 (million)
% 13.61/3.13 % (29149)------------------------------
% 13.61/3.13 % (29149)------------------------------
% 13.61/3.14 % (29151)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_28704 for (2984ds/668Mi)
% 13.61/3.18 % (29147)Instruction limit reached!
% 13.61/3.18 % (29147)------------------------------
% 13.61/3.18 % (29147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.61/3.18 % (29147)Termination reason: Unknown
% 13.61/3.18 % (29147)Termination phase: Saturation
% 13.61/3.18
% 13.61/3.18 % (29147)Memory used [KB]: 9722
% 13.61/3.18 % (29147)Time elapsed: 0.295 s
% 13.61/3.18 % (29147)Instructions burned: 997 (million)
% 13.61/3.18 % (29147)------------------------------
% 13.61/3.18 % (29147)------------------------------
% 13.61/3.19 % (29152)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_28704 for (2983ds/40Mi)
% 14.03/3.20 % (29152)Instruction limit reached!
% 14.03/3.20 % (29152)------------------------------
% 14.03/3.20 % (29152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.03/3.20 % (29152)Termination reason: Unknown
% 14.03/3.20 % (29152)Termination phase: shuffling
% 14.03/3.20
% 14.03/3.20 % (29152)Memory used [KB]: 2302
% 14.03/3.20 % (29152)Time elapsed: 0.013 s
% 14.03/3.20 % (29152)Instructions burned: 40 (million)
% 14.03/3.20 % (29152)------------------------------
% 14.03/3.20 % (29152)------------------------------
% 14.03/3.21 % (29153)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_28704 for (2983ds/294Mi)
% 14.03/3.22 % (29139)Instruction limit reached!
% 14.03/3.22 % (29139)------------------------------
% 14.03/3.22 % (29139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.03/3.22 % (29139)Termination reason: Unknown
% 14.03/3.22 % (29139)Termination phase: Saturation
% 14.03/3.22
% 14.03/3.22 % (29139)Memory used [KB]: 5117
% 14.03/3.22 % (29139)Time elapsed: 0.602 s
% 14.03/3.22 % (29139)Instructions burned: 1913 (million)
% 14.03/3.22 % (29139)------------------------------
% 14.03/3.22 % (29139)------------------------------
% 14.03/3.23 % (29154)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_28704 for (2983ds/187Mi)
% 14.03/3.28 % (29154)Instruction limit reached!
% 14.03/3.28 % (29154)------------------------------
% 14.03/3.28 % (29154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.03/3.28 % (29154)Termination reason: Unknown
% 14.03/3.28 % (29154)Termination phase: Saturation
% 14.03/3.28
% 14.03/3.28 % (29154)Memory used [KB]: 7675
% 14.03/3.28 % (29154)Time elapsed: 0.056 s
% 14.03/3.28 % (29154)Instructions burned: 188 (million)
% 14.03/3.28 % (29154)------------------------------
% 14.03/3.28 % (29154)------------------------------
% 14.03/3.29 % (29155)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_28704 for (2982ds/371Mi)
% 14.03/3.29 % (29153)Instruction limit reached!
% 14.03/3.29 % (29153)------------------------------
% 14.03/3.29 % (29153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.03/3.29 % (29153)Termination reason: Unknown
% 14.03/3.29 % (29153)Termination phase: Saturation
% 14.03/3.29
% 14.03/3.29 % (29153)Memory used [KB]: 7419
% 14.03/3.29 % (29153)Time elapsed: 0.083 s
% 14.03/3.29 % (29153)Instructions burned: 296 (million)
% 14.03/3.29 % (29153)------------------------------
% 14.03/3.29 % (29153)------------------------------
% 14.53/3.30 % (29150)Instruction limit reached!
% 14.53/3.30 % (29150)------------------------------
% 14.53/3.30 % (29150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.53/3.30 % (29150)Termination reason: Unknown
% 14.53/3.30 % (29150)Termination phase: Saturation
% 14.53/3.30
% 14.53/3.30 % (29150)Memory used [KB]: 9210
% 14.53/3.30 % (29150)Time elapsed: 0.257 s
% 14.53/3.30 % (29150)Instructions burned: 834 (million)
% 14.53/3.30 % (29150)------------------------------
% 14.53/3.30 % (29150)------------------------------
% 14.53/3.30 % (29156)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_28704 for (2982ds/1827Mi)
% 14.53/3.31 % (29157)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_28704 for (2982ds/70Mi)
% 14.53/3.33 % (29157)Instruction limit reached!
% 14.53/3.33 % (29157)------------------------------
% 14.53/3.33 % (29157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.53/3.33 % (29157)Termination reason: Unknown
% 14.53/3.33 % (29157)Termination phase: Property scanning
% 14.53/3.33
% 14.53/3.33 % (29157)Memory used [KB]: 2558
% 14.53/3.33 % (29157)Time elapsed: 0.020 s
% 14.53/3.33 % (29157)Instructions burned: 71 (million)
% 14.53/3.33 % (29157)------------------------------
% 14.53/3.33 % (29157)------------------------------
% 14.53/3.34 % (29158)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_28704 for (2982ds/316Mi)
% 14.53/3.35 % (29151)Instruction limit reached!
% 14.53/3.35 % (29151)------------------------------
% 14.53/3.35 % (29151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.53/3.35 % (29151)Termination reason: Unknown
% 14.53/3.35 % (29151)Termination phase: Saturation
% 14.53/3.35
% 14.53/3.35 % (29151)Memory used [KB]: 13944
% 14.53/3.35 % (29151)Time elapsed: 0.207 s
% 14.53/3.35 % (29151)Instructions burned: 671 (million)
% 14.53/3.35 % (29151)------------------------------
% 14.53/3.35 % (29151)------------------------------
% 14.53/3.36 % (29159)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_28704 for (2982ds/932Mi)
% 15.35/3.41 % (29155)Instruction limit reached!
% 15.35/3.41 % (29155)------------------------------
% 15.35/3.41 % (29155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.35/3.41 % (29155)Termination reason: Unknown
% 15.35/3.41 % (29155)Termination phase: Saturation
% 15.35/3.41
% 15.35/3.41 % (29155)Memory used [KB]: 8315
% 15.35/3.41 % (29155)Time elapsed: 0.121 s
% 15.35/3.41 % (29155)Instructions burned: 374 (million)
% 15.35/3.41 % (29155)------------------------------
% 15.35/3.41 % (29155)------------------------------
% 15.35/3.42 % (29160)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_28704 for (2981ds/4714Mi)
% 15.35/3.43 % (29158)Instruction limit reached!
% 15.35/3.43 % (29158)------------------------------
% 15.35/3.43 % (29158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.35/3.43 % (29158)Termination reason: Unknown
% 15.35/3.43 % (29158)Termination phase: Saturation
% 15.35/3.43
% 15.35/3.43 % (29158)Memory used [KB]: 8699
% 15.35/3.43 % (29158)Time elapsed: 0.090 s
% 15.35/3.43 % (29158)Instructions burned: 318 (million)
% 15.35/3.43 % (29158)------------------------------
% 15.35/3.43 % (29158)------------------------------
% 15.35/3.44 % (29161)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_28704 for (2981ds/8250Mi)
% 16.19/3.60 % (29140)Refutation not found, non-redundant clauses discarded% (29140)------------------------------
% 16.19/3.60 % (29140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/3.60 % (29140)Termination reason: Refutation not found, non-redundant clauses discarded
% 16.19/3.60
% 16.19/3.60 % (29140)Memory used [KB]: 8955
% 16.19/3.60 % (29140)Time elapsed: 0.942 s
% 16.19/3.60 % (29140)Instructions burned: 3125 (million)
% 16.19/3.60 % (29140)------------------------------
% 16.19/3.60 % (29140)------------------------------
% 16.19/3.61 % (29162)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_28704 for (2979ds/770Mi)
% 16.19/3.63 % (29159)Instruction limit reached!
% 16.19/3.63 % (29159)------------------------------
% 16.19/3.63 % (29159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/3.63 % (29159)Termination reason: Unknown
% 16.19/3.63 % (29159)Termination phase: Saturation
% 16.19/3.63
% 16.19/3.63 % (29159)Memory used [KB]: 11257
% 16.19/3.63 % (29159)Time elapsed: 0.272 s
% 16.19/3.63 % (29159)Instructions burned: 934 (million)
% 16.19/3.63 % (29159)------------------------------
% 16.19/3.63 % (29159)------------------------------
% 16.19/3.63 % (29162)Refutation not found, incomplete strategy
% 16.19/3.63 % (29162)------------------------------
% 16.19/3.63 % (29162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/3.63 % (29162)Termination reason: Refutation not found, incomplete strategy
% 16.19/3.63
% 16.19/3.63
% 16.19/3.63 % (29162)Memory used [KB]: 6908
% 16.19/3.63 % (29162)Time elapsed: 0.021 s
% 16.19/3.63 % (29162)Instructions burned: 63 (million)
% 16.19/3.63 % (29162)------------------------------
% 16.19/3.63 % (29162)------------------------------
% 16.19/3.64 % (29164)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_28704 for (2979ds/464Mi)
% 16.19/3.64 % (29163)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_28704 for (2979ds/794Mi)
% 16.71/3.79 % (29164)Instruction limit reached!
% 16.71/3.79 % (29164)------------------------------
% 16.71/3.79 % (29164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.71/3.79 % (29164)Termination reason: Unknown
% 16.71/3.79 % (29164)Termination phase: Saturation
% 16.71/3.79
% 16.71/3.79 % (29164)Memory used [KB]: 8187
% 16.71/3.79 % (29164)Time elapsed: 0.168 s
% 16.71/3.79 % (29164)Instructions burned: 465 (million)
% 16.71/3.79 % (29164)------------------------------
% 16.71/3.79 % (29164)------------------------------
% 16.71/3.80 % (29165)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_28704 for (2977ds/1376Mi)
% 17.07/3.86 % (29135)Instruction limit reached!
% 17.07/3.86 % (29135)------------------------------
% 17.07/3.86 % (29135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.86 % (29135)Termination reason: Unknown
% 17.07/3.86 % (29135)Termination phase: Saturation
% 17.07/3.86
% 17.07/3.86 % (29135)Memory used [KB]: 14456
% 17.07/3.86 % (29135)Time elapsed: 1.364 s
% 17.07/3.86 % (29135)Instructions burned: 4438 (million)
% 17.07/3.86 % (29135)------------------------------
% 17.07/3.86 % (29135)------------------------------
% 17.07/3.87 % (29166)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_28704 for (2976ds/906Mi)
% 17.07/3.89 % (29156)Instruction limit reached!
% 17.07/3.89 % (29156)------------------------------
% 17.07/3.89 % (29156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.89 % (29156)Termination reason: Unknown
% 17.07/3.89 % (29156)Termination phase: Saturation
% 17.07/3.89
% 17.07/3.89 % (29156)Memory used [KB]: 10874
% 17.07/3.89 % (29156)Time elapsed: 0.584 s
% 17.07/3.89 % (29156)Instructions burned: 1829 (million)
% 17.07/3.89 % (29156)------------------------------
% 17.07/3.89 % (29156)------------------------------
% 17.07/3.89 % (29163)Instruction limit reached!
% 17.07/3.89 % (29163)------------------------------
% 17.07/3.89 % (29163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.89 % (29163)Termination reason: Unknown
% 17.07/3.89 % (29163)Termination phase: Saturation
% 17.07/3.89
% 17.07/3.89 % (29163)Memory used [KB]: 6524
% 17.07/3.89 % (29163)Time elapsed: 0.248 s
% 17.07/3.89 % (29163)Instructions burned: 796 (million)
% 17.07/3.89 % (29163)------------------------------
% 17.07/3.89 % (29163)------------------------------
% 17.07/3.90 % (29167)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_28704 for (2976ds/434Mi)
% 18.10/3.90 % (29168)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_28704 for (2976ds/865Mi)
% 20.07/4.03 % (29167)Instruction limit reached!
% 20.07/4.03 % (29167)------------------------------
% 20.07/4.03 % (29167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.03 % (29167)Termination reason: Unknown
% 20.07/4.03 % (29167)Termination phase: Saturation
% 20.07/4.03
% 20.07/4.03 % (29167)Memory used [KB]: 8187
% 20.07/4.03 % (29167)Time elapsed: 0.133 s
% 20.07/4.03 % (29167)Instructions burned: 435 (million)
% 20.07/4.03 % (29167)------------------------------
% 20.07/4.03 % (29167)------------------------------
% 20.07/4.04 % (29169)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_28704 for (2975ds/593Mi)
% 20.07/4.09 % (29138)Instruction limit reached!
% 20.07/4.09 % (29138)------------------------------
% 20.07/4.09 % (29138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.09 % (29138)Termination reason: Unknown
% 20.07/4.09 % (29138)Termination phase: Saturation
% 20.07/4.09
% 20.07/4.09 % (29138)Memory used [KB]: 14456
% 20.07/4.09 % (29138)Time elapsed: 1.548 s
% 20.07/4.09 % (29138)Instructions burned: 5205 (million)
% 20.07/4.09 % (29138)------------------------------
% 20.07/4.09 % (29138)------------------------------
% 20.07/4.10 % (29170)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_28704 for (2974ds/443Mi)
% 20.66/4.16 % (29168)Instruction limit reached!
% 20.66/4.16 % (29168)------------------------------
% 20.66/4.16 % (29168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.66/4.16 % (29168)Termination reason: Unknown
% 20.66/4.16 % (29168)Termination phase: Saturation
% 20.66/4.16
% 20.66/4.16 % (29168)Memory used [KB]: 9594
% 20.66/4.16 % (29168)Time elapsed: 0.259 s
% 20.66/4.16 % (29168)Instructions burned: 865 (million)
% 20.66/4.16 % (29168)------------------------------
% 20.66/4.16 % (29168)------------------------------
% 20.66/4.17 % (29171)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_28704 for (2974ds/594Mi)
% 20.66/4.19 % (29166)Instruction limit reached!
% 20.66/4.19 % (29166)------------------------------
% 20.66/4.19 % (29166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.66/4.19 % (29166)Termination reason: Unknown
% 20.66/4.19 % (29166)Termination phase: Saturation
% 20.66/4.19
% 20.66/4.19 % (29166)Memory used [KB]: 13048
% 20.66/4.19 % (29166)Time elapsed: 0.324 s
% 20.66/4.19 % (29166)Instructions burned: 906 (million)
% 20.66/4.19 % (29166)------------------------------
% 20.66/4.19 % (29166)------------------------------
% 20.97/4.20 % (29172)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_28704 for (2973ds/327Mi)
% 20.97/4.20 % (29169)Instruction limit reached!
% 20.97/4.20 % (29169)------------------------------
% 20.97/4.20 % (29169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.20 % (29169)Termination reason: Unknown
% 20.97/4.20 % (29169)Termination phase: Saturation
% 20.97/4.20
% 20.97/4.20 % (29169)Memory used [KB]: 9722
% 20.97/4.20 % (29169)Time elapsed: 0.167 s
% 20.97/4.20 % (29169)Instructions burned: 595 (million)
% 20.97/4.20 % (29169)------------------------------
% 20.97/4.20 % (29169)------------------------------
% 20.97/4.21 % (29173)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_28704 for (2973ds/5411Mi)
% 20.97/4.22 % (29165)Instruction limit reached!
% 20.97/4.22 % (29165)------------------------------
% 20.97/4.22 % (29165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.22 % (29165)Termination reason: Unknown
% 20.97/4.22 % (29165)Termination phase: Saturation
% 20.97/4.22
% 20.97/4.22 % (29165)Memory used [KB]: 13688
% 20.97/4.22 % (29165)Time elapsed: 0.445 s
% 20.97/4.22 % (29165)Instructions burned: 1379 (million)
% 20.97/4.22 % (29165)------------------------------
% 20.97/4.22 % (29165)------------------------------
% 20.97/4.23 % (29174)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_28704 for (2973ds/1762Mi)
% 20.97/4.23 % (29170)Instruction limit reached!
% 20.97/4.23 % (29170)------------------------------
% 20.97/4.23 % (29170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.23 % (29170)Termination reason: Unknown
% 20.97/4.23 % (29170)Termination phase: Saturation
% 20.97/4.23
% 20.97/4.23 % (29170)Memory used [KB]: 8315
% 20.97/4.23 % (29170)Time elapsed: 0.160 s
% 20.97/4.23 % (29170)Instructions burned: 445 (million)
% 20.97/4.23 % (29170)------------------------------
% 20.97/4.23 % (29170)------------------------------
% 20.97/4.24 % (29173)Refutation not found, incomplete strategy
% 20.97/4.24 % (29173)------------------------------
% 20.97/4.24 % (29173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.24 % (29173)Termination reason: Refutation not found, incomplete strategy
% 20.97/4.24
% 20.97/4.24
% 20.97/4.24 % (29173)Memory used [KB]: 7036
% 20.97/4.24 % (29173)Time elapsed: 0.053 s
% 20.97/4.24 % (29173)Instructions burned: 85 (million)
% 20.97/4.24 % (29173)------------------------------
% 20.97/4.24 % (29173)------------------------------
% 20.97/4.24 % (29175)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_28704 for (2973ds/96Mi)
% 20.97/4.25 % (29176)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_28704 for (2973ds/503Mi)
% 20.97/4.27 % (29175)Instruction limit reached!
% 20.97/4.27 % (29175)------------------------------
% 20.97/4.27 % (29175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.27 % (29175)Termination reason: Unknown
% 20.97/4.27 % (29175)Termination phase: Preprocessing 1
% 20.97/4.27
% 20.97/4.27 % (29175)Memory used [KB]: 2814
% 20.97/4.27 % (29175)Time elapsed: 0.027 s
% 20.97/4.27 % (29175)Instructions burned: 97 (million)
% 20.97/4.27 % (29175)------------------------------
% 20.97/4.27 % (29175)------------------------------
% 20.97/4.28 % (29177)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_28704 for (2972ds/90Mi)
% 21.60/4.30 % (29172)Instruction limit reached!
% 21.60/4.30 % (29172)------------------------------
% 21.60/4.30 % (29172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.60/4.30 % (29172)Termination reason: Unknown
% 21.60/4.30 % (29172)Termination phase: Saturation
% 21.60/4.30
% 21.60/4.30 % (29172)Memory used [KB]: 8443
% 21.60/4.30 % (29172)Time elapsed: 0.101 s
% 21.60/4.30 % (29172)Instructions burned: 329 (million)
% 21.60/4.30 % (29172)------------------------------
% 21.60/4.30 % (29172)------------------------------
% 21.60/4.31 % (29177)Instruction limit reached!
% 21.60/4.31 % (29177)------------------------------
% 21.60/4.31 % (29177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.60/4.31 % (29177)Termination reason: Unknown
% 21.60/4.31 % (29177)Termination phase: Property scanning
% 21.60/4.31
% 21.60/4.31 % (29177)Memory used [KB]: 2942
% 21.60/4.31 % (29177)Time elapsed: 0.029 s
% 21.60/4.31 % (29177)Instructions burned: 92 (million)
% 21.60/4.31 % (29177)------------------------------
% 21.60/4.31 % (29177)------------------------------
% 21.60/4.31 % (29178)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_28704 for (2972ds/593Mi)
% 21.60/4.32 % (29179)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_28704 for (2972ds/1512Mi)
% 21.60/4.35 % (29171)Instruction limit reached!
% 21.60/4.35 % (29171)------------------------------
% 21.60/4.35 % (29171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.60/4.35 % (29171)Termination reason: Unknown
% 21.60/4.35 % (29171)Termination phase: Saturation
% 21.60/4.35
% 21.60/4.35 % (29171)Memory used [KB]: 7931
% 21.60/4.35 % (29171)Time elapsed: 0.209 s
% 21.60/4.35 % (29171)Instructions burned: 596 (million)
% 21.60/4.35 % (29171)------------------------------
% 21.60/4.35 % (29171)------------------------------
% 21.60/4.36 % (29180)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_28704 for (2972ds/569Mi)
% 21.60/4.40 % (29176)Instruction limit reached!
% 21.60/4.40 % (29176)------------------------------
% 21.60/4.40 % (29176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.60/4.40 % (29176)Termination reason: Unknown
% 21.60/4.40 % (29176)Termination phase: Saturation
% 21.60/4.40
% 21.60/4.40 % (29176)Memory used [KB]: 8955
% 21.60/4.40 % (29176)Time elapsed: 0.148 s
% 21.60/4.40 % (29176)Instructions burned: 504 (million)
% 21.60/4.40 % (29176)------------------------------
% 21.60/4.40 % (29176)------------------------------
% 22.15/4.41 % (29181)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_28704 for (2971ds/501Mi)
% 22.15/4.49 % (29178)Instruction limit reached!
% 22.15/4.49 % (29178)------------------------------
% 22.15/4.49 % (29178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.15/4.49 % (29178)Termination reason: Unknown
% 22.15/4.49 % (29178)Termination phase: Saturation
% 22.15/4.49
% 22.15/4.49 % (29178)Memory used [KB]: 9210
% 22.15/4.49 % (29178)Time elapsed: 0.183 s
% 22.15/4.49 % (29178)Instructions burned: 595 (million)
% 22.15/4.49 % (29178)------------------------------
% 22.15/4.49 % (29178)------------------------------
% 22.69/4.50 % (29182)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_28704 for (2970ds/562Mi)
% 22.69/4.52 % (29180)Instruction limit reached!
% 22.69/4.52 % (29180)------------------------------
% 22.69/4.52 % (29180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.69/4.52 % (29180)Termination reason: Unknown
% 22.69/4.52 % (29180)Termination phase: Saturation
% 22.69/4.52
% 22.69/4.52 % (29180)Memory used [KB]: 8827
% 22.69/4.52 % (29180)Time elapsed: 0.160 s
% 22.69/4.52 % (29180)Instructions burned: 569 (million)
% 22.69/4.52 % (29180)------------------------------
% 22.69/4.52 % (29180)------------------------------
% 22.69/4.53 % (29183)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_28704 for (2970ds/406Mi)
% 22.69/4.56 % (29181)Instruction limit reached!
% 22.69/4.56 % (29181)------------------------------
% 22.69/4.56 % (29181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.69/4.56 % (29181)Termination reason: Unknown
% 22.69/4.56 % (29181)Termination phase: Saturation
% 22.69/4.56
% 22.69/4.56 % (29181)Memory used [KB]: 10234
% 22.69/4.56 % (29181)Time elapsed: 0.150 s
% 22.69/4.56 % (29181)Instructions burned: 501 (million)
% 22.69/4.56 % (29181)------------------------------
% 22.69/4.56 % (29181)------------------------------
% 22.69/4.57 % (29184)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_28704 for (2970ds/582Mi)
% 23.22/4.65 % (29183)Instruction limit reached!
