%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT232^1 : 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 : n003.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 08:45:14 AM UTC 2026
% Result : Theorem 185.79s 27.61s
% Output : Refutation 185.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT232^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 06:12:25 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : DAT232^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.43 % Domain : Data Structures
% 0.16/0.43 % Problem : Red-black trees 415
% 0.16/0.43 % Version : [Bla16] axioms : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.43 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Bla16]
% 0.16/0.43 % Names : rbt_impl__415.p [Bla16]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.16/0.43 % Syntax : Number of formulae : 331 ( 112 unt; 72 typ; 0 def)
% 0.16/0.43 % Number of atoms : 854 ( 326 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 13 ( 3 avg)
% 0.16/0.43 % Number of connectives : 4737 ( 168 ~; 28 |; 111 &;4120 @)
% 0.16/0.43 % ( 0 <=>; 310 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 23 ( 8 avg)
% 0.16/0.43 % Number of types : 4 ( 3 usr)
% 0.16/0.43 % Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 70 ( 69 usr; 20 con; 0-7 aty)
% 0.16/0.43 % Number of variables : 1191 ( 23 ^;1000 !; 108 ?;1191 :)
% 0.16/0.43 % ( 60 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.43 % SPC : TH1_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.43 % 2016-07-13 14:41:06.898
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 %----Could-be-implicit typings (9)
% 0.16/0.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.16/0.43 rBT_Im1923302023_color: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.16/0.43 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.43 product_prod: $tType > $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Option_Ooption,type,
% 0.16/0.43 option: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_List_Olist,type,
% 0.16/0.43 list: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_Set_Oset,type,
% 0.16/0.43 set: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_t_itself,type,
% 0.16/0.43 itself: $tType > $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_tf_b,type,
% 0.16/0.43 b: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(ty_tf_a,type,
% 0.16/0.43 a: $tType ).
% 0.16/0.43
% 0.16/0.43 %----Explicit typings (63)
% 0.16/0.43 thf(sy_cl_HOL_Otype,type,
% 0.16/0.43 type:
% 0.16/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_cl_Orderings_Oorder,type,
% 0.16/0.43 order:
% 0.16/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Fun_Oinj__on,type,
% 0.16/0.43 inj_on:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Oappend,type,
% 0.16/0.43 append:
% 0.16/0.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Obind,type,
% 0.16/0.43 bind:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Odistinct,type,
% 0.16/0.43 distinct:
% 0.16/0.43 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Oextract,type,
% 0.16/0.43 extract:
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > ( option @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Olist_OCons,type,
% 0.16/0.43 cons:
% 0.16/0.43 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Olist_ONil,type,
% 0.16/0.43 nil:
% 0.16/0.43 !>[A: $tType] : ( list @ A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Olist_Oset,type,
% 0.16/0.43 set2:
% 0.16/0.43 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Olistrel1,type,
% 0.16/0.43 listrel1:
% 0.16/0.43 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Oord_Olexordp,type,
% 0.16/0.43 lexordp:
% 0.16/0.43 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.16/0.43 lexordp_eq:
% 0.16/0.43 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Oproduct__lists,type,
% 0.16/0.43 product_lists:
% 0.16/0.43 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Osublists,type,
% 0.16/0.43 sublists:
% 0.16/0.43 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_List_Ounion,type,
% 0.16/0.43 union:
% 0.16/0.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Map_Odom,type,
% 0.16/0.43 dom:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Map_Omap__of,type,
% 0.16/0.43 map_of:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Option_Ooption_ONone,type,
% 0.16/0.43 none:
% 0.16/0.43 !>[A: $tType] : ( option @ A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Option_Ooption_OSome,type,
% 0.16/0.43 some:
% 0.16/0.43 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.16/0.43 ord_less:
% 0.16/0.43 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 0.16/0.43 strict_mono:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.43 product_Pair:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Pure_Otype,type,
% 0.16/0.43 type2:
% 0.16/0.43 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 0.16/0.43 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 0.16/0.43 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of,type,
% 0.16/0.43 rBT_Im1805589839lor_of:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > rBT_Im1923302023_color ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 0.16/0.43 rBT_Im954575269ntries:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1,type,
% 0.16/0.43 rBT_Im1040612427e_inv1:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv2,type,
% 0.16/0.43 rBT_Im1040612428e_inv2:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys,type,
% 0.16/0.43 rBT_Im380146495e_keys:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt,type,
% 0.16/0.43 rBT_Im862805236is_rbt:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 0.16/0.43 rBT_Im1259024060reater:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 0.16/0.43 rBT_Im2075124343t_less:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 0.16/0.43 rBT_Im35466040lookup:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 0.16/0.43 rBT_Im759614907sorted:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.16/0.43 rBT_Im480247531Branch:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.16/0.43 rBT_Im418718756_Empty:
% 0.16/0.43 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_OCollect,type,
% 0.16/0.43 collect:
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set_Othe__elem,type,
% 0.16/0.43 the_elem:
% 0.16/0.43 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 0.16/0.43 set_greaterThan:
% 0.16/0.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 0.16/0.43 set_lessThan:
% 0.16/0.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_Transitive__Closure_Oacyclic,type,
% 0.16/0.43 transitive_acyclic:
% 0.16/0.43 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_c_member,type,
% 0.16/0.43 member:
% 0.16/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_b____,type,
% 0.16/0.43 b2: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_c____,type,
% 0.16/0.43 c: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_k,type,
% 0.16/0.43 k: a ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_l,type,
% 0.16/0.43 l: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_less,type,
% 0.16/0.43 less: a > a > $o ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_r,type,
% 0.16/0.43 r: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_s____,type,
% 0.16/0.43 s: b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_t____,type,
% 0.16/0.43 t: b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_va____,type,
% 0.16/0.43 va: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vb____,type,
% 0.16/0.43 vb: a ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vc____,type,
% 0.16/0.43 vc: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vd____,type,
% 0.16/0.43 vd: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_ve____,type,
% 0.16/0.43 ve: a ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vf____,type,
% 0.16/0.43 vf: rBT_Im246033960le_rbt @ a @ b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vg____,type,
% 0.16/0.43 vg: b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_vii____,type,
% 0.16/0.43 vii: b ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_x____,type,
% 0.16/0.43 x: a ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_y____,type,
% 0.16/0.43 y: a ).
% 0.16/0.43
% 0.16/0.43 thf(sy_v_z____,type,
% 0.16/0.43 z: a ).
% 0.16/0.43
% 0.16/0.43 %----Relevant facts (255)
% 0.16/0.43 thf(fact_0_local_Oantisym__conv3,axiom,
% 0.16/0.43 ! [Y: a,X: a] :
% 0.16/0.43 ( ~ ( less @ Y @ X )
% 0.16/0.43 => ( ( ~ ( less @ X @ Y ) )
% 0.16/0.43 = ( X = Y ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.antisym_conv3
% 0.16/0.43 thf(fact_1_local_Odual__order_Oasym,axiom,
% 0.16/0.43 ! [B2: a,A2: a] :
% 0.16/0.43 ( ( less @ B2 @ A2 )
% 0.16/0.43 => ~ ( less @ A2 @ B2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.dual_order.asym
% 0.16/0.43 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.43 ! [B2: a,A2: a] :
% 0.16/0.43 ( ( less @ B2 @ A2 )
% 0.16/0.43 => ( A2 != B2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.dual_order.strict_implies_not_eq
% 0.16/0.43 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 0.16/0.43 ! [B2: a,A2: a,C: a] :
% 0.16/0.43 ( ( less @ B2 @ A2 )
% 0.16/0.43 => ( ( less @ C @ B2 )
% 0.16/0.43 => ( less @ C @ A2 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.dual_order.strict_trans
% 0.16/0.43 thf(fact_4_local_Oless__asym,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_asym
% 0.16/0.43 thf(fact_5_local_Oless__asym_H,axiom,
% 0.16/0.43 ! [A2: a,B2: a] :
% 0.16/0.43 ( ( less @ A2 @ B2 )
% 0.16/0.43 => ~ ( less @ B2 @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_asym'
% 0.16/0.43 thf(fact_6_local_Oless__imp__neq,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( X != Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_imp_neq
% 0.16/0.43 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( X != Y ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_imp_not_eq
% 0.16/0.43 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( Y != X ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_imp_not_eq2
% 0.16/0.43 thf(fact_9_local_Oless__imp__not__less,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_imp_not_less
% 0.16/0.43 thf(fact_10_local_Oless__imp__triv,axiom,
% 0.16/0.43 ! [X: a,Y: a,P: $o] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( ( less @ Y @ X )
% 0.16/0.43 => P ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_imp_triv
% 0.16/0.43 thf(fact_11_local_Oless__irrefl,axiom,
% 0.16/0.43 ! [X: a] :
% 0.16/0.43 ~ ( less @ X @ X ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_irrefl
% 0.16/0.43 thf(fact_12_local_Oless__linear,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 | ( X = Y )
% 0.16/0.43 | ( less @ Y @ X ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_linear
% 0.16/0.43 thf(fact_13_local_Oless__not__sym,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ~ ( less @ Y @ X ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_not_sym
% 0.16/0.43 thf(fact_14_local_Oless__trans,axiom,
% 0.16/0.43 ! [X: a,Y: a,Z: a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( ( less @ Y @ Z )
% 0.16/0.43 => ( less @ X @ Z ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.less_trans
% 0.16/0.43 thf(fact_15_local_Olinorder__cases,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ~ ( less @ X @ Y )
% 0.16/0.43 => ( ( X != Y )
% 0.16/0.43 => ( less @ Y @ X ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.linorder_cases
% 0.16/0.43 thf(fact_16_local_OneqE,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( X != Y )
% 0.16/0.43 => ( ~ ( less @ X @ Y )
% 0.16/0.43 => ( less @ Y @ X ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.neqE
% 0.16/0.43 thf(fact_17_local_Oneq__iff,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( X != Y )
% 0.16/0.43 = ( ( less @ X @ Y )
% 0.16/0.43 | ( less @ Y @ X ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.neq_iff
% 0.16/0.43 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 0.16/0.43 ! [X: a,Y: a] :
% 0.16/0.43 ( ( ~ ( less @ X @ Y ) )
% 0.16/0.43 = ( ( less @ Y @ X )
% 0.16/0.43 | ( X = Y ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.not_less_iff_gr_or_eq
% 0.16/0.43 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 0.16/0.43 ! [A2: a,B2: a,C: a] :
% 0.16/0.43 ( ( A2 = B2 )
% 0.16/0.43 => ( ( less @ B2 @ C )
% 0.16/0.43 => ( less @ A2 @ C ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.ord_eq_less_trans
% 0.16/0.43 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 0.16/0.43 ! [A2: a,B2: a,C: a] :
% 0.16/0.43 ( ( less @ A2 @ B2 )
% 0.16/0.43 => ( ( B2 = C )
% 0.16/0.43 => ( less @ A2 @ C ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.ord_less_eq_trans
% 0.16/0.43 thf(fact_21_local_Oorder_Oasym,axiom,
% 0.16/0.43 ! [A2: a,B2: a] :
% 0.16/0.43 ( ( less @ A2 @ B2 )
% 0.16/0.43 => ~ ( less @ B2 @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.order.asym
% 0.16/0.43 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 0.16/0.43 ! [A2: a] :
% 0.16/0.43 ~ ( less @ A2 @ A2 ) ).
% 0.16/0.43
% 0.16/0.43 % local.order.irrefl
% 0.16/0.43 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 0.16/0.43 ! [A2: a,B2: a] :
% 0.16/0.43 ( ( less @ A2 @ B2 )
% 0.16/0.43 => ( A2 != B2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.order.strict_implies_not_eq
% 0.16/0.43 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 0.16/0.43 ! [A2: a,B2: a,C: a] :
% 0.16/0.43 ( ( less @ A2 @ B2 )
% 0.16/0.43 => ( ( less @ B2 @ C )
% 0.16/0.43 => ( less @ A2 @ C ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.order.strict_trans
% 0.16/0.43 thf(fact_25_assms_I2_J,axiom,
% 0.16/0.43 rBT_Im759614907sorted @ a @ b @ less @ r ).
% 0.16/0.43
% 0.16/0.43 % assms(2)
% 0.16/0.43 thf(fact_26_assms_I1_J,axiom,
% 0.16/0.43 rBT_Im759614907sorted @ a @ b @ less @ l ).
% 0.16/0.43
% 0.16/0.43 % assms(1)
% 0.16/0.43 thf(fact_27_local_Orbt__less__trans,axiom,
% 0.16/0.43 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 0.16/0.43 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 0.16/0.43 => ( ( less @ X @ Y )
% 0.16/0.43 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_less_trans
% 0.16/0.43 thf(fact_28_local_Orbt__greater__trans,axiom,
% 0.16/0.43 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 0.16/0.43 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_greater_trans
% 0.16/0.43 thf(fact_29_rbt_Oinject,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 0.16/0.43 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.16/0.43 = ( ( X21 = Y21 )
% 0.16/0.43 & ( X22 = Y22 )
% 0.16/0.43 & ( X23 = Y23 )
% 0.16/0.43 & ( X24 = Y24 )
% 0.16/0.43 & ( X25 = Y25 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % rbt.inject
% 0.16/0.43 thf(fact_30_assms_I3_J,axiom,
% 0.16/0.43 rBT_Im2075124343t_less @ a @ b @ less @ k @ l ).
% 0.16/0.43
% 0.16/0.43 % assms(3)
% 0.16/0.43 thf(fact_31_assms_I4_J,axiom,
% 0.16/0.43 rBT_Im1259024060reater @ a @ b @ less @ k @ r ).
% 0.16/0.43
% 0.16/0.43 % assms(4)
% 0.16/0.43 thf(fact_32_local_Orbt__sorted_Osimps_I2_J,axiom,
% 0.16/0.43 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.43 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V @ R ) )
% 0.16/0.43 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.16/0.43 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.16/0.43 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.16/0.43 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_sorted.simps(2)
% 0.16/0.43 thf(fact_33_local_Orbt__greater__simps_I2_J,axiom,
% 0.16/0.43 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.16/0.43 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.16/0.43 = ( ( less @ K @ Kt )
% 0.16/0.43 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 0.16/0.43 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_greater_simps(2)
% 0.16/0.43 thf(fact_34_local_Ostrict__mono__eq,axiom,
% 0.16/0.43 ! [B: $tType] :
% 0.16/0.43 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.43 => ! [F: a > B,X: a,Y: a] :
% 0.16/0.43 ( ( strict_mono @ a @ B @ less @ F )
% 0.16/0.43 => ( ( ( F @ X )
% 0.16/0.43 = ( F @ Y ) )
% 0.16/0.43 = ( X = Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.strict_mono_eq
% 0.16/0.43 thf(fact_35_ord_Orbt__greater__simps_I2_J,axiom,
% 0.16/0.43 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.16/0.43 ( ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.16/0.43 = ( ( Less @ K @ Kt )
% 0.16/0.43 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Lt )
% 0.16/0.43 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_greater_simps(2)
% 0.16/0.43 thf(fact_36_local_Orbt__less__simps_I2_J,axiom,
% 0.16/0.43 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.16/0.43 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.16/0.43 = ( ( less @ Kt @ K )
% 0.16/0.43 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 0.16/0.43 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_less_simps(2)
% 0.16/0.43 thf(fact_37__C1_C,axiom,
% 0.16/0.43 rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 0.16/0.43
% 0.16/0.43 % "1"
% 0.16/0.43 thf(fact_38__092_060open_062x_A_060_Ay_A_092_060and_062_ABranch_AB_Ava_Avb_Avg_Avc_A_124_092_060guillemotleft_062_Ax_092_060close_062,axiom,
% 0.16/0.43 ( ( less @ x @ y )
% 0.16/0.43 & ( rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % \<open>x < y \<and> Branch B va vb vg vc |\<guillemotleft> x\<close>
% 0.16/0.43 thf(fact_39_local_Ois__rbt__rbt__sorted,axiom,
% 0.16/0.43 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.43 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.16/0.43 => ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.is_rbt_rbt_sorted
% 0.16/0.43 thf(fact_40__C5__4_Oprems_C_I4_J,axiom,
% 0.16/0.43 rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ).
% 0.16/0.43
% 0.16/0.43 % "5_4.prems"(4)
% 0.16/0.43 thf(fact_41__C5__4_Oprems_C_I2_J,axiom,
% 0.16/0.43 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ).
% 0.16/0.43
% 0.16/0.43 % "5_4.prems"(2)
% 0.16/0.43 thf(fact_42_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) )
% 0.16/0.43 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 0.16/0.43 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 0.16/0.43 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 0.16/0.43 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_sorted.simps(2)
% 0.16/0.43 thf(fact_43_ord_Orbt__less__simps_I2_J,axiom,
% 0.16/0.43 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.16/0.43 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.16/0.43 = ( ( Less @ Kt @ K )
% 0.16/0.43 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Lt )
% 0.16/0.43 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_less_simps(2)
% 0.16/0.43 thf(fact_44_color_Odistinct_I1_J,axiom,
% 0.16/0.43 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 0.16/0.43
% 0.16/0.43 % color.distinct(1)
% 0.16/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.43 ! [A: $tType,A2: A,P: A > $o] :
% 0.16/0.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.16/0.43 = ( P @ A2 ) ) ).
% 0.16/0.43
% 0.16/0.43 % mem_Collect_eq
% 0.16/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.43 ! [A: $tType,A3: set @ A] :
% 0.16/0.43 ( ( collect @ A
% 0.16/0.43 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.16/0.43 = A3 ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_mem_eq
% 0.16/0.43 thf(fact_47_Collect__cong,axiom,
% 0.16/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( P @ X3 )
% 0.16/0.43 = ( Q @ X3 ) )
% 0.16/0.43 => ( ( collect @ A @ P )
% 0.16/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % Collect_cong
% 0.16/0.43 thf(fact_48_ext,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ( ( F @ X3 )
% 0.16/0.43 = ( G @ X3 ) )
% 0.16/0.43 => ( F = G ) ) ).