% 23.22/4.65 % (29183)------------------------------
% 23.22/4.65 % (29183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.22/4.65 % (29183)Termination reason: Unknown
% 23.22/4.65 % (29183)Termination phase: Saturation
% 23.22/4.65
% 23.22/4.65 % (29183)Memory used [KB]: 8827
% 23.22/4.65 % (29183)Time elapsed: 0.125 s
% 23.22/4.65 % (29183)Instructions burned: 406 (million)
% 23.22/4.65 % (29183)------------------------------
% 23.22/4.65 % (29183)------------------------------
% 23.22/4.66 % (29185)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_28704 for (2969ds/456Mi)
% 23.22/4.67 % (29182)Instruction limit reached!
% 23.22/4.67 % (29182)------------------------------
% 23.22/4.67 % (29182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.22/4.67 % (29182)Termination reason: Unknown
% 23.22/4.67 % (29182)Termination phase: Saturation
% 23.22/4.67
% 23.22/4.67 % (29182)Memory used [KB]: 8571
% 23.22/4.67 % (29182)Time elapsed: 0.165 s
% 23.22/4.67 % (29182)Instructions burned: 564 (million)
% 23.22/4.67 % (29182)------------------------------
% 23.22/4.67 % (29182)------------------------------
% 23.22/4.68 % (29186)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_28704 for (2968ds/393Mi)
% 23.74/4.72 % (29160)Instruction limit reached!
% 23.74/4.72 % (29160)------------------------------
% 23.74/4.72 % (29160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.72 % (29160)Termination reason: Unknown
% 23.74/4.72 % (29160)Termination phase: Saturation
% 23.74/4.72
% 23.74/4.72 % (29160)Memory used [KB]: 13560
% 23.74/4.72 % (29160)Time elapsed: 1.296 s
% 23.74/4.72 % (29160)Instructions burned: 4714 (million)
% 23.74/4.72 % (29160)------------------------------
% 23.74/4.72 % (29160)------------------------------
% 23.74/4.72 % (29179)Instruction limit reached!
% 23.74/4.72 % (29179)------------------------------
% 23.74/4.72 % (29179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.72 % (29179)Termination reason: Unknown
% 23.74/4.72 % (29179)Termination phase: Saturation
% 23.74/4.72
% 23.74/4.72 % (29179)Memory used [KB]: 10490
% 23.74/4.72 % (29179)Time elapsed: 0.404 s
% 23.74/4.72 % (29179)Instructions burned: 1514 (million)
% 23.74/4.72 % (29179)------------------------------
% 23.74/4.72 % (29179)------------------------------
% 23.74/4.73 % (29187)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_28704 for (2968ds/1335Mi)
% 23.74/4.73 % (29188)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_28704 for (2968ds/3373Mi)
% 23.74/4.73 % (29174)Instruction limit reached!
% 23.74/4.73 % (29174)------------------------------
% 23.74/4.73 % (29174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.73 % (29174)Termination reason: Unknown
% 23.74/4.73 % (29174)Termination phase: Saturation
% 23.74/4.73
% 23.74/4.73 % (29174)Memory used [KB]: 10618
% 23.74/4.73 % (29174)Time elapsed: 0.533 s
% 23.74/4.73 % (29174)Instructions burned: 1762 (million)
% 23.74/4.73 % (29174)------------------------------
% 23.74/4.73 % (29174)------------------------------
% 23.74/4.74 % (29189)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_28704 for (2968ds/474Mi)
% 23.74/4.75 % (29184)Instruction limit reached!
% 23.74/4.75 % (29184)------------------------------
% 23.74/4.75 % (29184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.75 % (29184)Termination reason: Unknown
% 23.74/4.75 % (29184)Termination phase: Saturation
% 23.74/4.75
% 23.74/4.75 % (29184)Memory used [KB]: 8827
% 23.74/4.75 % (29184)Time elapsed: 0.184 s
% 23.74/4.75 % (29184)Instructions burned: 583 (million)
% 23.74/4.75 % (29184)------------------------------
% 23.74/4.75 % (29184)------------------------------
% 23.74/4.76 % (29190)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_28704 for (2968ds/157Mi)
% 23.74/4.79 % (29186)Instruction limit reached!
% 23.74/4.79 % (29186)------------------------------
% 23.74/4.79 % (29186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.79 % (29186)Termination reason: Unknown
% 23.74/4.79 % (29186)Termination phase: Saturation
% 23.74/4.79
% 23.74/4.79 % (29186)Memory used [KB]: 7803
% 23.74/4.79 % (29186)Time elapsed: 0.110 s
% 23.74/4.79 % (29186)Instructions burned: 394 (million)
% 23.74/4.79 % (29186)------------------------------
% 23.74/4.79 % (29186)------------------------------
% 23.74/4.80 % (29191)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_28704 for (2967ds/590Mi)
% 25.11/4.80 % (29190)Instruction limit reached!
% 25.11/4.80 % (29190)------------------------------
% 25.11/4.80 % (29190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.11/4.80 % (29190)Termination reason: Unknown
% 25.11/4.80 % (29190)Termination phase: Property scanning
% 25.11/4.80
% 25.11/4.80 % (29190)Memory used [KB]: 2814
% 25.11/4.80 % (29190)Time elapsed: 0.045 s
% 25.11/4.80 % (29190)Instructions burned: 159 (million)
% 25.11/4.80 % (29190)------------------------------
% 25.11/4.80 % (29190)------------------------------
% 25.11/4.80 % (29185)Instruction limit reached!
% 25.11/4.80 % (29185)------------------------------
% 25.11/4.80 % (29185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.11/4.80 % (29185)Termination reason: Unknown
% 25.11/4.80 % (29185)Termination phase: Saturation
% 25.11/4.80
% 25.11/4.80 % (29185)Memory used [KB]: 9338
% 25.11/4.80 % (29185)Time elapsed: 0.143 s
% 25.11/4.80 % (29185)Instructions burned: 456 (million)
% 25.11/4.80 % (29185)------------------------------
% 25.11/4.80 % (29185)------------------------------
% 25.11/4.81 % (29192)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_28704 for (2967ds/104Mi)
% 25.11/4.81 % (29193)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_28704 for (2967ds/414Mi)
% 25.11/4.84 % (29192)Instruction limit reached!
% 25.11/4.84 % (29192)------------------------------
% 25.11/4.84 % (29192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.11/4.84 % (29192)Termination reason: Unknown
% 25.11/4.84 % (29192)Termination phase: Property scanning
% 25.11/4.84
% 25.11/4.84 % (29192)Memory used [KB]: 2942
% 25.11/4.84 % (29192)Time elapsed: 0.032 s
% 25.11/4.84 % (29192)Instructions burned: 104 (million)
% 25.11/4.84 % (29192)------------------------------
% 25.11/4.84 % (29192)------------------------------
% 25.11/4.85 % (29194)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_28704 for (2967ds/715Mi)
% 25.11/4.89 % (29189)Instruction limit reached!
% 25.11/4.89 % (29189)------------------------------
% 25.11/4.89 % (29189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.11/4.89 % (29189)Termination reason: Unknown
% 25.11/4.89 % (29189)Termination phase: Saturation
% 25.11/4.89
% 25.11/4.89 % (29189)Memory used [KB]: 8443
% 25.11/4.89 % (29189)Time elapsed: 0.147 s
% 25.11/4.89 % (29189)Instructions burned: 475 (million)
% 25.11/4.89 % (29189)------------------------------
% 25.11/4.89 % (29189)------------------------------
% 25.61/4.90 % (29195)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_28704 for (2966ds/961Mi)
% 25.61/4.93 % (29193)Instruction limit reached!
% 25.61/4.93 % (29193)------------------------------
% 25.61/4.93 % (29193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.61/4.93 % (29193)Termination reason: Unknown
% 25.61/4.93 % (29193)Termination phase: Saturation
% 25.61/4.93
% 25.61/4.93 % (29193)Memory used [KB]: 8571
% 25.61/4.93 % (29193)Time elapsed: 0.118 s
% 25.61/4.93 % (29193)Instructions burned: 416 (million)
% 25.61/4.93 % (29193)------------------------------
% 25.61/4.93 % (29193)------------------------------
% 25.61/4.94 % (29196)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_28704 for (2966ds/1213Mi)
% 25.61/4.97 % (29191)Instruction limit reached!
% 25.61/4.97 % (29191)------------------------------
% 25.61/4.97 % (29191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.61/4.97 % (29191)Termination reason: Unknown
% 25.61/4.97 % (29191)Termination phase: Saturation
% 25.61/4.97
% 25.61/4.97 % (29191)Memory used [KB]: 8827
% 25.61/4.97 % (29191)Time elapsed: 0.173 s
% 25.61/4.97 % (29191)Instructions burned: 593 (million)
% 25.61/4.97 % (29191)------------------------------
% 25.61/4.97 % (29191)------------------------------
% 25.61/4.98 % (29197)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_28704 for (2965ds/1979Mi)
% 27.08/5.07 % (29194)Instruction limit reached!
% 27.08/5.07 % (29194)------------------------------
% 27.08/5.07 % (29194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.08/5.07 % (29194)Termination reason: Unknown
% 27.08/5.07 % (29194)Termination phase: Saturation
% 27.08/5.07
% 27.08/5.07 % (29194)Memory used [KB]: 5245
% 27.08/5.07 % (29194)Time elapsed: 0.218 s
% 27.08/5.07 % (29194)Instructions burned: 715 (million)
% 27.08/5.07 % (29194)------------------------------
% 27.08/5.07 % (29194)------------------------------
% 27.08/5.08 % (29198)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_28704 for (2964ds/481Mi)
% 27.08/5.12 % (29187)Instruction limit reached!
% 27.08/5.12 % (29187)------------------------------
% 27.08/5.12 % (29187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.08/5.12 % (29187)Termination reason: Unknown
% 27.08/5.12 % (29187)Termination phase: Saturation
% 27.08/5.12
% 27.08/5.12 % (29187)Memory used [KB]: 9594
% 27.08/5.12 % (29187)Time elapsed: 0.396 s
% 27.08/5.12 % (29187)Instructions burned: 1336 (million)
% 27.08/5.12 % (29187)------------------------------
% 27.08/5.12 % (29187)------------------------------
% 27.77/5.13 % (29199)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_28704 for (2964ds/783Mi)
% 28.12/5.20 % (29195)Instruction limit reached!
% 28.12/5.20 % (29195)------------------------------
% 28.12/5.20 % (29195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.12/5.20 % (29195)Termination reason: Unknown
% 28.12/5.20 % (29195)Termination phase: Saturation
% 28.12/5.20
% 28.12/5.20 % (29195)Memory used [KB]: 8443
% 28.12/5.20 % (29195)Time elapsed: 0.302 s
% 28.12/5.20 % (29195)Instructions burned: 962 (million)
% 28.12/5.20 % (29195)------------------------------
% 28.12/5.20 % (29195)------------------------------
% 28.12/5.21 % (29200)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_28704 for (2963ds/432Mi)
% 28.12/5.23 % (29198)Instruction limit reached!
% 28.12/5.23 % (29198)------------------------------
% 28.12/5.23 % (29198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.12/5.23 % (29198)Termination reason: Unknown
% 28.12/5.23 % (29198)Termination phase: Saturation
% 28.12/5.23
% 28.12/5.23 % (29198)Memory used [KB]: 8059
% 28.12/5.23 % (29198)Time elapsed: 0.147 s
% 28.12/5.23 % (29198)Instructions burned: 482 (million)
% 28.12/5.23 % (29198)------------------------------
% 28.12/5.23 % (29198)------------------------------
% 28.12/5.23 % (29201)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_28704 for (2963ds/1670Mi)
% 28.68/5.31 % (29196)Instruction limit reached!
% 28.68/5.31 % (29196)------------------------------
% 28.68/5.31 % (29196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.68/5.31 % (29196)Termination reason: Unknown
% 28.68/5.31 % (29196)Termination phase: Saturation
% 28.68/5.31
% 28.68/5.31 % (29196)Memory used [KB]: 10874
% 28.68/5.31 % (29196)Time elapsed: 0.376 s
% 28.68/5.31 % (29196)Instructions burned: 1213 (million)
% 28.68/5.31 % (29196)------------------------------
% 28.68/5.31 % (29196)------------------------------
% 28.68/5.32 % (29202)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_28704 for (2962ds/90Mi)
% 28.68/5.34 % (29200)Instruction limit reached!
% 28.68/5.34 % (29200)------------------------------
% 28.68/5.34 % (29200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.68/5.34 % (29200)Termination reason: Unknown
% 28.68/5.34 % (29200)Termination phase: Saturation
% 28.68/5.34
% 28.68/5.34 % (29200)Memory used [KB]: 7931
% 28.68/5.34 % (29200)Time elapsed: 0.131 s
% 28.68/5.34 % (29200)Instructions burned: 433 (million)
% 28.68/5.34 % (29200)------------------------------
% 28.68/5.34 % (29200)------------------------------
% 28.68/5.35 % (29203)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_28704 for (2962ds/346Mi)
% 28.68/5.35 % (29202)Instruction limit reached!
% 28.68/5.35 % (29202)------------------------------
% 28.68/5.35 % (29202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.68/5.35 % (29202)Termination reason: Unknown
% 28.68/5.35 % (29202)Termination phase: Property scanning
% 28.68/5.35
% 28.68/5.35 % (29202)Memory used [KB]: 2942
% 28.68/5.35 % (29202)Time elapsed: 0.029 s
% 28.68/5.35 % (29202)Instructions burned: 91 (million)
% 28.68/5.35 % (29202)------------------------------
% 28.68/5.35 % (29202)------------------------------
% 28.68/5.36 % (29204)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_28704 for (2962ds/401Mi)
% 28.68/5.37 % (29199)Instruction limit reached!
% 28.68/5.37 % (29199)------------------------------
% 28.68/5.37 % (29199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.68/5.37 % (29199)Termination reason: Unknown
% 28.68/5.37 % (29199)Termination phase: Saturation
% 28.68/5.37
% 28.68/5.37 % (29199)Memory used [KB]: 9466
% 28.68/5.37 % (29199)Time elapsed: 0.236 s
% 28.68/5.37 % (29199)Instructions burned: 784 (million)
% 28.68/5.37 % (29199)------------------------------
% 28.68/5.37 % (29199)------------------------------
% 28.68/5.38 % (29205)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_28704 for (2961ds/6454Mi)
% 29.43/5.45 % (29203)Instruction limit reached!
% 29.43/5.45 % (29203)------------------------------
% 29.43/5.45 % (29203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.45 % (29203)Termination reason: Unknown
% 29.43/5.45 % (29203)Termination phase: Saturation
% 29.43/5.45
% 29.43/5.45 % (29203)Memory used [KB]: 8059
% 29.43/5.45 % (29203)Time elapsed: 0.104 s
% 29.43/5.45 % (29203)Instructions burned: 346 (million)
% 29.43/5.45 % (29203)------------------------------
% 29.43/5.45 % (29203)------------------------------
% 29.43/5.46 % (29206)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_28704 for (2961ds/283Mi)
% 29.43/5.47 % (29204)Instruction limit reached!
% 29.43/5.47 % (29204)------------------------------
% 29.43/5.47 % (29204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.47 % (29204)Termination reason: Unknown
% 29.43/5.47 % (29204)Termination phase: Saturation
% 29.43/5.47
% 29.43/5.47 % (29204)Memory used [KB]: 8699
% 29.43/5.47 % (29204)Time elapsed: 0.112 s
% 29.43/5.47 % (29204)Instructions burned: 401 (million)
% 29.43/5.47 % (29204)------------------------------
% 29.43/5.47 % (29204)------------------------------
% 29.43/5.48 % (29207)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_28704 for (2960ds/865Mi)
% 29.97/5.55 % (29206)Instruction limit reached!
% 29.97/5.55 % (29206)------------------------------
% 29.97/5.55 % (29206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.55 % (29206)Termination reason: Unknown
% 29.97/5.55 % (29206)Termination phase: Saturation
% 29.97/5.55
% 29.97/5.55 % (29206)Memory used [KB]: 8059
% 29.97/5.55 % (29206)Time elapsed: 0.087 s
% 29.97/5.55 % (29206)Instructions burned: 285 (million)
% 29.97/5.55 % (29206)------------------------------
% 29.97/5.55 % (29206)------------------------------
% 29.97/5.56 % (29208)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_28704 for (2960ds/4528Mi)
% 29.97/5.58 % (29208)Refutation not found, incomplete strategy
% 29.97/5.58 % (29208)------------------------------
% 29.97/5.58 % (29208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.58 % (29208)Termination reason: Refutation not found, incomplete strategy
% 29.97/5.58
% 29.97/5.58
% 29.97/5.58 % (29208)Memory used [KB]: 2302
% 29.97/5.58 % (29208)Time elapsed: 0.021 s
% 29.97/5.58 % (29208)Instructions burned: 64 (million)
% 29.97/5.58 % (29208)------------------------------
% 29.97/5.58 % (29208)------------------------------
% 29.97/5.59 % (29209)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_28704 for (2959ds/1001Mi)
% 30.40/5.60 % (29197)Instruction limit reached!
% 30.40/5.60 % (29197)------------------------------
% 30.40/5.60 % (29197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.40/5.60 % (29197)Termination reason: Unknown
% 30.40/5.60 % (29197)Termination phase: Saturation
% 30.40/5.60
% 30.40/5.60 % (29197)Memory used [KB]: 10490
% 30.40/5.60 % (29197)Time elapsed: 0.627 s
% 30.40/5.60 % (29197)Instructions burned: 1982 (million)
% 30.40/5.60 % (29197)------------------------------
% 30.40/5.60 % (29197)------------------------------
% 30.40/5.61 % (29210)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_28704 for (2959ds/102Mi)
% 30.40/5.64 % (29210)Instruction limit reached!
% 30.40/5.64 % (29210)------------------------------
% 30.40/5.64 % (29210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.40/5.64 % (29210)Termination reason: Unknown
% 30.40/5.64 % (29210)Termination phase: Preprocessing 3
% 30.40/5.64
% 30.40/5.64 % (29210)Memory used [KB]: 2814
% 30.40/5.64 % (29210)Time elapsed: 0.029 s
% 30.40/5.64 % (29210)Instructions burned: 104 (million)
% 30.40/5.64 % (29210)------------------------------
% 30.40/5.64 % (29210)------------------------------
% 30.40/5.65 % (29211)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_28704 for (2959ds/952Mi)
% 30.65/5.73 % (29201)Instruction limit reached!
% 30.65/5.73 % (29201)------------------------------
% 30.65/5.73 % (29201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.73 % (29201)Termination reason: Unknown
% 30.65/5.73 % (29201)Termination phase: Saturation
% 30.65/5.73
% 30.65/5.73 % (29201)Memory used [KB]: 11641
% 30.65/5.73 % (29201)Time elapsed: 0.496 s
% 30.65/5.73 % (29201)Instructions burned: 1672 (million)
% 30.65/5.73 % (29201)------------------------------
% 30.65/5.73 % (29201)------------------------------
% 30.65/5.74 % (29212)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_28704 for (2958ds/578Mi)
% 30.65/5.76 % (29207)Instruction limit reached!
% 30.65/5.76 % (29207)------------------------------
% 30.65/5.76 % (29207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.76 % (29207)Termination reason: Unknown
% 30.65/5.76 % (29207)Termination phase: Saturation
% 30.65/5.76
% 30.65/5.76 % (29207)Memory used [KB]: 10746
% 30.65/5.76 % (29207)Time elapsed: 0.274 s
% 30.65/5.76 % (29207)Instructions burned: 865 (million)
% 30.65/5.76 % (29207)------------------------------
% 30.65/5.76 % (29207)------------------------------
% 30.65/5.77 % (29213)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_28704 for (2958ds/643Mi)
% 30.65/5.78 % (29188)Instruction limit reached!
% 30.65/5.78 % (29188)------------------------------
% 30.65/5.78 % (29188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.78 % (29188)Termination reason: Unknown
% 30.65/5.78 % (29188)Termination phase: Saturation
% 30.65/5.78
% 30.65/5.78 % (29188)Memory used [KB]: 13688
% 30.65/5.78 % (29188)Time elapsed: 1.051 s
% 30.65/5.78 % (29188)Instructions burned: 3376 (million)
% 30.65/5.78 % (29188)------------------------------
% 30.65/5.78 % (29188)------------------------------
% 30.65/5.79 % (29214)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_28704 for (2957ds/865Mi)
% 31.73/5.90 % (29209)Instruction limit reached!
% 31.73/5.90 % (29209)------------------------------
% 31.73/5.90 % (29209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.90 % (29209)Termination reason: Unknown
% 31.73/5.90 % (29209)Termination phase: Saturation
% 31.73/5.90
% 31.73/5.90 % (29209)Memory used [KB]: 10362
% 31.73/5.90 % (29209)Time elapsed: 0.315 s
% 31.73/5.90 % (29209)Instructions burned: 1002 (million)
% 31.73/5.90 % (29209)------------------------------
% 31.73/5.90 % (29209)------------------------------
% 31.73/5.91 % (29212)Instruction limit reached!
% 31.73/5.91 % (29212)------------------------------
% 31.73/5.91 % (29212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.91 % (29212)Termination reason: Unknown
% 31.73/5.91 % (29212)Termination phase: Saturation
% 31.73/5.91
% 31.73/5.91 % (29212)Memory used [KB]: 9210
% 31.73/5.91 % (29212)Time elapsed: 0.167 s
% 31.73/5.91 % (29212)Instructions burned: 578 (million)
% 31.73/5.91 % (29212)------------------------------
% 31.73/5.91 % (29212)------------------------------
% 31.73/5.91 % (29215)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_28704 for (2956ds/1174Mi)
% 31.73/5.92 % (29216)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_28704 for (2956ds/644Mi)
% 31.73/5.95 % (29211)Instruction limit reached!
% 31.73/5.95 % (29211)------------------------------
% 31.73/5.95 % (29211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.95 % (29211)Termination reason: Unknown
% 31.73/5.95 % (29211)Termination phase: Saturation
% 31.73/5.95
% 31.73/5.95 % (29211)Memory used [KB]: 9722
% 31.73/5.95 % (29211)Time elapsed: 0.295 s
% 31.73/5.95 % (29211)Instructions burned: 954 (million)
% 31.73/5.95 % (29211)------------------------------
% 31.73/5.95 % (29211)------------------------------
% 31.73/5.95 % (29213)Instruction limit reached!