% 0.16/0.43
% 0.16/0.43 % ext
% 0.16/0.43 thf(fact_49_color_Oinduct,axiom,
% 0.16/0.43 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 0.16/0.43 ( ( P @ rBT_Impl_Mirabelle_R )
% 0.16/0.43 => ( ( P @ rBT_Impl_Mirabelle_B )
% 0.16/0.43 => ( P @ Color ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % color.induct
% 0.16/0.43 thf(fact_50_color_Oexhaust,axiom,
% 0.16/0.43 ! [Y: rBT_Im1923302023_color] :
% 0.16/0.43 ( ( Y != rBT_Impl_Mirabelle_R )
% 0.16/0.43 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 0.16/0.43
% 0.16/0.43 % color.exhaust
% 0.16/0.43 thf(fact_51_local_Olexordp__eq__antisym,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 0.16/0.43 => ( Xs = Ys ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_antisym
% 0.16/0.43 thf(fact_52_local_Olexordp__eq__trans,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 0.16/0.43 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_trans
% 0.16/0.43 thf(fact_53_local_Olexordp__eq__refl,axiom,
% 0.16/0.43 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_refl
% 0.16/0.43 thf(fact_54_local_Olexordp__eq__linear,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_linear
% 0.16/0.43 thf(fact_55__C5__4_Oprems_C_I1_J,axiom,
% 0.16/0.43 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 0.16/0.43
% 0.16/0.43 % "5_4.prems"(1)
% 0.16/0.43 thf(fact_56__C5__4_Oprems_C_I3_J,axiom,
% 0.16/0.43 rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 0.16/0.43
% 0.16/0.43 % "5_4.prems"(3)
% 0.16/0.43 thf(fact_57_ord_Ois__rbt__rbt__sorted,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( rBT_Im862805236is_rbt @ A @ B @ Less @ T )
% 0.16/0.43 => ( rBT_Im759614907sorted @ A @ B @ Less @ T ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.is_rbt_rbt_sorted
% 0.16/0.43 thf(fact_58_local_OgreaterThan__def,axiom,
% 0.16/0.43 ! [L: a] :
% 0.16/0.43 ( ( set_greaterThan @ a @ less @ L )
% 0.16/0.43 = ( collect @ a @ ( less @ L ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.greaterThan_def
% 0.16/0.43 thf(fact_59_local_OlessThan__def,axiom,
% 0.16/0.43 ! [U: a] :
% 0.16/0.43 ( ( set_lessThan @ a @ less @ U )
% 0.16/0.43 = ( collect @ a
% 0.16/0.43 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lessThan_def
% 0.16/0.43 thf(fact_60_local_OEmpty__is__rbt,axiom,
% 0.16/0.43 ! [B: $tType] : ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.Empty_is_rbt
% 0.16/0.43 thf(fact_61_local_Ostrict__mono__less,axiom,
% 0.16/0.43 ! [B: $tType] :
% 0.16/0.43 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.43 => ! [F: a > B,X: a,Y: a] :
% 0.16/0.43 ( ( strict_mono @ a @ B @ less @ F )
% 0.16/0.43 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 0.16/0.43 = ( less @ X @ Y ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.strict_mono_less
% 0.16/0.43 thf(fact_62_local_Ostrict__mono__def,axiom,
% 0.16/0.43 ! [B: $tType] :
% 0.16/0.43 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.43 => ! [F: a > B] :
% 0.16/0.43 ( ( strict_mono @ a @ B @ less @ F )
% 0.16/0.43 = ( ! [X2: a,Y2: a] :
% 0.16/0.43 ( ( less @ X2 @ Y2 )
% 0.16/0.43 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.strict_mono_def
% 0.16/0.43 thf(fact_63_local_Ostrict__monoI,axiom,
% 0.16/0.43 ! [B: $tType] :
% 0.16/0.43 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.43 => ! [F: a > B] :
% 0.16/0.43 ( ! [X3: a,Y3: a] :
% 0.16/0.43 ( ( less @ X3 @ Y3 )
% 0.16/0.43 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.16/0.43 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.strict_monoI
% 0.16/0.43 thf(fact_64_local_Ostrict__monoD,axiom,
% 0.16/0.43 ! [B: $tType] :
% 0.16/0.43 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.43 => ! [F: a > B,X: a,Y: a] :
% 0.16/0.43 ( ( strict_mono @ a @ B @ less @ F )
% 0.16/0.43 => ( ( less @ X @ Y )
% 0.16/0.43 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.strict_monoD
% 0.16/0.43 thf(fact_65_local_Olexordp__eq_ONil,axiom,
% 0.16/0.43 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.Nil
% 0.16/0.43 thf(fact_66_local_Orbt__sorted_Osimps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_sorted.simps(1)
% 0.16/0.43 thf(fact_67_local_OlessThan__iff,axiom,
% 0.16/0.43 ! [I: a,K: a] :
% 0.16/0.43 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 0.16/0.43 = ( less @ I @ K ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lessThan_iff
% 0.16/0.43 thf(fact_68_local_OgreaterThan__iff,axiom,
% 0.16/0.43 ! [I: a,K: a] :
% 0.16/0.43 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 0.16/0.43 = ( less @ K @ I ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.greaterThan_iff
% 0.16/0.43 thf(fact_69_local_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.43 ! [Xs: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 0.16/0.43 = ( Xs
% 0.16/0.43 = ( nil @ a ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_simps(2)
% 0.16/0.43 thf(fact_70_local_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.43 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_simps(1)
% 0.16/0.43 thf(fact_71_local_Orbt__less__simps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_less_simps(1)
% 0.16/0.43 thf(fact_72_local_Orbt__greater__simps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.rbt_greater_simps(1)
% 0.16/0.43 thf(fact_73_rbt_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.16/0.43 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.16/0.43
% 0.16/0.43 % rbt.distinct(1)
% 0.16/0.43 thf(fact_74_rbt_Oinduct,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.43 => ( ! [X1: rBT_Im1923302023_color,X26: rBT_Im246033960le_rbt @ A @ B,X32: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( P @ X26 )
% 0.16/0.43 => ( ( P @ X5 )
% 0.16/0.43 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X26 @ X32 @ X4 @ X5 ) ) ) )
% 0.16/0.43 => ( P @ Rbt ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % rbt.induct
% 0.16/0.43 thf(fact_75_rbt_Oexhaust,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( Y
% 0.16/0.43 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.43 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % rbt.exhaust
% 0.16/0.43 thf(fact_76_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_sorted.simps(1)
% 0.16/0.43 thf(fact_77_ord_Orbt__less__simps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_less_simps(1)
% 0.16/0.43 thf(fact_78_ord_Orbt__greater__simps_I1_J,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.rbt_greater_simps(1)
% 0.16/0.43 thf(fact_79_ord_OEmpty__is__rbt,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im862805236is_rbt @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.Empty_is_rbt
% 0.16/0.43 thf(fact_80_rbt__cases,axiom,
% 0.16/0.43 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( ( T
% 0.16/0.43 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.43 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( T
% 0.16/0.43 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K2 @ V2 @ R2 ) )
% 0.16/0.43 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.43 ( T
% 0.16/0.43 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K2 @ V2 @ R2 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % rbt_cases
% 0.16/0.43 thf(fact_81_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq_simps(1)
% 0.16/0.43 thf(fact_82_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.16/0.43 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.16/0.43 = ( Xs
% 0.16/0.43 = ( nil @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq_simps(2)
% 0.16/0.43 thf(fact_83_local_Olexordp__eq_Ocases,axiom,
% 0.16/0.43 ! [A1: list @ a,A22: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.16/0.43 => ( ( ( A1
% 0.16/0.43 = ( nil @ a ) )
% 0.16/0.43 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 0.16/0.43 => ( ! [X3: a] :
% 0.16/0.43 ( ? [Xs2: list @ a] :
% 0.16/0.43 ( A1
% 0.16/0.43 = ( cons @ a @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Y3: a] :
% 0.16/0.43 ( ? [Ys2: list @ a] :
% 0.16/0.43 ( A22
% 0.16/0.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ~ ( less @ X3 @ Y3 ) ) )
% 0.16/0.43 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Ys2: list @ a] :
% 0.16/0.43 ( ( A22
% 0.16/0.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ~ ( less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( less @ Y3 @ X3 )
% 0.16/0.43 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.cases
% 0.16/0.43 thf(fact_84_local_Olexordp__eq_Oinducts,axiom,
% 0.16/0.43 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ X12 @ X27 )
% 0.16/0.43 => ( ! [X1: list @ a] : ( P @ ( nil @ a ) @ X1 )
% 0.16/0.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.16/0.43 ( ( less @ X3 @ Y3 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.16/0.43 ( ~ ( less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( less @ Y3 @ X3 )
% 0.16/0.43 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 0.16/0.43 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 0.16/0.43 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.inducts
% 0.16/0.43 thf(fact_85_local_Olexordp__eq_Osimps,axiom,
% 0.16/0.43 ! [A1: list @ a,A22: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.16/0.43 = ( ? [Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( nil @ a ) )
% 0.16/0.43 & ( A22 = Ys3 ) )
% 0.16/0.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A22
% 0.16/0.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.16/0.43 & ( less @ X2 @ Y2 ) )
% 0.16/0.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A22
% 0.16/0.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.16/0.43 & ~ ( less @ X2 @ Y2 )
% 0.16/0.43 & ~ ( less @ Y2 @ X2 )
% 0.16/0.43 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.simps
% 0.16/0.43 thf(fact_86_ord_Olexordp__eq_ONil,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.Nil
% 0.16/0.43 thf(fact_87_local_Olexordp__eq_OCons,axiom,
% 0.16/0.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.Cons
% 0.16/0.43 thf(fact_88_local_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ~ ( less @ X @ Y )
% 0.16/0.43 => ( ~ ( less @ Y @ X )
% 0.16/0.43 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq.Cons_eq
% 0.16/0.43 thf(fact_89_list_Oinject,axiom,
% 0.16/0.43 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.16/0.43 ( ( ( cons @ A @ X21 @ X22 )
% 0.16/0.43 = ( cons @ A @ Y21 @ Y22 ) )
% 0.16/0.43 = ( ( X21 = Y21 )
% 0.16/0.43 & ( X22 = Y22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list.inject
% 0.16/0.43 thf(fact_90_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.43 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.16/0.43 = ( ( Less @ X @ Y )
% 0.16/0.43 | ( ~ ( Less @ Y @ X )
% 0.16/0.43 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq_simps(4)
% 0.16/0.43 thf(fact_91_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 0.16/0.43 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq_simps(3)
% 0.16/0.43 thf(fact_92_local_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.43 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 0.16/0.43 = ( ( less @ X @ Y )
% 0.16/0.43 | ( ~ ( less @ Y @ X )
% 0.16/0.43 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_simps(4)
% 0.16/0.43 thf(fact_93_local_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.43 ! [X: a,Xs: list @ a] :
% 0.16/0.43 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_simps(3)
% 0.16/0.43 thf(fact_94_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.16/0.43 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 0.16/0.43 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.16/0.43 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 0.16/0.43 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.16/0.43 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % map_tailrec_rev.induct
% 0.16/0.43 thf(fact_95_list__nonempty__induct,axiom,
% 0.16/0.43 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.16/0.43 ( ( Xs
% 0.16/0.43 != ( nil @ A ) )
% 0.16/0.43 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.43 => ( ! [X3: A,Xs2: list @ A] :
% 0.16/0.43 ( ( Xs2
% 0.16/0.43 != ( nil @ A ) )
% 0.16/0.43 => ( ( P @ Xs2 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 0.16/0.43 => ( P @ Xs ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list_nonempty_induct
% 0.16/0.43 thf(fact_96_remdups__adj_Oinduct,axiom,
% 0.16/0.43 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.16/0.43 ( ( P @ ( nil @ A ) )
% 0.16/0.43 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.43 => ( ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.16/0.43 ( ( ( X3 = Y3 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.16/0.43 => ( ( ( X3 != Y3 )
% 0.16/0.43 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.16/0.43 => ( P @ A0 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % remdups_adj.induct
% 0.16/0.43 thf(fact_97_remdups__adj_Ocases,axiom,
% 0.16/0.43 ! [A: $tType,X: list @ A] :
% 0.16/0.43 ( ( X
% 0.16/0.43 != ( nil @ A ) )
% 0.16/0.43 => ( ! [X3: A] :
% 0.16/0.43 ( X
% 0.16/0.43 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.43 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.16/0.43 ( X
% 0.16/0.43 != ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % remdups_adj.cases
% 0.16/0.43 thf(fact_98_transpose_Ocases,axiom,
% 0.16/0.43 ! [A: $tType,X: list @ ( list @ A )] :
% 0.16/0.43 ( ( X
% 0.16/0.43 != ( nil @ ( list @ A ) ) )
% 0.16/0.43 => ( ! [Xss: list @ ( list @ A )] :
% 0.16/0.43 ( X
% 0.16/0.43 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.16/0.43 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.16/0.43 ( X
% 0.16/0.43 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % transpose.cases
% 0.16/0.43 thf(fact_99_splice_Oinduct,axiom,
% 0.16/0.43 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.43 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.16/0.43 => ( ! [V2: A,Va: list @ A] : ( P @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) )
% 0.16/0.43 => ( ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 0.16/0.43 ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % splice.induct
% 0.16/0.43 thf(fact_100_list__induct2_H,axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.16/0.43 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.43 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 0.16/0.43 => ( ! [Y3: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ! [X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 0.16/0.43 ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list_induct2'
% 0.16/0.43 thf(fact_101_neq__Nil__conv,axiom,
% 0.16/0.43 ! [A: $tType,Xs: list @ A] :
% 0.16/0.43 ( ( Xs
% 0.16/0.43 != ( nil @ A ) )
% 0.16/0.43 = ( ? [Y2: A,Ys3: list @ A] :
% 0.16/0.43 ( Xs
% 0.16/0.43 = ( cons @ A @ Y2 @ Ys3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % neq_Nil_conv
% 0.16/0.43 thf(fact_102_list_Oinducts,axiom,
% 0.16/0.43 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.16/0.43 ( ( P @ ( nil @ A ) )
% 0.16/0.43 => ( ! [X1: A,X26: list @ A] :
% 0.16/0.43 ( ( P @ X26 )
% 0.16/0.43 => ( P @ ( cons @ A @ X1 @ X26 ) ) )
% 0.16/0.43 => ( P @ List ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list.inducts
% 0.16/0.43 thf(fact_103_list_Oexhaust,axiom,
% 0.16/0.43 ! [A: $tType,Y: list @ A] :
% 0.16/0.43 ( ( Y
% 0.16/0.43 != ( nil @ A ) )
% 0.16/0.43 => ~ ! [X212: A,X222: list @ A] :
% 0.16/0.43 ( Y
% 0.16/0.43 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list.exhaust
% 0.16/0.43 thf(fact_104_list_OdiscI,axiom,
% 0.16/0.43 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.16/0.43 ( ( List
% 0.16/0.43 = ( cons @ A @ X21 @ X22 ) )
% 0.16/0.43 => ( List
% 0.16/0.43 != ( nil @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % list.discI
% 0.16/0.43 thf(fact_105_list_Odistinct_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,X21: A,X22: list @ A] :
% 0.16/0.43 ( ( nil @ A )
% 0.16/0.43 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.16/0.43
% 0.16/0.43 % list.distinct(1)
% 0.16/0.43 thf(fact_106_not__Cons__self2,axiom,
% 0.16/0.43 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.43 ( ( cons @ A @ X @ Xs )
% 0.16/0.43 != Xs ) ).
% 0.16/0.43
% 0.16/0.43 % not_Cons_self2
% 0.16/0.43 thf(fact_107_ord_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.43 ( ~ ( Less @ X @ Y )
% 0.16/0.43 => ( ~ ( Less @ Y @ X )
% 0.16/0.43 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 0.16/0.43 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.Cons_eq
% 0.16/0.43 thf(fact_108_ord_Olexordp__eq_OCons,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.43 ( ( Less @ X @ Y )
% 0.16/0.43 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.Cons
% 0.16/0.43 thf(fact_109_ord_Olexordp__eq_Oinducts,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.16/0.43 ( ( lexordp_eq @ A @ Less @ X12 @ X27 )
% 0.16/0.43 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.16/0.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.43 ( ( Less @ X3 @ Y3 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.43 ( ~ ( Less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( Less @ Y3 @ X3 )
% 0.16/0.43 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 0.16/0.43 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 0.16/0.43 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.inducts
% 0.16/0.43 thf(fact_110_ord_Olexordp__eq_Osimps,axiom,
% 0.16/0.43 ! [A: $tType] :
% 0.16/0.43 ( ( lexordp_eq @ A )
% 0.16/0.43 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.16/0.43 ( ? [Ys3: list @ A] :
% 0.16/0.43 ( ( A12
% 0.16/0.43 = ( nil @ A ) )
% 0.16/0.43 & ( A23 = Ys3 ) )
% 0.16/0.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.43 ( ( A12
% 0.16/0.43 = ( cons @ A @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A23
% 0.16/0.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.16/0.43 & ( Less2 @ X2 @ Y2 ) )
% 0.16/0.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.43 ( ( A12
% 0.16/0.43 = ( cons @ A @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A23
% 0.16/0.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.16/0.43 & ~ ( Less2 @ X2 @ Y2 )
% 0.16/0.43 & ~ ( Less2 @ Y2 @ X2 )
% 0.16/0.43 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.simps
% 0.16/0.43 thf(fact_111_ord_Olexordp__eq_Ocases,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.16/0.43 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 0.16/0.43 => ( ( ( A1
% 0.16/0.43 = ( nil @ A ) )
% 0.16/0.43 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 0.16/0.43 => ( ! [X3: A] :
% 0.16/0.43 ( ? [Xs2: list @ A] :
% 0.16/0.43 ( A1
% 0.16/0.43 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Y3: A] :
% 0.16/0.43 ( ? [Ys2: list @ A] :
% 0.16/0.43 ( A22
% 0.16/0.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.16/0.43 => ~ ( Less @ X3 @ Y3 ) ) )
% 0.16/0.43 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Ys2: list @ A] :
% 0.16/0.43 ( ( A22
% 0.16/0.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ~ ( Less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( Less @ Y3 @ X3 )
% 0.16/0.43 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq.cases
% 0.16/0.43 thf(fact_112_ord_Olexordp__eq__refl,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_eq_refl
% 0.16/0.43 thf(fact_113_local_Olexordp_ONil,axiom,
% 0.16/0.43 ! [Y: a,Ys: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ Y @ Ys ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.Nil
% 0.16/0.43 thf(fact_114_local_Olexordp_Ocases,axiom,
% 0.16/0.43 ! [A1: list @ a,A22: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ A1 @ A22 )
% 0.16/0.43 => ( ( ( A1
% 0.16/0.43 = ( nil @ a ) )
% 0.16/0.43 => ! [Y3: a,Ys2: list @ a] :
% 0.16/0.43 ( A22
% 0.16/0.43 != ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( ! [X3: a] :
% 0.16/0.43 ( ? [Xs2: list @ a] :
% 0.16/0.43 ( A1
% 0.16/0.43 = ( cons @ a @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Y3: a] :
% 0.16/0.43 ( ? [Ys2: list @ a] :
% 0.16/0.43 ( A22
% 0.16/0.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ~ ( less @ X3 @ Y3 ) ) )
% 0.16/0.43 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X3 @ Xs2 ) )
% 0.16/0.43 => ! [Ys2: list @ a] :
% 0.16/0.43 ( ( A22
% 0.16/0.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ~ ( less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( less @ Y3 @ X3 )
% 0.16/0.43 => ~ ( lexordp @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.cases
% 0.16/0.43 thf(fact_115_local_Olexordp_Oinducts,axiom,
% 0.16/0.43 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.16/0.43 ( ( lexordp @ a @ less @ X12 @ X27 )
% 0.16/0.43 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.16/0.43 ( ( less @ X3 @ Y3 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.16/0.43 ( ~ ( less @ X3 @ Y3 )
% 0.16/0.43 => ( ~ ( less @ Y3 @ X3 )
% 0.16/0.43 => ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 0.16/0.43 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 0.16/0.43 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.inducts
% 0.16/0.43 thf(fact_116_local_Olexordp_Osimps,axiom,
% 0.16/0.43 ! [A1: list @ a,A22: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ A1 @ A22 )
% 0.16/0.43 = ( ? [Y2: a,Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( nil @ a ) )
% 0.16/0.43 & ( A22
% 0.16/0.43 = ( cons @ a @ Y2 @ Ys3 ) ) )
% 0.16/0.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A22
% 0.16/0.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.16/0.43 & ( less @ X2 @ Y2 ) )
% 0.16/0.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.16/0.43 ( ( A1
% 0.16/0.43 = ( cons @ a @ X2 @ Xs3 ) )
% 0.16/0.43 & ( A22
% 0.16/0.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.16/0.43 & ~ ( less @ X2 @ Y2 )
% 0.16/0.43 & ~ ( less @ Y2 @ X2 )
% 0.16/0.43 & ( lexordp @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.simps
% 0.16/0.43 thf(fact_117_local_Olexordp__cases,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( ( ( Xs
% 0.16/0.43 = ( nil @ a ) )
% 0.16/0.43 => ! [Y3: a,Ys4: list @ a] :
% 0.16/0.43 ( Ys
% 0.16/0.43 != ( cons @ a @ Y3 @ Ys4 ) ) )
% 0.16/0.43 => ( ! [X3: a] :
% 0.16/0.43 ( ? [Xs4: list @ a] :
% 0.16/0.43 ( Xs
% 0.16/0.43 = ( cons @ a @ X3 @ Xs4 ) )
% 0.16/0.43 => ! [Y3: a] :
% 0.16/0.43 ( ? [Ys4: list @ a] :
% 0.16/0.43 ( Ys
% 0.16/0.43 = ( cons @ a @ Y3 @ Ys4 ) )
% 0.16/0.43 => ~ ( less @ X3 @ Y3 ) ) )
% 0.16/0.43 => ~ ! [X3: a,Xs4: list @ a] :
% 0.16/0.43 ( ( Xs
% 0.16/0.43 = ( cons @ a @ X3 @ Xs4 ) )
% 0.16/0.43 => ! [Ys4: list @ a] :
% 0.16/0.43 ( ( Ys
% 0.16/0.43 = ( cons @ a @ X3 @ Ys4 ) )
% 0.16/0.43 => ~ ( lexordp @ a @ less @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_cases
% 0.16/0.43 thf(fact_118_local_Olexordp__induct,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 0.16/0.43 => ( ! [X3: a,Xs2: list @ a,Y3: a,Ys2: list @ a] :
% 0.16/0.43 ( ( less @ X3 @ Y3 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.16/0.43 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 0.16/0.43 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 0.16/0.43 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_induct
% 0.16/0.43 thf(fact_119_local_Olexordp__antisym,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_antisym
% 0.16/0.43 thf(fact_120_local_Olexordp__irreflexive,axiom,
% 0.16/0.43 ! [Xs: list @ a] :
% 0.16/0.43 ( ! [X3: a] :
% 0.16/0.43 ~ ( less @ X3 @ X3 )
% 0.16/0.43 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_irreflexive
% 0.16/0.43 thf(fact_121_local_Olexordp__irreflexive_H,axiom,
% 0.16/0.43 ! [Xs: list @ a] :
% 0.16/0.43 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_irreflexive'
% 0.16/0.43 thf(fact_122_local_Olexordp__linear,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 | ( Xs = Ys )
% 0.16/0.43 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_linear
% 0.16/0.43 thf(fact_123_local_Olexordp__trans,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( ( lexordp @ a @ less @ Ys @ Zs )
% 0.16/0.43 => ( lexordp @ a @ less @ Xs @ Zs ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_trans
% 0.16/0.43 thf(fact_124_local_Olexordp_OCons,axiom,
% 0.16/0.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( less @ X @ Y )
% 0.16/0.43 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.Cons
% 0.16/0.43 thf(fact_125_local_Olexordp_OCons__eq,axiom,
% 0.16/0.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ~ ( less @ X @ Y )
% 0.16/0.43 => ( ~ ( less @ Y @ X )
% 0.16/0.43 => ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp.Cons_eq
% 0.16/0.43 thf(fact_126_local_Olexordp__conv__lexordp__eq,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 = ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 & ~ ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_conv_lexordp_eq
% 0.16/0.43 thf(fact_127_local_Olexordp__eq__conv__lexord,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.16/0.43 = ( ( Xs = Ys )
% 0.16/0.43 | ( lexordp @ a @ less @ Xs @ Ys ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_eq_conv_lexord
% 0.16/0.43 thf(fact_128_local_Olexordp__into__lexordp__eq,axiom,
% 0.16/0.43 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.43 => ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_into_lexordp_eq
% 0.16/0.43 thf(fact_129_ord_Olexordp__simps_I3_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.43 ( ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.16/0.43 = ( ( Less @ X @ Y )
% 0.16/0.43 | ( ~ ( Less @ Y @ X )
% 0.16/0.43 & ( lexordp @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_simps(3)
% 0.16/0.43 thf(fact_130_ord_Olexordp__simps_I1_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Ys: list @ A] :
% 0.16/0.43 ( ( lexordp @ A @ Less @ ( nil @ A ) @ Ys )
% 0.16/0.43 = ( Ys
% 0.16/0.43 != ( nil @ A ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_simps(1)
% 0.16/0.43 thf(fact_131_ord_Olexordp__simps_I2_J,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.16/0.43 ~ ( lexordp @ A @ Less @ Xs @ ( nil @ A ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_simps(2)
% 0.16/0.43 thf(fact_132_local_Olexordp__simps_I3_J,axiom,
% 0.16/0.43 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 0.16/0.43 = ( ( less @ X @ Y )
% 0.16/0.43 | ( ~ ( less @ Y @ X )
% 0.16/0.43 & ( lexordp @ a @ less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_simps(3)
% 0.16/0.43 thf(fact_133_local_Olexordp__simps_I2_J,axiom,
% 0.16/0.43 ! [Xs: list @ a] :
% 0.16/0.43 ~ ( lexordp @ a @ less @ Xs @ ( nil @ a ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_simps(2)
% 0.16/0.43 thf(fact_134_local_Olexordp__simps_I1_J,axiom,
% 0.16/0.43 ! [Ys: list @ a] :
% 0.16/0.43 ( ( lexordp @ a @ less @ ( nil @ a ) @ Ys )
% 0.16/0.43 = ( Ys
% 0.16/0.43 != ( nil @ a ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % local.lexordp_simps(1)
% 0.16/0.43 thf(fact_135_ord_Olexordp__irreflexive,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.16/0.43 ( ! [X3: A] :
% 0.16/0.43 ~ ( Less @ X3 @ X3 )
% 0.16/0.43 => ~ ( lexordp @ A @ Less @ Xs @ Xs ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp_irreflexive
% 0.16/0.43 thf(fact_136_ord_Olexordp_OCons__eq,axiom,
% 0.16/0.43 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.43 ( ~ ( Less @ X @ Y )
% 0.16/0.43 => ( ~ ( Less @ Y @ X )
% 0.16/0.43 => ( ( lexordp @ A @ Less @ Xs @ Ys )
% 0.16/0.43 => ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 % ord.lexordp.Cons_eq
% 0.16/0.44 thf(fact_137_ord_Olexordp_OCons,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( Less @ X @ Y )
% 0.16/0.44 => ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp.Cons
% 0.16/0.44 thf(fact_138_ord_Olexordp__into__lexordp__eq,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( lexordp @ A @ Less @ Xs @ Ys )
% 0.16/0.44 => ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_into_lexordp_eq
% 0.16/0.44 thf(fact_139_ord_Olexordp_ONil,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Y: A,Ys: list @ A] : ( lexordp @ A @ Less @ ( nil @ A ) @ ( cons @ A @ Y @ Ys ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp.Nil
% 0.16/0.44 thf(fact_140_ord_Olexordp_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.16/0.44 ( ( lexordp @ A @ Less @ A1 @ A22 )
% 0.16/0.44 => ( ( ( A1
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ! [Y3: A,Ys2: list @ A] :
% 0.16/0.44 ( A22
% 0.16/0.44 != ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.16/0.44 => ( ! [X3: A] :
% 0.16/0.44 ( ? [Xs2: list @ A] :
% 0.16/0.44 ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Y3: A] :
% 0.16/0.44 ( ? [Ys2: list @ A] :
% 0.16/0.44 ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.16/0.44 => ~ ( Less @ X3 @ Y3 ) ) )
% 0.16/0.44 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.16/0.44 ( ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Ys2: list @ A] :
% 0.16/0.44 ( ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.16/0.44 => ( ~ ( Less @ X3 @ Y3 )
% 0.16/0.44 => ( ~ ( Less @ Y3 @ X3 )
% 0.16/0.44 => ~ ( lexordp @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp.cases
% 0.16/0.44 thf(fact_141_ord_Olexordp_Osimps,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lexordp @ A )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.16/0.44 ( ? [Y2: A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( A23
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys3 ) ) )
% 0.16/0.44 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X2 @ Xs3 ) )
% 0.16/0.44 & ( A23
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.16/0.44 & ( Less2 @ X2 @ Y2 ) )
% 0.16/0.44 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X2 @ Xs3 ) )
% 0.16/0.44 & ( A23
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.16/0.44 & ~ ( Less2 @ X2 @ Y2 )
% 0.16/0.44 & ~ ( Less2 @ Y2 @ X2 )
% 0.16/0.44 & ( lexordp @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp.simps
% 0.16/0.44 thf(fact_142_ord_Olexordp_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.16/0.44 ( ( lexordp @ A @ Less @ X12 @ X27 )
% 0.16/0.44 => ( ! [Y3: A,Ys2: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys2 ) )
% 0.16/0.44 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ( Less @ X3 @ Y3 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.16/0.44 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ~ ( Less @ X3 @ Y3 )
% 0.16/0.44 => ( ~ ( Less @ Y3 @ X3 )
% 0.16/0.44 => ( ( lexordp @ A @ Less @ Xs2 @ Ys2 )
% 0.16/0.44 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 0.16/0.44 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp.inducts
% 0.16/0.44 thf(fact_143_local_Olexordp__append__rightI,axiom,
% 0.16/0.44 ! [Ys: list @ a,Xs: list @ a] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 != ( nil @ a ) )
% 0.16/0.44 => ( lexordp @ a @ less @ Xs @ ( append @ a @ Xs @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.lexordp_append_rightI
% 0.16/0.44 thf(fact_144_local_Olexordp__iff,axiom,
% 0.16/0.44 ! [Xs: list @ a,Ys: list @ a] :
% 0.16/0.44 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.16/0.44 = ( ? [X2: a,Vs: list @ a] :
% 0.16/0.44 ( Ys
% 0.16/0.44 = ( append @ a @ Xs @ ( cons @ a @ X2 @ Vs ) ) )
% 0.16/0.44 | ? [Us: list @ a,A5: a,B3: a,Vs: list @ a,Ws: list @ a] :
% 0.16/0.44 ( ( less @ A5 @ B3 )
% 0.16/0.44 & ( Xs
% 0.16/0.44 = ( append @ a @ Us @ ( cons @ a @ A5 @ Vs ) ) )
% 0.16/0.44 & ( Ys
% 0.16/0.44 = ( append @ a @ Us @ ( cons @ a @ B3 @ Ws ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.lexordp_iff
% 0.16/0.44 thf(fact_145_local_Olexordp__append__left__rightI,axiom,
% 0.16/0.44 ! [X: a,Y: a,Us2: list @ a,Xs: list @ a,Ys: list @ a] :
% 0.16/0.44 ( ( less @ X @ Y )
% 0.16/0.44 => ( lexordp @ a @ less @ ( append @ a @ Us2 @ ( cons @ a @ X @ Xs ) ) @ ( append @ a @ Us2 @ ( cons @ a @ Y @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.lexordp_append_left_rightI
% 0.16/0.44 thf(fact_146_sublists_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( sublists @ A @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sublists.simps(1)
% 0.16/0.44 thf(fact_147_local_Olexordp__append__leftI,axiom,
% 0.16/0.44 ! [Us2: list @ a,Vs2: list @ a,Xs: list @ a] :
% 0.16/0.44 ( ( lexordp @ a @ less @ Us2 @ Vs2 )
% 0.16/0.44 => ( lexordp @ a @ less @ ( append @ a @ Xs @ Us2 ) @ ( append @ a @ Xs @ Vs2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.lexordp_append_leftI
% 0.16/0.44 thf(fact_148_local_Olexordp__append__leftD,axiom,
% 0.16/0.44 ! [Xs: list @ a,Us2: list @ a,Vs2: list @ a] :
% 0.16/0.44 ( ( lexordp @ a @ less @ ( append @ a @ Xs @ Us2 ) @ ( append @ a @ Xs @ Vs2 ) )
% 0.16/0.44 => ( ! [A4: a] :
% 0.16/0.44 ~ ( less @ A4 @ A4 )
% 0.16/0.44 => ( lexordp @ a @ less @ Us2 @ Vs2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.lexordp_append_leftD
% 0.16/0.44 thf(fact_149_same__append__eq,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = ( append @ A @ Xs @ Zs ) )
% 0.16/0.44 = ( Ys = Zs ) ) ).