% 31.73/5.95 % (29213)------------------------------
% 31.73/5.95 % (29213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.95 % (29213)Termination reason: Unknown
% 31.73/5.95 % (29213)Termination phase: Saturation
% 31.73/5.95
% 31.73/5.95 % (29213)Memory used [KB]: 9850
% 31.73/5.95 % (29213)Time elapsed: 0.187 s
% 31.73/5.95 % (29213)Instructions burned: 643 (million)
% 31.73/5.95 % (29213)------------------------------
% 31.73/5.95 % (29213)------------------------------
% 31.73/5.96 % (29217)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_28704 for (2956ds/1201Mi)
% 31.73/5.96 % (29218)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_28704 for (2956ds/1046Mi)
% 31.73/5.98 % (29161)Instruction limit reached!
% 31.73/5.98 % (29161)------------------------------
% 31.73/5.98 % (29161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.98 % (29161)Termination reason: Unknown
% 31.73/5.98 % (29161)Termination phase: Saturation
% 31.73/5.98
% 31.73/5.98 % (29161)Memory used [KB]: 17526
% 31.73/5.98 % (29161)Time elapsed: 2.563 s
% 31.73/5.98 % (29161)Instructions burned: 8251 (million)
% 31.73/5.98 % (29161)------------------------------
% 31.73/5.98 % (29161)------------------------------
% 31.73/5.99 % (29219)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_28704 for (2955ds/222Mi)
% 34.09/6.05 % (29219)Instruction limit reached!
% 34.09/6.05 % (29219)------------------------------
% 34.09/6.05 % (29219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.05 % (29219)Termination reason: Unknown
% 34.09/6.05 % (29219)Termination phase: Saturation
% 34.09/6.05
% 34.09/6.05 % (29219)Memory used [KB]: 7675
% 34.09/6.05 % (29219)Time elapsed: 0.063 s
% 34.09/6.05 % (29219)Instructions burned: 224 (million)
% 34.09/6.05 % (29219)------------------------------
% 34.09/6.05 % (29219)------------------------------
% 34.09/6.06 % (29214)Instruction limit reached!
% 34.09/6.06 % (29214)------------------------------
% 34.09/6.06 % (29214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.06 % (29214)Termination reason: Unknown
% 34.09/6.06 % (29214)Termination phase: Saturation
% 34.09/6.06
% 34.09/6.06 % (29214)Memory used [KB]: 9978
% 34.09/6.06 % (29214)Time elapsed: 0.269 s
% 34.09/6.06 % (29214)Instructions burned: 866 (million)
% 34.09/6.06 % (29214)------------------------------
% 34.09/6.06 % (29214)------------------------------
% 34.09/6.06 % (29220)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_28704 for (2955ds/68Mi)
% 34.09/6.07 % (29221)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_28704 for (2954ds/454Mi)
% 34.09/6.08 % (29220)Instruction limit reached!
% 34.09/6.08 % (29220)------------------------------
% 34.09/6.08 % (29220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.08 % (29220)Termination reason: Unknown
% 34.09/6.08 % (29220)Termination phase: Preprocessing 3
% 34.09/6.08
% 34.09/6.08 % (29220)Memory used [KB]: 2430
% 34.09/6.08 % (29220)Time elapsed: 0.024 s
% 34.09/6.08 % (29220)Instructions burned: 70 (million)
% 34.09/6.08 % (29220)------------------------------
% 34.09/6.08 % (29220)------------------------------
% 34.09/6.09 % (29222)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_28704 for (2954ds/360Mi)
% 34.09/6.12 % (29216)Instruction limit reached!
% 34.09/6.12 % (29216)------------------------------
% 34.09/6.12 % (29216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.12 % (29216)Termination reason: Unknown
% 34.09/6.12 % (29216)Termination phase: Saturation
% 34.09/6.12
% 34.09/6.12 % (29216)Memory used [KB]: 10490
% 34.09/6.12 % (29216)Time elapsed: 0.203 s
% 34.09/6.12 % (29216)Instructions burned: 644 (million)
% 34.09/6.12 % (29216)------------------------------
% 34.09/6.12 % (29216)------------------------------
% 34.71/6.13 % (29223)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_28704 for (2954ds/157Mi)
% 34.71/6.17 % (29223)Instruction limit reached!
% 34.71/6.17 % (29223)------------------------------
% 34.71/6.17 % (29223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.17 % (29223)Termination reason: Unknown
% 34.71/6.17 % (29223)Termination phase: Property scanning
% 34.71/6.17
% 34.71/6.17 % (29223)Memory used [KB]: 2814
% 34.71/6.17 % (29223)Time elapsed: 0.043 s
% 34.71/6.17 % (29223)Instructions burned: 157 (million)
% 34.71/6.17 % (29223)------------------------------
% 34.71/6.17 % (29223)------------------------------
% 34.71/6.18 % (29224)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_28704 for (2953ds/5061Mi)
% 34.71/6.19 % (29222)Instruction limit reached!
% 34.71/6.19 % (29222)------------------------------
% 34.71/6.19 % (29222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.19 % (29222)Termination reason: Unknown
% 34.71/6.19 % (29222)Termination phase: Saturation
% 34.71/6.19
% 34.71/6.19 % (29222)Memory used [KB]: 8699
% 34.71/6.19 % (29222)Time elapsed: 0.100 s
% 34.71/6.19 % (29222)Instructions burned: 360 (million)
% 34.71/6.19 % (29222)------------------------------
% 34.71/6.19 % (29222)------------------------------
% 34.71/6.20 % (29221)Instruction limit reached!
% 34.71/6.20 % (29221)------------------------------
% 34.71/6.20 % (29221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.71/6.20 % (29221)Termination reason: Unknown
% 34.71/6.20 % (29221)Termination phase: Saturation
% 34.71/6.20
% 34.71/6.20 % (29221)Memory used [KB]: 13176
% 34.71/6.20 % (29221)Time elapsed: 0.131 s
% 34.71/6.20 % (29221)Instructions burned: 455 (million)
% 34.71/6.20 % (29221)------------------------------
% 34.71/6.20 % (29221)------------------------------
% 35.16/6.20 % (29225)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_28704 for (2953ds/2401Mi)
% 35.16/6.21 % (29226)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_28704 for (2953ds/5798Mi)
% 35.16/6.27 % (29218)Instruction limit reached!
% 35.16/6.27 % (29218)------------------------------
% 35.16/6.27 % (29218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.16/6.27 % (29218)Termination reason: Unknown
% 35.16/6.27 % (29218)Termination phase: Saturation
% 35.16/6.27
% 35.16/6.27 % (29218)Memory used [KB]: 8955
% 35.16/6.27 % (29218)Time elapsed: 0.307 s
% 35.16/6.27 % (29218)Instructions burned: 1048 (million)
% 35.16/6.27 % (29218)------------------------------
% 35.16/6.27 % (29218)------------------------------
% 35.16/6.28 % (29227)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_28704 for (2952ds/346Mi)
% 35.16/6.28 % (29215)Instruction limit reached!
% 35.16/6.28 % (29215)------------------------------
% 35.16/6.28 % (29215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.16/6.28 % (29215)Termination reason: Unknown
% 35.16/6.28 % (29215)Termination phase: Saturation
% 35.16/6.28
% 35.16/6.28 % (29215)Memory used [KB]: 12025
% 35.16/6.28 % (29215)Time elapsed: 0.370 s
% 35.16/6.28 % (29215)Instructions burned: 1176 (million)
% 35.16/6.28 % (29215)------------------------------
% 35.16/6.28 % (29215)------------------------------
% 35.16/6.29 % (29228)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_28704 for (2952ds/1321Mi)
% 35.69/6.30 % (29217)Instruction limit reached!
% 35.69/6.30 % (29217)------------------------------
% 35.69/6.30 % (29217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.30 % (29217)Termination reason: Unknown
% 35.69/6.30 % (29217)Termination phase: Saturation
% 35.69/6.30
% 35.69/6.30 % (29217)Memory used [KB]: 11641
% 35.69/6.30 % (29217)Time elapsed: 0.344 s
% 35.69/6.30 % (29217)Instructions burned: 1203 (million)
% 35.69/6.30 % (29217)------------------------------
% 35.69/6.30 % (29217)------------------------------
% 35.69/6.31 % (29229)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_28704 for (2952ds/1312Mi)
% 35.69/6.38 % (29227)Instruction limit reached!
% 35.69/6.38 % (29227)------------------------------
% 35.69/6.38 % (29227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.38 % (29227)Termination reason: Unknown
% 35.69/6.38 % (29227)Termination phase: Saturation
% 35.69/6.38
% 35.69/6.38 % (29227)Memory used [KB]: 8059
% 35.69/6.38 % (29227)Time elapsed: 0.105 s
% 35.69/6.38 % (29227)Instructions burned: 348 (million)
% 35.69/6.38 % (29227)------------------------------
% 35.69/6.38 % (29227)------------------------------
% 35.69/6.39 % (29230)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_28704 for (2951ds/672Mi)
% 36.11/6.60 % (29230)Instruction limit reached!
% 36.11/6.60 % (29230)------------------------------
% 36.11/6.60 % (29230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.11/6.60 % (29230)Termination reason: Unknown
% 36.11/6.60 % (29230)Termination phase: Saturation
% 36.11/6.60
% 36.11/6.60 % (29230)Memory used [KB]: 8955
% 36.11/6.60 % (29230)Time elapsed: 0.211 s
% 36.11/6.60 % (29230)Instructions burned: 674 (million)
% 36.11/6.60 % (29230)------------------------------
% 36.11/6.60 % (29230)------------------------------
% 36.11/6.61 % (29231)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_28704 for (2949ds/1897Mi)
% 36.11/6.68 % (29228)Instruction limit reached!
% 36.11/6.68 % (29228)------------------------------
% 36.11/6.68 % (29228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.11/6.68 % (29228)Termination reason: Unknown
% 36.11/6.68 % (29228)Termination phase: Saturation
% 36.11/6.68
% 36.11/6.68 % (29228)Memory used [KB]: 8059
% 36.11/6.68 % (29228)Time elapsed: 0.392 s
% 36.11/6.68 % (29228)Instructions burned: 1321 (million)
% 36.11/6.68 % (29228)------------------------------
% 36.11/6.68 % (29228)------------------------------
% 36.11/6.69 % (29232)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_28704 for (2948ds/1202Mi)
% 36.84/6.70 % (29229)Instruction limit reached!
% 36.84/6.70 % (29229)------------------------------
% 36.84/6.70 % (29229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.84/6.70 % (29229)Termination reason: Unknown
% 36.84/6.70 % (29229)Termination phase: Saturation
% 36.84/6.70
% 36.84/6.70 % (29229)Memory used [KB]: 9850
% 36.84/6.70 % (29229)Time elapsed: 0.391 s
% 36.84/6.70 % (29229)Instructions burned: 1314 (million)
% 36.84/6.70 % (29229)------------------------------
% 36.84/6.70 % (29229)------------------------------
% 36.84/6.71 % (29233)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_28704 for (2948ds/1493Mi)
% 37.45/6.95 % (29225)Instruction limit reached!
% 37.45/6.95 % (29225)------------------------------
% 37.45/6.95 % (29225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.45/6.95 % (29225)Termination reason: Unknown
% 37.45/6.95 % (29225)Termination phase: Saturation
% 37.45/6.95
% 37.45/6.95 % (29225)Memory used [KB]: 12665
% 37.45/6.95 % (29225)Time elapsed: 0.749 s
% 37.45/6.95 % (29225)Instructions burned: 2401 (million)
% 37.45/6.95 % (29225)------------------------------
% 37.45/6.95 % (29225)------------------------------
% 37.45/6.96 % (29234)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_28704 for (2946ds/7679Mi)
% 41.11/7.06 % (29232)Instruction limit reached!
% 41.11/7.06 % (29232)------------------------------
% 41.11/7.06 % (29232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.11/7.06 % (29232)Termination reason: Unknown
% 41.11/7.06 % (29232)Termination phase: Saturation
% 41.11/7.06
% 41.11/7.06 % (29232)Memory used [KB]: 6652
% 41.11/7.06 % (29232)Time elapsed: 0.369 s
% 41.11/7.06 % (29232)Instructions burned: 1204 (million)
% 41.11/7.06 % (29232)------------------------------
% 41.11/7.06 % (29232)------------------------------
% 41.11/7.07 % (29235)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_28704 for (2945ds/340Mi)
% 41.77/7.14 % (29233)Instruction limit reached!
% 41.77/7.14 % (29233)------------------------------
% 41.77/7.14 % (29233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.14 % (29233)Termination reason: Unknown
% 41.77/7.14 % (29233)Termination phase: Saturation
% 41.77/7.14
% 41.77/7.14 % (29233)Memory used [KB]: 9338
% 41.77/7.14 % (29233)Time elapsed: 0.429 s
% 41.77/7.14 % (29233)Instructions burned: 1493 (million)
% 41.77/7.14 % (29233)------------------------------
% 41.77/7.14 % (29233)------------------------------
% 41.77/7.15 % (29236)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_28704 for (2944ds/3672Mi)
% 41.77/7.17 % (29235)Instruction limit reached!
% 41.77/7.17 % (29235)------------------------------
% 41.77/7.17 % (29235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.17 % (29235)Termination reason: Unknown
% 41.77/7.17 % (29235)Termination phase: Saturation
% 41.77/7.17
% 41.77/7.17 % (29235)Memory used [KB]: 8187
% 41.77/7.17 % (29235)Time elapsed: 0.097 s
% 41.77/7.17 % (29235)Instructions burned: 341 (million)
% 41.77/7.17 % (29235)------------------------------
% 41.77/7.17 % (29235)------------------------------
% 41.77/7.18 % (29237)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_28704 for (2944ds/1535Mi)
% 42.28/7.20 % (29231)Instruction limit reached!
% 42.28/7.20 % (29231)------------------------------
% 42.28/7.20 % (29231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.28/7.20 % (29231)Termination reason: Unknown
% 42.28/7.20 % (29231)Termination phase: Saturation
% 42.28/7.20
% 42.28/7.20 % (29231)Memory used [KB]: 10490
% 42.28/7.20 % (29231)Time elapsed: 0.594 s
% 42.28/7.20 % (29231)Instructions burned: 1899 (million)
% 42.28/7.20 % (29231)------------------------------
% 42.28/7.20 % (29231)------------------------------
% 42.28/7.21 % (29238)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_28704 for (2943ds/4637Mi)
% 42.69/7.39 % (29205)Refutation not found, non-redundant clauses discarded% (29205)------------------------------
% 42.69/7.39 % (29205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.69/7.39 % (29205)Termination reason: Refutation not found, non-redundant clauses discarded
% 42.69/7.39
% 42.69/7.39 % (29205)Memory used [KB]: 11769
% 42.69/7.39 % (29205)Time elapsed: 2.014 s
% 42.69/7.39 % (29205)Instructions burned: 6352 (million)
% 42.69/7.39 % (29205)------------------------------
% 42.69/7.39 % (29205)------------------------------
% 43.09/7.40 % (29239)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_28704 for (2941ds/3174Mi)
% 43.69/7.62 % (29237)Instruction limit reached!
% 43.69/7.62 % (29237)------------------------------
% 43.69/7.62 % (29237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.69/7.62 % (29237)Termination reason: Unknown
% 43.69/7.62 % (29237)Termination phase: Saturation
% 43.69/7.62
% 43.69/7.62 % (29237)Memory used [KB]: 13304
% 43.69/7.62 % (29237)Time elapsed: 0.467 s
% 43.69/7.62 % (29237)Instructions burned: 1538 (million)
% 43.69/7.62 % (29237)------------------------------
% 43.69/7.62 % (29237)------------------------------
% 43.69/7.63 % (29240)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_28704 for (2939ds/307Mi)
% 43.69/7.70 % (29224)Instruction limit reached!
% 43.69/7.70 % (29224)------------------------------
% 43.69/7.70 % (29224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.69/7.70 % (29224)Termination reason: Unknown
% 43.69/7.70 % (29224)Termination phase: Saturation
% 43.69/7.70
% 43.69/7.70 % (29224)Memory used [KB]: 13816
% 43.69/7.70 % (29224)Time elapsed: 1.518 s
% 43.69/7.70 % (29224)Instructions burned: 5061 (million)
% 43.69/7.70 % (29224)------------------------------
% 43.69/7.70 % (29224)------------------------------
% 42.94/7.71 % (29241)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_28704 for (2938ds/3619Mi)
% 42.94/7.72 % (29240)Instruction limit reached!
% 42.94/7.72 % (29240)------------------------------
% 42.94/7.72 % (29240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.72 % (29240)Termination reason: Unknown
% 42.94/7.72 % (29240)Termination phase: Saturation
% 42.94/7.72
% 42.94/7.72 % (29240)Memory used [KB]: 7803
% 42.94/7.72 % (29240)Time elapsed: 0.087 s
% 42.94/7.72 % (29240)Instructions burned: 307 (million)
% 42.94/7.72 % (29240)------------------------------
% 42.94/7.72 % (29240)------------------------------
% 42.94/7.72 % (29242)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_28704 for (2938ds/2325Mi)
% 44.76/7.89 % (29226)Instruction limit reached!
% 44.76/7.89 % (29226)------------------------------
% 44.76/7.89 % (29226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.76/7.89 % (29226)Termination reason: Unknown
% 44.76/7.89 % (29226)Termination phase: Saturation
% 44.76/7.89
% 44.76/7.89 % (29226)Memory used [KB]: 9210
% 44.76/7.89 % (29226)Time elapsed: 1.682 s
% 44.76/7.89 % (29226)Instructions burned: 5798 (million)
% 44.76/7.89 % (29226)------------------------------
% 44.76/7.89 % (29226)------------------------------
% 44.96/7.90 % (29243)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_28704 for (2936ds/2341Mi)
% 48.84/8.17 % (29242)Refutation not found, non-redundant clauses discarded% (29242)------------------------------
% 48.84/8.17 % (29242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.84/8.17 % (29242)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.84/8.17
% 48.84/8.17 % (29242)Memory used [KB]: 11897
% 48.84/8.17 % (29242)Time elapsed: 0.444 s
% 48.84/8.17 % (29242)Instructions burned: 1444 (million)
% 48.84/8.17 % (29242)------------------------------
% 48.84/8.17 % (29242)------------------------------
% 48.84/8.18 % (29244)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_28704 for (2933ds/7257Mi)
% 49.95/8.31 % (29236)Instruction limit reached!
% 49.95/8.31 % (29236)------------------------------
% 49.95/8.31 % (29236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.95/8.31 % (29236)Termination reason: Unknown
% 49.95/8.31 % (29236)Termination phase: Saturation
% 49.95/8.31
% 49.95/8.31 % (29236)Memory used [KB]: 13816
% 49.95/8.31 % (29236)Time elapsed: 1.183 s
% 49.95/8.31 % (29236)Instructions burned: 3674 (million)
% 49.95/8.31 % (29236)------------------------------
% 49.95/8.31 % (29236)------------------------------
% 49.95/8.32 % (29245)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_28704 for (2932ds/3710Mi)
% 49.95/8.39 % (29239)Instruction limit reached!
% 49.95/8.39 % (29239)------------------------------
% 49.95/8.39 % (29239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.95/8.39 % (29239)Termination reason: Unknown
% 49.95/8.39 % (29239)Termination phase: Saturation
% 49.95/8.39
% 49.95/8.39 % (29239)Memory used [KB]: 13816
% 49.95/8.39 % (29239)Time elapsed: 0.990 s
% 49.95/8.39 % (29239)Instructions burned: 3175 (million)
% 49.95/8.39 % (29239)------------------------------
% 49.95/8.39 % (29239)------------------------------
% 50.47/8.40 % (29246)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_28704 for (2931ds/326Mi)
% 50.86/8.51 % (29246)Instruction limit reached!
% 50.86/8.51 % (29246)------------------------------
% 50.86/8.51 % (29246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.86/8.51 % (29246)Termination reason: Unknown
% 50.86/8.51 % (29246)Termination phase: Saturation
% 50.86/8.51
% 50.86/8.51 % (29246)Memory used [KB]: 7675
% 50.86/8.51 % (29246)Time elapsed: 0.109 s
% 50.86/8.51 % (29246)Instructions burned: 326 (million)
% 50.86/8.51 % (29246)------------------------------
% 50.86/8.51 % (29246)------------------------------
% 50.86/8.52 % (29247)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_28704 for (2930ds/1100Mi)
% 51.39/8.62 % (29238)Instruction limit reached!
% 51.39/8.62 % (29238)------------------------------
% 51.39/8.62 % (29238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.39/8.62 % (29238)Termination reason: Unknown
% 51.39/8.62 % (29238)Termination phase: Saturation
% 51.39/8.62
% 51.39/8.62 % (29238)Memory used [KB]: 11129
% 51.39/8.62 % (29238)Time elapsed: 1.431 s
% 51.39/8.62 % (29238)Instructions burned: 4640 (million)
% 51.39/8.62 % (29238)------------------------------
% 51.39/8.62 % (29238)------------------------------
% 51.39/8.63 % (29248)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_28704 for (2929ds/406Mi)
% 51.39/8.64 % (29243)Instruction limit reached!
% 51.39/8.64 % (29243)------------------------------
% 51.39/8.64 % (29243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.39/8.64 % (29243)Termination reason: Unknown
% 51.39/8.64 % (29243)Termination phase: Saturation
% 51.39/8.64
% 51.39/8.64 % (29243)Memory used [KB]: 10362
% 51.39/8.64 % (29243)Time elapsed: 0.740 s
% 51.39/8.64 % (29243)Instructions burned: 2343 (million)
% 51.39/8.64 % (29243)------------------------------
% 51.39/8.64 % (29243)------------------------------
% 51.39/8.65 % (29249)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_28704 for (2929ds/1871Mi)
% 51.67/8.76 % (29248)Instruction limit reached!
% 51.67/8.76 % (29248)------------------------------
% 51.67/8.76 % (29248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.67/8.76 % (29248)Termination reason: Unknown
% 51.67/8.76 % (29248)Termination phase: Saturation
% 51.67/8.76
% 51.67/8.76 % (29248)Memory used [KB]: 8827
% 51.67/8.76 % (29248)Time elapsed: 0.129 s
% 51.67/8.76 % (29248)Instructions burned: 408 (million)
% 51.67/8.76 % (29248)------------------------------
% 51.67/8.76 % (29248)------------------------------
% 51.67/8.77 % (29250)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_28704 for (2928ds/1194Mi)
% 51.67/8.79 % (29241)Instruction limit reached!
% 51.67/8.79 % (29241)------------------------------
% 51.67/8.79 % (29241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.67/8.79 % (29241)Termination reason: Unknown
% 51.67/8.79 % (29241)Termination phase: Saturation
% 51.67/8.79
% 51.67/8.79 % (29241)Memory used [KB]: 14583
% 51.67/8.79 % (29241)Time elapsed: 1.087 s
% 51.67/8.79 % (29241)Instructions burned: 3621 (million)
% 51.67/8.79 % (29241)------------------------------
% 51.67/8.79 % (29241)------------------------------
% 52.02/8.80 % (29251)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_28704 for (2927ds/474Mi)
% 52.02/8.86 % (29247)Instruction limit reached!