% 0.16/0.44
% 0.16/0.44 % same_append_eq
% 0.16/0.44 thf(fact_150_append__same__eq,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Ys @ Xs )
% 0.16/0.44 = ( append @ A @ Zs @ Xs ) )
% 0.16/0.44 = ( Ys = Zs ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_same_eq
% 0.16/0.44 thf(fact_151_append__assoc,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.44 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_assoc
% 0.16/0.44 thf(fact_152_append__Nil2,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A] :
% 0.16/0.44 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.16/0.44 = Xs ) ).
% 0.16/0.44
% 0.16/0.44 % append_Nil2
% 0.16/0.44 thf(fact_153_append__self__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = Xs )
% 0.16/0.44 = ( Ys
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_self_conv
% 0.16/0.44 thf(fact_154_self__append__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.44 = ( Ys
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % self_append_conv
% 0.16/0.44 thf(fact_155_append__self__conv2,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = Ys )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_self_conv2
% 0.16/0.44 thf(fact_156_self__append__conv2,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % self_append_conv2
% 0.16/0.44 thf(fact_157_Nil__is__append__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ( nil @ A )
% 0.16/0.44 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.44 = ( ( Xs
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( Ys
% 0.16/0.44 = ( nil @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Nil_is_append_conv
% 0.16/0.44 thf(fact_158_append__is__Nil__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 = ( ( Xs
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( Ys
% 0.16/0.44 = ( nil @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_is_Nil_conv
% 0.16/0.44 thf(fact_159_append1__eq__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.44 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.16/0.44 = ( ( Xs = Ys )
% 0.16/0.44 & ( X = Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append1_eq_conv
% 0.16/0.44 thf(fact_160_ord_Olexordp__append__leftD,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 0.16/0.44 ( ( lexordp @ A @ Less @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 0.16/0.44 => ( ! [A4: A] :
% 0.16/0.44 ~ ( Less @ A4 @ A4 )
% 0.16/0.44 => ( lexordp @ A @ Less @ Us2 @ Vs2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_append_leftD
% 0.16/0.44 thf(fact_161_ord_Olexordp__append__leftI,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 0.16/0.44 ( ( lexordp @ A @ Less @ Us2 @ Vs2 )
% 0.16/0.44 => ( lexordp @ A @ Less @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_append_leftI
% 0.16/0.44 thf(fact_162_append__Cons,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.16/0.44 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_Cons
% 0.16/0.44 thf(fact_163_Cons__eq__appendI,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( ( cons @ A @ X @ Xs1 )
% 0.16/0.44 = Ys )
% 0.16/0.44 => ( ( Xs
% 0.16/0.44 = ( append @ A @ Xs1 @ Zs ) )
% 0.16/0.44 => ( ( cons @ A @ X @ Xs )
% 0.16/0.44 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Cons_eq_appendI
% 0.16/0.44 thf(fact_164_eq__Nil__appendI,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( Xs = Ys )
% 0.16/0.44 => ( Xs
% 0.16/0.44 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % eq_Nil_appendI
% 0.16/0.44 thf(fact_165_append__Nil,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A] :
% 0.16/0.44 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.16/0.44 = Ys ) ).
% 0.16/0.44
% 0.16/0.44 % append_Nil
% 0.16/0.44 thf(fact_166_append__eq__append__conv2,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = ( append @ A @ Zs @ Ts ) )
% 0.16/0.44 = ( ? [Us: list @ A] :
% 0.16/0.44 ( ( ( Xs
% 0.16/0.44 = ( append @ A @ Zs @ Us ) )
% 0.16/0.44 & ( ( append @ A @ Us @ Ys )
% 0.16/0.44 = Ts ) )
% 0.16/0.44 | ( ( ( append @ A @ Xs @ Us )
% 0.16/0.44 = Zs )
% 0.16/0.44 & ( Ys
% 0.16/0.44 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_eq_append_conv2
% 0.16/0.44 thf(fact_167_append__eq__appendI,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Xs @ Xs1 )
% 0.16/0.44 = Zs )
% 0.16/0.44 => ( ( Ys
% 0.16/0.44 = ( append @ A @ Xs1 @ Us2 ) )
% 0.16/0.44 => ( ( append @ A @ Xs @ Ys )
% 0.16/0.44 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_eq_appendI
% 0.16/0.44 thf(fact_168_rev__nonempty__induct,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A] :
% 0.16/0.44 ( ( Xs2
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( ( P @ Xs2 )
% 0.16/0.44 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 0.16/0.44 => ( P @ Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rev_nonempty_induct
% 0.16/0.44 thf(fact_169_append__eq__Cons__conv,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( ( append @ A @ Ys @ Zs )
% 0.16/0.44 = ( cons @ A @ X @ Xs ) )
% 0.16/0.44 = ( ( ( Ys
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( Zs
% 0.16/0.44 = ( cons @ A @ X @ Xs ) ) )
% 0.16/0.44 | ? [Ys5: list @ A] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 = ( cons @ A @ X @ Ys5 ) )
% 0.16/0.44 & ( ( append @ A @ Ys5 @ Zs )
% 0.16/0.44 = Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_eq_Cons_conv
% 0.16/0.44 thf(fact_170_Cons__eq__append__conv,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.44 = ( append @ A @ Ys @ Zs ) )
% 0.16/0.44 = ( ( ( Ys
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( ( cons @ A @ X @ Xs )
% 0.16/0.44 = Zs ) )
% 0.16/0.44 | ? [Ys5: list @ A] :
% 0.16/0.44 ( ( ( cons @ A @ X @ Ys5 )
% 0.16/0.44 = Ys )
% 0.16/0.44 & ( Xs
% 0.16/0.44 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Cons_eq_append_conv
% 0.16/0.44 thf(fact_171_rev__exhaust,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ~ ! [Ys2: list @ A,Y3: A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 != ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rev_exhaust
% 0.16/0.44 thf(fact_172_rev__induct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.16/0.44 ( ( P @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A] :
% 0.16/0.44 ( ( P @ Xs2 )
% 0.16/0.44 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 0.16/0.44 => ( P @ Xs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % rev_induct
% 0.16/0.44 thf(fact_173_ord_Olexordp__append__left__rightI,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Us2: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( Less @ X @ Y )
% 0.16/0.44 => ( lexordp @ A @ Less @ ( append @ A @ Us2 @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_append_left_rightI
% 0.16/0.44 thf(fact_174_ord_Olexordp__append__rightI,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A,Less: A > A > $o,Xs: list @ A] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( lexordp @ A @ Less @ Xs @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_append_rightI
% 0.16/0.44 thf(fact_175_keys__simps_I2_J,axiom,
% 0.16/0.44 ! [D: $tType,C2: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ C2 @ D,K: C2,V: D,R: rBT_Im246033960le_rbt @ C2 @ D] :
% 0.16/0.44 ( ( rBT_Im380146495e_keys @ C2 @ D @ ( rBT_Im480247531Branch @ C2 @ D @ C @ L @ K @ V @ R ) )
% 0.16/0.44 = ( append @ C2 @ ( rBT_Im380146495e_keys @ C2 @ D @ L ) @ ( cons @ C2 @ K @ ( rBT_Im380146495e_keys @ C2 @ D @ R ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % keys_simps(2)
% 0.16/0.44 thf(fact_176_product__lists_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % product_lists.simps(1)
% 0.16/0.44 thf(fact_177_bind__simps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.16/0.44 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 0.16/0.44 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bind_simps(2)
% 0.16/0.44 thf(fact_178_bind__simps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.16/0.44 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.16/0.44 = ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % bind_simps(1)
% 0.16/0.44 thf(fact_179_keys__simps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( rBT_Im380146495e_keys @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.44 = ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % keys_simps(1)
% 0.16/0.44 thf(fact_180_non__empty__rbt__keys,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( T
% 0.16/0.44 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.44 => ( ( rBT_Im380146495e_keys @ A @ B @ T )
% 0.16/0.44 != ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % non_empty_rbt_keys
% 0.16/0.44 thf(fact_181_local_Orbt__greater__prop,axiom,
% 0.16/0.44 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 0.16/0.44 = ( ! [X2: a] :
% 0.16/0.44 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 0.16/0.44 => ( less @ K @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_greater_prop
% 0.16/0.44 thf(fact_182_local_Orbt__less__prop,axiom,
% 0.16/0.44 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 0.16/0.44 = ( ! [X2: a] :
% 0.16/0.44 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 0.16/0.44 => ( less @ X2 @ K ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_less_prop
% 0.16/0.44 thf(fact_183_local_Ostrict__mono__imp__inj__on,axiom,
% 0.16/0.44 ! [B: $tType] :
% 0.16/0.44 ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.44 => ! [F: a > B,A3: set @ a] :
% 0.16/0.44 ( ( strict_mono @ a @ B @ less @ F )
% 0.16/0.44 => ( inj_on @ a @ B @ F @ A3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.strict_mono_imp_inj_on
% 0.16/0.44 thf(fact_184_list__bind__cong,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 0.16/0.44 ( ( Xs = Ys )
% 0.16/0.44 => ( ! [X3: A] :
% 0.16/0.44 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 => ( ( F @ X3 )
% 0.16/0.44 = ( G @ X3 ) ) )
% 0.16/0.44 => ( ( bind @ A @ B @ Xs @ F )
% 0.16/0.44 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_bind_cong
% 0.16/0.44 thf(fact_185_split__list__first__prop__iff,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ( ? [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X2 ) ) )
% 0.16/0.44 = ( ? [Ys3: list @ A,X2: A] :
% 0.16/0.44 ( ? [Zs2: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 0.16/0.44 & ( P @ X2 )
% 0.16/0.44 & ! [Y2: A] :
% 0.16/0.44 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys3 ) )
% 0.16/0.44 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_first_prop_iff
% 0.16/0.44 thf(fact_186_split__list__last__prop__iff,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ( ? [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X2 ) ) )
% 0.16/0.44 = ( ? [Ys3: list @ A,X2: A,Zs2: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 0.16/0.44 & ( P @ X2 )
% 0.16/0.44 & ! [Y2: A] :
% 0.16/0.44 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 0.16/0.44 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_last_prop_iff
% 0.16/0.44 thf(fact_187_in__set__conv__decomp__first,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.16/0.44 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % in_set_conv_decomp_first
% 0.16/0.44 thf(fact_188_in__set__conv__decomp__last,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.16/0.44 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % in_set_conv_decomp_last
% 0.16/0.44 thf(fact_189_split__list__first__propE,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ~ ! [Ys2: list @ A,X3: A] :
% 0.16/0.44 ( ? [Zs3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 => ( ( P @ X3 )
% 0.16/0.44 => ~ ! [Xa: A] :
% 0.16/0.44 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.16/0.44 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_first_propE
% 0.16/0.44 thf(fact_190_split__list__last__propE,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ~ ! [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 => ( ( P @ X3 )
% 0.16/0.44 => ~ ! [Xa: A] :
% 0.16/0.44 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.16/0.44 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_last_propE
% 0.16/0.44 thf(fact_191_split__list__first__prop,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ? [Ys2: list @ A,X3: A] :
% 0.16/0.44 ( ? [Zs3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 & ( P @ X3 )
% 0.16/0.44 & ! [Xa: A] :
% 0.16/0.44 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.16/0.44 => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_first_prop
% 0.16/0.44 thf(fact_192_split__list__last__prop,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 & ( P @ X3 )
% 0.16/0.44 & ! [Xa: A] :
% 0.16/0.44 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.16/0.44 => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_last_prop
% 0.16/0.44 thf(fact_193_in__set__conv__decomp,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % in_set_conv_decomp
% 0.16/0.44 thf(fact_194_split__list__propE,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ~ ! [Ys2: list @ A,X3: A] :
% 0.16/0.44 ( ? [Zs3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 => ~ ( P @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_propE
% 0.16/0.44 thf(fact_195_split__list__first,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.16/0.44 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_first
% 0.16/0.44 thf(fact_196_split__list__prop,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.16/0.44 ( ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X6 ) )
% 0.16/0.44 => ? [Ys2: list @ A,X3: A] :
% 0.16/0.44 ( ? [Zs3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.16/0.44 & ( P @ X3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_prop
% 0.16/0.44 thf(fact_197_split__list__last,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.16/0.44 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list_last
% 0.16/0.44 thf(fact_198_split__list,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % split_list
% 0.16/0.44 thf(fact_199_list_Oset__cases,axiom,
% 0.16/0.44 ! [A: $tType,E: A,A2: list @ A] :
% 0.16/0.44 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.16/0.44 => ( ! [Z2: list @ A] :
% 0.16/0.44 ( A2
% 0.16/0.44 != ( cons @ A @ E @ Z2 ) )
% 0.16/0.44 => ~ ! [Z1: A,Z2: list @ A] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( cons @ A @ Z1 @ Z2 ) )
% 0.16/0.44 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.set_cases
% 0.16/0.44 thf(fact_200_set__ConsD,axiom,
% 0.16/0.44 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.16/0.44 => ( ( Y = X )
% 0.16/0.44 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % set_ConsD
% 0.16/0.44 thf(fact_201_list_Oset__intros_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.set_intros(1)
% 0.16/0.44 thf(fact_202_list_Oset__intros_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 0.16/0.44 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 0.16/0.44 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.set_intros(2)
% 0.16/0.44 thf(fact_203_ord_Orbt__less__prop,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( rBT_Im2075124343t_less @ A @ B )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,K3: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ! [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.16/0.44 => ( Less2 @ X2 @ K3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_less_prop
% 0.16/0.44 thf(fact_204_ord_Orbt__greater__prop,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( rBT_Im1259024060reater @ A @ B )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,K3: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ! [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.16/0.44 => ( Less2 @ K3 @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_greater_prop
% 0.16/0.44 thf(fact_205_local_Odistinct__keys,axiom,
% 0.16/0.44 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.16/0.44 => ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.distinct_keys
% 0.16/0.44 thf(fact_206_the__elem__set,axiom,
% 0.16/0.44 ! [A: $tType,X: A] :
% 0.16/0.44 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.16/0.44 = X ) ).
% 0.16/0.44
% 0.16/0.44 % the_elem_set
% 0.16/0.44 thf(fact_207_ord_OgreaterThan__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( set_greaterThan @ A )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,L3: A] : ( collect @ A @ ( Less2 @ L3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.greaterThan_def
% 0.16/0.44 thf(fact_208_distinct__product__lists,axiom,
% 0.16/0.44 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.16/0.44 ( ! [X3: list @ A] :
% 0.16/0.44 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.16/0.44 => ( distinct @ A @ X3 ) )
% 0.16/0.44 => ( distinct @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct_product_lists
% 0.16/0.44 thf(fact_209_distinct_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.44 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( distinct @ A @ Xs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct.simps(2)
% 0.16/0.44 thf(fact_210_distinct_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct.simps(1)
% 0.16/0.44 thf(fact_211_distinct__length__2__or__more,axiom,
% 0.16/0.44 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 0.16/0.44 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 0.16/0.44 = ( ( A2 != B2 )
% 0.16/0.44 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 0.16/0.44 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct_length_2_or_more
% 0.16/0.44 thf(fact_212_distinct__singleton,axiom,
% 0.16/0.44 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct_singleton
% 0.16/0.44 thf(fact_213_not__distinct__decomp,axiom,
% 0.16/0.44 ! [A: $tType,Ws2: list @ A] :
% 0.16/0.44 ( ~ ( distinct @ A @ Ws2 )
% 0.16/0.44 => ? [Xs2: list @ A,Ys2: list @ A,Zs3: list @ A,Y3: A] :
% 0.16/0.44 ( Ws2
% 0.16/0.44 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ ( append @ A @ Ys2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % not_distinct_decomp
% 0.16/0.44 thf(fact_214_not__distinct__conv__prefix,axiom,
% 0.16/0.44 ! [A: $tType,As2: list @ A] :
% 0.16/0.44 ( ( ~ ( distinct @ A @ As2 ) )
% 0.16/0.44 = ( ? [Xs3: list @ A,Y2: A,Ys3: list @ A] :
% 0.16/0.44 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 0.16/0.44 & ( distinct @ A @ Xs3 )
% 0.16/0.44 & ( As2
% 0.16/0.44 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % not_distinct_conv_prefix
% 0.16/0.44 thf(fact_215_ord_OlessThan__iff,axiom,
% 0.16/0.44 ! [A: $tType,I: A,Less: A > A > $o,K: A] :
% 0.16/0.44 ( ( member @ A @ I @ ( set_lessThan @ A @ Less @ K ) )
% 0.16/0.44 = ( Less @ I @ K ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lessThan_iff
% 0.16/0.44 thf(fact_216_ord_OgreaterThan__iff,axiom,
% 0.16/0.44 ! [A: $tType,I: A,Less: A > A > $o,K: A] :
% 0.16/0.44 ( ( member @ A @ I @ ( set_greaterThan @ A @ Less @ K ) )
% 0.16/0.44 = ( Less @ K @ I ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.greaterThan_iff
% 0.16/0.44 thf(fact_217_ord_OlessThan__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( set_lessThan @ A )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,U2: A] :
% 0.16/0.44 ( collect @ A
% 0.16/0.44 @ ^ [X2: A] : ( Less2 @ X2 @ U2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lessThan_def
% 0.16/0.44 thf(fact_218_local_Oset__entries__inject,axiom,
% 0.16/0.44 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.16/0.44 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.16/0.44 => ( ( ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) )
% 0.16/0.44 = ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) )
% 0.16/0.44 = ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.16/0.44 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.set_entries_inject
% 0.16/0.44 thf(fact_219_distinct__union,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( distinct @ A @ ( union @ A @ Xs @ Ys ) )
% 0.16/0.44 = ( distinct @ A @ Ys ) ) ).
% 0.16/0.44
% 0.16/0.44 % distinct_union
% 0.16/0.44 thf(fact_220_entries_Osimps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.44 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % entries.simps(1)
% 0.16/0.44 thf(fact_221_local_Oentries__rbt__lookup,axiom,
% 0.16/0.44 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.16/0.44 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.16/0.44 => ( ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.16/0.44 = ( rBT_Im954575269ntries @ a @ B @ T22 ) )
% 0.16/0.44 = ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.entries_rbt_lookup
% 0.16/0.44 thf(fact_222_local_Oentries__eqI,axiom,
% 0.16/0.44 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.16/0.44 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.16/0.44 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) )
% 0.16/0.44 => ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.16/0.44 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.entries_eqI
% 0.16/0.44 thf(fact_223_local_Orbt__lookup__from__in__tree,axiom,
% 0.16/0.44 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B,K: a] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.16/0.44 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.16/0.44 => ( ! [V2: B] :
% 0.16/0.44 ( ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V2 ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) ) )
% 0.16/0.44 = ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V2 ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 @ K )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 @ K ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_from_in_tree
% 0.16/0.44 thf(fact_224_local_Orbt__lookup__keys,axiom,
% 0.16/0.44 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.16/0.44 => ( ( dom @ a @ B @ ( rBT_Im35466040lookup @ a @ B @ less @ T ) )
% 0.16/0.44 = ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_keys
% 0.16/0.44 thf(fact_225_entries_Osimps_I2_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ K @ V @ R ) )
% 0.16/0.44 = ( append @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ L ) @ ( cons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V ) @ ( rBT_Im954575269ntries @ A @ B @ R ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % entries.simps(2)
% 0.16/0.44 thf(fact_226_entry__in__tree__keys,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,K: A,V: B,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V ) @ ( set2 @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ T ) ) )
% 0.16/0.44 => ( member @ A @ K @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % entry_in_tree_keys
% 0.16/0.44 thf(fact_227_keys__entries,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( member @ A @ K @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) )
% 0.16/0.44 = ( ? [V3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ T ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % keys_entries
% 0.16/0.44 thf(fact_228_local_OacyclicI__order,axiom,
% 0.16/0.44 ! [B: $tType,R: set @ ( product_prod @ B @ B ),F: B > a] :
% 0.16/0.44 ( ! [A4: B,B4: B] :
% 0.16/0.44 ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A4 @ B4 ) @ R )
% 0.16/0.44 => ( less @ ( F @ B4 ) @ ( F @ A4 ) ) )
% 0.16/0.44 => ( transitive_acyclic @ B @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.acyclicI_order
% 0.16/0.44 thf(fact_229_local_Orbt__lookup__in__tree,axiom,
% 0.16/0.44 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.16/0.44 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.16/0.44 = ( some @ B @ V ) )
% 0.16/0.44 = ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_in_tree
% 0.16/0.44 thf(fact_230_local_Orbt__lookup_Osimps_I2_J,axiom,
% 0.16/0.44 ! [B: $tType,K: a,X: a,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( ( less @ K @ X )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ L @ K ) ) )
% 0.16/0.44 & ( ~ ( less @ K @ X )
% 0.16/0.44 => ( ( ( less @ X @ K )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ R @ K ) ) )
% 0.16/0.44 & ( ~ ( less @ X @ K )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( some @ B @ Y ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup.simps(2)
% 0.16/0.44 thf(fact_231_splice_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 0.16/0.44 ( ! [Ys2: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 0.16/0.44 => ( ! [V2: A,Va: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) ) )
% 0.16/0.44 => ~ ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % splice.cases
% 0.16/0.44 thf(fact_232_map__tailrec__rev_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 0.16/0.44 ( ! [F2: A > B,Bs: list @ B] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 0.16/0.44 => ~ ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_tailrec_rev.cases
% 0.16/0.44 thf(fact_233_ord_Orbt__lookup_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,X: A,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( ( Less @ K @ X )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( rBT_Im35466040lookup @ A @ B @ Less @ L @ K ) ) )
% 0.16/0.44 & ( ~ ( Less @ K @ X )
% 0.16/0.44 => ( ( ( Less @ X @ K )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( rBT_Im35466040lookup @ A @ B @ Less @ R @ K ) ) )
% 0.16/0.44 & ( ~ ( Less @ X @ K )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.16/0.44 = ( some @ B @ Y ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_lookup.simps(2)
% 0.16/0.44 thf(fact_234_local_Omap__of__entries,axiom,
% 0.16/0.44 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.16/0.44 => ( ( map_of @ a @ B @ ( rBT_Im954575269ntries @ a @ B @ T ) )
% 0.16/0.44 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.map_of_entries
% 0.16/0.44 thf(fact_235_local_Orbt__lookup_Osimps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,K: a] :
% 0.16/0.44 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 0.16/0.44 = ( none @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup.simps(1)
% 0.16/0.44 thf(fact_236_local_Orbt__lookup__Empty,axiom,
% 0.16/0.44 ! [B: $tType] :
% 0.16/0.44 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 0.16/0.44 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_Empty
% 0.16/0.44 thf(fact_237_local_Orbt__lookup__rbt__less,axiom,
% 0.16/0.44 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.16/0.44 = ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_rbt_less
% 0.16/0.44 thf(fact_238_local_Orbt__lookup__rbt__greater,axiom,
% 0.16/0.44 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.16/0.44 = ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.rbt_lookup_rbt_greater
% 0.16/0.44 thf(fact_239_ord_Orbt__lookup__Empty,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,Less: A > A > $o] :
% 0.16/0.44 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.16/0.44 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_lookup_Empty
% 0.16/0.44 thf(fact_240_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Less: A > A > $o,K: A] :
% 0.16/0.44 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 0.16/0.44 = ( none @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_lookup.simps(1)
% 0.16/0.44 thf(fact_241_ord_Orbt__lookup__rbt__less,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ T )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 0.16/0.44 = ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_lookup_rbt_less
% 0.16/0.44 thf(fact_242_ord_Orbt__lookup__rbt__greater,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.16/0.44 ( ( rBT_Im1259024060reater @ A @ B @ Less @ K @ T )
% 0.16/0.44 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 0.16/0.44 = ( none @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.rbt_lookup_rbt_greater
% 0.16/0.44 thf(fact_243_order__class_OacyclicI__order,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [R: set @ ( product_prod @ B @ B ),F: B > A] :
% 0.16/0.44 ( ! [A4: B,B4: B] :
% 0.16/0.44 ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A4 @ B4 ) @ R )
% 0.16/0.44 => ( ord_less @ A @ ( F @ B4 ) @ ( F @ A4 ) ) )
% 0.16/0.44 => ( transitive_acyclic @ B @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % order_class.acyclicI_order
% 0.16/0.44 thf(fact_244_dom__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( dom @ A @ B )
% 0.16/0.44 = ( ^ [M: A > ( option @ B )] :
% 0.16/0.44 ( collect @ A
% 0.16/0.44 @ ^ [A5: A] :
% 0.16/0.44 ( ( M @ A5 )
% 0.16/0.44 != ( none @ B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % dom_def
% 0.16/0.44 thf(fact_245_extract__Some__iff,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o,Xs: list @ A,Ys: list @ A,Y: A,Zs: list @ A] :
% 0.16/0.44 ( ( ( extract @ A @ P @ Xs )
% 0.16/0.44 = ( some @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) @ ( product_Pair @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) @ Ys @ ( product_Pair @ A @ ( list @ A ) @ Y @ Zs ) ) ) )
% 0.16/0.44 = ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys @ ( cons @ A @ Y @ Zs ) ) )
% 0.16/0.44 & ( P @ Y )
% 0.16/0.44 & ~ ? [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 0.16/0.44 & ( P @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % extract_Some_iff
% 0.16/0.44 thf(fact_246_extract__SomeE,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o,Xs: list @ A,Ys: list @ A,Y: A,Zs: list @ A] :
% 0.16/0.44 ( ( ( extract @ A @ P @ Xs )
% 0.16/0.44 = ( some @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) @ ( product_Pair @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) @ Ys @ ( product_Pair @ A @ ( list @ A ) @ Y @ Zs ) ) ) )
% 0.16/0.44 => ( ( Xs
% 0.16/0.44 = ( append @ A @ Ys @ ( cons @ A @ Y @ Zs ) ) )
% 0.16/0.44 & ( P @ Y )
% 0.16/0.44 & ~ ? [X6: A] :
% 0.16/0.44 ( ( member @ A @ X6 @ ( set2 @ A @ Ys ) )
% 0.16/0.44 & ( P @ X6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % extract_SomeE
% 0.16/0.44 thf(fact_247_extract__Nil__code,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o] :
% 0.16/0.44 ( ( extract @ A @ P @ ( nil @ A ) )
% 0.16/0.44 = ( none @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % extract_Nil_code
% 0.16/0.44 thf(fact_248_extract__None__iff,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o,Xs: list @ A] :
% 0.16/0.44 ( ( ( extract @ A @ P @ Xs )
% 0.16/0.44 = ( none @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) )
% 0.16/0.44 = ( ~ ? [X2: A] :
% 0.16/0.44 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.16/0.44 & ( P @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % extract_None_iff
% 0.16/0.44 thf(fact_249_snoc__listrel1__snoc__iff,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 0.16/0.44 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.16/0.44 & ( X = Y ) )
% 0.16/0.44 | ( ( Xs = Ys )
% 0.16/0.44 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % snoc_listrel1_snoc_iff
% 0.16/0.44 thf(fact_250_local_Ois__rbt__def,axiom,
% 0.16/0.44 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.16/0.44 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.16/0.44 = ( ( rBT_Im1040612427e_inv1 @ a @ B @ T )
% 0.16/0.44 & ( rBT_Im1040612428e_inv2 @ a @ B @ T )
% 0.16/0.44 & ( ( rBT_Im1805589839lor_of @ a @ B @ T )
% 0.16/0.44 = rBT_Impl_Mirabelle_B )
% 0.16/0.44 & ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.is_rbt_def
% 0.16/0.44 thf(fact_251_Cons__listrel1__Cons,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 0.16/0.44 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 0.16/0.44 & ( Xs = Ys ) )
% 0.16/0.44 | ( ( X = Y )
% 0.16/0.44 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Cons_listrel1_Cons
% 0.16/0.44 thf(fact_252_listrel1I2,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 0.16/0.44 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.16/0.44 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrel1I2
% 0.16/0.44 thf(fact_253_append__listrel1I,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs2: list @ A] :
% 0.16/0.44 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 0.16/0.44 & ( Us2 = Vs2 ) )
% 0.16/0.44 | ( ( Xs = Ys )
% 0.16/0.44 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs2 ) @ ( listrel1 @ A @ R ) ) ) )
% 0.16/0.44 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % append_listrel1I
% 0.16/0.44 thf(fact_254_not__listrel1__Nil,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 0.16/0.44 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 0.16/0.44
% 0.16/0.44 % not_listrel1_Nil
% 0.16/0.44
% 0.16/0.44 %----Type constructors (3)
% 0.16/0.44 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.16/0.44 ! [A6: $tType,A7: $tType] :
% 0.16/0.44 ( ( order @ A7 @ ( type2 @ A7 ) )
% 0.16/0.44 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.16/0.44 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.16/0.44 order @ $o @ ( type2 @ $o ) ).
% 0.16/0.44
% 0.16/0.44 %----Conjectures (1)
% 0.16/0.44 thf(conj_0,conjecture,
% 0.16/0.44 ( ( less @ y @ z )
% 0.16/0.44 & ( rBT_Im1259024060reater @ a @ b @ less @ z @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 2.45/1.45 ---- Embedded in THF ---
% 2.45/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.45/1.45 %%% Generated on Tue Feb 24 06:12:26 EST 2026
% 2.45/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.45/1.45 %%% Logic specification used:
% 2.45/1.45 %%% thf(spec, logic, $$dhol).
% 2.45/1.45
% 2.45/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2DTF30182.p
% 2.45/1.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor, type, rBT_Im1923302023_color: $tType).
% 2.45/1.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt, type, rBT_Im246033960le_rbt: ($tType > ($tType > $tType))).
% 2.45/1.45 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.45/1.45 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.45/1.45 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.45/1.45 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.45/1.45 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.45/1.45 thf(ty_tf_b, type, b: $tType).
% 2.45/1.45 thf(ty_tf_a, type, a: $tType).
% 2.45/1.45 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.45/1.45 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.45/1.45 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 2.45/1.45 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.45/1.45 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.45/1.45 thf(sy_c_List_Odistinct, type, distinct: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.45/1.45 thf(sy_c_List_Oextract, type, extract: (!> [A:$tType]: (((A > $o) > ((list @ A) > (option @ ((product_prod @ (list @ A)) @ ((product_prod @ A) @ (list @ A))))))))).
% 2.45/1.45 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.45/1.45 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.45/1.45 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.45/1.45 thf(sy_c_List_Olistrel1, type, listrel1: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > (set @ ((product_prod @ (list @ A)) @ (list @ A))))))).
% 2.45/1.45 thf(sy_c_List_Oord_Olexordp, type, lexordp: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.45/1.45 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.45/1.45 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.45/1.45 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.45/1.45 thf(sy_c_List_Ounion, type, union: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.45/1.45 thf(sy_c_Map_Odom, type, dom: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > (set @ A))))).
% 2.45/1.45 thf(sy_c_Map_Omap__of, type, map_of: (!> [A:$tType,B:$tType]: (((list @ ((product_prod @ A) @ B)) > (A > (option @ B)))))).
% 2.45/1.45 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.45/1.45 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.45/1.45 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.45/1.45 thf(sy_c_Orderings_Oorder_Ostrict__mono, type, strict_mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.45/1.45 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.45/1.45 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of, type, rBT_Im1805589839lor_of: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > rBT_Im1923302023_color)))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries, type, rBT_Im954575269ntries: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (list @ ((product_prod @ A) @ B)))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1, type, rBT_Im1040612427e_inv1: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv2, type, rBT_Im1040612428e_inv2: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys, type, rBT_Im380146495e_keys: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (list @ A))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt, type, rBT_Im862805236is_rbt: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater, type, rBT_Im1259024060reater: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less, type, rBT_Im2075124343t_less: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup, type, rBT_Im35466040lookup: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (option @ B))))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted, type, rBT_Im759614907sorted: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch, type, rBT_Im480247531Branch: (!> [A:$tType,B:$tType]: ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.45/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty, type, rBT_Im418718756_Empty: (!> [A:$tType,B:$tType]: (((rBT_Im246033960le_rbt @ A) @ B)))).
% 2.45/1.45 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.45/1.45 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.45/1.45 thf(sy_c_Set__Interval_Oord_OgreaterThan, type, set_greaterThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.45/1.45 thf(sy_c_Set__Interval_Oord_OlessThan, type, set_lessThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.45/1.45 thf(sy_c_Transitive__Closure_Oacyclic, type, transitive_acyclic: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.45/1.45 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.45/1.45 thf(sy_v_b____, type, b2: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_c____, type, c: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_k, type, k: a).
% 2.45/1.45 thf(sy_v_l, type, l: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_less, type, less: (a > (a > $o))).
% 2.45/1.45 thf(sy_v_r, type, r: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_s____, type, s: b).
% 2.45/1.45 thf(sy_v_t____, type, t: b).
% 2.45/1.45 thf(sy_v_va____, type, va: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_vb____, type, vb: a).
% 2.45/1.45 thf(sy_v_vc____, type, vc: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_vd____, type, vd: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_ve____, type, ve: a).
% 2.45/1.45 thf(sy_v_vf____, type, vf: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.45/1.45 thf(sy_v_vg____, type, vg: b).
% 2.45/1.45 thf(sy_v_vii____, type, vii: b).
% 2.45/1.45 thf(sy_v_x____, type, x: a).
% 2.45/1.45 thf(sy_v_y____, type, y: a).
% 2.45/1.45 thf(sy_v_z____, type, z: a).
% 2.45/1.45 thf(fact_0_local_Oantisym__conv3, axiom, (! [Y:a,X:a]: (((~ (((less @ Y) @ X))) => ((~ (((less @ X) @ Y))) = (X = Y)))))).
% 2.45/1.45 thf(fact_1_local_Odual__order_Oasym, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (~ (((less @ A2) @ B2))))))).
% 2.45/1.45 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (A2 != B2))))).
% 2.45/1.45 thf(fact_3_local_Odual__order_Ostrict__trans, axiom, (! [B2:a,A2:a,C:a]: ((((less @ B2) @ A2) => (((less @ C) @ B2) => ((less @ C) @ A2)))))).
% 2.45/1.45 thf(fact_4_local_Oless__asym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.45/1.45 thf(fact_5_local_Oless__asym_H, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.45/1.45 thf(fact_6_local_Oless__imp__neq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.45/1.45 thf(fact_7_local_Oless__imp__not__eq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.45/1.45 thf(fact_8_local_Oless__imp__not__eq2, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (Y != X))))).
% 2.45/1.45 thf(fact_9_local_Oless__imp__not__less, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.45/1.45 thf(fact_10_local_Oless__imp__triv, axiom, (! [X:a,Y:a,P:$o]: ((((less @ X) @ Y) => (((less @ Y) @ X) => P))))).
% 2.45/1.45 thf(fact_11_local_Oless__irrefl, axiom, (! [X:a]: ((~ (((less @ X) @ X)))))).
% 2.45/1.45 thf(fact_12_local_Oless__linear, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) | ((X = Y) | ((less @ Y) @ X)))))).
% 2.45/1.45 thf(fact_13_local_Oless__not__sym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.45/1.45 thf(fact_14_local_Oless__trans, axiom, (! [X:a,Y:a,Z:a]: ((((less @ X) @ Y) => (((less @ Y) @ Z) => ((less @ X) @ Z)))))).
% 2.45/1.45 thf(fact_15_local_Olinorder__cases, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) => ((X != Y) => ((less @ Y) @ X)))))).
% 2.45/1.45 thf(fact_16_local_OneqE, axiom, (! [X:a,Y:a]: (((X != Y) => ((~ (((less @ X) @ Y))) => ((less @ Y) @ X)))))).
% 2.45/1.45 thf(fact_17_local_Oneq__iff, axiom, (! [X:a,Y:a]: (((X != Y) = (((less @ X) @ Y) | ((less @ Y) @ X)))))).
% 2.45/1.45 thf(fact_18_local_Onot__less__iff__gr__or__eq, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) = (((less @ Y) @ X) | (X = Y)))))).
% 2.45/1.45 thf(fact_19_local_Oord__eq__less__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.45/1.45 thf(fact_20_local_Oord__less__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => ((B2 = C) => ((less @ A2) @ C)))))).
% 2.45/1.45 thf(fact_21_local_Oorder_Oasym, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.45/1.45 thf(fact_22_local_Oorder_Oirrefl, axiom, (! [A2:a]: ((~ (((less @ A2) @ A2)))))).
% 2.45/1.45 thf(fact_23_local_Oorder_Ostrict__implies__not__eq, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (A2 != B2))))).
% 2.45/1.45 thf(fact_24_local_Oorder_Ostrict__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.45/1.45 thf(fact_25_assms_I2_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ r)).
% 2.45/1.45 thf(fact_26_assms_I1_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ l)).
% 2.45/1.45 thf(fact_27_local_Orbt__less__trans, axiom, (! [C2:$tType,X:a,T:((rBT_Im246033960le_rbt @ a) @ C2),Y:a]: (((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ X) @ T) => (((less @ X) @ Y) => (((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ Y) @ T)))))).
% 2.45/1.45 thf(fact_28_local_Orbt__greater__trans, axiom, (! [C2:$tType,X:a,Y:a,T:((rBT_Im246033960le_rbt @ a) @ C2)]: ((((less @ X) @ Y) => ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ Y) @ T) => (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ X) @ T)))))).
% 2.45/1.45 thf(fact_29_rbt_Oinject, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25) = (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & ((X22 = Y22) & ((X23 = Y23) & ((X24 = Y24) & (X25 = Y25))))))))).
% 2.45/1.45 thf(fact_30_assms_I3_J, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ k) @ l)).
% 2.45/1.45 thf(fact_31_assms_I4_J, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ r)).
% 2.45/1.45 thf(fact_32_local_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ C) @ L) @ K) @ V) @ R)) = ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) & ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) & (((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) & ((((rBT_Im759614907sorted @ a) @ B) @ less) @ R)))))))).
% 2.45/1.45 thf(fact_33_local_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.45/1.45 thf(fact_34_local_Ostrict__mono__eq, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((F @ X) = (F @ Y)) = (X = Y))))))))).
% 2.45/1.45 thf(fact_35_ord_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ Rt))))))).
% 2.45/1.45 thf(fact_36_local_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.45/1.45 thf(fact_37__C1_C, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ y) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ va) @ vb) @ vg) @ vc))).
% 2.45/1.45 thf(fact_38__092_060open_062x_A_060_Ay_A_092_060and_062_ABranch_AB_Ava_Avb_Avg_Avc_A_124_092_060guillemotleft_062_Ax_092_060close_062, axiom, (((less @ x) @ y) & (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ x) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ va) @ vb) @ vg) @ vc)))).
% 2.45/1.45 thf(fact_39_local_Ois__rbt__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ T))))).
% 2.45/1.45 thf(fact_40__C5__4_Oprems_C_I4_J, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ x) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ b2) @ y) @ s) @ c)) @ z) @ t) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ vd) @ ve) @ vii) @ vf)))).
% 2.45/1.45 thf(fact_41__C5__4_Oprems_C_I2_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ b2) @ y) @ s) @ c)) @ z) @ t) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ vd) @ ve) @ vii) @ vf)))).
% 2.45/1.45 thf(fact_42_ord_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im759614907sorted @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C) @ L) @ K) @ V) @ R)) = ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ L) & ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ R) & (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ L) & ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ R)))))))).
% 2.45/1.45 thf(fact_43_ord_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ Rt))))))).
% 2.45/1.45 thf(fact_44_color_Odistinct_I1_J, axiom, (rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B)).
% 2.45/1.45 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.45/1.45 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.45/1.45 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.45/1.45 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.45/1.45 thf(fact_49_color_Oinduct, axiom, (! [P:(rBT_Im1923302023_color > $o),Color:rBT_Im1923302023_color]: (((P @ rBT_Impl_Mirabelle_R) => ((P @ rBT_Impl_Mirabelle_B) => (P @ Color)))))).
% 2.45/1.45 thf(fact_50_color_Oexhaust, axiom, (! [Y:rBT_Im1923302023_color]: (((Y != rBT_Impl_Mirabelle_R) => (Y = rBT_Impl_Mirabelle_B))))).
% 2.45/1.45 thf(fact_51_local_Olexordp__eq__antisym, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => (((((lexordp_eq @ a) @ less) @ Ys) @ Xs) => (Xs = Ys)))))).
% 2.45/1.45 thf(fact_52_local_Olexordp__eq__trans, axiom, (! [Xs:(list @ a),Ys:(list @ a),Zs:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => (((((lexordp_eq @ a) @ less) @ Ys) @ Zs) => ((((lexordp_eq @ a) @ less) @ Xs) @ Zs)))))).
% 2.45/1.45 thf(fact_53_local_Olexordp__eq__refl, axiom, (! [Xs:(list @ a)]: (((((lexordp_eq @ a) @ less) @ Xs) @ Xs)))).
% 2.45/1.45 thf(fact_54_local_Olexordp__eq__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) | ((((lexordp_eq @ a) @ less) @ Ys) @ Xs))))).
% 2.45/1.45 thf(fact_55__C5__4_Oprems_C_I1_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ va) @ vb) @ vg) @ vc))).
% 2.45/1.45 thf(fact_56__C5__4_Oprems_C_I3_J, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ x) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ va) @ vb) @ vg) @ vc))).
% 2.45/1.45 thf(fact_57_ord_Ois__rbt__rbt__sorted, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),T:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im862805236is_rbt @ A) @ B) @ Less) @ T) => ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ T))))).
% 2.45/1.45 thf(fact_58_local_OgreaterThan__def, axiom, (! [L:a]: (((((set_greaterThan @ a) @ less) @ L) = ((collect @ a) @ (less @ L)))))).
% 2.45/1.45 thf(fact_59_local_OlessThan__def, axiom, (! [U:a]: (((((set_lessThan @ a) @ less) @ U) = ((collect @ a) @ (^ [X2:a]: (((less @ X2) @ U)))))))).
% 2.45/1.45 thf(fact_60_local_OEmpty__is__rbt, axiom, (! [B:$tType]: (((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.45/1.45 thf(fact_61_local_Ostrict__mono__less, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => ((((ord_less @ B) @ (F @ X)) @ (F @ Y)) = ((less @ X) @ Y))))))))).
% 2.45/1.45 thf(fact_62_local_Ostrict__mono__def, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: ((((((strict_mono @ a) @ B) @ less) @ F) = (! [X2:a,Y2:a]: ((((less @ X2) @ Y2) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y2)))))))))))).
% 2.45/1.45 thf(fact_63_local_Ostrict__monoI, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: (((! [X3:a,Y3:a]: ((((less @ X3) @ Y3) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y3))))) => ((((strict_mono @ a) @ B) @ less) @ F)))))))).
% 2.45/1.45 thf(fact_64_local_Ostrict__monoD, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((less @ X) @ Y) => (((ord_less @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.45/1.45 thf(fact_65_local_Olexordp__eq_ONil, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.45/1.45 thf(fact_66_local_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType]: (((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.45/1.45 thf(fact_67_local_OlessThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_lessThan @ a) @ less) @ K)) = ((less @ I) @ K))))).
% 2.45/1.45 thf(fact_68_local_OgreaterThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_greaterThan @ a) @ less) @ K)) = ((less @ K) @ I))))).
% 2.45/1.45 thf(fact_69_local_Olexordp__eq__simps_I2_J, axiom, (! [Xs:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ (nil @ a)) = (Xs = (nil @ a)))))).
% 2.45/1.45 thf(fact_70_local_Olexordp__eq__simps_I1_J, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.45/1.45 thf(fact_71_local_Orbt__less__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.45/1.45 thf(fact_72_local_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.45/1.45 thf(fact_73_rbt_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((rBT_Im418718756_Empty @ A) @ B) != (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25))))).
% 2.45/1.45 thf(fact_74_rbt_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > $o),Rbt:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) => ((! [X1:rBT_Im1923302023_color,X26:((rBT_Im246033960le_rbt @ A) @ B),X32:A,X4:B,X5:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ X26) => ((P @ X5) => (P @ (((((((rBT_Im480247531Branch @ A) @ B) @ X1) @ X26) @ X32) @ X4) @ X5)))))) => (P @ Rbt)))))).