% 52.02/8.86 % (29247)------------------------------
% 52.02/8.86 % (29247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.02/8.86 % (29247)Termination reason: Unknown
% 52.02/8.86 % (29247)Termination phase: Saturation
% 52.02/8.86
% 52.02/8.86 % (29247)Memory used [KB]: 12153
% 52.02/8.86 % (29247)Time elapsed: 0.343 s
% 52.02/8.86 % (29247)Instructions burned: 1100 (million)
% 52.02/8.86 % (29247)------------------------------
% 52.02/8.86 % (29247)------------------------------
% 52.02/8.87 % (29252)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_28704 for (2927ds/3115Mi)
% 52.49/8.94 % (29251)Instruction limit reached!
% 52.49/8.94 % (29251)------------------------------
% 52.49/8.94 % (29251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.49/8.94 % (29251)Termination reason: Unknown
% 52.49/8.94 % (29251)Termination phase: Saturation
% 52.49/8.94
% 52.49/8.94 % (29251)Memory used [KB]: 8443
% 52.49/8.94 % (29251)Time elapsed: 0.143 s
% 52.49/8.94 % (29251)Instructions burned: 475 (million)
% 52.49/8.94 % (29251)------------------------------
% 52.49/8.94 % (29251)------------------------------
% 52.49/8.95 % (29253)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_28704 for (2926ds/831Mi)
% 55.87/9.14 % (29250)Instruction limit reached!
% 55.87/9.14 % (29250)------------------------------
% 55.87/9.14 % (29250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.87/9.14 % (29250)Termination reason: Unknown
% 55.87/9.14 % (29250)Termination phase: Saturation
% 55.87/9.14
% 55.87/9.14 % (29250)Memory used [KB]: 10106
% 55.87/9.14 % (29250)Time elapsed: 0.370 s
% 55.87/9.14 % (29250)Instructions burned: 1196 (million)
% 55.87/9.14 % (29250)------------------------------
% 55.87/9.14 % (29250)------------------------------
% 55.87/9.15 % (29254)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_28704 for (2924ds/1188Mi)
% 56.33/9.21 % (29253)Instruction limit reached!
% 56.33/9.21 % (29253)------------------------------
% 56.33/9.21 % (29253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.33/9.21 % (29253)Termination reason: Unknown
% 56.33/9.21 % (29253)Termination phase: Saturation
% 56.33/9.21
% 56.33/9.21 % (29253)Memory used [KB]: 10874
% 56.33/9.21 % (29253)Time elapsed: 0.256 s
% 56.33/9.21 % (29253)Instructions burned: 831 (million)
% 56.33/9.21 % (29253)------------------------------
% 56.33/9.21 % (29253)------------------------------
% 56.33/9.22 % (29255)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_28704 for (2923ds/2868Mi)
% 56.33/9.23 % (29249)Instruction limit reached!
% 56.33/9.23 % (29249)------------------------------
% 56.33/9.23 % (29249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.33/9.23 % (29249)Termination reason: Unknown
% 56.33/9.23 % (29249)Termination phase: Saturation
% 56.33/9.23
% 56.33/9.23 % (29249)Memory used [KB]: 12665
% 56.33/9.23 % (29249)Time elapsed: 0.581 s
% 56.33/9.23 % (29249)Instructions burned: 1873 (million)
% 56.33/9.23 % (29249)------------------------------
% 56.33/9.23 % (29249)------------------------------
% 56.33/9.24 % (29256)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_28704 for (2923ds/1516Mi)
% 56.33/9.25 % (29234)Instruction limit reached!
% 56.33/9.25 % (29234)------------------------------
% 56.33/9.25 % (29234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.33/9.25 % (29234)Termination reason: Unknown
% 56.33/9.25 % (29234)Termination phase: Saturation
% 56.33/9.25
% 56.33/9.25 % (29234)Memory used [KB]: 14967
% 56.33/9.25 % (29234)Time elapsed: 2.292 s
% 56.33/9.25 % (29234)Instructions burned: 7682 (million)
% 56.33/9.25 % (29234)------------------------------
% 56.33/9.25 % (29234)------------------------------
% 56.33/9.26 % (29257)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_28704 for (2923ds/2321Mi)
% 57.06/9.41 % (29245)Instruction limit reached!
% 57.06/9.41 % (29245)------------------------------
% 57.06/9.41 % (29245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.06/9.41 % (29245)Termination reason: Unknown
% 57.06/9.41 % (29245)Termination phase: Saturation
% 57.06/9.41
% 57.06/9.41 % (29245)Memory used [KB]: 19317
% 57.06/9.41 % (29245)Time elapsed: 1.091 s
% 57.06/9.41 % (29245)Instructions burned: 3711 (million)
% 57.06/9.41 % (29245)------------------------------
% 57.06/9.41 % (29245)------------------------------
% 57.06/9.42 % (29258)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_28704 for (2921ds/2812Mi)
% 57.28/9.51 % (29254)Instruction limit reached!
% 57.28/9.51 % (29254)------------------------------
% 57.28/9.51 % (29254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.28/9.51 % (29254)Termination reason: Unknown
% 57.28/9.51 % (29254)Termination phase: Saturation
% 57.28/9.51
% 57.28/9.51 % (29254)Memory used [KB]: 9722
% 57.28/9.51 % (29254)Time elapsed: 0.365 s
% 57.28/9.51 % (29254)Instructions burned: 1191 (million)
% 57.28/9.51 % (29254)------------------------------
% 57.28/9.51 % (29254)------------------------------
% 57.28/9.52 % (29259)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_28704 for (2920ds/4604Mi)
% 58.05/9.70 % (29256)Instruction limit reached!
% 58.05/9.70 % (29256)------------------------------
% 58.05/9.70 % (29256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.05/9.70 % (29256)Termination reason: Unknown
% 58.05/9.70 % (29256)Termination phase: Saturation
% 58.05/9.70
% 58.05/9.70 % (29256)Memory used [KB]: 9210
% 58.05/9.70 % (29256)Time elapsed: 0.462 s
% 58.05/9.70 % (29256)Instructions burned: 1518 (million)
% 58.05/9.70 % (29256)------------------------------
% 58.05/9.70 % (29256)------------------------------
% 58.05/9.71 % (29260)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_28704 for (2918ds/2678Mi)
% 58.05/9.78 % (29252)Instruction limit reached!
% 58.05/9.78 % (29252)------------------------------
% 58.05/9.78 % (29252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.05/9.78 % (29252)Termination reason: Unknown
% 58.05/9.78 % (29252)Termination phase: Saturation
% 58.05/9.78
% 58.05/9.78 % (29252)Memory used [KB]: 12792
% 58.05/9.78 % (29252)Time elapsed: 0.917 s
% 58.05/9.78 % (29252)Instructions burned: 3118 (million)
% 58.05/9.78 % (29252)------------------------------
% 58.05/9.78 % (29252)------------------------------
% 58.05/9.80 % (29261)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_28704 for (2917ds/643Mi)
% 58.83/9.91 % (29257)Instruction limit reached!
% 58.83/9.91 % (29257)------------------------------
% 58.83/9.91 % (29257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.83/9.91 % (29257)Termination reason: Unknown
% 58.83/9.91 % (29257)Termination phase: Saturation
% 58.83/9.91
% 58.83/9.91 % (29257)Memory used [KB]: 12153
% 58.83/9.91 % (29257)Time elapsed: 0.648 s
% 58.83/9.91 % (29257)Instructions burned: 2323 (million)
% 58.83/9.91 % (29257)------------------------------
% 58.83/9.91 % (29257)------------------------------
% 58.83/9.92 % (29262)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_28704 for (2916ds/458Mi)
% 58.83/9.99 % (29261)Instruction limit reached!
% 58.83/9.99 % (29261)------------------------------
% 58.83/9.99 % (29261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.83/9.99 % (29261)Termination reason: Unknown
% 58.83/9.99 % (29261)Termination phase: Saturation
% 58.83/9.99
% 58.83/9.99 % (29261)Memory used [KB]: 9850
% 58.83/9.99 % (29261)Time elapsed: 0.191 s
% 58.83/9.99 % (29261)Instructions burned: 644 (million)
% 58.83/9.99 % (29261)------------------------------
% 58.83/9.99 % (29261)------------------------------
% 58.83/10.00 % (29263)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_28704 for (2915ds/2546Mi)
% 62.21/10.03 % (29255)Instruction limit reached!
% 62.21/10.03 % (29255)------------------------------
% 62.21/10.03 % (29255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.21/10.03 % (29255)Termination reason: Unknown
% 62.21/10.03 % (29255)Termination phase: Saturation
% 62.21/10.03
% 62.21/10.03 % (29255)Memory used [KB]: 12409
% 62.21/10.03 % (29255)Time elapsed: 0.811 s
% 62.21/10.03 % (29255)Instructions burned: 2869 (million)
% 62.21/10.03 % (29255)------------------------------
% 62.21/10.03 % (29255)------------------------------
% 62.21/10.04 % (29264)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_28704 for (2915ds/1432Mi)
% 62.21/10.05 % (29262)Instruction limit reached!
% 62.21/10.05 % (29262)------------------------------
% 62.21/10.05 % (29262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.21/10.05 % (29262)Termination reason: Unknown
% 62.21/10.05 % (29262)Termination phase: Saturation
% 62.21/10.05
% 62.21/10.05 % (29262)Memory used [KB]: 8827
% 62.21/10.05 % (29262)Time elapsed: 0.131 s
% 62.21/10.05 % (29262)Instructions burned: 458 (million)
% 62.21/10.05 % (29262)------------------------------
% 62.21/10.05 % (29262)------------------------------
% 62.21/10.06 % (29265)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_28704 for (2915ds/386Mi)
% 62.76/10.16 % (29265)Instruction limit reached!
% 62.76/10.16 % (29265)------------------------------
% 62.76/10.16 % (29265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.76/10.16 % (29265)Termination reason: Unknown
% 62.76/10.16 % (29265)Termination phase: Saturation
% 62.76/10.16
% 62.76/10.16 % (29265)Memory used [KB]: 8699
% 62.76/10.16 % (29265)Time elapsed: 0.108 s
% 62.76/10.16 % (29265)Instructions burned: 386 (million)
% 62.76/10.16 % (29265)------------------------------
% 62.76/10.16 % (29265)------------------------------
% 62.76/10.18 % (29266)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_28704 for (2913ds/360Mi)
% 63.22/10.28 % (29266)Instruction limit reached!
% 63.22/10.28 % (29266)------------------------------
% 63.22/10.28 % (29266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.22/10.28 % (29266)Termination reason: Unknown
% 63.22/10.28 % (29266)Termination phase: Saturation
% 63.22/10.28
% 63.22/10.28 % (29266)Memory used [KB]: 8571
% 63.22/10.28 % (29266)Time elapsed: 0.105 s
% 63.22/10.28 % (29266)Instructions burned: 362 (million)
% 63.22/10.28 % (29266)------------------------------
% 63.22/10.28 % (29266)------------------------------
% 63.22/10.29 % (29267)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_28704 for (2912ds/5446Mi)
% 63.83/10.31 % (29258)Instruction limit reached!
% 63.83/10.31 % (29258)------------------------------
% 63.83/10.31 % (29258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.83/10.31 % (29258)Termination reason: Unknown
% 63.83/10.31 % (29258)Termination phase: Saturation
% 63.83/10.31
% 63.83/10.31 % (29258)Memory used [KB]: 12665
% 63.83/10.31 % (29258)Time elapsed: 0.893 s
% 63.83/10.31 % (29258)Instructions burned: 2814 (million)
% 63.83/10.31 % (29258)------------------------------
% 63.83/10.31 % (29258)------------------------------
% 63.83/10.32 % (29268)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_28704 for (2912ds/2573Mi)
% 63.83/10.35 % (29244)Instruction limit reached!
% 63.83/10.35 % (29244)------------------------------
% 63.83/10.35 % (29244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.83/10.35 % (29244)Termination reason: Unknown
% 63.83/10.35 % (29244)Termination phase: Saturation
% 63.83/10.35
% 63.83/10.35 % (29244)Memory used [KB]: 17526
% 63.83/10.35 % (29244)Time elapsed: 2.169 s
% 63.83/10.35 % (29244)Instructions burned: 7258 (million)
% 63.83/10.35 % (29244)------------------------------
% 63.83/10.35 % (29244)------------------------------
% 63.83/10.36 % (29269)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_28704 for (2912ds/2655Mi)
% 64.23/10.44 % (29264)Instruction limit reached!
% 64.23/10.44 % (29264)------------------------------
% 64.23/10.44 % (29264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.23/10.44 % (29264)Termination reason: Unknown
% 64.23/10.44 % (29264)Termination phase: Saturation
% 64.23/10.44
% 64.23/10.44 % (29264)Memory used [KB]: 12153
% 64.23/10.44 % (29264)Time elapsed: 0.401 s
% 64.23/10.44 % (29264)Instructions burned: 1432 (million)
% 64.23/10.44 % (29264)------------------------------
% 64.23/10.44 % (29264)------------------------------
% 64.23/10.45 % (29270)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_28704 for (2911ds/2781Mi)
% 64.94/10.51 % (29260)Instruction limit reached!
% 64.94/10.51 % (29260)------------------------------
% 64.94/10.51 % (29260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.94/10.51 % (29260)Termination reason: Unknown
% 64.94/10.51 % (29260)Termination phase: Saturation
% 64.94/10.51
% 64.94/10.51 % (29260)Memory used [KB]: 12665
% 64.94/10.51 % (29260)Time elapsed: 0.808 s
% 64.94/10.51 % (29260)Instructions burned: 2680 (million)
% 64.94/10.51 % (29260)------------------------------
% 64.94/10.51 % (29260)------------------------------
% 64.94/10.52 % (29271)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_28704 for (2910ds/307Mi)
% 65.17/10.61 % (29271)Instruction limit reached!
% 65.17/10.61 % (29271)------------------------------
% 65.17/10.61 % (29271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.17/10.61 % (29271)Termination reason: Unknown
% 65.17/10.61 % (29271)Termination phase: Saturation
% 65.17/10.61
% 65.17/10.61 % (29271)Memory used [KB]: 7803
% 65.17/10.61 % (29271)Time elapsed: 0.090 s
% 65.17/10.61 % (29271)Instructions burned: 309 (million)
% 65.17/10.61 % (29271)------------------------------
% 65.17/10.61 % (29271)------------------------------
% 65.17/10.62 % (29272)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_28704 for (2909ds/1548Mi)
% 65.68/10.81 % (29263)Instruction limit reached!
% 65.68/10.81 % (29263)------------------------------
% 65.68/10.81 % (29263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.68/10.81 % (29263)Termination reason: Unknown
% 65.68/10.81 % (29263)Termination phase: Saturation
% 65.68/10.81
% 65.68/10.81 % (29263)Memory used [KB]: 12025
% 65.68/10.81 % (29263)Time elapsed: 0.814 s
% 65.68/10.81 % (29263)Instructions burned: 2547 (million)
% 65.68/10.81 % (29263)------------------------------
% 65.68/10.81 % (29263)------------------------------
% 65.68/10.82 % (29273)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_28704 for (2907ds/5214Mi)
% 65.68/10.87 % (29259)Instruction limit reached!
% 65.68/10.87 % (29259)------------------------------
% 65.68/10.87 % (29259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.68/10.87 % (29259)Termination reason: Unknown
% 65.68/10.87 % (29259)Termination phase: Saturation
% 65.68/10.87
% 65.68/10.87 % (29259)Memory used [KB]: 10362
% 65.68/10.87 % (29259)Time elapsed: 1.354 s
% 65.68/10.87 % (29259)Instructions burned: 4604 (million)
% 65.68/10.87 % (29259)------------------------------
% 65.68/10.87 % (29259)------------------------------
% 65.68/10.88 % (29274)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_28704 for (2906ds/3201Mi)
% 69.21/11.08 % (29272)Instruction limit reached!
% 69.21/11.08 % (29272)------------------------------
% 69.21/11.08 % (29272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.08 % (29272)Termination reason: Unknown
% 69.21/11.08 % (29272)Termination phase: Saturation
% 69.21/11.08
% 69.21/11.08 % (29272)Memory used [KB]: 10106
% 69.21/11.08 % (29272)Time elapsed: 0.455 s
% 69.21/11.08 % (29272)Instructions burned: 1550 (million)
% 69.21/11.08 % (29272)------------------------------
% 69.21/11.08 % (29272)------------------------------
% 69.21/11.09 % (29275)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_28704 for (2904ds/454Mi)
% 69.21/11.09 % (29268)Instruction limit reached!
% 69.21/11.09 % (29268)------------------------------
% 69.21/11.09 % (29268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.21/11.09 % (29268)Termination reason: Unknown
% 69.21/11.09 % (29268)Termination phase: Saturation
% 69.21/11.09
% 69.21/11.09 % (29268)Memory used [KB]: 12281
% 69.21/11.09 % (29268)Time elapsed: 0.775 s
% 69.21/11.09 % (29268)Instructions burned: 2576 (million)
% 69.21/11.09 % (29268)------------------------------
% 69.21/11.09 % (29268)------------------------------
% 69.21/11.10 % (29276)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_28704 for (2904ds/3049Mi)
% 69.85/11.15 % (29269)Instruction limit reached!
% 69.85/11.15 % (29269)------------------------------
% 69.85/11.15 % (29269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.85/11.15 % (29269)Termination reason: Unknown
% 69.85/11.15 % (29269)Termination phase: Saturation
% 69.85/11.15
% 69.85/11.15 % (29269)Memory used [KB]: 18166
% 69.85/11.15 % (29269)Time elapsed: 0.796 s
% 69.85/11.15 % (29269)Instructions burned: 2657 (million)
% 69.85/11.15 % (29269)------------------------------
% 69.85/11.15 % (29269)------------------------------
% 69.85/11.16 % (29277)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_28704 for (2904ds/7311Mi)
% 70.20/11.22 % (29275)Instruction limit reached!
% 70.20/11.22 % (29275)------------------------------
% 70.20/11.22 % (29275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.20/11.22 % (29275)Termination reason: Unknown
% 70.20/11.22 % (29275)Termination phase: Saturation
% 70.20/11.22
% 70.20/11.22 % (29275)Memory used [KB]: 13176
% 70.20/11.22 % (29275)Time elapsed: 0.132 s
% 70.20/11.22 % (29275)Instructions burned: 457 (million)
% 70.20/11.22 % (29275)------------------------------
% 70.20/11.22 % (29275)------------------------------
% 70.20/11.23 % (29278)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_28704 for (2903ds/6804Mi)
% 70.73/11.32 % (29270)Instruction limit reached!
% 70.73/11.32 % (29270)------------------------------
% 70.73/11.32 % (29270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.73/11.32 % (29270)Termination reason: Unknown
% 70.73/11.32 % (29270)Termination phase: Saturation
% 70.73/11.32
% 70.73/11.32 % (29270)Memory used [KB]: 6268
% 70.73/11.32 % (29270)Time elapsed: 0.869 s
% 70.73/11.32 % (29270)Instructions burned: 2783 (million)
% 70.73/11.32 % (29270)------------------------------
% 70.73/11.32 % (29270)------------------------------
% 70.73/11.33 % (29279)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_28704 for (2902ds/1683Mi)
% 72.29/11.86 % (29274)Instruction limit reached!
% 72.29/11.86 % (29274)------------------------------
% 72.29/11.86 % (29274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.29/11.86 % (29274)Termination reason: Unknown
% 72.29/11.86 % (29274)Termination phase: Saturation
% 72.29/11.86
% 72.29/11.86 % (29274)Memory used [KB]: 13176
% 72.29/11.86 % (29274)Time elapsed: 0.974 s
% 72.29/11.86 % (29274)Instructions burned: 3203 (million)
% 72.29/11.86 % (29274)------------------------------
% 72.29/11.86 % (29274)------------------------------
% 72.29/11.86 % (29279)Instruction limit reached!
% 72.29/11.86 % (29279)------------------------------
% 72.29/11.86 % (29279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.29/11.86 % (29279)Termination reason: Unknown
% 72.29/11.86 % (29279)Termination phase: Saturation
% 72.29/11.86
% 72.29/11.86 % (29279)Memory used [KB]: 10618
% 72.29/11.86 % (29279)Time elapsed: 0.553 s
% 72.29/11.86 % (29279)Instructions burned: 1685 (million)
% 72.29/11.86 % (29279)------------------------------
% 72.29/11.86 % (29279)------------------------------
% 72.29/11.87 % (29280)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_28704 for (2897ds/4688Mi)
% 72.29/11.87 % (29281)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_28704 for (2896ds/2207Mi)
% 73.09/12.01 % (29267)Instruction limit reached!
% 73.09/12.01 % (29267)------------------------------
% 73.09/12.01 % (29267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.09/12.01 % (29267)Termination reason: Unknown
% 73.09/12.01 % (29267)Termination phase: Saturation
% 73.09/12.01
% 73.09/12.01 % (29267)Memory used [KB]: 20084
% 73.09/12.01 % (29267)Time elapsed: 1.719 s
% 73.09/12.01 % (29267)Instructions burned: 5446 (million)
% 73.09/12.01 % (29267)------------------------------
% 73.09/12.01 % (29267)------------------------------
% 73.09/12.02 % (29282)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=8216:si=on:rtra=on_0 on DTF2THF_28704 for (2895ds/8216Mi)
% 76.22/12.06 % (29276)Instruction limit reached!
% 76.22/12.06 % (29276)------------------------------
% 76.22/12.06 % (29276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.22/12.06 % (29276)Termination reason: Unknown
% 76.22/12.06 % (29276)Termination phase: Saturation
% 76.22/12.06
% 76.22/12.06 % (29276)Memory used [KB]: 11513
% 76.22/12.06 % (29276)Time elapsed: 0.984 s
% 76.22/12.06 % (29276)Instructions burned: 3050 (million)
% 76.22/12.06 % (29276)------------------------------
% 76.22/12.06 % (29276)------------------------------
% 76.22/12.08 % (29283)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_28704 for (2894ds/430Mi)
% 76.77/12.20 % (29283)Instruction limit reached!