% 2.45/1.45 thf(fact_75_rbt_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((rBT_Im246033960le_rbt @ A) @ B)]: (((Y != ((rBT_Im418718756_Empty @ A) @ B)) => (~ ((! [X212:rBT_Im1923302023_color,X222:((rBT_Im246033960le_rbt @ A) @ B),X232:A,X242:B,X252:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y != (((((((rBT_Im480247531Branch @ A) @ B) @ X212) @ X222) @ X232) @ X242) @ X252)))))))))).
% 2.45/1.45 thf(fact_76_ord_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.45/1.45 thf(fact_77_ord_Orbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.45/1.45 thf(fact_78_ord_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.45/1.45 thf(fact_79_ord_OEmpty__is__rbt, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: (((((rBT_Im862805236is_rbt @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.45/1.45 thf(fact_80_rbt__cases, axiom, (! [B:$tType,A:$tType,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((T != ((rBT_Im418718756_Empty @ A) @ B)) => ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K2:A,V2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ K2) @ V2) @ R2)))) => (~ ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K2:A,V2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ K2) @ V2) @ R2))))))))))).
% 2.45/1.45 thf(fact_81_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.45/1.45 thf(fact_82_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.45/1.45 thf(fact_83_local_Olexordp__eq_Ocases, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ A1) @ A22) => (((A1 = (nil @ a)) => (! [Ys2:(list @ a)]: ((A22 != Ys2)))) => ((! [X3:a]: (((? [Xs2:(list @ a)]: ((A1 = (((cons @ a) @ X3) @ Xs2)))) => (! [Y3:a]: (((? [Ys2:(list @ a)]: ((A22 = (((cons @ a) @ Y3) @ Ys2)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Y3:a,Xs2:(list @ a)]: (((A1 = (((cons @ a) @ X3) @ Xs2)) => (! [Ys2:(list @ a)]: (((A22 = (((cons @ a) @ Y3) @ Ys2)) => ((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (~ (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.45/1.45 thf(fact_84_local_Olexordp__eq_Oinducts, axiom, (! [X12:(list @ a),X27:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp_eq @ a) @ less) @ X12) @ X27) => ((! [X1:(list @ a)]: (((P @ (nil @ a)) @ X1))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: (((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.45/1.45 thf(fact_85_local_Olexordp__eq_Osimps, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ A1) @ A22) = ((? [Ys3:(list @ a)]: (((A1 = (nil @ a)) & (A22 = Ys3)))) | ((? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((less @ X2) @ Y2))))) | (? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((~ (((less @ X2) @ Y2))) & ((~ (((less @ Y2) @ X2))) & ((((lexordp_eq @ a) @ less) @ Xs3) @ Ys3))))))))))))).
% 2.45/1.45 thf(fact_86_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.45/1.45 thf(fact_87_local_Olexordp__eq_OCons, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))).
% 2.45/1.45 thf(fact_88_local_Olexordp__eq_OCons__eq, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: (((~ (((less @ X) @ Y))) => ((~ (((less @ Y) @ X))) => (((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => ((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))))).
% 2.45/1.45 thf(fact_89_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.45/1.45 thf(fact_90_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less @ X) @ Y) | ((~ (((Less @ Y) @ X))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys))))))).
% 2.45/1.45 thf(fact_91_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A))))))).
% 2.45/1.45 thf(fact_92_local_Olexordp__eq__simps_I4_J, axiom, (! [X:a,Xs:(list @ a),Y:a,Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)) = (((less @ X) @ Y) | ((~ (((less @ Y) @ X))) & ((((lexordp_eq @ a) @ less) @ Xs) @ Ys))))))).
% 2.45/1.45 thf(fact_93_local_Olexordp__eq__simps_I3_J, axiom, (! [X:a,Xs:(list @ a)]: ((~ (((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (nil @ a))))))).
% 2.45/1.45 thf(fact_94_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X1))) => ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.45/1.45 thf(fact_95_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X3) @ Xs2)))))) => (P @ Xs))))))).
% 2.45/1.45 thf(fact_96_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y3:A,Xs2:(list @ A)]: ((((X3 = Y3) => (P @ (((cons @ A) @ X3) @ Xs2))) => (((X3 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.45/1.45 thf(fact_97_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X3:A]: ((X != (((cons @ A) @ X3) @ (nil @ A))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.45/1.45 thf(fact_98_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X3:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ Xss))))))))))).
% 2.45/1.45 thf(fact_99_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [V2:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V2) @ Va)) @ (nil @ A)))) => ((! [X3:A,Xs2:(list @ A),Y3:A,Ys2:(list @ A)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((P @ A0) @ A1))))))).
% 2.45/1.45 thf(fact_100_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys2)))) => ((! [X3:A,Xs2:(list @ A),Y3:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.45/1.45 thf(fact_101_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y2:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y2) @ Ys3)))))))).
% 2.45/1.45 thf(fact_102_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X26:(list @ A)]: (((P @ X26) => (P @ (((cons @ A) @ X1) @ X26))))) => (P @ List)))))).
% 2.45/1.45 thf(fact_103_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.45/1.45 thf(fact_104_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.45/1.45 thf(fact_105_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.45/1.45 thf(fact_106_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.45/1.45 thf(fact_107_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less @ X) @ Y))) => ((~ (((Less @ Y) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.45/1.45 thf(fact_108_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.45/1.45 thf(fact_109_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X12:(list @ A),X27:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X12) @ X27) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y3))) => ((~ (((Less @ Y3) @ X3))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.45/1.45 thf(fact_110_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys3)))) | ((? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((Less2 @ X2) @ Y2))))) | (? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((~ (((Less2 @ X2) @ Y2))) & ((~ (((Less2 @ Y2) @ X2))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys3))))))))))))))).
% 2.45/1.45 thf(fact_111_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A22 != Ys2)))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y3:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys2)))) => (~ (((Less @ X3) @ Y3))))))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys2)) => ((~ (((Less @ X3) @ Y3))) => ((~ (((Less @ Y3) @ X3))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.45/1.45 thf(fact_112_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.45/1.45 thf(fact_113_local_Olexordp_ONil, axiom, (! [Y:a,Ys:(list @ a)]: (((((lexordp @ a) @ less) @ (nil @ a)) @ (((cons @ a) @ Y) @ Ys))))).
% 2.45/1.45 thf(fact_114_local_Olexordp_Ocases, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp @ a) @ less) @ A1) @ A22) => (((A1 = (nil @ a)) => (! [Y3:a,Ys2:(list @ a)]: ((A22 != (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a]: (((? [Xs2:(list @ a)]: ((A1 = (((cons @ a) @ X3) @ Xs2)))) => (! [Y3:a]: (((? [Ys2:(list @ a)]: ((A22 = (((cons @ a) @ Y3) @ Ys2)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Y3:a,Xs2:(list @ a)]: (((A1 = (((cons @ a) @ X3) @ Xs2)) => (! [Ys2:(list @ a)]: (((A22 = (((cons @ a) @ Y3) @ Ys2)) => ((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (~ (((((lexordp @ a) @ less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.45/1.45 thf(fact_115_local_Olexordp_Oinducts, axiom, (! [X12:(list @ a),X27:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp @ a) @ less) @ X12) @ X27) => ((! [Y3:a,Ys2:(list @ a)]: (((P @ (nil @ a)) @ (((cons @ a) @ Y3) @ Ys2)))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: (((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (((((lexordp @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.45/1.45 thf(fact_116_local_Olexordp_Osimps, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp @ a) @ less) @ A1) @ A22) = ((? [Y2:a,Ys3:(list @ a)]: (((A1 = (nil @ a)) & (A22 = (((cons @ a) @ Y2) @ Ys3))))) | ((? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((less @ X2) @ Y2))))) | (? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((~ (((less @ X2) @ Y2))) & ((~ (((less @ Y2) @ X2))) & ((((lexordp @ a) @ less) @ Xs3) @ Ys3))))))))))))).
% 2.45/1.45 thf(fact_117_local_Olexordp__cases, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (((Xs = (nil @ a)) => (! [Y3:a,Ys4:(list @ a)]: ((Ys != (((cons @ a) @ Y3) @ Ys4))))) => ((! [X3:a]: (((? [Xs4:(list @ a)]: ((Xs = (((cons @ a) @ X3) @ Xs4)))) => (! [Y3:a]: (((? [Ys4:(list @ a)]: ((Ys = (((cons @ a) @ Y3) @ Ys4)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Xs4:(list @ a)]: (((Xs = (((cons @ a) @ X3) @ Xs4)) => (! [Ys4:(list @ a)]: (((Ys = (((cons @ a) @ X3) @ Ys4)) => (~ (((((lexordp @ a) @ less) @ Xs4) @ Ys4))))))))))))))))).
% 2.45/1.45 thf(fact_118_local_Olexordp__induct, axiom, (! [Xs:(list @ a),Ys:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => ((! [Y3:a,Ys2:(list @ a)]: (((P @ (nil @ a)) @ (((cons @ a) @ Y3) @ Ys2)))) => ((! [X3:a,Xs2:(list @ a),Y3:a,Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ X3) @ Ys2)))))) => ((P @ Xs) @ Ys)))))))).
% 2.45/1.45 thf(fact_119_local_Olexordp__antisym, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (~ (((((lexordp @ a) @ less) @ Ys) @ Xs))))))).
% 2.45/1.45 thf(fact_120_local_Olexordp__irreflexive, axiom, (! [Xs:(list @ a)]: (((! [X3:a]: ((~ (((less @ X3) @ X3))))) => (~ (((((lexordp @ a) @ less) @ Xs) @ Xs))))))).
% 2.45/1.45 thf(fact_121_local_Olexordp__irreflexive_H, axiom, (! [Xs:(list @ a)]: ((~ (((((lexordp @ a) @ less) @ Xs) @ Xs)))))).
% 2.45/1.45 thf(fact_122_local_Olexordp__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) | ((Xs = Ys) | ((((lexordp @ a) @ less) @ Ys) @ Xs)))))).
% 2.45/1.45 thf(fact_123_local_Olexordp__trans, axiom, (! [Xs:(list @ a),Ys:(list @ a),Zs:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (((((lexordp @ a) @ less) @ Ys) @ Zs) => ((((lexordp @ a) @ less) @ Xs) @ Zs)))))).
% 2.45/1.45 thf(fact_124_local_Olexordp_OCons, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))).
% 2.45/1.45 thf(fact_125_local_Olexordp_OCons__eq, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: (((~ (((less @ X) @ Y))) => ((~ (((less @ Y) @ X))) => (((((lexordp @ a) @ less) @ Xs) @ Ys) => ((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))))).
% 2.45/1.45 thf(fact_126_local_Olexordp__conv__lexordp__eq, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) = (((((lexordp_eq @ a) @ less) @ Xs) @ Ys) & (~ (((((lexordp_eq @ a) @ less) @ Ys) @ Xs)))))))).
% 2.45/1.45 thf(fact_127_local_Olexordp__eq__conv__lexord, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) = ((Xs = Ys) | ((((lexordp @ a) @ less) @ Xs) @ Ys)))))).
% 2.45/1.45 thf(fact_128_local_Olexordp__into__lexordp__eq, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => ((((lexordp_eq @ a) @ less) @ Xs) @ Ys))))).
% 2.45/1.45 thf(fact_129_ord_Olexordp__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less @ X) @ Y) | ((~ (((Less @ Y) @ X))) & ((((lexordp @ A) @ Less) @ Xs) @ Ys))))))).
% 2.45/1.45 thf(fact_130_ord_Olexordp__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: ((((((lexordp @ A) @ Less) @ (nil @ A)) @ Ys) = (Ys != (nil @ A)))))).
% 2.45/1.45 thf(fact_131_ord_Olexordp__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((~ (((((lexordp @ A) @ Less) @ Xs) @ (nil @ A))))))).
% 2.45/1.45 thf(fact_132_local_Olexordp__simps_I3_J, axiom, (! [X:a,Xs:(list @ a),Y:a,Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)) = (((less @ X) @ Y) | ((~ (((less @ Y) @ X))) & ((((lexordp @ a) @ less) @ Xs) @ Ys))))))).
% 2.45/1.45 thf(fact_133_local_Olexordp__simps_I2_J, axiom, (! [Xs:(list @ a)]: ((~ (((((lexordp @ a) @ less) @ Xs) @ (nil @ a))))))).
% 2.45/1.45 thf(fact_134_local_Olexordp__simps_I1_J, axiom, (! [Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ (nil @ a)) @ Ys) = (Ys != (nil @ a)))))).
% 2.45/1.45 thf(fact_135_ord_Olexordp__irreflexive, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((! [X3:A]: ((~ (((Less @ X3) @ X3))))) => (~ (((((lexordp @ A) @ Less) @ Xs) @ Xs))))))).
% 2.45/1.45 thf(fact_136_ord_Olexordp_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less @ X) @ Y))) => ((~ (((Less @ Y) @ X))) => (((((lexordp @ A) @ Less) @ Xs) @ Ys) => ((((lexordp @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.45/1.45 thf(fact_137_ord_Olexordp_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.45/1.45 thf(fact_138_ord_Olexordp__into__lexordp__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A),Ys:(list @ A)]: ((((((lexordp @ A) @ Less) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys))))).
% 2.45/1.45 thf(fact_139_ord_Olexordp_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Y:A,Ys:(list @ A)]: (((((lexordp @ A) @ Less) @ (nil @ A)) @ (((cons @ A) @ Y) @ Ys))))).
% 2.45/1.45 thf(fact_140_ord_Olexordp_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp @ A) @ Less) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Y3:A,Ys2:(list @ A)]: ((A22 != (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y3:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys2)))) => (~ (((Less @ X3) @ Y3))))))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys2)) => ((~ (((Less @ X3) @ Y3))) => ((~ (((Less @ Y3) @ X3))) => (~ (((((lexordp @ A) @ Less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.45/1.45 thf(fact_141_ord_Olexordp_Osimps, axiom, (! [A:$tType]: (((lexordp @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Y2:A,Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = (((cons @ A) @ Y2) @ Ys3))))) | ((? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((Less2 @ X2) @ Y2))))) | (? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((~ (((Less2 @ X2) @ Y2))) & ((~ (((Less2 @ Y2) @ X2))) & ((((lexordp @ A) @ Less2) @ Xs3) @ Ys3))))))))))))))).
% 2.45/1.45 thf(fact_142_ord_Olexordp_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X12:(list @ A),X27:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp @ A) @ Less) @ X12) @ X27) => ((! [Y3:A,Ys2:(list @ A)]: (((P @ (nil @ A)) @ (((cons @ A) @ Y3) @ Ys2)))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y3))) => ((~ (((Less @ Y3) @ X3))) => (((((lexordp @ A) @ Less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.45/1.45 thf(fact_143_local_Olexordp__append__rightI, axiom, (! [Ys:(list @ a),Xs:(list @ a)]: (((Ys != (nil @ a)) => ((((lexordp @ a) @ less) @ Xs) @ (((append @ a) @ Xs) @ Ys)))))).
% 2.45/1.45 thf(fact_144_local_Olexordp__iff, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) = ((? [X2:a,Vs:(list @ a)]: ((Ys = (((append @ a) @ Xs) @ (((cons @ a) @ X2) @ Vs))))) | (? [Us:(list @ a),A5:a,B3:a,Vs:(list @ a),Ws:(list @ a)]: ((((less @ A5) @ B3) & ((Xs = (((append @ a) @ Us) @ (((cons @ a) @ A5) @ Vs))) & (Ys = (((append @ a) @ Us) @ (((cons @ a) @ B3) @ Ws)))))))))))).
% 2.45/1.45 thf(fact_145_local_Olexordp__append__left__rightI, axiom, (! [X:a,Y:a,Us2:(list @ a),Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp @ a) @ less) @ (((append @ a) @ Us2) @ (((cons @ a) @ X) @ Xs))) @ (((append @ a) @ Us2) @ (((cons @ a) @ Y) @ Ys))))))).
% 2.45/1.45 thf(fact_146_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.45/1.45 thf(fact_147_local_Olexordp__append__leftI, axiom, (! [Us2:(list @ a),Vs2:(list @ a),Xs:(list @ a)]: ((((((lexordp @ a) @ less) @ Us2) @ Vs2) => ((((lexordp @ a) @ less) @ (((append @ a) @ Xs) @ Us2)) @ (((append @ a) @ Xs) @ Vs2)))))).
% 2.45/1.45 thf(fact_148_local_Olexordp__append__leftD, axiom, (! [Xs:(list @ a),Us2:(list @ a),Vs2:(list @ a)]: ((((((lexordp @ a) @ less) @ (((append @ a) @ Xs) @ Us2)) @ (((append @ a) @ Xs) @ Vs2)) => ((! [A4:a]: ((~ (((less @ A4) @ A4))))) => ((((lexordp @ a) @ less) @ Us2) @ Vs2)))))).
% 2.45/1.45 thf(fact_149_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.45/1.45 thf(fact_150_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.45/1.45 thf(fact_151_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.45/1.45 thf(fact_152_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.45/1.45 thf(fact_153_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.45/1.45 thf(fact_154_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.45/1.45 thf(fact_155_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.45/1.45 thf(fact_156_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.45/1.45 thf(fact_157_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.45/1.45 thf(fact_158_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.45/1.45 thf(fact_159_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.45/1.45 thf(fact_160_ord_Olexordp__append__leftD, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A),Us2:(list @ A),Vs2:(list @ A)]: ((((((lexordp @ A) @ Less) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2)) => ((! [A4:A]: ((~ (((Less @ A4) @ A4))))) => ((((lexordp @ A) @ Less) @ Us2) @ Vs2)))))).
% 2.45/1.45 thf(fact_161_ord_Olexordp__append__leftI, axiom, (! [A:$tType,Less:(A > (A > $o)),Us2:(list @ A),Vs2:(list @ A),Xs:(list @ A)]: ((((((lexordp @ A) @ Less) @ Us2) @ Vs2) => ((((lexordp @ A) @ Less) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2)))))).
% 2.45/1.45 thf(fact_162_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.45/1.45 thf(fact_163_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs))))))).
% 2.45/1.45 thf(fact_164_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.45/1.45 thf(fact_165_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.45/1.45 thf(fact_166_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us)) & ((((append @ A) @ Us) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs) & (Ys = (((append @ A) @ Us) @ Ts)))))))))).
% 2.45/1.45 thf(fact_167_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Us2))))))).
% 2.45/1.45 thf(fact_168_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.45/1.45 thf(fact_169_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs) = Xs))))))))).
% 2.45/1.45 thf(fact_170_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X) @ Ys5) = Ys) & (Xs = (((append @ A) @ Ys5) @ Zs)))))))))).
% 2.45/1.45 thf(fact_171_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys2:(list @ A),Y3:A]: ((Xs != (((append @ A) @ Ys2) @ (((cons @ A) @ Y3) @ (nil @ A)))))))))))).
% 2.45/1.45 thf(fact_172_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.45/1.45 thf(fact_173_ord_Olexordp__append__left__rightI, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Us2:(list @ A),Xs:(list @ A),Ys:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp @ A) @ Less) @ (((append @ A) @ Us2) @ (((cons @ A) @ X) @ Xs))) @ (((append @ A) @ Us2) @ (((cons @ A) @ Y) @ Ys))))))).
% 2.45/1.45 thf(fact_174_ord_Olexordp__append__rightI, axiom, (! [A:$tType,Ys:(list @ A),Less:(A > (A > $o)),Xs:(list @ A)]: (((Ys != (nil @ A)) => ((((lexordp @ A) @ Less) @ Xs) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.45/1.45 thf(fact_175_keys__simps_I2_J, axiom, (! [D:$tType,C2:$tType,C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ C2) @ D),K:C2,V:D,R:((rBT_Im246033960le_rbt @ C2) @ D)]: (((((rBT_Im380146495e_keys @ C2) @ D) @ (((((((rBT_Im480247531Branch @ C2) @ D) @ C) @ L) @ K) @ V) @ R)) = (((append @ C2) @ (((rBT_Im380146495e_keys @ C2) @ D) @ L)) @ (((cons @ C2) @ K) @ (((rBT_Im380146495e_keys @ C2) @ D) @ R))))))).
% 2.45/1.45 thf(fact_176_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.45/1.45 thf(fact_177_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F) = (((append @ A) @ (F @ X)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 2.45/1.45 thf(fact_178_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 2.45/1.45 thf(fact_179_keys__simps_I1_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im380146495e_keys @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (nil @ A))))).
% 2.45/1.45 thf(fact_180_non__empty__rbt__keys, axiom, (! [B:$tType,A:$tType,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((T != ((rBT_Im418718756_Empty @ A) @ B)) => ((((rBT_Im380146495e_keys @ A) @ B) @ T) != (nil @ A)))))).
% 2.45/1.45 thf(fact_181_local_Orbt__greater__prop, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ T) = (! [X2:a]: (((((member @ a) @ X2) @ ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))) => ((less @ K) @ X2)))))))).
% 2.45/1.45 thf(fact_182_local_Orbt__less__prop, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ T) = (! [X2:a]: (((((member @ a) @ X2) @ ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))) => ((less @ X2) @ K)))))))).
% 2.45/1.45 thf(fact_183_local_Ostrict__mono__imp__inj__on, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),A3:(set @ a)]: ((((((strict_mono @ a) @ B) @ less) @ F) => ((((inj_on @ a) @ B) @ F) @ A3)))))))).
% 2.45/1.45 thf(fact_184_list__bind__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F:(A > (list @ B)),G:(A > (list @ B))]: (((Xs = Ys) => ((! [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) => ((F @ X3) = (G @ X3))))) => (((((bind @ A) @ B) @ Xs) @ F) = ((((bind @ A) @ B) @ Ys) @ G))))))).
% 2.45/1.45 thf(fact_185_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) = (? [Ys3:(list @ A),X2:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs2))))) & ((P @ X2) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Y2)))))))))))))).
% 2.45/1.45 thf(fact_186_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) = (? [Ys3:(list @ A),X2:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs2))) & ((P @ X2) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Y2)))))))))))))).
% 2.45/1.45 thf(fact_187_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.45/1.45 thf(fact_188_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs2))))))))))).
% 2.45/1.45 thf(fact_189_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (~ ((! [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) => ((P @ X3) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.45/1.45 thf(fact_190_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (~ ((! [Ys2:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))) => ((P @ X3) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))))))).
% 2.45/1.45 thf(fact_191_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (? [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))).
% 2.45/1.45 thf(fact_192_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (? [Ys2:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))).
% 2.45/1.45 thf(fact_193_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))))))))).
% 2.45/1.45 thf(fact_194_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (~ ((! [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) => (~ ((P @ X3)))))))))))).
% 2.45/1.45 thf(fact_195_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.45/1.45 thf(fact_196_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Xs)) & (P @ X6)))) => (? [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) & (P @ X3)))))))).
% 2.45/1.45 thf(fact_197_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.45/1.45 thf(fact_198_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.45/1.45 thf(fact_199_list_Oset__cases, axiom, (! [A:$tType,E:A,A2:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.45/1.45 thf(fact_200_set__ConsD, axiom, (! [A:$tType,Y:A,X:A,Xs:(list @ A)]: (((((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs))) => ((Y = X) | (((member @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 2.45/1.45 thf(fact_201_list_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(list @ A)]: ((((member @ A) @ A1) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22)))))).
% 2.45/1.45 thf(fact_202_list_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(list @ A),A1:A]: (((((member @ A) @ X) @ ((set2 @ A) @ A22)) => (((member @ A) @ X) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22))))))).
% 2.45/1.45 thf(fact_203_ord_Orbt__less__prop, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im2075124343t_less @ A) @ B) = (^ [Less2:(A > (A > $o)),K3:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => ((Less2 @ X2) @ K3)))))))))).