% 76.77/12.20 % (29283)------------------------------
% 76.77/12.20 % (29283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.77/12.20 % (29283)Termination reason: Unknown
% 76.77/12.20 % (29283)Termination phase: Saturation
% 76.77/12.20
% 76.77/12.20 % (29283)Memory used [KB]: 8699
% 76.77/12.20 % (29283)Time elapsed: 0.123 s
% 76.77/12.20 % (29283)Instructions burned: 430 (million)
% 76.77/12.20 % (29283)------------------------------
% 76.77/12.20 % (29283)------------------------------
% 77.13/12.21 % (29300)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_28704 for (2893ds/2012Mi)
% 77.78/12.36 % (29273)Refutation not found, non-redundant clauses discarded% (29273)------------------------------
% 77.78/12.36 % (29273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.78/12.36 % (29273)Termination reason: Refutation not found, non-redundant clauses discarded
% 77.78/12.36
% 77.78/12.36 % (29273)Memory used [KB]: 19317
% 77.78/12.36 % (29273)Time elapsed: 1.547 s
% 77.78/12.36 % (29273)Instructions burned: 5144 (million)
% 77.78/12.36 % (29273)------------------------------
% 77.78/12.36 % (29273)------------------------------
% 77.78/12.38 % (29301)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_28704 for (2891ds/631Mi)
% 78.65/12.56 % (29281)Instruction limit reached!
% 78.65/12.56 % (29281)------------------------------
% 78.65/12.56 % (29281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.65/12.56 % (29281)Termination reason: Unknown
% 78.65/12.56 % (29281)Termination phase: Saturation
% 78.65/12.56
% 78.65/12.56 % (29281)Memory used [KB]: 11385
% 78.65/12.56 % (29281)Time elapsed: 0.693 s
% 78.65/12.56 % (29281)Instructions burned: 2208 (million)
% 78.65/12.56 % (29281)------------------------------
% 78.65/12.56 % (29281)------------------------------
% 78.65/12.57 % (29302)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_28704 for (2890ds/8785Mi)
% 78.65/12.57 % (29301)Instruction limit reached!
% 78.65/12.57 % (29301)------------------------------
% 78.65/12.57 % (29301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.65/12.57 % (29301)Termination reason: Unknown
% 78.65/12.57 % (29301)Termination phase: Saturation
% 78.65/12.57
% 78.65/12.57 % (29301)Memory used [KB]: 10490
% 78.65/12.57 % (29301)Time elapsed: 0.200 s
% 78.65/12.57 % (29301)Instructions burned: 633 (million)
% 78.65/12.57 % (29301)------------------------------
% 78.65/12.57 % (29301)------------------------------
% 78.65/12.58 % (29303)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_28704 for (2889ds/739Mi)
% 79.83/12.82 % (29303)Instruction limit reached!
% 79.83/12.82 % (29303)------------------------------
% 79.83/12.82 % (29303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.83/12.82 % (29303)Termination reason: Unknown
% 79.83/12.82 % (29303)Termination phase: Saturation
% 79.83/12.82
% 79.83/12.82 % (29303)Memory used [KB]: 9722
% 79.83/12.82 % (29303)Time elapsed: 0.232 s
% 79.83/12.82 % (29303)Instructions burned: 740 (million)
% 79.83/12.82 % (29303)------------------------------
% 79.83/12.82 % (29303)------------------------------
% 79.83/12.82 % (29300)Instruction limit reached!
% 79.83/12.82 % (29300)------------------------------
% 79.83/12.82 % (29300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.83/12.82 % (29300)Termination reason: Unknown
% 79.83/12.82 % (29300)Termination phase: Saturation
% 79.83/12.82
% 79.83/12.82 % (29300)Memory used [KB]: 19957
% 79.83/12.82 % (29300)Time elapsed: 0.619 s
% 79.83/12.82 % (29300)Instructions burned: 2015 (million)
% 79.83/12.82 % (29300)------------------------------
% 79.83/12.82 % (29300)------------------------------
% 79.83/12.83 % (29304)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_28704 for (2887ds/5473Mi)
% 79.83/12.84 % (29305)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_28704 for (2887ds/43570Mi)
% 79.83/12.86 % (29305)Refutation not found, incomplete strategy
% 79.83/12.86 % (29305)------------------------------
% 79.83/12.86 % (29305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.83/12.86 % (29305)Termination reason: Refutation not found, incomplete strategy
% 79.83/12.86
% 79.83/12.86
% 79.83/12.86 % (29305)Memory used [KB]: 7036
% 79.83/12.86 % (29305)Time elapsed: 0.029 s
% 79.83/12.86 % (29305)Instructions burned: 88 (million)
% 79.83/12.86 % (29305)------------------------------
% 79.83/12.86 % (29305)------------------------------
% 79.83/12.87 % (29306)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_28704 for (2887ds/8382Mi)
% 83.96/13.19 % (29280)Instruction limit reached!
% 83.96/13.19 % (29280)------------------------------
% 83.96/13.19 % (29280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.96/13.19 % (29280)Termination reason: Unknown
% 83.96/13.19 % (29280)Termination phase: Saturation
% 83.96/13.19
% 83.96/13.19 % (29280)Memory used [KB]: 12281
% 83.96/13.19 % (29280)Time elapsed: 1.327 s
% 83.96/13.19 % (29280)Instructions burned: 4690 (million)
% 83.96/13.19 % (29280)------------------------------
% 83.96/13.19 % (29280)------------------------------
% 84.46/13.20 % (29307)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_28704 for (2883ds/407Mi)
% 84.46/13.29 % (29278)Instruction limit reached!
% 84.46/13.29 % (29278)------------------------------
% 84.46/13.29 % (29278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.46/13.29 % (29278)Termination reason: Unknown
% 84.46/13.29 % (29278)Termination phase: Saturation
% 84.46/13.29
% 84.46/13.29 % (29278)Memory used [KB]: 12537
% 84.46/13.29 % (29278)Time elapsed: 2.087 s
% 84.46/13.29 % (29278)Instructions burned: 6804 (million)
% 84.46/13.29 % (29278)------------------------------
% 84.46/13.29 % (29278)------------------------------
% 85.06/13.30 % (29308)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_28704 for (2882ds/2971Mi)
% 85.06/13.33 % (29307)Instruction limit reached!
% 85.06/13.33 % (29307)------------------------------
% 85.06/13.33 % (29307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.06/13.33 % (29307)Termination reason: Unknown
% 85.06/13.33 % (29307)Termination phase: Saturation
% 85.06/13.33
% 85.06/13.33 % (29307)Memory used [KB]: 8827
% 85.06/13.33 % (29307)Time elapsed: 0.128 s
% 85.06/13.33 % (29307)Instructions burned: 408 (million)
% 85.06/13.33 % (29307)------------------------------
% 85.06/13.33 % (29307)------------------------------
% 85.06/13.34 % (29309)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_28704 for (2882ds/9822Mi)
% 85.71/13.42 % (29277)Instruction limit reached!
% 85.71/13.42 % (29277)------------------------------
% 85.71/13.42 % (29277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.71/13.42 % (29277)Termination reason: Unknown
% 85.71/13.42 % (29277)Termination phase: Saturation
% 85.71/13.42
% 85.71/13.42 % (29277)Memory used [KB]: 14967
% 85.71/13.42 % (29277)Time elapsed: 2.274 s
% 85.71/13.42 % (29277)Instructions burned: 7311 (million)
% 85.71/13.42 % (29277)------------------------------
% 85.71/13.42 % (29277)------------------------------
% 85.71/13.43 % (29310)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_28704 for (2881ds/8425Mi)
% 90.98/14.15 % (29308)Instruction limit reached!
% 90.98/14.15 % (29308)------------------------------
% 90.98/14.15 % (29308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.98/14.15 % (29308)Termination reason: Unknown
% 90.98/14.15 % (29308)Termination phase: Saturation
% 90.98/14.15
% 90.98/14.15 % (29308)Memory used [KB]: 12409
% 90.98/14.15 % (29308)Time elapsed: 0.847 s
% 90.98/14.15 % (29308)Instructions burned: 2973 (million)
% 90.98/14.15 % (29308)------------------------------
% 90.98/14.15 % (29308)------------------------------
% 90.98/14.16 % (29312)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_28704 for (2874ds/3107Mi)
% 93.26/14.51 % (29282)Instruction limit reached!
% 93.26/14.51 % (29282)------------------------------
% 93.26/14.51 % (29282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.26/14.51 % (29282)Termination reason: Unknown
% 93.26/14.51 % (29282)Termination phase: Saturation
% 93.26/14.51
% 93.26/14.51 % (29282)Memory used [KB]: 12153
% 93.26/14.51 % (29282)Time elapsed: 2.497 s
% 93.26/14.51 % (29282)Instructions burned: 8218 (million)
% 93.26/14.51 % (29282)------------------------------
% 93.26/14.51 % (29282)------------------------------
% 93.26/14.52 % (29459)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_28704 for (2870ds/7967Mi)
% 93.26/14.56 % (29304)Instruction limit reached!
% 93.26/14.56 % (29304)------------------------------
% 93.26/14.56 % (29304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.26/14.56 % (29304)Termination reason: Unknown
% 93.26/14.56 % (29304)Termination phase: Saturation
% 93.26/14.56
% 93.26/14.56 % (29304)Memory used [KB]: 14967
% 93.26/14.56 % (29304)Time elapsed: 1.734 s
% 93.26/14.56 % (29304)Instructions burned: 5473 (million)
% 93.26/14.56 % (29304)------------------------------
% 93.26/14.56 % (29304)------------------------------
% 93.26/14.57 % (29474)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_28704 for (2869ds/3629Mi)
% 97.30/15.08 % (29312)Instruction limit reached!
% 97.30/15.08 % (29312)------------------------------
% 97.30/15.08 % (29312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.30/15.08 % (29312)Termination reason: Unknown
% 97.30/15.08 % (29312)Termination phase: Saturation
% 97.30/15.08
% 97.30/15.08 % (29312)Memory used [KB]: 21492
% 97.30/15.08 % (29312)Time elapsed: 0.921 s
% 97.30/15.08 % (29312)Instructions burned: 3107 (million)
% 97.30/15.08 % (29312)------------------------------
% 97.30/15.08 % (29312)------------------------------
% 97.30/15.09 % (29691)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_28704 for (2864ds/939Mi)
% 99.00/15.31 % (29302)Instruction limit reached!
% 99.00/15.31 % (29302)------------------------------
% 99.00/15.31 % (29302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.00/15.31 % (29302)Termination reason: Unknown
% 99.00/15.31 % (29302)Termination phase: Saturation
% 99.00/15.31
% 99.00/15.31 % (29302)Memory used [KB]: 17398
% 99.00/15.31 % (29302)Time elapsed: 2.737 s
% 99.00/15.31 % (29302)Instructions burned: 8787 (million)
% 99.00/15.31 % (29302)------------------------------
% 99.00/15.31 % (29302)------------------------------
% 99.00/15.32 % (29762)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_28704 for (2862ds/1188Mi)
% 99.00/15.38 % (29691)Instruction limit reached!
% 99.00/15.38 % (29691)------------------------------
% 99.00/15.38 % (29691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.00/15.38 % (29691)Termination reason: Unknown
% 99.00/15.38 % (29691)Termination phase: Saturation
% 99.00/15.38
% 99.00/15.38 % (29691)Memory used [KB]: 9338
% 99.00/15.38 % (29691)Time elapsed: 0.290 s
% 99.00/15.38 % (29691)Instructions burned: 940 (million)
% 99.00/15.38 % (29691)------------------------------
% 99.00/15.38 % (29691)------------------------------
% 99.00/15.39 % (29793)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_28704 for (2861ds/3205Mi)
% 99.83/15.46 % (29306)Instruction limit reached!
% 99.83/15.46 % (29306)------------------------------
% 99.83/15.46 % (29306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.83/15.46 % (29306)Termination reason: Unknown
% 99.83/15.46 % (29306)Termination phase: Saturation
% 99.83/15.46
% 99.83/15.46 % (29306)Memory used [KB]: 21108
% 99.83/15.46 % (29306)Time elapsed: 2.584 s
% 99.83/15.46 % (29306)Instructions burned: 8382 (million)
% 99.83/15.46 % (29306)------------------------------
% 99.83/15.46 % (29306)------------------------------
% 99.83/15.47 % (29833)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_28704 for (2861ds/865Mi)
% 100.69/15.65 % (29474)Instruction limit reached!
% 100.69/15.65 % (29474)------------------------------
% 100.69/15.65 % (29474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.69/15.65 % (29474)Termination reason: Unknown
% 100.69/15.65 % (29474)Termination phase: Saturation
% 100.69/15.65
% 100.69/15.65 % (29474)Memory used [KB]: 12920
% 100.69/15.65 % (29474)Time elapsed: 1.086 s
% 100.69/15.65 % (29474)Instructions burned: 3629 (million)
% 100.69/15.65 % (29474)------------------------------
% 100.69/15.65 % (29474)------------------------------
% 100.69/15.66 % (29901)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_28704 for (2859ds/7469Mi)
% 100.69/15.70 % (29762)Instruction limit reached!
% 100.69/15.70 % (29762)------------------------------
% 100.69/15.70 % (29762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.69/15.70 % (29762)Termination reason: Unknown
% 100.69/15.70 % (29762)Termination phase: Saturation
% 100.69/15.70
% 100.69/15.70 % (29762)Memory used [KB]: 9850
% 100.69/15.70 % (29762)Time elapsed: 0.380 s
% 100.69/15.70 % (29762)Instructions burned: 1189 (million)
% 100.69/15.70 % (29762)------------------------------
% 100.69/15.70 % (29762)------------------------------
% 101.05/15.71 % (29924)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_28704 for (2858ds/4165Mi)
% 101.05/15.75 % (29833)Instruction limit reached!
% 101.05/15.75 % (29833)------------------------------
% 101.05/15.75 % (29833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.05/15.75 % (29833)Termination reason: Unknown
% 101.05/15.75 % (29833)Termination phase: Saturation
% 101.05/15.75
% 101.05/15.75 % (29833)Memory used [KB]: 9978
% 101.05/15.75 % (29833)Time elapsed: 0.279 s
% 101.05/15.75 % (29833)Instructions burned: 866 (million)
% 101.05/15.75 % (29833)------------------------------
% 101.05/15.75 % (29833)------------------------------
% 101.05/15.76 % (29942)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_28704 for (2858ds/13468Mi)
% 102.34/15.97 % (29310)Instruction limit reached!
% 102.34/15.97 % (29310)------------------------------
% 102.34/15.97 % (29310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.34/15.97 % (29310)Termination reason: Unknown
% 102.34/15.97 % (29310)Termination phase: Saturation
% 102.34/15.97
% 102.34/15.97 % (29310)Memory used [KB]: 13944
% 102.34/15.97 % (29310)Time elapsed: 2.545 s
% 102.34/15.97 % (29310)Instructions burned: 8425 (million)
% 102.34/15.97 % (29310)------------------------------
% 102.34/15.97 % (29310)------------------------------
% 102.34/15.98 % (29943)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_28704 for (2855ds/2635Mi)
% 105.51/16.21 % (29459)Instruction limit reached!
% 105.51/16.21 % (29459)------------------------------
% 105.51/16.21 % (29459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.51/16.21 % (29459)Termination reason: Unknown
% 105.51/16.21 % (29459)Termination phase: Saturation
% 105.51/16.21
% 105.51/16.21 % (29459)Memory used [KB]: 12281
% 105.51/16.21 % (29459)Time elapsed: 1.683 s
% 105.51/16.21 % (29459)Instructions burned: 7969 (million)
% 105.51/16.21 % (29459)------------------------------
% 105.51/16.21 % (29459)------------------------------
% 105.51/16.22 % (29944)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_28704 for (2853ds/631Mi)
% 106.13/16.31 % (29309)Instruction limit reached!
% 106.13/16.31 % (29309)------------------------------
% 106.13/16.31 % (29309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.13/16.31 % (29309)Termination reason: Unknown
% 106.13/16.31 % (29309)Termination phase: Saturation
% 106.13/16.31
% 106.13/16.31 % (29309)Memory used [KB]: 22003
% 106.13/16.31 % (29309)Time elapsed: 2.972 s
% 106.13/16.31 % (29309)Instructions burned: 9823 (million)
% 106.13/16.31 % (29309)------------------------------
% 106.13/16.31 % (29309)------------------------------
% 106.13/16.32 % (29945)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_28704 for (2852ds/15557Mi)
% 106.13/16.38 % (29793)Instruction limit reached!
% 106.13/16.38 % (29793)------------------------------
% 106.13/16.38 % (29793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.13/16.38 % (29793)Termination reason: Unknown
% 106.13/16.38 % (29793)Termination phase: Saturation
% 106.13/16.38
% 106.13/16.38 % (29793)Memory used [KB]: 14456
% 106.13/16.38 % (29793)Time elapsed: 0.992 s
% 106.13/16.38 % (29793)Instructions burned: 3207 (million)
% 106.13/16.38 % (29793)------------------------------
% 106.13/16.38 % (29793)------------------------------
% 106.13/16.39 % (29946)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_28704 for (2851ds/2142Mi)
% 106.67/16.40 % (29944)Instruction limit reached!
% 106.67/16.40 % (29944)------------------------------
% 106.67/16.40 % (29944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.67/16.40 % (29944)Termination reason: Unknown
% 106.67/16.40 % (29944)Termination phase: Saturation
% 106.67/16.40
% 106.67/16.40 % (29944)Memory used [KB]: 9850
% 106.67/16.40 % (29944)Time elapsed: 0.184 s
% 106.67/16.40 % (29944)Instructions burned: 631 (million)
% 106.67/16.40 % (29944)------------------------------
% 106.67/16.40 % (29944)------------------------------
% 106.67/16.41 % (29947)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_28704 for (2851ds/5624Mi)
% 108.46/16.81 % (29943)Instruction limit reached!
% 108.46/16.81 % (29943)------------------------------
% 108.46/16.81 % (29943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.46/16.81 % (29943)Termination reason: Unknown
% 108.46/16.81 % (29943)Termination phase: Saturation
% 108.46/16.81
% 108.46/16.81 % (29943)Memory used [KB]: 14839
% 108.46/16.81 % (29943)Time elapsed: 0.830 s
% 108.46/16.81 % (29943)Instructions burned: 2635 (million)
% 108.46/16.81 % (29943)------------------------------
% 108.46/16.81 % (29943)------------------------------
% 108.46/16.82 % (29948)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_28704 for (2847ds/1665Mi)
% 108.79/17.01 % (29924)Instruction limit reached!
% 108.79/17.01 % (29924)------------------------------
% 108.79/17.01 % (29924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.79/17.01 % (29924)Termination reason: Unknown
% 108.79/17.01 % (29924)Termination phase: Saturation
% 108.79/17.01
% 108.79/17.01 % (29924)Memory used [KB]: 16758
% 108.79/17.01 % (29924)Time elapsed: 1.303 s
% 108.79/17.01 % (29924)Instructions burned: 4166 (million)
% 108.79/17.01 % (29924)------------------------------
% 108.79/17.01 % (29924)------------------------------
% 108.79/17.02 % (29949)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_28704 for (2845ds/64912Mi)
% 111.32/17.04 % (29949)Refutation not found, incomplete strategy
% 111.32/17.04 % (29949)------------------------------
% 111.32/17.04 % (29949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.32/17.04 % (29949)Termination reason: Refutation not found, incomplete strategy
% 111.32/17.04
% 111.32/17.04
% 111.32/17.04 % (29949)Memory used [KB]: 2302
% 111.32/17.04 % (29949)Time elapsed: 0.042 s
% 111.32/17.04 % (29949)Instructions burned: 59 (million)
% 111.32/17.04 % (29949)------------------------------
% 111.32/17.04 % (29949)------------------------------
% 111.32/17.05 % (29950)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_28704 for (2845ds/7801Mi)
% 111.32/17.07 % (29946)Instruction limit reached!
% 111.32/17.07 % (29946)------------------------------
% 111.32/17.07 % (29946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.32/17.07 % (29946)Termination reason: Unknown
% 111.32/17.07 % (29946)Termination phase: Saturation
% 111.32/17.07
% 111.32/17.07 % (29946)Memory used [KB]: 10234
% 111.32/17.07 % (29946)Time elapsed: 0.679 s
% 111.32/17.07 % (29946)Instructions burned: 2143 (million)
% 111.32/17.07 % (29946)------------------------------
% 111.32/17.07 % (29946)------------------------------
% 111.32/17.08 % (29951)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_28704 for (2844ds/15194Mi)
% 112.78/17.32 % (29948)Instruction limit reached!
% 112.78/17.32 % (29948)------------------------------
% 112.78/17.32 % (29948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.78/17.32 % (29948)Termination reason: Unknown
% 112.78/17.32 % (29948)Termination phase: Saturation
% 112.78/17.32
% 112.78/17.32 % (29948)Memory used [KB]: 11897
% 112.78/17.32 % (29948)Time elapsed: 0.500 s
% 112.78/17.32 % (29948)Instructions burned: 1667 (million)
% 112.78/17.32 % (29948)------------------------------
% 112.78/17.32 % (29948)------------------------------
% 112.78/17.33 % (29952)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_28704 for (2842ds/6753Mi)
% 115.22/17.92 % (29901)Instruction limit reached!
% 115.22/17.92 % (29901)------------------------------
% 115.22/17.92 % (29901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.22/17.92 % (29901)Termination reason: Unknown
% 115.22/17.92 % (29901)Termination phase: Saturation
% 115.22/17.92
% 115.22/17.92 % (29901)Memory used [KB]: 12537
% 115.22/17.92 % (29901)Time elapsed: 2.257 s
% 115.22/17.92 % (29901)Instructions burned: 7472 (million)
% 115.22/17.92 % (29901)------------------------------
% 115.22/17.92 % (29901)------------------------------
% 115.22/17.93 % (29953)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_28704 for (2836ds/1003Mi)
% 119.03/18.14 % (29947)Instruction limit reached!
% 119.03/18.14 % (29947)------------------------------
% 119.03/18.14 % (29947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.03/18.14 % (29947)Termination reason: Unknown
% 119.03/18.14 % (29947)Termination phase: Saturation
% 119.03/18.14
% 119.03/18.14 % (29947)Memory used [KB]: 13560
% 119.03/18.14 % (29947)Time elapsed: 1.729 s
% 119.03/18.14 % (29947)Instructions burned: 5624 (million)
% 119.03/18.14 % (29947)------------------------------
% 119.03/18.14 % (29947)------------------------------
% 119.03/18.15 % (29954)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_28704 for (2834ds/13018Mi)
% 119.52/18.22 % (29953)Instruction limit reached!
% 119.52/18.22 % (29953)------------------------------
% 119.52/18.22 % (29953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.52/18.22 % (29953)Termination reason: Unknown
% 119.52/18.22 % (29953)Termination phase: Saturation
% 119.52/18.22
% 119.52/18.22 % (29953)Memory used [KB]: 8571
% 119.52/18.22 % (29953)Time elapsed: 0.286 s
% 119.52/18.22 % (29953)Instructions burned: 1004 (million)
% 119.52/18.22 % (29953)------------------------------
% 119.52/18.22 % (29953)------------------------------
% 119.52/18.23 % (29955)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_28704 for (2833ds/1267Mi)
% 121.55/18.62 % (29955)Instruction limit reached!
% 121.55/18.62 % (29955)------------------------------
% 121.55/18.62 % (29955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.55/18.62 % (29955)Termination reason: Unknown
% 121.55/18.62 % (29955)Termination phase: Saturation
% 121.55/18.62
% 121.55/18.62 % (29955)Memory used [KB]: 8955
% 121.55/18.62 % (29955)Time elapsed: 0.391 s
% 121.55/18.62 % (29955)Instructions burned: 1270 (million)
% 121.55/18.62 % (29955)------------------------------
% 121.55/18.62 % (29955)------------------------------
% 121.55/18.63 % (29956)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_28704 for (2829ds/2570Mi)
% 125.36/19.08 % (29952)Instruction limit reached!
% 125.36/19.08 % (29952)------------------------------
% 125.36/19.08 % (29952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.36/19.08 % (29952)Termination reason: Unknown
% 125.36/19.08 % (29952)Termination phase: Saturation
% 125.36/19.08
% 125.36/19.08 % (29952)Memory used [KB]: 23283
% 125.36/19.08 % (29952)Time elapsed: 1.745 s
% 125.36/19.08 % (29952)Instructions burned: 6755 (million)
% 125.36/19.08 % (29952)------------------------------
% 125.36/19.08 % (29952)------------------------------
% 125.36/19.09 % (29957)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_28704 for (2824ds/13163Mi)
% 127.06/19.37 % (29956)Instruction limit reached!
% 127.06/19.37 % (29956)------------------------------
% 127.06/19.37 % (29956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.06/19.37 % (29956)Termination reason: Unknown
% 127.06/19.37 % (29956)Termination phase: Saturation
% 127.06/19.37
% 127.06/19.37 % (29956)Memory used [KB]: 10874
% 127.06/19.37 % (29956)Time elapsed: 0.747 s
% 127.06/19.37 % (29956)Instructions burned: 2572 (million)
% 127.06/19.37 % (29956)------------------------------
% 127.06/19.37 % (29956)------------------------------
% 127.06/19.38 % (29958)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_28704 for (2821ds/5087Mi)
% 127.65/19.44 % (29950)Instruction limit reached!
% 127.65/19.44 % (29950)------------------------------
% 127.65/19.44 % (29950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.65/19.44 % (29950)Termination reason: Unknown
% 127.65/19.44 % (29950)Termination phase: Saturation
% 127.65/19.44
% 127.65/19.44 % (29950)Memory used [KB]: 12665
% 127.65/19.44 % (29950)Time elapsed: 2.393 s
% 127.65/19.44 % (29950)Instructions burned: 7801 (million)
% 127.65/19.44 % (29950)------------------------------
% 127.65/19.44 % (29950)------------------------------
% 127.65/19.45 % (29959)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_28704 for (2821ds/10380Mi)
% 129.72/20.00 % (29942)Instruction limit reached!
% 129.72/20.00 % (29942)------------------------------
% 129.72/20.00 % (29942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 129.72/20.00 % (29942)Termination reason: Unknown
% 129.72/20.00 % (29942)Termination phase: Saturation
% 129.72/20.00
% 129.72/20.00 % (29942)Memory used [KB]: 26225
% 129.72/20.00 % (29942)Time elapsed: 4.249 s
% 129.72/20.00 % (29942)Instructions burned: 13469 (million)
% 129.72/20.00 % (29942)------------------------------
% 129.72/20.00 % (29942)------------------------------
% 129.72/20.02 % (29960)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_28704 for (2815ds/4218Mi)
% 137.62/20.92 % (29960)Refutation not found, non-redundant clauses discarded% (29960)------------------------------
% 137.62/20.92 % (29960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.62/20.92 % (29960)Termination reason: Refutation not found, non-redundant clauses discarded
% 137.62/20.92
% 137.62/20.92 % (29960)Memory used [KB]: 8827
% 137.62/20.92 % (29960)Time elapsed: 0.908 s
% 137.62/20.92 % (29960)Instructions burned: 3002 (million)
% 137.62/20.92 % (29960)------------------------------
% 137.62/20.92 % (29960)------------------------------
% 137.62/20.93 % (29961)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_28704 for (2806ds/3971Mi)
% 137.62/20.96 % (29945)Instruction limit reached!
% 137.62/20.96 % (29945)------------------------------
% 137.62/20.96 % (29945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.62/20.96 % (29945)Termination reason: Unknown
% 137.62/20.96 % (29945)Termination phase: Saturation
% 137.62/20.96
% 137.62/20.96 % (29945)Memory used [KB]: 23027
% 137.62/20.96 % (29945)Time elapsed: 4.636 s
% 137.62/20.96 % (29945)Instructions burned: 15557 (million)
% 137.62/20.96 % (29945)------------------------------
% 137.62/20.96 % (29945)------------------------------
% 137.62/20.96 % (29958)Instruction limit reached!
% 137.62/20.96 % (29958)------------------------------
% 137.62/20.96 % (29958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.62/20.96 % (29958)Termination reason: Unknown
% 137.62/20.96 % (29958)Termination phase: Saturation
% 137.62/20.96
% 137.62/20.96 % (29958)Memory used [KB]: 14072
% 137.62/20.96 % (29958)Time elapsed: 1.584 s
% 137.62/20.96 % (29958)Instructions burned: 5087 (million)
% 137.62/20.96 % (29958)------------------------------
% 137.62/20.96 % (29958)------------------------------
% 137.62/20.97 % (29962)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_28704 for (2806ds/14014Mi)
% 137.62/20.97 % (29963)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_28704 for (2806ds/8517Mi)
% 144.83/21.80 % (29951)Instruction limit reached!
% 144.83/21.80 % (29951)------------------------------
% 144.83/21.80 % (29951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 144.83/21.80 % (29951)Termination reason: Unknown
% 144.83/21.80 % (29951)Termination phase: Saturation
% 144.83/21.80
% 144.83/21.80 % (29951)Memory used [KB]: 21748
% 144.83/21.80 % (29951)Time elapsed: 4.724 s
% 144.83/21.80 % (29951)Instructions burned: 15196 (million)
% 144.83/21.80 % (29951)------------------------------
% 144.83/21.80 % (29951)------------------------------
% 144.83/21.81 % (29964)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_28704 for (2797ds/10148Mi)
% 146.41/22.02 % (29961)Instruction limit reached!
% 146.41/22.02 % (29961)------------------------------
% 146.41/22.02 % (29961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.41/22.02 % (29961)Termination reason: Unknown
% 146.41/22.02 % (29961)Termination phase: Saturation
% 146.41/22.02
% 146.41/22.02 % (29961)Memory used [KB]: 11257
% 146.41/22.02 % (29961)Time elapsed: 1.093 s
% 146.41/22.02 % (29961)Instructions burned: 3971 (million)
% 146.41/22.02 % (29961)------------------------------
% 146.41/22.02 % (29961)------------------------------
% 146.41/22.04 % (29965)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_28704 for (2795ds/9078Mi)
% 147.04/22.18 % (29954)Instruction limit reached!
% 147.04/22.18 % (29954)------------------------------
% 147.04/22.18 % (29954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.04/22.18 % (29954)Termination reason: Unknown
% 147.04/22.18 % (29954)Termination phase: Saturation
% 147.04/22.18
% 147.04/22.18 % (29954)Memory used [KB]: 31726
% 147.04/22.18 % (29954)Time elapsed: 4.036 s
% 147.04/22.18 % (29954)Instructions burned: 13019 (million)
% 147.04/22.18 % (29954)------------------------------
% 147.04/22.18 % (29954)------------------------------
% 147.04/22.19 % (29966)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_28704 for (2793ds/16164Mi)
% 147.98/22.35 % (29959)Instruction limit reached!
% 147.98/22.35 % (29959)------------------------------
% 147.98/22.35 % (29959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.98/22.35 % (29959)Termination reason: Unknown
% 147.98/22.35 % (29959)Termination phase: Saturation
% 147.98/22.35
% 147.98/22.35 % (29959)Memory used [KB]: 10490
% 147.98/22.35 % (29959)Time elapsed: 2.904 s
% 147.98/22.35 % (29959)Instructions burned: 10381 (million)
% 147.98/22.35 % (29959)------------------------------
% 147.98/22.35 % (29959)------------------------------
% 147.98/22.36 % (29967)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_28704 for (2792ds/6102Mi)
% 153.42/23.06 % (29957)Instruction limit reached!
% 153.42/23.06 % (29957)------------------------------
% 153.42/23.06 % (29957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.42/23.06 % (29957)Termination reason: Unknown
% 153.42/23.06 % (29957)Termination phase: Saturation
% 153.42/23.06
% 153.42/23.06 % (29957)Memory used [KB]: 23283
% 153.42/23.06 % (29957)Time elapsed: 3.968 s
% 153.42/23.06 % (29957)Instructions burned: 13164 (million)
% 153.42/23.06 % (29957)------------------------------
% 153.42/23.06 % (29957)------------------------------
% 153.42/23.07 % (29968)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_28704 for (2785ds/10308Mi)
% 156.31/23.52 % (29963)Instruction limit reached!
% 156.31/23.52 % (29963)------------------------------
% 156.31/23.52 % (29963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.31/23.52 % (29963)Termination reason: Unknown
% 156.31/23.52 % (29963)Termination phase: Saturation
% 156.31/23.52
% 156.31/23.52 % (29963)Memory used [KB]: 20084
% 156.31/23.52 % (29963)Time elapsed: 2.546 s
% 156.31/23.52 % (29963)Instructions burned: 8519 (million)
% 156.31/23.52 % (29963)------------------------------
% 156.31/23.52 % (29963)------------------------------
% 156.31/23.53 % (29969)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_28704 for (2780ds/4041Mi)
% 160.47/24.10 % (29967)Instruction limit reached!
% 160.47/24.10 % (29967)------------------------------
% 160.47/24.10 % (29967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 160.47/24.10 % (29967)Termination reason: Unknown
% 160.47/24.10 % (29967)Termination phase: Saturation
% 160.47/24.10
% 160.47/24.10 % (29967)Memory used [KB]: 31342
% 160.47/24.10 % (29967)Time elapsed: 1.734 s
% 160.47/24.10 % (29967)Instructions burned: 6104 (million)
% 160.47/24.10 % (29967)------------------------------
% 160.47/24.10 % (29967)------------------------------
% 160.47/24.11 % (29970)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_28704 for (2774ds/6901Mi)
% 164.60/24.73 % (29965)Instruction limit reached!
% 164.60/24.73 % (29965)------------------------------
% 164.60/24.73 % (29965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.60/24.73 % (29965)Termination reason: Unknown
% 164.60/24.73 % (29965)Termination phase: Saturation
% 164.60/24.73
% 164.60/24.73 % (29965)Memory used [KB]: 23283
% 164.60/24.73 % (29965)Time elapsed: 2.700 s
% 164.60/24.73 % (29965)Instructions burned: 9080 (million)
% 164.60/24.73 % (29965)------------------------------
% 164.60/24.73 % (29965)------------------------------
% 164.60/24.74 % (29969)Instruction limit reached!
% 164.60/24.74 % (29969)------------------------------
% 164.60/24.74 % (29969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.60/24.74 % (29969)Termination reason: Unknown
% 164.60/24.74 % (29969)Termination phase: Saturation
% 164.60/24.74
% 164.60/24.74 % (29969)Memory used [KB]: 11513
% 164.60/24.74 % (29969)Time elapsed: 1.214 s
% 164.60/24.74 % (29969)Instructions burned: 4042 (million)
% 164.60/24.74 % (29969)------------------------------
% 164.60/24.74 % (29969)------------------------------
% 164.60/24.75 % (29972)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_28704 for (2768ds/5576Mi)
% 164.60/24.75 % (29973)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_28704 for (2768ds/2014Mi)
% 164.60/24.79 % (29964)Instruction limit reached!
% 164.60/24.79 % (29964)------------------------------
% 164.60/24.79 % (29964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.60/24.79 % (29964)Termination reason: Unknown
% 164.60/24.79 % (29964)Termination phase: Saturation
% 164.60/24.79
% 164.60/24.79 % (29964)Memory used [KB]: 14839
% 164.60/24.79 % (29964)Time elapsed: 2.977 s
% 164.60/24.79 % (29964)Instructions burned: 10148 (million)
% 164.60/24.79 % (29964)------------------------------
% 164.60/24.79 % (29964)------------------------------
% 165.11/24.80 % (29974)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_28704 for (2767ds/5115Mi)
% 169.38/25.31 % (29962)Instruction limit reached!
% 169.38/25.31 % (29962)------------------------------
% 169.38/25.31 % (29962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.38/25.31 % (29962)Termination reason: Unknown
% 169.38/25.31 % (29962)Termination phase: Saturation
% 169.38/25.31
% 169.38/25.31 % (29962)Memory used [KB]: 31598
% 169.38/25.31 % (29962)Time elapsed: 4.340 s
% 169.38/25.31 % (29962)Instructions burned: 14016 (million)
% 169.38/25.31 % (29962)------------------------------
% 169.38/25.31 % (29962)------------------------------
% 169.38/25.32 % (29975)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_28704 for (2762ds/13001Mi)
% 169.38/25.38 % (29973)Instruction limit reached!
% 169.38/25.38 % (29973)------------------------------
% 169.38/25.38 % (29973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.38/25.38 % (29973)Termination reason: Unknown
% 169.38/25.38 % (29973)Termination phase: Saturation
% 169.38/25.38
% 169.38/25.38 % (29973)Memory used [KB]: 15607
% 169.38/25.38 % (29973)Time elapsed: 0.626 s
% 169.38/25.38 % (29973)Instructions burned: 2014 (million)
% 169.38/25.38 % (29973)------------------------------
% 169.38/25.38 % (29973)------------------------------
% 169.38/25.39 % (29976)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_28704 for (2761ds/11105Mi)
% 175.72/26.26 % (29970)Instruction limit reached!
% 175.72/26.26 % (29970)------------------------------
% 175.72/26.26 % (29970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.72/26.26 % (29970)Termination reason: Unknown
% 175.72/26.26 % (29970)Termination phase: Saturation
% 175.72/26.26
% 175.72/26.26 % (29970)Memory used [KB]: 19189
% 175.72/26.26 % (29970)Time elapsed: 2.150 s
% 175.72/26.26 % (29970)Instructions burned: 6904 (million)
% 175.72/26.26 % (29970)------------------------------
% 175.72/26.26 % (29970)------------------------------
% 175.72/26.27 % (29977)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=13832:si=on:rtra=on_0 on DTF2THF_28704 for (2752ds/13832Mi)
% 175.72/26.29 % (29974)Instruction limit reached!
% 175.72/26.29 % (29974)------------------------------
% 175.72/26.29 % (29974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.72/26.29 % (29974)Termination reason: Unknown
% 175.72/26.29 % (29974)Termination phase: Saturation
% 175.72/26.29
% 175.72/26.29 % (29974)Memory used [KB]: 26481
% 175.72/26.29 % (29974)Time elapsed: 1.486 s
% 175.72/26.29 % (29974)Instructions burned: 5117 (million)
% 175.72/26.29 % (29974)------------------------------
% 175.72/26.29 % (29974)------------------------------
% 175.72/26.30 % (29978)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on DTF2THF_28704 for (2752ds/32887Mi)
% 176.40/26.30 % (29968)Refutation not found, non-redundant clauses discarded% (29968)------------------------------
% 176.40/26.30 % (29968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.40/26.30 % (29968)Termination reason: Refutation not found, non-redundant clauses discarded
% 176.40/26.30
% 176.40/26.30 % (29968)Memory used [KB]: 16247
% 176.40/26.30 % (29968)Time elapsed: 3.236 s
% 176.40/26.30 % (29968)Instructions burned: 10301 (million)
% 176.40/26.30 % (29968)------------------------------
% 176.40/26.30 % (29968)------------------------------
% 176.40/26.31 % (29979)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on DTF2THF_28704 for (2752ds/3362Mi)
% 176.81/26.49 % (29972)Instruction limit reached!
% 176.81/26.49 % (29972)------------------------------
% 176.81/26.49 % (29972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.81/26.49 % (29972)Termination reason: Unknown
% 176.81/26.49 % (29972)Termination phase: Saturation
% 176.81/26.49
% 176.81/26.49 % (29972)Memory used [KB]: 13560
% 176.81/26.49 % (29972)Time elapsed: 1.749 s
% 176.81/26.49 % (29972)Instructions burned: 5576 (million)
% 176.81/26.49 % (29972)------------------------------
% 176.81/26.49 % (29972)------------------------------
% 177.22/26.50 % (29980)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on DTF2THF_28704 for (2750ds/24965Mi)
% 177.83/26.76 % (29966)Instruction limit reached!
% 177.83/26.76 % (29966)------------------------------
% 177.83/26.76 % (29966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 177.83/26.76 % (29966)Termination reason: Unknown
% 177.83/26.76 % (29966)Termination phase: Saturation
% 177.83/26.76
% 177.83/26.76 % (29966)Memory used [KB]: 19829
% 177.83/26.76 % (29966)Time elapsed: 4.563 s
% 177.83/26.76 % (29966)Instructions burned: 16164 (million)
% 177.83/26.76 % (29966)------------------------------
% 177.83/26.76 % (29966)------------------------------
% 177.83/26.77 % (29981)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on DTF2THF_28704 for (2747ds/15705Mi)
% 182.75/27.20 % (29980)First to succeed.
% 182.75/27.21 % (29980)Refutation found. Thanks to Tanya!
% 182.75/27.21 % SZS status Theorem for DTF2THF_28704
% 182.75/27.21 % SZS output start Proof for DTF2THF_28704
% 182.75/27.21 thf(type_def_5, type, itself: ($tType) > $tType).
% 182.75/27.21 thf(type_def_7, type, list: ($tType) > $tType).
% 182.75/27.21 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 182.75/27.21 thf(type_def_9, type, set: ($tType) > $tType).
% 182.75/27.21 thf(type_def_10, type, nat: $tType).
% 182.75/27.21 thf(type_def_11, type, tree: ($tType) > $tType).
% 182.75/27.21 thf(type_def_12, type, splay_2011811431op_s_t: ($tType) > $tType).
% 182.75/27.21 thf(type_def_13, type, a: $tType).
% 182.75/27.21 thf(func_def_0, type, splay_2011811431op_s_t: ($tType) > $tType).
% 182.75/27.21 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 182.75/27.21 thf(func_def_2, type, tree: ($tType) > $tType).
% 182.75/27.21 thf(func_def_3, type, list: ($tType) > $tType).
% 182.75/27.21 thf(func_def_4, type, set: ($tType) > $tType).
% 182.75/27.21 thf(func_def_5, type, nat: $tType).
% 182.75/27.21 thf(func_def_6, type, itself: ($tType) > $tType).
% 182.75/27.21 thf(func_def_7, type, a: $tType).
% 182.75/27.21 thf(func_def_8, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_9, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_11, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_12, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_13, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_14, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_15, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_16, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_17, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_18, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_19, type, semiring_numeral_div: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_20, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_21, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_22, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_23, type, condit1037483654norder: !>[X0: $tType]:(itself @ X0 > $o)).
% 182.75/27.21 thf(func_def_24, type, one_one: !>[X0: $tType]:(X0)).
% 182.75/27.21 thf(func_def_25, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 182.75/27.21 thf(func_def_26, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 182.75/27.21 thf(func_def_27, type, distinct: !>[X0: $tType]:(list @ X0 > $o)).
% 182.75/27.21 thf(func_def_28, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 182.75/27.21 thf(func_def_29, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 182.75/27.21 thf(func_def_30, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 182.75/27.21 thf(func_def_31, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2)).
% 182.75/27.21 thf(func_def_32, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 182.75/27.21 thf(func_def_33, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 182.75/27.21 thf(func_def_34, type, type2: !>[X0: $tType]:(itself @ X0)).
% 182.75/27.21 thf(func_def_35, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 182.75/27.21 thf(func_def_36, type, set_fo292404081st_nat: !>[X0: $tType]:((nat > X0 > X0) > nat > nat > X0 > X0)).
% 182.75/27.21 thf(func_def_37, type, set_fo2092542664at_rel: !>[X0: $tType]:(product_prod @ (nat > X0 > X0) @ product_prod @ nat @ product_prod @ nat @ X0 > product_prod @ (nat > X0 > X0) @ product_prod @ nat @ product_prod @ nat @ X0 > $o)).
% 182.75/27.21 thf(func_def_38, type, splay_delete: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_39, type, splay_insert: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_40, type, splay_is_root: !>[X0: $tType]:(X0 > tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_41, type, splay_splay: !>[X0: $tType]:(X0 > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_42, type, splay_splay_max: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_43, type, splay_splay_rel: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > product_prod @ X0 @ tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_44, type, splay_859309299xt_s_t: !>[X0: $tType]:(splay_2011811431op_s_t @ X0 > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_45, type, splay_1102316486_t_rel: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_46, type, splay_705249169Delete: !>[X0: $tType]:(X0 > splay_2011811431op_s_t @ X0)).
% 182.75/27.21 thf(func_def_47, type, splay_1105473951Insert: !>[X0: $tType]:(X0 > splay_2011811431op_s_t @ X0)).
% 182.75/27.21 thf(func_def_48, type, splay_2088287777_Splay: !>[X0: $tType]:(X0 > splay_2011811431op_s_t @ X0)).
% 182.75/27.21 thf(func_def_49, type, splay_549499974op_s_t: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > (X0 > X1) > splay_2011811431op_s_t @ X0 > X1)).
% 182.75/27.21 thf(func_def_50, type, splay_2144473850op_s_t: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > (X0 > X1) > splay_2011811431op_s_t @ X0 > X1)).
% 182.75/27.21 thf(func_def_51, type, splay_434753539op_s_t: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > splay_2011811431op_s_t @ X0 > splay_2011811431op_s_t @ X1 > $o)).
% 182.75/27.21 thf(func_def_52, type, splay_1816468620op_s_t: !>[X0: $tType]:(splay_2011811431op_s_t @ X0 > set @ X0)).
% 182.75/27.21 thf(func_def_53, type, splay_914434265_splay: !>[X0: $tType]:(X0 > tree @ X0 > nat)).
% 182.75/27.21 thf(func_def_54, type, splay_878424299ay_max: !>[X0: $tType]:(tree @ X0 > nat)).
% 182.75/27.21 thf(func_def_55, type, splay_1816415694ax_rel: !>[X0: $tType]:(tree @ X0 > tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_56, type, inorder: !>[X0: $tType]:(tree @ X0 > list @ X0)).