% 2.45/1.45 thf(fact_204_ord_Orbt__greater__prop, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1259024060reater @ A) @ B) = (^ [Less2:(A > (A > $o)),K3:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => ((Less2 @ K3) @ X2)))))))))).
% 2.45/1.45 thf(fact_205_local_Odistinct__keys, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((distinct @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T)))))).
% 2.45/1.45 thf(fact_206_the__elem__set, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.45/1.45 thf(fact_207_ord_OgreaterThan__def, axiom, (! [A:$tType]: (((set_greaterThan @ A) = (^ [Less2:(A > (A > $o)),L3:A]: (((collect @ A) @ (Less2 @ L3)))))))).
% 2.45/1.45 thf(fact_208_distinct__product__lists, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: (((! [X3:(list @ A)]: (((((member @ (list @ A)) @ X3) @ ((set2 @ (list @ A)) @ Xss2)) => ((distinct @ A) @ X3)))) => ((distinct @ (list @ A)) @ ((product_lists @ A) @ Xss2)))))).
% 2.45/1.45 thf(fact_209_distinct_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ X) @ Xs)) = ((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) & ((distinct @ A) @ Xs)))))).
% 2.45/1.45 thf(fact_210_distinct_Osimps_I1_J, axiom, (! [A:$tType]: (((distinct @ A) @ (nil @ A))))).
% 2.45/1.45 thf(fact_211_distinct__length__2__or__more, axiom, (! [A:$tType,A2:A,B2:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ A2) @ (((cons @ A) @ B2) @ Xs))) = ((A2 != B2) & (((distinct @ A) @ (((cons @ A) @ A2) @ Xs)) & ((distinct @ A) @ (((cons @ A) @ B2) @ Xs)))))))).
% 2.45/1.45 thf(fact_212_distinct__singleton, axiom, (! [A:$tType,X:A]: (((distinct @ A) @ (((cons @ A) @ X) @ (nil @ A)))))).
% 2.45/1.45 thf(fact_213_not__distinct__decomp, axiom, (! [A:$tType,Ws2:(list @ A)]: (((~ (((distinct @ A) @ Ws2))) => (? [Xs2:(list @ A),Ys2:(list @ A),Zs3:(list @ A),Y3:A]: ((Ws2 = (((append @ A) @ Xs2) @ (((append @ A) @ (((cons @ A) @ Y3) @ (nil @ A))) @ (((append @ A) @ Ys2) @ (((append @ A) @ (((cons @ A) @ Y3) @ (nil @ A))) @ Zs3))))))))))).
% 2.45/1.45 thf(fact_214_not__distinct__conv__prefix, axiom, (! [A:$tType,As2:(list @ A)]: (((~ (((distinct @ A) @ As2))) = (? [Xs3:(list @ A),Y2:A,Ys3:(list @ A)]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Xs3)) & (((distinct @ A) @ Xs3) & (As2 = (((append @ A) @ Xs3) @ (((cons @ A) @ Y2) @ Ys3))))))))))).
% 2.45/1.45 thf(fact_215_ord_OlessThan__iff, axiom, (! [A:$tType,I:A,Less:(A > (A > $o)),K:A]: (((((member @ A) @ I) @ (((set_lessThan @ A) @ Less) @ K)) = ((Less @ I) @ K))))).
% 2.45/1.45 thf(fact_216_ord_OgreaterThan__iff, axiom, (! [A:$tType,I:A,Less:(A > (A > $o)),K:A]: (((((member @ A) @ I) @ (((set_greaterThan @ A) @ Less) @ K)) = ((Less @ K) @ I))))).
% 2.45/1.45 thf(fact_217_ord_OlessThan__def, axiom, (! [A:$tType]: (((set_lessThan @ A) = (^ [Less2:(A > (A > $o)),U2:A]: (((collect @ A) @ (^ [X2:A]: (((Less2 @ X2) @ U2)))))))))).
% 2.45/1.45 thf(fact_218_local_Oset__entries__inject, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => ((((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T1)) = ((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T22))) = ((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)))))))).
% 2.45/1.45 thf(fact_219_distinct__union, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((distinct @ A) @ (((union @ A) @ Xs) @ Ys)) = ((distinct @ A) @ Ys))))).
% 2.45/1.45 thf(fact_220_entries_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im954575269ntries @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (nil @ ((product_prod @ A) @ B)))))).
% 2.45/1.45 thf(fact_221_local_Oentries__rbt__lookup, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => (((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ T1) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T22)))))))).
% 2.45/1.45 thf(fact_222_local_Oentries__eqI, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T1) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T22)) => ((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)))))))).
% 2.45/1.45 thf(fact_223_local_Orbt__lookup__from__in__tree, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B),K:a]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => ((! [V2:B]: (((((member @ ((product_prod @ a) @ B)) @ ((((product_Pair @ a) @ B) @ K) @ V2)) @ ((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T1))) = (((member @ ((product_prod @ a) @ B)) @ ((((product_Pair @ a) @ B) @ K) @ V2)) @ ((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T22)))))) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T1) @ K) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ T22) @ K)))))))).
% 2.45/1.45 thf(fact_224_local_Orbt__lookup__keys, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((dom @ a) @ B) @ ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T)) = ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))))))).
% 2.45/1.45 thf(fact_225_entries_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Uu:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im954575269ntries @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Uu) @ L) @ K) @ V) @ R)) = (((append @ ((product_prod @ A) @ B)) @ (((rBT_Im954575269ntries @ A) @ B) @ L)) @ (((cons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ K) @ V)) @ (((rBT_Im954575269ntries @ A) @ B) @ R))))))).
% 2.45/1.45 thf(fact_226_entry__in__tree__keys, axiom, (! [B:$tType,A:$tType,K:A,V:B,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ K) @ V)) @ ((set2 @ ((product_prod @ A) @ B)) @ (((rBT_Im954575269ntries @ A) @ B) @ T))) => (((member @ A) @ K) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T))))))).
% 2.45/1.45 thf(fact_227_keys__entries, axiom, (! [A:$tType,B:$tType,K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ A) @ K) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T))) = (? [V3:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ K) @ V3)) @ ((set2 @ ((product_prod @ A) @ B)) @ (((rBT_Im954575269ntries @ A) @ B) @ T))))))))).
% 2.45/1.45 thf(fact_228_local_OacyclicI__order, axiom, (! [B:$tType,R:(set @ ((product_prod @ B) @ B)),F:(B > a)]: (((! [A4:B,B4:B]: (((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ A4) @ B4)) @ R) => ((less @ (F @ B4)) @ (F @ A4))))) => ((transitive_acyclic @ B) @ R))))).
% 2.45/1.45 thf(fact_229_local_Orbt__lookup__in__tree, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => (((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = ((some @ B) @ V)) = (((member @ ((product_prod @ a) @ B)) @ ((((product_Pair @ a) @ B) @ K) @ V)) @ ((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T)))))))).
% 2.45/1.45 thf(fact_230_local_Orbt__lookup_Osimps_I2_J, axiom, (! [B:$tType,K:a,X:a,Uu:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ a) @ B),Y:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K) @ X) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ L) @ K))) & ((~ (((less @ K) @ X))) => ((((less @ X) @ K) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ R) @ K))) & ((~ (((less @ X) @ K))) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = ((some @ B) @ Y))))))))).
% 2.45/1.45 thf(fact_231_splice_Ocases, axiom, (! [A:$tType,X:((product_prod @ (list @ A)) @ (list @ A))]: (((! [Ys2:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (nil @ A)) @ Ys2)))) => ((! [V2:A,Va:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ V2) @ Va)) @ (nil @ A))))) => (~ ((! [X3:A,Xs2:(list @ A),Y3:A,Ys2:(list @ A)]: ((X != ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2)))))))))))).
% 2.45/1.45 thf(fact_232_map__tailrec__rev_Ocases, axiom, (! [A:$tType,B:$tType,X:((product_prod @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B)))]: (((! [F2:(A > B),Bs:(list @ B)]: ((X != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (nil @ A)) @ Bs))))) => (~ ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: ((X != ((((product_Pair @ (A > B)) @ ((product_prod @ (list @ A)) @ (list @ B))) @ F2) @ ((((product_Pair @ (list @ A)) @ (list @ B)) @ (((cons @ A) @ A4) @ As)) @ Bs))))))))))).
% 2.45/1.45 thf(fact_233_ord_Orbt__lookup_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A,X:A,Uu:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),Y:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((Less @ K) @ X) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ A) @ B) @ Less) @ L) @ K))) & ((~ (((Less @ K) @ X))) => ((((Less @ X) @ K) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ A) @ B) @ Less) @ R) @ K))) & ((~ (((Less @ X) @ K))) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = ((some @ B) @ Y))))))))).
% 2.45/1.45 thf(fact_234_local_Omap__of__entries, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((map_of @ a) @ B) @ (((rBT_Im954575269ntries @ a) @ B) @ T)) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T)))))).
% 2.45/1.45 thf(fact_235_local_Orbt__lookup_Osimps_I1_J, axiom, (! [B:$tType,K:a]: (((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) @ K) = (none @ B))))).
% 2.45/1.45 thf(fact_236_local_Orbt__lookup__Empty, axiom, (! [B:$tType]: ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) = (^ [X2:a]: ((none @ B))))))).
% 2.45/1.45 thf(fact_237_local_Orbt__lookup__rbt__less, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ T) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = (none @ B)))))).
% 2.45/1.45 thf(fact_238_local_Orbt__lookup__rbt__greater, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ T) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = (none @ B)))))).
% 2.45/1.45 thf(fact_239_ord_Orbt__lookup__Empty, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B)) = (^ [X2:A]: ((none @ B))))))).
% 2.45/1.45 thf(fact_240_ord_Orbt__lookup_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A]: (((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) = (none @ B))))).
% 2.45/1.45 thf(fact_241_ord_Orbt__lookup__rbt__less, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ T) @ K) = (none @ B)))))).
% 2.45/1.45 thf(fact_242_ord_Orbt__lookup__rbt__greater, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ T) @ K) = (none @ B)))))).
% 2.45/1.45 thf(fact_243_order__class_OacyclicI__order, axiom, (! [A:$tType,B:$tType]: ((((order @ A) @ (type2 @ A)) => (! [R:(set @ ((product_prod @ B) @ B)),F:(B > A)]: (((! [A4:B,B4:B]: (((((member @ ((product_prod @ B) @ B)) @ ((((product_Pair @ B) @ B) @ A4) @ B4)) @ R) => (((ord_less @ A) @ (F @ B4)) @ (F @ A4))))) => ((transitive_acyclic @ B) @ R)))))))).
% 2.45/1.45 thf(fact_244_dom__def, axiom, (! [B:$tType,A:$tType]: ((((dom @ A) @ B) = (^ [M:(A > (option @ B))]: (((collect @ A) @ (^ [A5:A]: (((M @ A5) != (none @ B))))))))))).
% 2.45/1.45 thf(fact_245_extract__Some__iff, axiom, (! [A:$tType,P:(A > $o),Xs:(list @ A),Ys:(list @ A),Y:A,Zs:(list @ A)]: ((((((extract @ A) @ P) @ Xs) = ((some @ ((product_prod @ (list @ A)) @ ((product_prod @ A) @ (list @ A)))) @ ((((product_Pair @ (list @ A)) @ ((product_prod @ A) @ (list @ A))) @ Ys) @ ((((product_Pair @ A) @ (list @ A)) @ Y) @ Zs)))) = ((Xs = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ Zs))) & ((P @ Y) & (~ ((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Ys)) & (P @ X2)))))))))))).
% 2.45/1.45 thf(fact_246_extract__SomeE, axiom, (! [A:$tType,P:(A > $o),Xs:(list @ A),Ys:(list @ A),Y:A,Zs:(list @ A)]: ((((((extract @ A) @ P) @ Xs) = ((some @ ((product_prod @ (list @ A)) @ ((product_prod @ A) @ (list @ A)))) @ ((((product_Pair @ (list @ A)) @ ((product_prod @ A) @ (list @ A))) @ Ys) @ ((((product_Pair @ A) @ (list @ A)) @ Y) @ Zs)))) => ((Xs = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ Zs))) & ((P @ Y) & (~ ((? [X6:A]: (((((member @ A) @ X6) @ ((set2 @ A) @ Ys)) & (P @ X6)))))))))))).
% 2.45/1.45 thf(fact_247_extract__Nil__code, axiom, (! [A:$tType,P:(A > $o)]: (((((extract @ A) @ P) @ (nil @ A)) = (none @ ((product_prod @ (list @ A)) @ ((product_prod @ A) @ (list @ A)))))))).
% 2.45/1.45 thf(fact_248_extract__None__iff, axiom, (! [A:$tType,P:(A > $o),Xs:(list @ A)]: ((((((extract @ A) @ P) @ Xs) = (none @ ((product_prod @ (list @ A)) @ ((product_prod @ A) @ (list @ A))))) = (~ ((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))))))))).
% 2.45/1.45 thf(fact_249_snoc__listrel1__snoc__iff, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A,R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A))))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) & (X = Y)) | ((Xs = Ys) & (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R))))))).
% 2.45/1.45 thf(fact_250_local_Ois__rbt__def, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) = ((((rBT_Im1040612427e_inv1 @ a) @ B) @ T) & ((((rBT_Im1040612428e_inv2 @ a) @ B) @ T) & (((((rBT_Im1805589839lor_of @ a) @ B) @ T) = rBT_Impl_Mirabelle_B) & ((((rBT_Im759614907sorted @ a) @ B) @ less) @ T)))))))).
% 2.45/1.45 thf(fact_251_Cons__listrel1__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A),R:(set @ ((product_prod @ A) @ A))]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys))) @ ((listrel1 @ A) @ R)) = (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ R) & (Xs = Ys)) | ((X = Y) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)))))))).
% 2.45/1.45 thf(fact_252_listrel1I2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A)),X:A]: (((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ X) @ Ys))) @ ((listrel1 @ A) @ R)))))).
% 2.45/1.45 thf(fact_253_append__listrel1I, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),R:(set @ ((product_prod @ A) @ A)),Us2:(list @ A),Vs2:(list @ A)]: (((((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ Ys)) @ ((listrel1 @ A) @ R)) & (Us2 = Vs2)) | ((Xs = Ys) & (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Us2) @ Vs2)) @ ((listrel1 @ A) @ R)))) => (((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Ys) @ Vs2))) @ ((listrel1 @ A) @ R)))))).
% 2.45/1.45 thf(fact_254_not__listrel1__Nil, axiom, (! [A:$tType,Xs:(list @ A),R:(set @ ((product_prod @ A) @ A))]: ((~ ((((member @ ((product_prod @ (list @ A)) @ (list @ A))) @ ((((product_Pair @ (list @ A)) @ (list @ A)) @ Xs) @ (nil @ A))) @ ((listrel1 @ A) @ R))))))).
% 2.45/1.45 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: ((((order @ A7) @ (type2 @ A7)) => ((order @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.45/1.45 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A6:$tType]: (((order @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.45/1.45 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.45/1.45 thf(conj_0, conjecture, (((less @ y) @ z) & (((((rBT_Im1259024060reater @ a) @ b) @ less) @ z) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ vd) @ ve) @ vii) @ vf)))).
% 2.45/1.45 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2DTF30182.p
% 2.45/1.45 ------------------------
% 2.45/1.48 ---- Cleaned THF ---
% 2.45/1.48 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 2.45/1.48 rBT_Im1923302023_color: $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 2.45/1.48 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_Product__Type_Oprod,type,
% 2.45/1.48 product_prod: $tType > $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_Option_Ooption,type,
% 2.45/1.48 option: $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_List_Olist,type,
% 2.45/1.48 list: $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_Set_Oset,type,
% 2.45/1.48 set: $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_t_itself,type,
% 2.45/1.48 itself: $tType > $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_tf_b,type,
% 2.45/1.48 b: $tType ).
% 2.45/1.48
% 2.45/1.48 thf(ty_tf_a,type,
% 2.45/1.48 a: $tType ).
% 2.45/1.48
% 2.45/1.48 thf(sy_cl_HOL_Otype,type,
% 2.45/1.48 type:
% 2.45/1.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_cl_Orderings_Oorder,type,
% 2.45/1.48 order:
% 2.45/1.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Fun_Oinj__on,type,
% 2.45/1.48 inj_on:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Oappend,type,
% 2.45/1.48 append:
% 2.45/1.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Obind,type,
% 2.45/1.48 bind:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Odistinct,type,
% 2.45/1.48 distinct:
% 2.45/1.48 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Oextract,type,
% 2.45/1.48 extract:
% 2.45/1.48 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > ( option @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Olist_OCons,type,
% 2.45/1.48 cons:
% 2.45/1.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Olist_ONil,type,
% 2.45/1.48 nil:
% 2.45/1.48 !>[A: $tType] : ( list @ A ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Olist_Oset,type,
% 2.45/1.48 set2:
% 2.45/1.48 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Olistrel1,type,
% 2.45/1.48 listrel1:
% 2.45/1.48 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > ( set @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Oord_Olexordp,type,
% 2.45/1.48 lexordp:
% 2.45/1.48 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.45/1.48 lexordp_eq:
% 2.45/1.48 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Oproduct__lists,type,
% 2.45/1.48 product_lists:
% 2.45/1.48 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Osublists,type,
% 2.45/1.48 sublists:
% 2.45/1.48 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_List_Ounion,type,
% 2.45/1.48 union:
% 2.45/1.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Map_Odom,type,
% 2.45/1.48 dom:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Map_Omap__of,type,
% 2.45/1.48 map_of:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Option_Ooption_ONone,type,
% 2.45/1.48 none:
% 2.45/1.48 !>[A: $tType] : ( option @ A ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Option_Ooption_OSome,type,
% 2.45/1.48 some:
% 2.45/1.48 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.45/1.48 ord_less:
% 2.45/1.48 !>[A: $tType] : ( A > A > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 2.45/1.48 strict_mono:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Product__Type_OPair,type,
% 2.45/1.48 product_Pair:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Pure_Otype,type,
% 2.45/1.48 type2:
% 2.45/1.48 !>[A: $tType] : ( itself @ A ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 2.45/1.48 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 2.45/1.48 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of,type,
% 2.45/1.48 rBT_Im1805589839lor_of:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > rBT_Im1923302023_color ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 2.45/1.48 rBT_Im954575269ntries:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1,type,
% 2.45/1.48 rBT_Im1040612427e_inv1:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv2,type,
% 2.45/1.48 rBT_Im1040612428e_inv2:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys,type,
% 2.45/1.48 rBT_Im380146495e_keys:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt,type,
% 2.45/1.48 rBT_Im862805236is_rbt:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 2.45/1.48 rBT_Im1259024060reater:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 2.45/1.48 rBT_Im2075124343t_less:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 2.45/1.48 rBT_Im35466040lookup:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 2.45/1.48 rBT_Im759614907sorted:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 2.45/1.48 rBT_Im480247531Branch:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 2.45/1.48 rBT_Im418718756_Empty:
% 2.45/1.48 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Set_OCollect,type,
% 2.45/1.48 collect:
% 2.45/1.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Set_Othe__elem,type,
% 2.45/1.48 the_elem:
% 2.45/1.48 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 2.45/1.48 set_greaterThan:
% 2.45/1.48 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 2.45/1.48 set_lessThan:
% 2.45/1.48 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_Transitive__Closure_Oacyclic,type,
% 2.45/1.48 transitive_acyclic:
% 2.45/1.48 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_c_member,type,
% 2.45/1.48 member:
% 2.45/1.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_b____,type,
% 2.45/1.48 b2: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_c____,type,
% 2.45/1.48 c: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_k,type,
% 2.45/1.48 k: a ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_l,type,
% 2.45/1.48 l: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_less,type,
% 2.45/1.48 less: a > a > $o ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_r,type,
% 2.45/1.48 r: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_s____,type,
% 2.45/1.48 s: b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_t____,type,
% 2.45/1.48 t: b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_va____,type,
% 2.45/1.48 va: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vb____,type,
% 2.45/1.48 vb: a ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vc____,type,
% 2.45/1.48 vc: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vd____,type,
% 2.45/1.48 vd: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_ve____,type,
% 2.45/1.48 ve: a ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vf____,type,
% 2.45/1.48 vf: rBT_Im246033960le_rbt @ a @ b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vg____,type,
% 2.45/1.48 vg: b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_vii____,type,
% 2.45/1.48 vii: b ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_x____,type,
% 2.45/1.48 x: a ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_y____,type,
% 2.45/1.48 y: a ).
% 2.45/1.48
% 2.45/1.48 thf(sy_v_z____,type,
% 2.45/1.48 z: a ).
% 2.45/1.48
% 2.45/1.48 thf(fact_0_local_Oantisym__conv3,axiom,
% 2.45/1.48 ! [Y: a,X: a] :
% 2.45/1.48 ( ~ ( less @ Y @ X )
% 2.45/1.48 => ( ( ~ ( less @ X @ Y ) )
% 2.45/1.48 = ( X = Y ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_1_local_Odual__order_Oasym,axiom,
% 2.45/1.48 ! [B2: a,A2: a] :
% 2.45/1.48 ( ( less @ B2 @ A2 )
% 2.45/1.48 => ~ ( less @ A2 @ B2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 2.45/1.48 ! [B2: a,A2: a] :
% 2.45/1.48 ( ( less @ B2 @ A2 )
% 2.45/1.48 => ( A2 != B2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 2.45/1.48 ! [B2: a,A2: a,C: a] :
% 2.45/1.48 ( ( less @ B2 @ A2 )
% 2.45/1.48 => ( ( less @ C @ B2 )
% 2.45/1.48 => ( less @ C @ A2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_4_local_Oless__asym,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ~ ( less @ Y @ X ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_5_local_Oless__asym_H,axiom,
% 2.45/1.48 ! [A2: a,B2: a] :
% 2.45/1.48 ( ( less @ A2 @ B2 )
% 2.45/1.48 => ~ ( less @ B2 @ A2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_6_local_Oless__imp__neq,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( X != Y ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( X != Y ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( Y != X ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_9_local_Oless__imp__not__less,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ~ ( less @ Y @ X ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_10_local_Oless__imp__triv,axiom,
% 2.45/1.48 ! [X: a,Y: a,P: $o] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( ( less @ Y @ X )
% 2.45/1.48 => P ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_11_local_Oless__irrefl,axiom,
% 2.45/1.48 ! [X: a] :
% 2.45/1.48 ~ ( less @ X @ X ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_12_local_Oless__linear,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 | ( X = Y )
% 2.45/1.48 | ( less @ Y @ X ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_13_local_Oless__not__sym,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ~ ( less @ Y @ X ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_14_local_Oless__trans,axiom,
% 2.45/1.48 ! [X: a,Y: a,Z: a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( ( less @ Y @ Z )
% 2.45/1.48 => ( less @ X @ Z ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_15_local_Olinorder__cases,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ~ ( less @ X @ Y )
% 2.45/1.48 => ( ( X != Y )
% 2.45/1.48 => ( less @ Y @ X ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_16_local_OneqE,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( X != Y )
% 2.45/1.48 => ( ~ ( less @ X @ Y )
% 2.45/1.48 => ( less @ Y @ X ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_17_local_Oneq__iff,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( X != Y )
% 2.45/1.48 = ( ( less @ X @ Y )
% 2.45/1.48 | ( less @ Y @ X ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 2.45/1.48 ! [X: a,Y: a] :
% 2.45/1.48 ( ( ~ ( less @ X @ Y ) )
% 2.45/1.48 = ( ( less @ Y @ X )
% 2.45/1.48 | ( X = Y ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 2.45/1.48 ! [A2: a,B2: a,C: a] :
% 2.45/1.48 ( ( A2 = B2 )
% 2.45/1.48 => ( ( less @ B2 @ C )
% 2.45/1.48 => ( less @ A2 @ C ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 2.45/1.48 ! [A2: a,B2: a,C: a] :
% 2.45/1.48 ( ( less @ A2 @ B2 )
% 2.45/1.48 => ( ( B2 = C )
% 2.45/1.48 => ( less @ A2 @ C ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_21_local_Oorder_Oasym,axiom,
% 2.45/1.48 ! [A2: a,B2: a] :
% 2.45/1.48 ( ( less @ A2 @ B2 )
% 2.45/1.48 => ~ ( less @ B2 @ A2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 2.45/1.48 ! [A2: a] :
% 2.45/1.48 ~ ( less @ A2 @ A2 ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 2.45/1.48 ! [A2: a,B2: a] :
% 2.45/1.48 ( ( less @ A2 @ B2 )
% 2.45/1.48 => ( A2 != B2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 2.45/1.48 ! [A2: a,B2: a,C: a] :
% 2.45/1.48 ( ( less @ A2 @ B2 )
% 2.45/1.48 => ( ( less @ B2 @ C )
% 2.45/1.48 => ( less @ A2 @ C ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_25_assms_I2_J,axiom,
% 2.45/1.48 rBT_Im759614907sorted @ a @ b @ less @ r ).