% 182.75/27.21 thf(func_def_57, type, linorder_bst: !>[X0: $tType]:(tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_58, type, linorder_bst_eq: !>[X0: $tType]:(tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_59, type, linorder_bst_eq_rel: !>[X0: $tType]:(tree @ X0 > tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_60, type, linorder_bst_rel: !>[X0: $tType]:(tree @ X0 > tree @ X0 > $o)).
% 182.75/27.21 thf(func_def_61, type, preorder2: !>[X0: $tType]:(tree @ X0 > list @ X0)).
% 182.75/27.21 thf(func_def_62, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 182.75/27.21 thf(func_def_63, type, node: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_64, type, set_tree: !>[X0: $tType]:(tree @ X0 > set @ X0)).
% 182.75/27.21 thf(func_def_65, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 182.75/27.21 thf(func_def_66, type, lex_prod: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 182.75/27.21 thf(func_def_67, type, measure: !>[X0: $tType]:((X0 > nat) > set @ product_prod @ X0 @ X0)).
% 182.75/27.21 thf(func_def_68, type, same_fst: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1)).
% 182.75/27.21 thf(func_def_69, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 182.75/27.21 thf(func_def_70, type, a2: tree @ a).
% 182.75/27.21 thf(func_def_71, type, f: splay_2011811431op_s_t @ a).
% 182.75/27.21 thf(func_def_93, type, sK1: (nat > nat) > nat).
% 182.75/27.21 thf(func_def_94, type, sK2: (nat > nat) > nat).
% 182.75/27.21 thf(func_def_95, type, sK3: !>[X0: $tType, X1: $tType]:((splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > (X1 > X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_96, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_97, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_98, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_99, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_100, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (splay_2011811431op_s_t @ X1 > splay_2011811431op_s_t @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_101, type, sK9: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_102, type, sK10: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_103, type, sK11: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_104, type, sK12: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_105, type, sK13: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_106, type, sK14: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_107, type, sK15: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_108, type, sK16: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_109, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X2)).
% 182.75/27.21 thf(func_def_110, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X4)).
% 182.75/27.21 thf(func_def_111, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X3)).
% 182.75/27.21 thf(func_def_112, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X2)).
% 182.75/27.21 thf(func_def_113, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X0)).
% 182.75/27.21 thf(func_def_114, type, sK22: !>[X0: $tType]:(splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_115, type, sK23: !>[X0: $tType]:(splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_116, type, sK24: !>[X0: $tType]:(splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_117, type, sK25: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_118, type, sK26: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_119, type, sK27: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_120, type, sK28: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_121, type, sK29: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_122, type, sK30: (nat > $o) > nat).
% 182.75/27.21 thf(func_def_123, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > $o) > X2)).
% 182.75/27.21 thf(func_def_124, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > $o) > X4)).
% 182.75/27.21 thf(func_def_125, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X3)).
% 182.75/27.21 thf(func_def_126, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X2)).
% 182.75/27.21 thf(func_def_127, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X0)).
% 182.75/27.21 thf(func_def_128, type, sK36: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_129, type, sK37: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_130, type, sK38: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_131, type, sK39: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_132, type, sK40: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_133, type, sK41: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_134, type, sK42: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_135, type, sK43: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_136, type, sK44: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_137, type, sK45: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_138, type, sK46: (nat > $o) > nat).
% 182.75/27.21 thf(func_def_139, type, sK47: !>[X0: $tType]:(nat > (X0 > nat) > X0 > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_140, type, sK48: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_141, type, sK49: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_142, type, sK50: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_143, type, sK51: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_144, type, sK52: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_145, type, sK53: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_146, type, sK54: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_147, type, sK55: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 182.75/27.21 thf(func_def_148, type, sK56: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 182.75/27.21 thf(func_def_149, type, sK57: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_150, type, sK58: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_151, type, sK59: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_152, type, sK60: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_153, type, sK61: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_154, type, sK62: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_155, type, sK63: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_156, type, sK64: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_157, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X2 @ X1 > X1)).
% 182.75/27.21 thf(func_def_158, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X2 @ X1 > X2)).
% 182.75/27.21 thf(func_def_159, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X1 @ product_prod @ X2 @ X0 > X1)).
% 182.75/27.21 thf(func_def_160, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1)).
% 182.75/27.21 thf(func_def_161, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3)).
% 182.75/27.21 thf(func_def_162, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X2)).
% 182.75/27.21 thf(func_def_163, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X1)).
% 182.75/27.21 thf(func_def_164, type, sK72: !>[X0: $tType]:($o > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_165, type, sK73: !>[X0: $tType]:($o > tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_166, type, sK74: !>[X0: $tType]:($o > tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_167, type, sK75: !>[X0: $tType]:($o > tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_168, type, sK76: !>[X0: $tType]:($o > tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_169, type, sK77: !>[X0: $tType]:(nat > (X0 > nat) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_170, type, sK78: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_171, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > $o) > X1)).
% 182.75/27.21 thf(func_def_172, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > $o) > X3)).
% 182.75/27.21 thf(func_def_173, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2)).
% 182.75/27.21 thf(func_def_174, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_175, type, sK83: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 182.75/27.21 thf(func_def_176, type, sK84: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_177, type, sK85: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_178, type, sK86: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_179, type, sK87: !>[X0: $tType]:((splay_2011811431op_s_t @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_180, type, sK88: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_181, type, sK89: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_182, type, sK90: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_183, type, sK91: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_184, type, sK92: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_185, type, sK93: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_186, type, sK94: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_187, type, sK95: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_188, type, sK96: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_189, type, sK97: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_190, type, sK98: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_191, type, sK99: !>[X0: $tType]:(product_prod @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_192, type, sK100: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 182.75/27.21 thf(func_def_193, type, sK101: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 182.75/27.21 thf(func_def_194, type, sK102: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_195, type, sK103: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_196, type, sK104: !>[X0: $tType]:(tree @ X0 > tree @ X0 > splay_2011811431op_s_t @ X0 > X0)).
% 182.75/27.21 thf(func_def_197, type, sK105: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_198, type, sK106: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_199, type, sK107: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_200, type, sK108: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_201, type, sK109: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_202, type, sK110: !>[X0: $tType]:(product_prod @ splay_2011811431op_s_t @ X0 @ tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_203, type, sK111: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 182.75/27.21 thf(func_def_204, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1)).
% 182.75/27.21 thf(func_def_205, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2)).
% 182.75/27.21 thf(func_def_206, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1)).
% 182.75/27.21 thf(func_def_207, type, sK115: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_208, type, sK116: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_209, type, sK117: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_210, type, sK118: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 182.75/27.21 thf(func_def_211, type, sK119: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_212, type, sK120: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 182.75/27.21 thf(func_def_213, type, sK121: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_214, type, sK122: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_215, type, sK123: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_216, type, sK124: !>[X0: $tType]:(tree @ X0 > X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_217, type, sK125: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_218, type, sK126: !>[X0: $tType]:(tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_219, type, sK127: !>[X0: $tType]:(tree @ X0 > tree @ X0)).
% 182.75/27.21 thf(func_def_220, type, sK128: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_221, type, sK129: !>[X0: $tType]:((tree @ X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_222, type, sK130: !>[X0: $tType]:((tree @ X0 > $o) > tree @ X0)).
% 182.75/27.21 thf(func_def_223, type, sK131: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X0)).
% 182.75/27.21 thf(func_def_224, type, sK132: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X0)).
% 182.75/27.21 thf(func_def_225, type, sK133: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X0)).
% 182.75/27.21 thf(func_def_226, type, sK134: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X1)).
% 182.75/27.21 thf(func_def_227, type, sK135: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X1)).
% 182.75/27.21 thf(func_def_228, type, sK136: !>[X0: $tType, X1: $tType]:(splay_2011811431op_s_t @ X0 > (X0 > X1 > $o) > splay_2011811431op_s_t @ X1 > X1)).
% 182.75/27.21 thf(func_def_229, type, sK137: !>[X0: $tType]:(X0 > tree @ X0 > X0)).
% 182.75/27.21 thf(func_def_230, type, sK138: !>[X0: $tType]:(tree @ X0 > X0 > X0)).
% 182.75/27.21 thf(func_def_231, type, sK139: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 182.75/27.21 thf(func_def_232, type, ph140: !>[X0: $tType]:(X0)).
% 182.75/27.21 thf(f5178,plain,(
% 182.75/27.21 $false),
% 182.75/27.21 inference(avatar_sat_refutation,[status(thm)],[f4640,f4649,f4856,f4859,f5177])).
% 182.75/27.21 thf(f5177,plain,(
% 182.75/27.21 spl0_8 | spl0_9 | ~spl0_23 | ~spl0_24),
% 182.75/27.21 inference(avatar_contradiction_clause,[status(thm)],[f5176])).
% 182.75/27.21 thf(f5176,plain,(
% 182.75/27.21 $false | (spl0_8 | spl0_9 | ~spl0_23 | ~spl0_24)),
% 182.75/27.21 inference(equality_resolution,[status(thm)],[f5152])).
% 182.75/27.21 thf(f5152,plain,(
% 182.75/27.21 ( ! [X0 : splay_2011811431op_s_t @ a] : ((f != X0)) ) | (spl0_8 | spl0_9 | ~spl0_23 | ~spl0_24)),
% 182.75/27.21 inference(equality_resolution,[status(thm)],[f5142])).
% 182.75/27.21 thf(f5142,plain,(
% 182.75/27.21 ( ! [X0 : splay_2011811431op_s_t @ a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | (X0 != X1)) ) | (spl0_8 | spl0_9 | ~spl0_23 | ~spl0_24)),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f5141,f4692])).
% 182.75/27.21 thf(f4692,plain,(
% 182.75/27.21 ( ! [X2 : splay_2011811431op_s_t @ a,X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_1105473951Insert @ a @ X0) != X2) | (f != X1) | (X1 != X2)) ) | ~spl0_23),
% 182.75/27.21 inference(superposition,[status(thm)],[f4672,f3513])).
% 182.75/27.21 thf(f3513,plain,(
% 182.75/27.21 ( ! [X3 : X2,X0 : X2,X1 : X2] : ((X0 = X1) | (X0 != X3) | (X1 != X3)) )),
% 182.75/27.21 inference(equality_resolution,[status(thm)],[f3382])).
% 182.75/27.21 thf(f3382,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (((splay_1105473951Insert @ X0 @ X3) != (splay_1105473951Insert @ X0 @ X2)) | (X1 = X3) | (X2 != X4) | (X1 != X4)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f1865,f3313])).
% 182.75/27.21 thf(f3313,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (((splay_1105473951Insert @ X0 @ X3) = (splay_1105473951Insert @ X0 @ X2)) | (X1 != X3) | (X1 != X2)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f1863,f1863])).
% 182.75/27.21 thf(f1863,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((splay_1105473951Insert @ X0 @ X1) = (splay_1105473951Insert @ X0 @ X2)) | (X1 != X2)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1862])).
% 182.75/27.21 thf(f1862,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 != X2) | (((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1)) = $true)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1860])).
% 182.75/27.21 thf(f1860,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((X2 = X1) = $false) | (((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1)) = $true)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1859])).
% 182.75/27.21 thf(f1859,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1)) = (X2 = X1))) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1858])).
% 182.75/27.21 thf(f1858,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((X2 = X1) = ((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1857])).
% 182.75/27.21 thf(f1857,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((^[Y0 : X0]: ((Y0 = X1) = ((splay_1105473951Insert @ X0 @ Y0) = (splay_1105473951Insert @ X0 @ X1)))) @ X2) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1856])).
% 182.75/27.21 thf(f1856,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (((!! @ X0 @ (^[Y0 : X0]: ((Y0 = X1) = ((splay_1105473951Insert @ X0 @ Y0) = (splay_1105473951Insert @ X0 @ X1))))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1855])).
% 182.75/27.21 thf(f1855,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : ((((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((Y1 = Y0) = ((splay_1105473951Insert @ X0 @ Y1) = (splay_1105473951Insert @ X0 @ Y0)))))) @ X1) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1134])).
% 182.75/27.21 thf(f1134,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((Y1 = Y0) = ((splay_1105473951Insert @ X0 @ Y1) = (splay_1105473951Insert @ X0 @ Y0))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f925])).
% 182.75/27.21 thf(f925,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((Y1 = Y0) = ((splay_1105473951Insert @ X0 @ Y1) = (splay_1105473951Insert @ X0 @ Y0))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f459])).
% 182.75/27.21 thf(f459,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((Y1 = Y0) = ((splay_1105473951Insert @ X0 @ Y1) = (splay_1105473951Insert @ X0 @ Y0))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f458])).
% 182.75/27.21 thf(f458,plain,(
% 182.75/27.21 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) = ((splay_1105473951Insert @ X0 @ X1) = (splay_1105473951Insert @ X0 @ X2)))),
% 182.75/27.21 inference(rectify,[status(thm)],[f14])).
% 182.75/27.21 thf(f14,axiom,(
% 182.75/27.21 ! [X0 : $tType,X9 : X0,X10 : X0] : ((X9 = X10) = ((splay_1105473951Insert @ X0 @ X9) = (splay_1105473951Insert @ X0 @ X10)))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_13_op_092_060_094sub_062s_092_060_094sub_062t_Oinject_I2_J)).
% 182.75/27.21 thf(f1865,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((splay_1105473951Insert @ X0 @ X1) != (splay_1105473951Insert @ X0 @ X2)) | (X1 = X2)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1864])).
% 182.75/27.21 thf(f1864,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1)) = $false)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1861])).
% 182.75/27.21 thf(f1861,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((X2 = X1) = $true) | (((splay_1105473951Insert @ X0 @ X2) = (splay_1105473951Insert @ X0 @ X1)) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1859])).
% 182.75/27.21 thf(f4672,plain,(
% 182.75/27.21 ( ! [X0 : a] : ((f != (splay_1105473951Insert @ a @ X0))) ) | ~spl0_23),
% 182.75/27.21 inference(equality_resolution,[status(thm)],[f4636])).
% 182.75/27.21 thf(f4636,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_1105473951Insert @ a @ X0) != X1) | (f != X1)) ) | ~spl0_23),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f4635])).
% 182.75/27.21 thf(f4635,definition,(
% 182.75/27.21 spl0_23 <=> ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_1105473951Insert @ a @ X0) != X1) | (f != X1))),
% 182.75/27.21 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 182.75/27.21 thf(f5141,plain,(
% 182.75/27.21 ( ! [X0 : splay_2011811431op_s_t @ a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ((splay_1105473951Insert @ a @ (sK22 @ a @ X0)) = X0) | (X0 != X1)) ) | (spl0_8 | spl0_9 | ~spl0_24)),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f5137,f4891])).
% 182.75/27.21 thf(f4891,plain,(
% 182.75/27.21 ( ! [X2 : splay_2011811431op_s_t @ a,X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_705249169Delete @ a @ X0) != X2) | (f != X1) | (X1 != X2)) ) | ~spl0_24),
% 182.75/27.21 inference(superposition,[status(thm)],[f4882,f3513])).
% 182.75/27.21 thf(f4882,plain,(
% 182.75/27.21 ( ! [X0 : a] : ((f != (splay_705249169Delete @ a @ X0))) ) | ~spl0_24),
% 182.75/27.21 inference(equality_resolution,[status(thm)],[f4841])).
% 182.75/27.21 thf(f4841,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_705249169Delete @ a @ X0) != X1) | (f != X1)) ) | ~spl0_24),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f4840])).
% 182.75/27.21 thf(f4840,definition,(
% 182.75/27.21 spl0_24 <=> ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ((splay_705249169Delete @ a @ X0) != X1))),
% 182.75/27.21 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 182.75/27.21 thf(f5137,plain,(
% 182.75/27.21 ( ! [X0 : splay_2011811431op_s_t @ a,X1 : splay_2011811431op_s_t @ a] : (((splay_705249169Delete @ a @ (sK24 @ a @ X0)) = X0) | (X0 != X1) | (f != X1) | ((splay_1105473951Insert @ a @ (sK22 @ a @ X0)) = X0)) ) | (spl0_8 | spl0_9)),
% 182.75/27.21 inference(superposition,[status(thm)],[f5116,f1365])).
% 182.75/27.21 thf(f1365,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | ((splay_705249169Delete @ X0 @ (sK24 @ X0 @ X1)) = X1)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1364])).
% 182.75/27.21 thf(f1364,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | (((splay_705249169Delete @ X0 @ (sK24 @ X0 @ X1)) = X1) = $true) | ((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1)) )),
% 182.75/27.21 inference(not_proxy_clausification,[status(thm)],[f1363])).
% 182.75/27.21 thf(f1363,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | ($false = (~ ((splay_705249169Delete @ X0 @ (sK24 @ X0 @ X1)) = X1)))) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1362])).
% 182.75/27.21 thf(f1362,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) | ($false = ((^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))) @ (sK24 @ X0 @ X1))) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1)) )),
% 182.75/27.21 inference(sigma_clausification,[status(thm)],[f1361])).
% 182.75/27.21 thf(f1361,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | ((!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1)))) = $false)) )),
% 182.75/27.21 inference(not_proxy_clausification,[status(thm)],[f1360])).
% 182.75/27.21 thf(f1360,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1359])).
% 182.75/27.21 thf(f1359,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1) = $true) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true)) )),
% 182.75/27.21 inference(not_proxy_clausification,[status(thm)],[f1358])).
% 182.75/27.21 thf(f1358,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (($false = (~ ((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1))) | ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1357])).
% 182.75/27.21 thf(f1357,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1) = $true) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ($false = (~ ((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1)))) )),
% 182.75/27.21 inference(not_proxy_clausification,[status(thm)],[f1356])).
% 182.75/27.21 thf(f1356,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((~ ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1)) = $false) | ($false = (~ ((splay_2088287777_Splay @ X0 @ (sK23 @ X0 @ X1)) = X1))) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1355])).
% 182.75/27.21 thf(f1355,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (($false = ((^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1))) @ (sK23 @ X0 @ X1))) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ((~ ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1)) = $false)) )),
% 182.75/27.21 inference(sigma_clausification,[status(thm)],[f1354])).
% 182.75/27.21 thf(f1354,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (($false = (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1))))) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ((~ ((splay_1105473951Insert @ X0 @ (sK22 @ X0 @ X1)) = X1)) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1353])).
% 182.75/27.21 thf(f1353,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((^[Y0 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y0) = X1))) @ (sK22 @ X0 @ X1)) = $false) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ($false = (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1)))))) )),
% 182.75/27.21 inference(sigma_clausification,[status(thm)],[f1352])).
% 182.75/27.21 thf(f1352,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (((!! @ X0 @ (^[Y0 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y0) = X1)))) = $false) | ((~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))) = $true) | ($false = (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1)))))) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1351])).
% 182.75/27.21 thf(f1351,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((!! @ X0 @ (^[Y0 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y0) = X1)))) => (~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1)))))) = $true) | ($false = (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1)))))) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1350])).
% 182.75/27.21 thf(f1350,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((!! @ X0 @ (^[Y0 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y0) = X1)))) => ((!! @ X0 @ (^[Y0 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y0) = X1)))) => (~ (!! @ X0 @ (^[Y0 : X0]: (~ ((splay_705249169Delete @ X0 @ Y0) = X1))))))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1349])).
% 182.75/27.21 thf(f1349,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : ((((^[Y0 : splay_2011811431op_s_t @ X0]: ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y1) = Y0)))) => ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y1) = Y0)))) => (~ (!! @ X0 @ (^[Y1 : X0]: (~ ((splay_705249169Delete @ X0 @ Y1) = Y0)))))))) @ X1) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1137])).
% 182.75/27.21 thf(f1137,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ splay_2011811431op_s_t @ X0 @ (^[Y0 : splay_2011811431op_s_t @ X0]: ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y1) = Y0)))) => ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y1) = Y0)))) => (~ (!! @ X0 @ (^[Y1 : X0]: (~ ((splay_705249169Delete @ X0 @ Y1) = Y0))))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f897])).
% 182.75/27.21 thf(f897,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((!! @ splay_2011811431op_s_t @ X0 @ (^[Y0 : splay_2011811431op_s_t @ X0]: ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y1) = Y0)))) => ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y1) = Y0)))) => (~ (!! @ X0 @ (^[Y1 : X0]: (~ ((splay_705249169Delete @ X0 @ Y1) = Y0))))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f787])).
% 182.75/27.21 thf(f787,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ splay_2011811431op_s_t @ X0 @ (^[Y0 : splay_2011811431op_s_t @ X0]: ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_2088287777_Splay @ X0 @ Y1) = Y0)))) => ((!! @ X0 @ (^[Y1 : X0]: (~ ((splay_1105473951Insert @ X0 @ Y1) = Y0)))) => (~ (!! @ X0 @ (^[Y1 : X0]: (~ ((splay_705249169Delete @ X0 @ Y1) = Y0))))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f786])).
% 182.75/27.21 thf(f786,plain,(
% 182.75/27.21 ! [X0 : $tType,X1 : splay_2011811431op_s_t @ X0] : (! [X2 : X0] : ((splay_2088287777_Splay @ X0 @ X2) != X1) => (! [X3 : X0] : ((splay_1105473951Insert @ X0 @ X3) != X1) => ~! [X4 : X0] : ((splay_705249169Delete @ X0 @ X4) != X1)))),
% 182.75/27.21 inference(rectify,[status(thm)],[f27])).
% 182.75/27.21 thf(f27,axiom,(
% 182.75/27.21 ! [X0 : $tType,X15 : splay_2011811431op_s_t @ X0] : (! [X21 : X0] : ((splay_2088287777_Splay @ X0 @ X21) != X15) => (! [X22 : X0] : ((splay_1105473951Insert @ X0 @ X22) != X15) => ~! [X23 : X0] : ((splay_705249169Delete @ X0 @ X23) != X15)))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_26_op_092_060_094sub_062s_092_060_094sub_062t_Oexhaust)).
% 182.75/27.21 thf(f5116,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_2088287777_Splay @ a @ X0) != X1) | (f != X1)) ) | (spl0_8 | spl0_9)),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f5115,f3747])).
% 182.75/27.21 thf(f3747,plain,(
% 182.75/27.21 ((linorder @ a @ type2 @ a) != $false) | spl0_9),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f3746])).
% 182.75/27.21 thf(f3746,definition,(
% 182.75/27.21 spl0_9 <=> ((linorder @ a @ type2 @ a) = $false)),
% 182.75/27.21 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 182.75/27.21 thf(f5115,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ((splay_2088287777_Splay @ a @ X0) != X1) | ((linorder @ a @ type2 @ a) = $false)) ) | (spl0_8 | spl0_9)),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f5114,f3735])).
% 182.75/27.21 thf(f3735,plain,(
% 182.75/27.21 ((linorder_bst @ a @ a2) != $false) | spl0_8),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f3734])).
% 182.75/27.21 thf(f3734,definition,(
% 182.75/27.21 spl0_8 <=> ((linorder_bst @ a @ a2) = $false)),
% 182.75/27.21 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 182.75/27.21 thf(f5114,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ((splay_2088287777_Splay @ a @ X0) != X1) | ((linorder_bst @ a @ a2) = $false) | ((linorder @ a @ type2 @ a) = $false)) ) | spl0_9),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f5107])).
% 182.75/27.21 thf(f5107,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_2088287777_Splay @ a @ X0) != X1) | ((linorder @ a @ type2 @ a) = $false) | (f != X1) | ((linorder_bst @ a @ a2) = $false) | ($false = $true)) ) | spl0_9),
% 182.75/27.21 inference(superposition,[status(thm)],[f4714,f1371])).
% 182.75/27.21 thf(f1371,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder_bst @ X0 @ (splay_splay @ X0 @ X1 @ X2)) = $true) | ($false = (linorder_bst @ X0 @ X2)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1370])).
% 182.75/27.21 thf(f1370,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder @ X0 @ type2 @ X0) = $false) | (((linorder_bst @ X0 @ X2) => (linorder_bst @ X0 @ (splay_splay @ X0 @ X1 @ X2))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1369])).
% 182.75/27.21 thf(f1369,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : ((((^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_splay @ X0 @ X1 @ Y0)))) @ X2) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1368])).
% 182.75/27.21 thf(f1368,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (((linorder @ X0 @ type2 @ X0) = $false) | ((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_splay @ X0 @ X1 @ Y0))))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1367])).
% 182.75/27.21 thf(f1367,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (($true = ((^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ Y0 @ Y1)))))) @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1366])).
% 182.75/27.21 thf(f1366,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ Y0 @ Y1))))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1050])).
% 182.75/27.21 thf(f1050,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f874])).
% 182.75/27.21 thf(f874,plain,(
% 182.75/27.21 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ Y0 @ Y1)))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f519])).
% 182.75/27.21 thf(f519,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f518])).
% 182.75/27.21 thf(f518,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : tree @ X0,X2 : X0] : ((linorder_bst @ X0 @ X1) => (linorder_bst @ X0 @ (splay_splay @ X0 @ X2 @ X1))))),
% 182.75/27.21 inference(rectify,[status(thm)],[f8])).
% 182.75/27.21 thf(f8,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X4 : tree @ X0,X5 : X0] : ((linorder_bst @ X0 @ X4) => (linorder_bst @ X0 @ (splay_splay @ X0 @ X5 @ X4))))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_7_bst__splay)).
% 182.75/27.21 thf(f4714,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder_bst @ a @ (splay_splay @ a @ X0 @ a2)) = $false) | (f != X1) | ((splay_2088287777_Splay @ a @ X0) != X1)) ) | spl0_9),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f4711,f3747])).
% 182.75/27.21 thf(f4711,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder @ a @ type2 @ a) = $false) | ((linorder_bst @ a @ (splay_splay @ a @ X0 @ a2)) = $false) | ((splay_2088287777_Splay @ a @ X0) != X1) | (f != X1)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f3538,f3054])).
% 182.75/27.21 thf(f3054,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : (((splay_splay @ X0 @ X2 @ X1) = (splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ X2) @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f3053])).
% 182.75/27.21 thf(f3053,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ X2) @ X1) = (splay_splay @ X0 @ X2 @ X1)) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3052])).
% 182.75/27.21 thf(f3052,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((^[Y0 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y0) @ X1) = (splay_splay @ X0 @ Y0 @ X1))) @ X2) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3051])).
% 182.75/27.21 thf(f3051,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : (((!! @ X0 @ (^[Y0 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y0) @ X1) = (splay_splay @ X0 @ Y0 @ X1)))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3050])).
% 182.75/27.21 thf(f3050,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : ((((^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y1) @ Y0) = (splay_splay @ X0 @ Y1 @ Y0))))) @ X1) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3049])).
% 182.75/27.21 thf(f3049,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y1) @ Y0) = (splay_splay @ X0 @ Y1 @ Y0)))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1078])).
% 182.75/27.21 thf(f1078,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y1) @ Y0) = (splay_splay @ X0 @ Y1 @ Y0))))))))) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f869])).
% 182.75/27.21 thf(f869,plain,(
% 182.75/27.21 ! [X0 : $tType] : ($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y1) @ Y0) = (splay_splay @ X0 @ Y1 @ Y0))))))))),
% 182.75/27.21 inference(closure,[status(thm)],[f441])).
% 182.75/27.21 thf(f441,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ Y1) @ Y0) = (splay_splay @ X0 @ Y1 @ Y0))))))))) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f440])).
% 182.75/27.21 thf(f440,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : tree @ X0] : ((splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ X1) @ X2) = (splay_splay @ X0 @ X1 @ X2)))),
% 182.75/27.21 inference(rectify,[status(thm)],[f10])).
% 182.75/27.21 thf(f10,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X5 : X0,X4 : tree @ X0] : ((splay_splay @ X0 @ X5 @ X4) = (splay_859309299xt_s_t @ X0 @ (splay_2088287777_Splay @ X0 @ X5) @ X4)))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_9_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I1_J)).
% 182.75/27.21 thf(f3538,plain,(
% 182.75/27.21 ( ! [X0 : splay_2011811431op_s_t @ a,X1 : splay_2011811431op_s_t @ a] : (($false = (linorder_bst @ a @ (splay_859309299xt_s_t @ a @ X0 @ a2))) | (f != X1) | (X0 != X1)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f2309,f3513])).
% 182.75/27.21 thf(f2309,plain,(
% 182.75/27.21 ((linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2)) = $false)),
% 182.75/27.21 inference(not_proxy_clausification,[status(thm)],[f1090])).
% 182.75/27.21 thf(f1090,plain,(
% 182.75/27.21 ((~ (linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2))) = $true)),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f635])).
% 182.75/27.21 thf(f635,plain,(
% 182.75/27.21 ((~ (linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2))) = $true)),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f634])).
% 182.75/27.21 thf(f634,plain,(
% 182.75/27.21 ~(linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2))),
% 182.75/27.21 inference(rectify,[status(thm)],[f288])).
% 182.75/27.21 thf(f288,negated_conjecture,(
% 182.75/27.21 ~(linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2))),
% 182.75/27.21 inference(negated_conjecture,[status(cth)],[f287])).
% 182.75/27.21 thf(f287,conjecture,(
% 182.75/27.21 (linorder_bst @ a @ (splay_859309299xt_s_t @ a @ f @ a2))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',conj_0)).
% 182.75/27.21 thf(f4859,plain,(
% 182.75/27.21 ~spl0_8),
% 182.75/27.21 inference(avatar_contradiction_clause,[status(thm)],[f4858])).
% 182.75/27.21 thf(f4858,plain,(
% 182.75/27.21 $false | ~spl0_8),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4857])).
% 182.75/27.21 thf(f4857,plain,(
% 182.75/27.21 ($false = $true) | ~spl0_8),
% 182.75/27.21 inference(backward_demodulation,[status(thm)],[f1142,f3736])).
% 182.75/27.21 thf(f3736,plain,(
% 182.75/27.21 ((linorder_bst @ a @ a2) = $false) | ~spl0_8),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f3734])).
% 182.75/27.21 thf(f1142,plain,(
% 182.75/27.21 ((linorder_bst @ a @ a2) = $true)),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f807])).
% 182.75/27.21 thf(f807,plain,(
% 182.75/27.21 ((linorder_bst @ a @ a2) = $true)),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f806])).
% 182.75/27.21 thf(f806,plain,(
% 182.75/27.21 (linorder_bst @ a @ a2)),
% 182.75/27.21 inference(rectify,[status(thm)],[f1])).
% 182.75/27.21 thf(f1,axiom,(
% 182.75/27.21 (linorder_bst @ a @ a2)),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_0__C2_C)).
% 182.75/27.21 thf(f4856,plain,(
% 182.75/27.21 spl0_24 | spl0_8 | spl0_9),
% 182.75/27.21 inference(avatar_split_clause,[status(thm)],[f4855,f3746,f3734,f4840])).
% 182.75/27.21 thf(f4855,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_705249169Delete @ a @ X0) != X1) | (f != X1) | ((linorder_bst @ a @ a2) = $false)) ) | spl0_9),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f4835,f3747])).
% 182.75/27.21 thf(f4835,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ((linorder_bst @ a @ a2) = $false) | ((linorder @ a @ type2 @ a) = $false) | ((splay_705249169Delete @ a @ X0) != X1)) ) | spl0_9),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4830])).
% 182.75/27.21 thf(f4830,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder @ a @ type2 @ a) = $false) | ($false = $true) | ((splay_705249169Delete @ a @ X0) != X1) | ((linorder_bst @ a @ a2) = $false) | (f != X1)) ) | spl0_9),
% 182.75/27.21 inference(superposition,[status(thm)],[f4684,f3110])).
% 182.75/27.21 thf(f3110,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder_bst @ X0 @ (splay_delete @ X0 @ X1 @ X2)) = $true) | ($false = (linorder_bst @ X0 @ X2)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f3109])).
% 182.75/27.21 thf(f3109,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder @ X0 @ type2 @ X0) = $false) | (((linorder_bst @ X0 @ X2) => (linorder_bst @ X0 @ (splay_delete @ X0 @ X1 @ X2))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3108])).
% 182.75/27.21 thf(f3108,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder @ X0 @ type2 @ X0) = $false) | (((^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_delete @ X0 @ X1 @ Y0)))) @ X2) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3107])).
% 182.75/27.21 thf(f3107,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_delete @ X0 @ X1 @ Y0))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3106])).
% 182.75/27.21 thf(f3106,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (($true = ((^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ Y0 @ Y1)))))) @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3105])).
% 182.75/27.21 thf(f3105,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ Y0 @ Y1))))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1122])).
% 182.75/27.21 thf(f1122,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f882])).
% 182.75/27.21 thf(f882,plain,(
% 182.75/27.21 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ Y0 @ Y1)))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f531])).
% 182.75/27.21 thf(f531,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f530])).
% 182.75/27.21 thf(f530,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : tree @ X0,X2 : X0] : ((linorder_bst @ X0 @ X1) => (linorder_bst @ X0 @ (splay_delete @ X0 @ X2 @ X1))))),
% 182.75/27.21 inference(rectify,[status(thm)],[f2])).
% 182.75/27.21 thf(f2,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X4 : tree @ X0,X5 : X0] : ((linorder_bst @ X0 @ X4) => (linorder_bst @ X0 @ (splay_delete @ X0 @ X5 @ X4))))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_1_bst__delete)).
% 182.75/27.21 thf(f4684,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (($false = (linorder_bst @ a @ (splay_delete @ a @ X0 @ a2))) | ((splay_705249169Delete @ a @ X0) != X1) | (f != X1)) ) | spl0_9),
% 182.75/27.21 inference(subsumption_resolution,[status(thm)],[f4682,f3747])).
% 182.75/27.21 thf(f4682,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_705249169Delete @ a @ X0) != X1) | ((linorder @ a @ type2 @ a) = $false) | ($false = (linorder_bst @ a @ (splay_delete @ a @ X0 @ a2))) | (f != X1)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f3538,f2336])).
% 182.75/27.21 thf(f2336,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : (((splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ X2) @ X1) = (splay_delete @ X0 @ X2 @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f2335])).
% 182.75/27.21 thf(f2335,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((splay_delete @ X0 @ X2 @ X1) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ X2) @ X1)) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f2334])).
% 182.75/27.21 thf(f2334,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((^[Y0 : X0]: ((splay_delete @ X0 @ Y0 @ X1) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y0) @ X1))) @ X2) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f2333])).
% 182.75/27.21 thf(f2333,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : (((!! @ X0 @ (^[Y0 : X0]: ((splay_delete @ X0 @ Y0 @ X1) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y0) @ X1)))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f2332])).
% 182.75/27.21 thf(f2332,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : ((((^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_delete @ X0 @ Y1 @ Y0) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y1) @ Y0))))) @ X1) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f2331])).
% 182.75/27.21 thf(f2331,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_delete @ X0 @ Y1 @ Y0) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y1) @ Y0)))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1057])).
% 182.75/27.21 thf(f1057,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_delete @ X0 @ Y1 @ Y0) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y1) @ Y0))))))))) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f868])).
% 182.75/27.21 thf(f868,plain,(
% 182.75/27.21 ! [X0 : $tType] : ($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_delete @ X0 @ Y1 @ Y0) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y1) @ Y0))))))))),
% 182.75/27.21 inference(closure,[status(thm)],[f651])).
% 182.75/27.21 thf(f651,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (($true = ((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_delete @ X0 @ Y1 @ Y0) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ Y1) @ Y0))))))))) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f650])).
% 182.75/27.21 thf(f650,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : tree @ X0] : ((splay_delete @ X0 @ X1 @ X2) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ X1) @ X2)))),
% 182.75/27.21 inference(rectify,[status(thm)],[f6])).
% 182.75/27.21 thf(f6,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X5 : X0,X4 : tree @ X0] : ((splay_delete @ X0 @ X5 @ X4) = (splay_859309299xt_s_t @ X0 @ (splay_705249169Delete @ X0 @ X5) @ X4)))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_5_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I3_J)).
% 182.75/27.21 thf(f4649,plain,(
% 182.75/27.21 ~spl0_9),
% 182.75/27.21 inference(avatar_contradiction_clause,[status(thm)],[f4648])).
% 182.75/27.21 thf(f4648,plain,(
% 182.75/27.21 $false | ~spl0_9),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4647])).
% 182.75/27.21 thf(f4647,plain,(
% 182.75/27.21 ($false = $true) | ~spl0_9),
% 182.75/27.21 inference(backward_demodulation,[status(thm)],[f1116,f3748])).
% 182.75/27.21 thf(f3748,plain,(
% 182.75/27.21 ((linorder @ a @ type2 @ a) = $false) | ~spl0_9),
% 182.75/27.21 inference(avatar_component_clause,[status(thm)],[f3746])).
% 182.75/27.21 thf(f1116,plain,(
% 182.75/27.21 ((linorder @ a @ type2 @ a) = $true)),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f607])).
% 182.75/27.21 thf(f607,plain,(
% 182.75/27.21 ((linorder @ a @ type2 @ a) = $true)),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f606])).
% 182.75/27.21 thf(f606,plain,(
% 182.75/27.21 (linorder @ a @ type2 @ a)),
% 182.75/27.21 inference(rectify,[status(thm)],[f286])).
% 182.75/27.21 thf(f286,axiom,(
% 182.75/27.21 (linorder @ a @ type2 @ a)),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',tfree_0)).
% 182.75/27.21 thf(f4640,plain,(
% 182.75/27.21 spl0_9 | spl0_23),
% 182.75/27.21 inference(avatar_split_clause,[status(thm)],[f4639,f4635,f3746])).
% 182.75/27.21 thf(f4639,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((splay_1105473951Insert @ a @ X0) != X1) | (f != X1) | ((linorder @ a @ type2 @ a) = $false)) )),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4638])).
% 182.75/27.21 thf(f4638,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder @ a @ type2 @ a) = $false) | (f != X1) | ((splay_1105473951Insert @ a @ X0) != X1) | ($false = $true)) )),
% 182.75/27.21 inference(forward_demodulation,[status(thm)],[f4624,f1142])).
% 182.75/27.21 thf(f4624,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder_bst @ a @ a2) = $false) | (f != X1) | ((linorder @ a @ type2 @ a) = $false) | ((splay_1105473951Insert @ a @ X0) != X1)) )),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4622])).
% 182.75/27.21 thf(f4622,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (($false = $true) | ((linorder_bst @ a @ a2) = $false) | ((splay_1105473951Insert @ a @ X0) != X1) | (f != X1) | ((linorder @ a @ type2 @ a) = $false)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f3230,f4609])).
% 182.75/27.21 thf(f4609,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder_bst @ a @ (splay_insert @ a @ X0 @ a2)) = $false) | ((splay_1105473951Insert @ a @ X0) != X1) | (f != X1)) )),
% 182.75/27.21 inference(trivial_inequality_removal,[status(thm)],[f4608])).
% 182.75/27.21 thf(f4608,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : ((f != X1) | ($false = $true) | ((linorder_bst @ a @ (splay_insert @ a @ X0 @ a2)) = $false) | ((splay_1105473951Insert @ a @ X0) != X1)) )),
% 182.75/27.21 inference(forward_demodulation,[status(thm)],[f4606,f1116])).
% 182.75/27.21 thf(f4606,plain,(
% 182.75/27.21 ( ! [X0 : a,X1 : splay_2011811431op_s_t @ a] : (((linorder_bst @ a @ (splay_insert @ a @ X0 @ a2)) = $false) | ((splay_1105473951Insert @ a @ X0) != X1) | (f != X1) | ((linorder @ a @ type2 @ a) = $false)) )),
% 182.75/27.21 inference(superposition,[status(thm)],[f3538,f1508])).
% 182.75/27.21 thf(f1508,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : (((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ X2) @ X1) = (splay_insert @ X0 @ X2 @ X1)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(equality_proxy_clausification,[status(thm)],[f1507])).
% 182.75/27.21 thf(f1507,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ X2) @ X1) = (splay_insert @ X0 @ X2 @ X1)) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1506])).
% 182.75/27.21 thf(f1506,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : X0,X1 : tree @ X0] : ((((^[Y0 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y0) @ X1) = (splay_insert @ X0 @ Y0 @ X1))) @ X2) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1505])).
% 182.75/27.21 thf(f1505,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : (((linorder @ X0 @ type2 @ X0) = $false) | ((!! @ X0 @ (^[Y0 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y0) @ X1) = (splay_insert @ X0 @ Y0 @ X1)))) = $true)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f1504])).
% 182.75/27.21 thf(f1504,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : tree @ X0] : (((linorder @ X0 @ type2 @ X0) = $false) | (((^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y1) @ Y0) = (splay_insert @ X0 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f1503])).
% 182.75/27.21 thf(f1503,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $false) | ((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y1) @ Y0) = (splay_insert @ X0 @ Y1 @ Y0)))))) = $true)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1111])).
% 182.75/27.21 thf(f1111,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y1) @ Y0) = (splay_insert @ X0 @ Y1 @ Y0))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f867])).
% 182.75/27.21 thf(f867,plain,(
% 182.75/27.21 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y1) @ Y0) = (splay_insert @ X0 @ Y1 @ Y0))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f673])).
% 182.75/27.21 thf(f673,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ tree @ X0 @ (^[Y0 : tree @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ Y1) @ Y0) = (splay_insert @ X0 @ Y1 @ Y0))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f672])).
% 182.75/27.21 thf(f672,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : tree @ X0] : ((splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ X1) @ X2) = (splay_insert @ X0 @ X1 @ X2)))),
% 182.75/27.21 inference(rectify,[status(thm)],[f7])).
% 182.75/27.21 thf(f7,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X5 : X0,X4 : tree @ X0] : ((splay_insert @ X0 @ X5 @ X4) = (splay_859309299xt_s_t @ X0 @ (splay_1105473951Insert @ X0 @ X5) @ X4)))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_6_nxt_092_060_094sub_062s_092_060_094sub_062t_Osimps_I2_J)).
% 182.75/27.21 thf(f3230,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (((linorder_bst @ X0 @ (splay_insert @ X0 @ X1 @ X2)) = $true) | ($false = (linorder_bst @ X0 @ X2)) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f3229])).
% 182.75/27.21 thf(f3229,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : (($true = ((linorder_bst @ X0 @ X2) => (linorder_bst @ X0 @ (splay_insert @ X0 @ X1 @ X2)))) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3228])).
% 182.75/27.21 thf(f3228,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : ((((^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_insert @ X0 @ X1 @ Y0)))) @ X2) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3227])).
% 182.75/27.21 thf(f3227,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (((!! @ tree @ X0 @ (^[Y0 : tree @ X0]: ((linorder_bst @ X0 @ Y0) => (linorder_bst @ X0 @ (splay_insert @ X0 @ X1 @ Y0))))) = $true) | ((linorder @ X0 @ type2 @ X0) = $false)) )),
% 182.75/27.21 inference(beta_eta_normalization,[status(thm)],[f3226])).
% 182.75/27.21 thf(f3226,plain,(
% 182.75/27.21 ( ! [X0 : $tType,X1 : X0] : (((linorder @ X0 @ type2 @ X0) = $false) | (((^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 182.75/27.21 inference(pi_clausification,[status(thm)],[f3225])).
% 182.75/27.21 thf(f3225,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $false) | ($true = (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ Y0 @ Y1))))))))) )),
% 182.75/27.21 inference(binary_proxy_clausification,[status(thm)],[f1089])).
% 182.75/27.21 thf(f1089,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(cnf_transformation,[status(thm)],[f883])).
% 182.75/27.21 thf(f883,plain,(
% 182.75/27.21 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ Y0 @ Y1)))))))) = $true)),
% 182.75/27.21 inference(closure,[status(thm)],[f831])).
% 182.75/27.21 thf(f831,plain,(
% 182.75/27.21 ( ! [X0 : $tType] : ((((linorder @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ tree @ X0 @ (^[Y1 : tree @ X0]: ((linorder_bst @ X0 @ Y1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ Y0 @ Y1)))))))) = $true)) )),
% 182.75/27.21 inference(fool_elimination,[status(thm)],[f830])).
% 182.75/27.21 thf(f830,plain,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : tree @ X0,X2 : X0] : ((linorder_bst @ X0 @ X1) => (linorder_bst @ X0 @ (splay_insert @ X0 @ X2 @ X1))))),
% 182.75/27.21 inference(rectify,[status(thm)],[f3])).
% 182.75/27.21 thf(f3,axiom,(
% 182.75/27.21 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X4 : tree @ X0,X5 : X0] : ((linorder_bst @ X0 @ X4) => (linorder_bst @ X0 @ (splay_insert @ X0 @ X5 @ X4))))),
% 182.75/27.21 file('/export/starexec/sandbox/tmp/tmp.hTzvDgvs46/DTF2THF_28704.p',fact_2_bst__insert)).
% 182.75/27.21 % SZS output end Proof for DTF2THF_28704
% 182.75/27.21 % (29980)------------------------------
% 182.75/27.21 % (29980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 182.75/27.21 % (29980)Termination reason: Refutation
% 182.75/27.21
% 182.75/27.21 % (29980)Memory used [KB]: 11001
% 182.75/27.21 % (29980)Time elapsed: 0.704 s
% 182.75/27.21 % (29980)Instructions burned: 2313 (million)
% 182.75/27.21 % (29980)------------------------------
% 182.75/27.21 % (29980)------------------------------
% 182.75/27.21 % (29039)Success in time 25.632 s
%------------------------------------------------------------------------------