% 2.45/1.48
% 2.45/1.48 thf(fact_26_assms_I1_J,axiom,
% 2.45/1.48 rBT_Im759614907sorted @ a @ b @ less @ l ).
% 2.45/1.48
% 2.45/1.48 thf(fact_27_local_Orbt__less__trans,axiom,
% 2.45/1.48 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 2.45/1.48 => ( ( less @ X @ Y )
% 2.45/1.48 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_28_local_Orbt__greater__trans,axiom,
% 2.45/1.48 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 2.45/1.48 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_29_rbt_Oinject,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 2.45/1.48 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 2.45/1.48 = ( ( X21 = Y21 )
% 2.45/1.48 & ( X22 = Y22 )
% 2.45/1.48 & ( X23 = Y23 )
% 2.45/1.48 & ( X24 = Y24 )
% 2.45/1.48 & ( X25 = Y25 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_30_assms_I3_J,axiom,
% 2.45/1.48 rBT_Im2075124343t_less @ a @ b @ less @ k @ l ).
% 2.45/1.48
% 2.45/1.48 thf(fact_31_assms_I4_J,axiom,
% 2.45/1.48 rBT_Im1259024060reater @ a @ b @ less @ k @ r ).
% 2.45/1.48
% 2.45/1.48 thf(fact_32_local_Orbt__sorted_Osimps_I2_J,axiom,
% 2.45/1.48 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V @ R ) )
% 2.45/1.48 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.45/1.48 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.45/1.48 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.45/1.48 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_33_local_Orbt__greater__simps_I2_J,axiom,
% 2.45/1.48 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.45/1.48 = ( ( less @ K @ Kt )
% 2.45/1.48 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 2.45/1.48 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_34_local_Ostrict__mono__eq,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B,X: a,Y: a] :
% 2.45/1.48 ( ( strict_mono @ a @ B @ less @ F )
% 2.45/1.48 => ( ( ( F @ X )
% 2.45/1.48 = ( F @ Y ) )
% 2.45/1.48 = ( X = Y ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_35_ord_Orbt__greater__simps_I2_J,axiom,
% 2.45/1.48 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.45/1.48 = ( ( Less @ K @ Kt )
% 2.45/1.48 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Lt )
% 2.45/1.48 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_36_local_Orbt__less__simps_I2_J,axiom,
% 2.45/1.48 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.45/1.48 = ( ( less @ Kt @ K )
% 2.45/1.48 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 2.45/1.48 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_37__C1_C,axiom,
% 2.45/1.48 rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_38__092_060open_062x_A_060_Ay_A_092_060and_062_ABranch_AB_Ava_Avb_Avg_Avc_A_124_092_060guillemotleft_062_Ax_092_060close_062,axiom,
% 2.45/1.48 ( ( less @ x @ y )
% 2.45/1.48 & ( rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_39_local_Ois__rbt__rbt__sorted,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.45/1.48 => ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_40__C5__4_Oprems_C_I4_J,axiom,
% 2.45/1.48 rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_41__C5__4_Oprems_C_I2_J,axiom,
% 2.45/1.48 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c ) @ z @ t @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_42_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) )
% 2.45/1.48 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 2.45/1.48 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 2.45/1.48 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 2.45/1.48 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_43_ord_Orbt__less__simps_I2_J,axiom,
% 2.45/1.48 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.45/1.48 = ( ( Less @ Kt @ K )
% 2.45/1.48 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Lt )
% 2.45/1.48 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_44_color_Odistinct_I1_J,axiom,
% 2.45/1.48 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 2.45/1.48
% 2.45/1.48 thf(fact_45_mem__Collect__eq,axiom,
% 2.45/1.48 ! [A: $tType,A2: A,P: A > $o] :
% 2.45/1.48 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.45/1.48 = ( P @ A2 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_46_Collect__mem__eq,axiom,
% 2.45/1.48 ! [A: $tType,A3: set @ A] :
% 2.45/1.48 ( ( collect @ A
% 2.45/1.48 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.45/1.48 = A3 ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_47_Collect__cong,axiom,
% 2.45/1.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.45/1.48 ( ! [X3: A] :
% 2.45/1.48 ( ( P @ X3 )
% 2.45/1.48 = ( Q @ X3 ) )
% 2.45/1.48 => ( ( collect @ A @ P )
% 2.45/1.48 = ( collect @ A @ Q ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_48_ext,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.45/1.48 ( ! [X3: A] :
% 2.45/1.48 ( ( F @ X3 )
% 2.45/1.48 = ( G @ X3 ) )
% 2.45/1.48 => ( F = G ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_49_color_Oinduct,axiom,
% 2.45/1.48 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 2.45/1.48 ( ( P @ rBT_Impl_Mirabelle_R )
% 2.45/1.48 => ( ( P @ rBT_Impl_Mirabelle_B )
% 2.45/1.48 => ( P @ Color ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_50_color_Oexhaust,axiom,
% 2.45/1.48 ! [Y: rBT_Im1923302023_color] :
% 2.45/1.48 ( ( Y != rBT_Impl_Mirabelle_R )
% 2.45/1.48 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_51_local_Olexordp__eq__antisym,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 2.45/1.48 => ( Xs = Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_52_local_Olexordp__eq__trans,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 2.45/1.48 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_53_local_Olexordp__eq__refl,axiom,
% 2.45/1.48 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_54_local_Olexordp__eq__linear,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_55__C5__4_Oprems_C_I1_J,axiom,
% 2.45/1.48 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_56__C5__4_Oprems_C_I3_J,axiom,
% 2.45/1.48 rBT_Im2075124343t_less @ a @ b @ less @ x @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ va @ vb @ vg @ vc ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_57_ord_Ois__rbt__rbt__sorted,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im862805236is_rbt @ A @ B @ Less @ T )
% 2.45/1.48 => ( rBT_Im759614907sorted @ A @ B @ Less @ T ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_58_local_OgreaterThan__def,axiom,
% 2.45/1.48 ! [L: a] :
% 2.45/1.48 ( ( set_greaterThan @ a @ less @ L )
% 2.45/1.48 = ( collect @ a @ ( less @ L ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_59_local_OlessThan__def,axiom,
% 2.45/1.48 ! [U: a] :
% 2.45/1.48 ( ( set_lessThan @ a @ less @ U )
% 2.45/1.48 = ( collect @ a
% 2.45/1.48 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_60_local_OEmpty__is__rbt,axiom,
% 2.45/1.48 ! [B: $tType] : ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_61_local_Ostrict__mono__less,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B,X: a,Y: a] :
% 2.45/1.48 ( ( strict_mono @ a @ B @ less @ F )
% 2.45/1.48 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 2.45/1.48 = ( less @ X @ Y ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_62_local_Ostrict__mono__def,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B] :
% 2.45/1.48 ( ( strict_mono @ a @ B @ less @ F )
% 2.45/1.48 = ( ! [X2: a,Y2: a] :
% 2.45/1.48 ( ( less @ X2 @ Y2 )
% 2.45/1.48 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_63_local_Ostrict__monoI,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B] :
% 2.45/1.48 ( ! [X3: a,Y3: a] :
% 2.45/1.48 ( ( less @ X3 @ Y3 )
% 2.45/1.48 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.45/1.48 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_64_local_Ostrict__monoD,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B,X: a,Y: a] :
% 2.45/1.48 ( ( strict_mono @ a @ B @ less @ F )
% 2.45/1.48 => ( ( less @ X @ Y )
% 2.45/1.48 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_65_local_Olexordp__eq_ONil,axiom,
% 2.45/1.48 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_66_local_Orbt__sorted_Osimps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_67_local_OlessThan__iff,axiom,
% 2.45/1.48 ! [I: a,K: a] :
% 2.45/1.48 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 2.45/1.48 = ( less @ I @ K ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_68_local_OgreaterThan__iff,axiom,
% 2.45/1.48 ! [I: a,K: a] :
% 2.45/1.48 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 2.45/1.48 = ( less @ K @ I ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_69_local_Olexordp__eq__simps_I2_J,axiom,
% 2.45/1.48 ! [Xs: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 2.45/1.48 = ( Xs
% 2.45/1.48 = ( nil @ a ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_70_local_Olexordp__eq__simps_I1_J,axiom,
% 2.45/1.48 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_71_local_Orbt__less__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_72_local_Orbt__greater__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_73_rbt_Odistinct_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im418718756_Empty @ A @ B )
% 2.45/1.48 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_74_rbt_Oinduct,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 => ( ! [X1: rBT_Im1923302023_color,X26: rBT_Im246033960le_rbt @ A @ B,X32: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( P @ X26 )
% 2.45/1.48 => ( ( P @ X5 )
% 2.45/1.48 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X26 @ X32 @ X4 @ X5 ) ) ) )
% 2.45/1.48 => ( P @ Rbt ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_75_rbt_Oexhaust,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( Y
% 2.45/1.48 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( Y
% 2.45/1.48 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_76_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_77_ord_Orbt__less__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_78_ord_Orbt__greater__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_79_ord_OEmpty__is__rbt,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im862805236is_rbt @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_80_rbt__cases,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( T
% 2.45/1.48 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( T
% 2.45/1.48 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K2 @ V2 @ R2 ) )
% 2.45/1.48 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( T
% 2.45/1.48 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K2 @ V2 @ R2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_81_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_82_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.45/1.48 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 2.45/1.48 = ( Xs
% 2.45/1.48 = ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_83_local_Olexordp__eq_Ocases,axiom,
% 2.45/1.48 ! [A1: list @ a,A22: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.45/1.48 => ( ( ( A1
% 2.45/1.48 = ( nil @ a ) )
% 2.45/1.48 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 2.45/1.48 => ( ! [X3: a] :
% 2.45/1.48 ( ? [Xs2: list @ a] :
% 2.45/1.48 ( A1
% 2.45/1.48 = ( cons @ a @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Y3: a] :
% 2.45/1.48 ( ? [Ys2: list @ a] :
% 2.45/1.48 ( A22
% 2.45/1.48 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ~ ( less @ X3 @ Y3 ) ) )
% 2.45/1.48 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Ys2: list @ a] :
% 2.45/1.48 ( ( A22
% 2.45/1.48 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ~ ( less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( less @ Y3 @ X3 )
% 2.45/1.48 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_84_local_Olexordp__eq_Oinducts,axiom,
% 2.45/1.48 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ X12 @ X27 )
% 2.45/1.48 => ( ! [X1: list @ a] : ( P @ ( nil @ a ) @ X1 )
% 2.45/1.48 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.45/1.48 ( ( less @ X3 @ Y3 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.45/1.48 ( ~ ( less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( less @ Y3 @ X3 )
% 2.45/1.48 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 2.45/1.48 => ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 2.45/1.48 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_85_local_Olexordp__eq_Osimps,axiom,
% 2.45/1.48 ! [A1: list @ a,A22: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.45/1.48 = ( ? [Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( nil @ a ) )
% 2.45/1.48 & ( A22 = Ys3 ) )
% 2.45/1.48 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A22
% 2.45/1.48 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.45/1.48 & ( less @ X2 @ Y2 ) )
% 2.45/1.48 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A22
% 2.45/1.48 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.45/1.48 & ~ ( less @ X2 @ Y2 )
% 2.45/1.48 & ~ ( less @ Y2 @ X2 )
% 2.45/1.48 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_86_ord_Olexordp__eq_ONil,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_87_local_Olexordp__eq_OCons,axiom,
% 2.45/1.48 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_88_local_Olexordp__eq_OCons__eq,axiom,
% 2.45/1.48 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ~ ( less @ X @ Y )
% 2.45/1.48 => ( ~ ( less @ Y @ X )
% 2.45/1.48 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_89_list_Oinject,axiom,
% 2.45/1.48 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.45/1.48 ( ( ( cons @ A @ X21 @ X22 )
% 2.45/1.48 = ( cons @ A @ Y21 @ Y22 ) )
% 2.45/1.48 = ( ( X21 = Y21 )
% 2.45/1.48 & ( X22 = Y22 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_90_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.45/1.48 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.45/1.48 = ( ( Less @ X @ Y )
% 2.45/1.48 | ( ~ ( Less @ Y @ X )
% 2.45/1.48 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_91_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 2.45/1.48 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_92_local_Olexordp__eq__simps_I4_J,axiom,
% 2.45/1.48 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 2.45/1.48 = ( ( less @ X @ Y )
% 2.45/1.48 | ( ~ ( less @ Y @ X )
% 2.45/1.48 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_93_local_Olexordp__eq__simps_I3_J,axiom,
% 2.45/1.48 ! [X: a,Xs: list @ a] :
% 2.45/1.48 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_94_map__tailrec__rev_Oinduct,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.45/1.48 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 2.45/1.48 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.45/1.48 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 2.45/1.48 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.45/1.48 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_95_list__nonempty__induct,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( Xs2
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( ( P @ Xs2 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 2.45/1.48 => ( P @ Xs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_96_remdups__adj_Oinduct,axiom,
% 2.45/1.48 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.45/1.48 ( ( P @ ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.45/1.48 => ( ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( ( X3 = Y3 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.45/1.48 => ( ( ( X3 != Y3 )
% 2.45/1.48 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 2.45/1.48 => ( P @ A0 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_97_remdups__adj_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,X: list @ A] :
% 2.45/1.48 ( ( X
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.45/1.48 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_98_transpose_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,X: list @ ( list @ A )] :
% 2.45/1.48 ( ( X
% 2.45/1.48 != ( nil @ ( list @ A ) ) )
% 2.45/1.48 => ( ! [Xss: list @ ( list @ A )] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.45/1.48 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_99_splice_Oinduct,axiom,
% 2.45/1.48 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.45/1.48 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.45/1.48 => ( ! [V2: A,Va: list @ A] : ( P @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 2.45/1.48 ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_100_list__induct2_H,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.45/1.48 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 2.45/1.48 => ( ! [Y3: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 2.45/1.48 ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_101_neq__Nil__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 = ( ? [Y2: A,Ys3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_102_list_Oinducts,axiom,
% 2.45/1.48 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.45/1.48 ( ( P @ ( nil @ A ) )
% 2.45/1.48 => ( ! [X1: A,X26: list @ A] :
% 2.45/1.48 ( ( P @ X26 )
% 2.45/1.48 => ( P @ ( cons @ A @ X1 @ X26 ) ) )
% 2.45/1.48 => ( P @ List ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_103_list_Oexhaust,axiom,
% 2.45/1.48 ! [A: $tType,Y: list @ A] :
% 2.45/1.48 ( ( Y
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ~ ! [X212: A,X222: list @ A] :
% 2.45/1.48 ( Y
% 2.45/1.48 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_104_list_OdiscI,axiom,
% 2.45/1.48 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.45/1.48 ( ( List
% 2.45/1.48 = ( cons @ A @ X21 @ X22 ) )
% 2.45/1.48 => ( List
% 2.45/1.48 != ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_105_list_Odistinct_I1_J,axiom,
% 2.45/1.48 ! [A: $tType,X21: A,X22: list @ A] :
% 2.45/1.48 ( ( nil @ A )
% 2.45/1.48 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_106_not__Cons__self2,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( cons @ A @ X @ Xs )
% 2.45/1.48 != Xs ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_107_ord_Olexordp__eq_OCons__eq,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ~ ( Less @ X @ Y )
% 2.45/1.48 => ( ~ ( Less @ Y @ X )
% 2.45/1.48 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_108_ord_Olexordp__eq_OCons,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( Less @ X @ Y )
% 2.45/1.48 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_109_ord_Olexordp__eq_Oinducts,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.45/1.48 ( ( lexordp_eq @ A @ Less @ X12 @ X27 )
% 2.45/1.48 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.45/1.48 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.45/1.48 ( ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.45/1.48 ( ~ ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( Less @ Y3 @ X3 )
% 2.45/1.48 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 2.45/1.48 => ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 2.45/1.48 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_110_ord_Olexordp__eq_Osimps,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( lexordp_eq @ A )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.45/1.48 ( ? [Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( A23 = Ys3 ) )
% 2.45/1.48 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( cons @ A @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A23
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.45/1.48 & ( Less2 @ X2 @ Y2 ) )
% 2.45/1.48 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( cons @ A @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A23
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.45/1.48 & ~ ( Less2 @ X2 @ Y2 )
% 2.45/1.48 & ~ ( Less2 @ Y2 @ X2 )
% 2.45/1.48 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_111_ord_Olexordp__eq_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.45/1.48 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 2.45/1.48 => ( ( ( A1
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 2.45/1.48 => ( ! [X3: A] :
% 2.45/1.48 ( ? [Xs2: list @ A] :
% 2.45/1.48 ( A1
% 2.45/1.48 = ( cons @ A @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Y3: A] :
% 2.45/1.48 ( ? [Ys2: list @ A] :
% 2.45/1.48 ( A22
% 2.45/1.48 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.45/1.48 => ~ ( Less @ X3 @ Y3 ) ) )
% 2.45/1.48 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ A @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Ys2: list @ A] :
% 2.45/1.48 ( ( A22
% 2.45/1.48 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ~ ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( Less @ Y3 @ X3 )
% 2.45/1.48 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_112_ord_Olexordp__eq__refl,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_113_local_Olexordp_ONil,axiom,
% 2.45/1.48 ! [Y: a,Ys: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ Y @ Ys ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_114_local_Olexordp_Ocases,axiom,
% 2.45/1.48 ! [A1: list @ a,A22: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ A1 @ A22 )
% 2.45/1.48 => ( ( ( A1
% 2.45/1.48 = ( nil @ a ) )
% 2.45/1.48 => ! [Y3: a,Ys2: list @ a] :
% 2.45/1.48 ( A22
% 2.45/1.48 != ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: a] :
% 2.45/1.48 ( ? [Xs2: list @ a] :
% 2.45/1.48 ( A1
% 2.45/1.48 = ( cons @ a @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Y3: a] :
% 2.45/1.48 ( ? [Ys2: list @ a] :
% 2.45/1.48 ( A22
% 2.45/1.48 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ~ ( less @ X3 @ Y3 ) ) )
% 2.45/1.48 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Ys2: list @ a] :
% 2.45/1.48 ( ( A22
% 2.45/1.48 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ~ ( less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( less @ Y3 @ X3 )
% 2.45/1.48 => ~ ( lexordp @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_115_local_Olexordp_Oinducts,axiom,
% 2.45/1.48 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.45/1.48 ( ( lexordp @ a @ less @ X12 @ X27 )
% 2.45/1.48 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.45/1.48 ( ( less @ X3 @ Y3 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.45/1.48 ( ~ ( less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( less @ Y3 @ X3 )
% 2.45/1.48 => ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 2.45/1.48 => ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 2.45/1.48 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_116_local_Olexordp_Osimps,axiom,
% 2.45/1.48 ! [A1: list @ a,A22: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ A1 @ A22 )
% 2.45/1.48 = ( ? [Y2: a,Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( nil @ a ) )
% 2.45/1.48 & ( A22
% 2.45/1.48 = ( cons @ a @ Y2 @ Ys3 ) ) )
% 2.45/1.48 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A22
% 2.45/1.48 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.45/1.48 & ( less @ X2 @ Y2 ) )
% 2.45/1.48 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ a @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A22
% 2.45/1.48 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.45/1.48 & ~ ( less @ X2 @ Y2 )
% 2.45/1.48 & ~ ( less @ Y2 @ X2 )
% 2.45/1.48 & ( lexordp @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_117_local_Olexordp__cases,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( ( ( Xs
% 2.45/1.48 = ( nil @ a ) )
% 2.45/1.48 => ! [Y3: a,Ys4: list @ a] :
% 2.45/1.48 ( Ys
% 2.45/1.48 != ( cons @ a @ Y3 @ Ys4 ) ) )
% 2.45/1.48 => ( ! [X3: a] :
% 2.45/1.48 ( ? [Xs4: list @ a] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( cons @ a @ X3 @ Xs4 ) )
% 2.45/1.48 => ! [Y3: a] :
% 2.45/1.48 ( ? [Ys4: list @ a] :
% 2.45/1.48 ( Ys
% 2.45/1.48 = ( cons @ a @ Y3 @ Ys4 ) )
% 2.45/1.48 => ~ ( less @ X3 @ Y3 ) ) )
% 2.45/1.48 => ~ ! [X3: a,Xs4: list @ a] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( cons @ a @ X3 @ Xs4 ) )
% 2.45/1.48 => ! [Ys4: list @ a] :
% 2.45/1.48 ( ( Ys
% 2.45/1.48 = ( cons @ a @ X3 @ Ys4 ) )
% 2.45/1.48 => ~ ( lexordp @ a @ less @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_118_local_Olexordp__induct,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ! [X3: a,Xs2: list @ a,Y3: a,Ys2: list @ a] :
% 2.45/1.48 ( ( less @ X3 @ Y3 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 2.45/1.48 => ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 2.45/1.48 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_119_local_Olexordp__antisym,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_120_local_Olexordp__irreflexive,axiom,
% 2.45/1.48 ! [Xs: list @ a] :
% 2.45/1.48 ( ! [X3: a] :
% 2.45/1.48 ~ ( less @ X3 @ X3 )
% 2.45/1.48 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_121_local_Olexordp__irreflexive_H,axiom,
% 2.45/1.48 ! [Xs: list @ a] :
% 2.45/1.48 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_122_local_Olexordp__linear,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 | ( Xs = Ys )
% 2.45/1.48 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_123_local_Olexordp__trans,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( ( lexordp @ a @ less @ Ys @ Zs )
% 2.45/1.48 => ( lexordp @ a @ less @ Xs @ Zs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_124_local_Olexordp_OCons,axiom,
% 2.45/1.48 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_125_local_Olexordp_OCons__eq,axiom,
% 2.45/1.48 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ~ ( less @ X @ Y )
% 2.45/1.48 => ( ~ ( less @ Y @ X )
% 2.45/1.48 => ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_126_local_Olexordp__conv__lexordp__eq,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 = ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 & ~ ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_127_local_Olexordp__eq__conv__lexord,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.45/1.48 = ( ( Xs = Ys )
% 2.45/1.48 | ( lexordp @ a @ less @ Xs @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_128_local_Olexordp__into__lexordp__eq,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_129_ord_Olexordp__simps_I3_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.45/1.48 = ( ( Less @ X @ Y )
% 2.45/1.48 | ( ~ ( Less @ Y @ X )
% 2.45/1.48 & ( lexordp @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_130_ord_Olexordp__simps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Ys: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ ( nil @ A ) @ Ys )
% 2.45/1.48 = ( Ys
% 2.45/1.48 != ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_131_ord_Olexordp__simps_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.45/1.48 ~ ( lexordp @ A @ Less @ Xs @ ( nil @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_132_local_Olexordp__simps_I3_J,axiom,
% 2.45/1.48 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 2.45/1.48 = ( ( less @ X @ Y )
% 2.45/1.48 | ( ~ ( less @ Y @ X )
% 2.45/1.48 & ( lexordp @ a @ less @ Xs @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_133_local_Olexordp__simps_I2_J,axiom,
% 2.45/1.48 ! [Xs: list @ a] :
% 2.45/1.48 ~ ( lexordp @ a @ less @ Xs @ ( nil @ a ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_134_local_Olexordp__simps_I1_J,axiom,
% 2.45/1.48 ! [Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ ( nil @ a ) @ Ys )
% 2.45/1.48 = ( Ys
% 2.45/1.48 != ( nil @ a ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_135_ord_Olexordp__irreflexive,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.45/1.48 ( ! [X3: A] :
% 2.45/1.48 ~ ( Less @ X3 @ X3 )
% 2.45/1.48 => ~ ( lexordp @ A @ Less @ Xs @ Xs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_136_ord_Olexordp_OCons__eq,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ~ ( Less @ X @ Y )
% 2.45/1.48 => ( ~ ( Less @ Y @ X )
% 2.45/1.48 => ( ( lexordp @ A @ Less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_137_ord_Olexordp_OCons,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( Less @ X @ Y )
% 2.45/1.48 => ( lexordp @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_138_ord_Olexordp__into__lexordp__eq,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ Xs @ Ys )
% 2.45/1.48 => ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_139_ord_Olexordp_ONil,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Y: A,Ys: list @ A] : ( lexordp @ A @ Less @ ( nil @ A ) @ ( cons @ A @ Y @ Ys ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_140_ord_Olexordp_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ A1 @ A22 )
% 2.45/1.48 => ( ( ( A1
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 => ! [Y3: A,Ys2: list @ A] :
% 2.45/1.48 ( A22
% 2.45/1.48 != ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: A] :
% 2.45/1.48 ( ? [Xs2: list @ A] :
% 2.45/1.48 ( A1
% 2.45/1.48 = ( cons @ A @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Y3: A] :
% 2.45/1.48 ( ? [Ys2: list @ A] :
% 2.45/1.48 ( A22
% 2.45/1.48 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.45/1.48 => ~ ( Less @ X3 @ Y3 ) ) )
% 2.45/1.48 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( A1
% 2.45/1.48 = ( cons @ A @ X3 @ Xs2 ) )
% 2.45/1.48 => ! [Ys2: list @ A] :
% 2.45/1.48 ( ( A22
% 2.45/1.48 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ~ ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( Less @ Y3 @ X3 )
% 2.45/1.48 => ~ ( lexordp @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_141_ord_Olexordp_Osimps,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( lexordp @ A )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.45/1.48 ( ? [Y2: A,Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( A23
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) ) )
% 2.45/1.48 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( cons @ A @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A23
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.45/1.48 & ( Less2 @ X2 @ Y2 ) )
% 2.45/1.48 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.45/1.48 ( ( A12
% 2.45/1.48 = ( cons @ A @ X2 @ Xs3 ) )
% 2.45/1.48 & ( A23
% 2.45/1.48 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.45/1.48 & ~ ( Less2 @ X2 @ Y2 )
% 2.45/1.48 & ~ ( Less2 @ Y2 @ X2 )
% 2.45/1.48 & ( lexordp @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_142_ord_Olexordp_Oinducts,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ X12 @ X27 )
% 2.45/1.48 => ( ! [Y3: A,Ys2: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys2 ) )
% 2.45/1.48 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.45/1.48 ( ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.45/1.48 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.45/1.48 ( ~ ( Less @ X3 @ Y3 )
% 2.45/1.48 => ( ~ ( Less @ Y3 @ X3 )
% 2.45/1.48 => ( ( lexordp @ A @ Less @ Xs2 @ Ys2 )
% 2.45/1.48 => ( ( P @ Xs2 @ Ys2 )
% 2.45/1.48 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 2.45/1.48 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_143_local_Olexordp__append__rightI,axiom,
% 2.45/1.48 ! [Ys: list @ a,Xs: list @ a] :
% 2.45/1.48 ( ( Ys
% 2.45/1.48 != ( nil @ a ) )
% 2.45/1.48 => ( lexordp @ a @ less @ Xs @ ( append @ a @ Xs @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_144_local_Olexordp__iff,axiom,
% 2.45/1.48 ! [Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.45/1.48 = ( ? [X2: a,Vs: list @ a] :
% 2.45/1.48 ( Ys
% 2.45/1.48 = ( append @ a @ Xs @ ( cons @ a @ X2 @ Vs ) ) )
% 2.45/1.48 | ? [Us: list @ a,A5: a,B3: a,Vs: list @ a,Ws: list @ a] :
% 2.45/1.48 ( ( less @ A5 @ B3 )
% 2.45/1.48 & ( Xs
% 2.45/1.48 = ( append @ a @ Us @ ( cons @ a @ A5 @ Vs ) ) )
% 2.45/1.48 & ( Ys
% 2.45/1.48 = ( append @ a @ Us @ ( cons @ a @ B3 @ Ws ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_145_local_Olexordp__append__left__rightI,axiom,
% 2.45/1.48 ! [X: a,Y: a,Us2: list @ a,Xs: list @ a,Ys: list @ a] :
% 2.45/1.48 ( ( less @ X @ Y )
% 2.45/1.48 => ( lexordp @ a @ less @ ( append @ a @ Us2 @ ( cons @ a @ X @ Xs ) ) @ ( append @ a @ Us2 @ ( cons @ a @ Y @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_146_sublists_Osimps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( sublists @ A @ ( nil @ A ) )
% 2.45/1.48 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_147_local_Olexordp__append__leftI,axiom,
% 2.45/1.48 ! [Us2: list @ a,Vs2: list @ a,Xs: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ Us2 @ Vs2 )
% 2.45/1.48 => ( lexordp @ a @ less @ ( append @ a @ Xs @ Us2 ) @ ( append @ a @ Xs @ Vs2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_148_local_Olexordp__append__leftD,axiom,
% 2.45/1.48 ! [Xs: list @ a,Us2: list @ a,Vs2: list @ a] :
% 2.45/1.48 ( ( lexordp @ a @ less @ ( append @ a @ Xs @ Us2 ) @ ( append @ a @ Xs @ Vs2 ) )
% 2.45/1.48 => ( ! [A4: a] :
% 2.45/1.48 ~ ( less @ A4 @ A4 )
% 2.45/1.48 => ( lexordp @ a @ less @ Us2 @ Vs2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_149_same__append__eq,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = ( append @ A @ Xs @ Zs ) )
% 2.45/1.48 = ( Ys = Zs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_150_append__same__eq,axiom,
% 2.45/1.48 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Ys @ Xs )
% 2.45/1.48 = ( append @ A @ Zs @ Xs ) )
% 2.45/1.48 = ( Ys = Zs ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_151_append__assoc,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.45/1.48 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.45/1.48 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_152_append__Nil2,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A] :
% 2.45/1.48 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.45/1.48 = Xs ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_153_append__self__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = Xs )
% 2.45/1.48 = ( Ys
% 2.45/1.48 = ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_154_self__append__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Xs @ Ys ) )
% 2.45/1.48 = ( Ys
% 2.45/1.48 = ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_155_append__self__conv2,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = Ys )
% 2.45/1.48 = ( Xs
% 2.45/1.48 = ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_156_self__append__conv2,axiom,
% 2.45/1.48 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.45/1.48 ( ( Ys
% 2.45/1.48 = ( append @ A @ Xs @ Ys ) )
% 2.45/1.48 = ( Xs
% 2.45/1.48 = ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_157_Nil__is__append__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( ( nil @ A )
% 2.45/1.48 = ( append @ A @ Xs @ Ys ) )
% 2.45/1.48 = ( ( Xs
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( Ys
% 2.45/1.48 = ( nil @ A ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_158_append__is__Nil__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 = ( ( Xs
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( Ys
% 2.45/1.48 = ( nil @ A ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_159_append1__eq__conv,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.45/1.48 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.45/1.48 = ( ( Xs = Ys )
% 2.45/1.48 & ( X = Y ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_160_ord_Olexordp__append__leftD,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 2.45/1.48 => ( ! [A4: A] :
% 2.45/1.48 ~ ( Less @ A4 @ A4 )
% 2.45/1.48 => ( lexordp @ A @ Less @ Us2 @ Vs2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_161_ord_Olexordp__append__leftI,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 2.45/1.48 ( ( lexordp @ A @ Less @ Us2 @ Vs2 )
% 2.45/1.48 => ( lexordp @ A @ Less @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_162_append__Cons,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.45/1.48 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_163_Cons__eq__appendI,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.45/1.48 ( ( ( cons @ A @ X @ Xs1 )
% 2.45/1.48 = Ys )
% 2.45/1.48 => ( ( Xs
% 2.45/1.48 = ( append @ A @ Xs1 @ Zs ) )
% 2.45/1.48 => ( ( cons @ A @ X @ Xs )
% 2.45/1.48 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_164_eq__Nil__appendI,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( Xs = Ys )
% 2.45/1.48 => ( Xs
% 2.45/1.48 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_165_append__Nil,axiom,
% 2.45/1.48 ! [A: $tType,Ys: list @ A] :
% 2.45/1.48 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.45/1.48 = Ys ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_166_append__eq__append__conv2,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = ( append @ A @ Zs @ Ts ) )
% 2.45/1.48 = ( ? [Us: list @ A] :
% 2.45/1.48 ( ( ( Xs
% 2.45/1.48 = ( append @ A @ Zs @ Us ) )
% 2.45/1.48 & ( ( append @ A @ Us @ Ys )
% 2.45/1.48 = Ts ) )
% 2.45/1.48 | ( ( ( append @ A @ Xs @ Us )
% 2.45/1.48 = Zs )
% 2.45/1.48 & ( Ys
% 2.45/1.48 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_167_append__eq__appendI,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us2: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Xs @ Xs1 )
% 2.45/1.48 = Zs )
% 2.45/1.48 => ( ( Ys
% 2.45/1.48 = ( append @ A @ Xs1 @ Us2 ) )
% 2.45/1.48 => ( ( append @ A @ Xs @ Ys )
% 2.45/1.48 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_168_rev__nonempty__induct,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( Xs2
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( ( P @ Xs2 )
% 2.45/1.48 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 2.45/1.48 => ( P @ Xs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_169_append__eq__Cons__conv,axiom,
% 2.45/1.48 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( ( append @ A @ Ys @ Zs )
% 2.45/1.48 = ( cons @ A @ X @ Xs ) )
% 2.45/1.48 = ( ( ( Ys
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( Zs
% 2.45/1.48 = ( cons @ A @ X @ Xs ) ) )
% 2.45/1.48 | ? [Ys5: list @ A] :
% 2.45/1.48 ( ( Ys
% 2.45/1.48 = ( cons @ A @ X @ Ys5 ) )
% 2.45/1.48 & ( ( append @ A @ Ys5 @ Zs )
% 2.45/1.48 = Xs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_170_Cons__eq__append__conv,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.45/1.48 ( ( ( cons @ A @ X @ Xs )
% 2.45/1.48 = ( append @ A @ Ys @ Zs ) )
% 2.45/1.48 = ( ( ( Ys
% 2.45/1.48 = ( nil @ A ) )
% 2.45/1.48 & ( ( cons @ A @ X @ Xs )
% 2.45/1.48 = Zs ) )
% 2.45/1.48 | ? [Ys5: list @ A] :
% 2.45/1.48 ( ( ( cons @ A @ X @ Ys5 )
% 2.45/1.48 = Ys )
% 2.45/1.48 & ( Xs
% 2.45/1.48 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_171_rev__exhaust,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ~ ! [Ys2: list @ A,Y3: A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 != ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_172_rev__induct,axiom,
% 2.45/1.48 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.45/1.48 ( ( P @ ( nil @ A ) )
% 2.45/1.48 => ( ! [X3: A,Xs2: list @ A] :
% 2.45/1.48 ( ( P @ Xs2 )
% 2.45/1.48 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 2.45/1.48 => ( P @ Xs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_173_ord_Olexordp__append__left__rightI,axiom,
% 2.45/1.48 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Us2: list @ A,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( Less @ X @ Y )
% 2.45/1.48 => ( lexordp @ A @ Less @ ( append @ A @ Us2 @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_174_ord_Olexordp__append__rightI,axiom,
% 2.45/1.48 ! [A: $tType,Ys: list @ A,Less: A > A > $o,Xs: list @ A] :
% 2.45/1.48 ( ( Ys
% 2.45/1.48 != ( nil @ A ) )
% 2.45/1.48 => ( lexordp @ A @ Less @ Xs @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_175_keys__simps_I2_J,axiom,
% 2.45/1.48 ! [D: $tType,C2: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ C2 @ D,K: C2,V: D,R: rBT_Im246033960le_rbt @ C2 @ D] :
% 2.45/1.48 ( ( rBT_Im380146495e_keys @ C2 @ D @ ( rBT_Im480247531Branch @ C2 @ D @ C @ L @ K @ V @ R ) )
% 2.45/1.48 = ( append @ C2 @ ( rBT_Im380146495e_keys @ C2 @ D @ L ) @ ( cons @ C2 @ K @ ( rBT_Im380146495e_keys @ C2 @ D @ R ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_176_product__lists_Osimps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.45/1.48 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_177_bind__simps_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 2.45/1.48 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 2.45/1.48 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_178_bind__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.45/1.48 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 2.45/1.48 = ( nil @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_179_keys__simps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType] :
% 2.45/1.48 ( ( rBT_Im380146495e_keys @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 = ( nil @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_180_non__empty__rbt__keys,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( T
% 2.45/1.48 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 => ( ( rBT_Im380146495e_keys @ A @ B @ T )
% 2.45/1.48 != ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_181_local_Orbt__greater__prop,axiom,
% 2.45/1.48 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 2.45/1.48 = ( ! [X2: a] :
% 2.45/1.48 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 2.45/1.48 => ( less @ K @ X2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_182_local_Orbt__less__prop,axiom,
% 2.45/1.48 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 2.45/1.48 = ( ! [X2: a] :
% 2.45/1.48 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 2.45/1.48 => ( less @ X2 @ K ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_183_local_Ostrict__mono__imp__inj__on,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( order @ B @ ( type2 @ B ) )
% 2.45/1.48 => ! [F: a > B,A3: set @ a] :
% 2.45/1.48 ( ( strict_mono @ a @ B @ less @ F )
% 2.45/1.48 => ( inj_on @ a @ B @ F @ A3 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_184_list__bind__cong,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 2.45/1.48 ( ( Xs = Ys )
% 2.45/1.48 => ( ! [X3: A] :
% 2.45/1.48 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 => ( ( F @ X3 )
% 2.45/1.48 = ( G @ X3 ) ) )
% 2.45/1.48 => ( ( bind @ A @ B @ Xs @ F )
% 2.45/1.48 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_185_split__list__first__prop__iff,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ( ? [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X2 ) ) )
% 2.45/1.48 = ( ? [Ys3: list @ A,X2: A] :
% 2.45/1.48 ( ? [Zs2: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 2.45/1.48 & ( P @ X2 )
% 2.45/1.48 & ! [Y2: A] :
% 2.45/1.48 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys3 ) )
% 2.45/1.48 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_186_split__list__last__prop__iff,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ( ? [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X2 ) ) )
% 2.45/1.48 = ( ? [Ys3: list @ A,X2: A,Zs2: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 2.45/1.48 & ( P @ X2 )
% 2.45/1.48 & ! [Y2: A] :
% 2.45/1.48 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 2.45/1.48 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_187_in__set__conv__decomp__first,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.45/1.48 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_188_in__set__conv__decomp__last,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.45/1.48 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_189_split__list__first__propE,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ~ ! [Ys2: list @ A,X3: A] :
% 2.45/1.48 ( ? [Zs3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 => ( ( P @ X3 )
% 2.45/1.48 => ~ ! [Xa: A] :
% 2.45/1.48 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.45/1.48 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_190_split__list__last__propE,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ~ ! [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 => ( ( P @ X3 )
% 2.45/1.48 => ~ ! [Xa: A] :
% 2.45/1.48 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.45/1.48 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_191_split__list__first__prop,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ? [Ys2: list @ A,X3: A] :
% 2.45/1.48 ( ? [Zs3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 & ( P @ X3 )
% 2.45/1.48 & ! [Xa: A] :
% 2.45/1.48 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.45/1.48 => ~ ( P @ Xa ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_192_split__list__last__prop,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 & ( P @ X3 )
% 2.45/1.48 & ! [Xa: A] :
% 2.45/1.48 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.45/1.48 => ~ ( P @ Xa ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_193_in__set__conv__decomp,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_194_split__list__propE,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ~ ! [Ys2: list @ A,X3: A] :
% 2.45/1.48 ( ? [Zs3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 => ~ ( P @ X3 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_195_split__list__first,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.45/1.48 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_196_split__list__prop,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.45/1.48 ( ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X6 ) )
% 2.45/1.48 => ? [Ys2: list @ A,X3: A] :
% 2.45/1.48 ( ? [Zs3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.45/1.48 & ( P @ X3 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_197_split__list__last,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.45/1.48 ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.45/1.48 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_198_split__list,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.45/1.48 ( Xs
% 2.45/1.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_199_list_Oset__cases,axiom,
% 2.45/1.48 ! [A: $tType,E: A,A2: list @ A] :
% 2.45/1.48 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 2.45/1.48 => ( ! [Z2: list @ A] :
% 2.45/1.48 ( A2
% 2.45/1.48 != ( cons @ A @ E @ Z2 ) )
% 2.45/1.48 => ~ ! [Z1: A,Z2: list @ A] :
% 2.45/1.48 ( ( A2
% 2.45/1.48 = ( cons @ A @ Z1 @ Z2 ) )
% 2.45/1.48 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_200_set__ConsD,axiom,
% 2.45/1.48 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.45/1.48 => ( ( Y = X )
% 2.45/1.48 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_201_list_Oset__intros_I1_J,axiom,
% 2.45/1.48 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_202_list_Oset__intros_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 2.45/1.48 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 2.45/1.48 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_203_ord_Orbt__less__prop,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ A @ B )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,K3: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ! [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.45/1.48 => ( Less2 @ X2 @ K3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_204_ord_Orbt__greater__prop,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ A @ B )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,K3: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ! [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.45/1.48 => ( Less2 @ K3 @ X2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_205_local_Odistinct__keys,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.45/1.48 => ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_206_the__elem__set,axiom,
% 2.45/1.48 ! [A: $tType,X: A] :
% 2.45/1.48 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.45/1.48 = X ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_207_ord_OgreaterThan__def,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( set_greaterThan @ A )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,L3: A] : ( collect @ A @ ( Less2 @ L3 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_208_distinct__product__lists,axiom,
% 2.45/1.48 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 2.45/1.48 ( ! [X3: list @ A] :
% 2.45/1.48 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 2.45/1.48 => ( distinct @ A @ X3 ) )
% 2.45/1.48 => ( distinct @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_209_distinct_Osimps_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A] :
% 2.45/1.48 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 2.45/1.48 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( distinct @ A @ Xs ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_210_distinct_Osimps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_211_distinct__length__2__or__more,axiom,
% 2.45/1.48 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 2.45/1.48 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 2.45/1.48 = ( ( A2 != B2 )
% 2.45/1.48 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 2.45/1.48 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_212_distinct__singleton,axiom,
% 2.45/1.48 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_213_not__distinct__decomp,axiom,
% 2.45/1.48 ! [A: $tType,Ws2: list @ A] :
% 2.45/1.48 ( ~ ( distinct @ A @ Ws2 )
% 2.45/1.48 => ? [Xs2: list @ A,Ys2: list @ A,Zs3: list @ A,Y3: A] :
% 2.45/1.48 ( Ws2
% 2.45/1.48 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ ( append @ A @ Ys2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_214_not__distinct__conv__prefix,axiom,
% 2.45/1.48 ! [A: $tType,As2: list @ A] :
% 2.45/1.48 ( ( ~ ( distinct @ A @ As2 ) )
% 2.45/1.48 = ( ? [Xs3: list @ A,Y2: A,Ys3: list @ A] :
% 2.45/1.48 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 2.45/1.48 & ( distinct @ A @ Xs3 )
% 2.45/1.48 & ( As2
% 2.45/1.48 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_215_ord_OlessThan__iff,axiom,
% 2.45/1.48 ! [A: $tType,I: A,Less: A > A > $o,K: A] :
% 2.45/1.48 ( ( member @ A @ I @ ( set_lessThan @ A @ Less @ K ) )
% 2.45/1.48 = ( Less @ I @ K ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_216_ord_OgreaterThan__iff,axiom,
% 2.45/1.48 ! [A: $tType,I: A,Less: A > A > $o,K: A] :
% 2.45/1.48 ( ( member @ A @ I @ ( set_greaterThan @ A @ Less @ K ) )
% 2.45/1.48 = ( Less @ K @ I ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_217_ord_OlessThan__def,axiom,
% 2.45/1.48 ! [A: $tType] :
% 2.45/1.48 ( ( set_lessThan @ A )
% 2.45/1.48 = ( ^ [Less2: A > A > $o,U2: A] :
% 2.45/1.48 ( collect @ A
% 2.45/1.48 @ ^ [X2: A] : ( Less2 @ X2 @ U2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_218_local_Oset__entries__inject,axiom,
% 2.45/1.48 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.45/1.48 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.45/1.48 => ( ( ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) )
% 2.45/1.48 = ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) )
% 2.45/1.48 = ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.45/1.48 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_219_distinct__union,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.45/1.48 ( ( distinct @ A @ ( union @ A @ Xs @ Ys ) )
% 2.45/1.48 = ( distinct @ A @ Ys ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_220_entries_Osimps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType] :
% 2.45/1.48 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_221_local_Oentries__rbt__lookup,axiom,
% 2.45/1.48 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.45/1.48 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.45/1.48 => ( ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.45/1.48 = ( rBT_Im954575269ntries @ a @ B @ T22 ) )
% 2.45/1.48 = ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_222_local_Oentries__eqI,axiom,
% 2.45/1.48 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.45/1.48 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.45/1.48 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) )
% 2.45/1.48 => ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.45/1.48 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_223_local_Orbt__lookup__from__in__tree,axiom,
% 2.45/1.48 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B,K: a] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.45/1.48 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.45/1.48 => ( ! [V2: B] :
% 2.45/1.48 ( ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V2 ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) ) )
% 2.45/1.48 = ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V2 ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 @ K )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 @ K ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_224_local_Orbt__lookup__keys,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.45/1.48 => ( ( dom @ a @ B @ ( rBT_Im35466040lookup @ a @ B @ less @ T ) )
% 2.45/1.48 = ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_225_entries_Osimps_I2_J,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ K @ V @ R ) )
% 2.45/1.48 = ( append @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ L ) @ ( cons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V ) @ ( rBT_Im954575269ntries @ A @ B @ R ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_226_entry__in__tree__keys,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,K: A,V: B,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V ) @ ( set2 @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ T ) ) )
% 2.45/1.48 => ( member @ A @ K @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_227_keys__entries,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( member @ A @ K @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) )
% 2.45/1.48 = ( ? [V3: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ K @ V3 ) @ ( set2 @ ( product_prod @ A @ B ) @ ( rBT_Im954575269ntries @ A @ B @ T ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_228_local_OacyclicI__order,axiom,
% 2.45/1.48 ! [B: $tType,R: set @ ( product_prod @ B @ B ),F: B > a] :
% 2.45/1.48 ( ! [A4: B,B4: B] :
% 2.45/1.48 ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A4 @ B4 ) @ R )
% 2.45/1.48 => ( less @ ( F @ B4 ) @ ( F @ A4 ) ) )
% 2.45/1.48 => ( transitive_acyclic @ B @ R ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_229_local_Orbt__lookup__in__tree,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.45/1.48 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.45/1.48 = ( some @ B @ V ) )
% 2.45/1.48 = ( member @ ( product_prod @ a @ B ) @ ( product_Pair @ a @ B @ K @ V ) @ ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_230_local_Orbt__lookup_Osimps_I2_J,axiom,
% 2.45/1.48 ! [B: $tType,K: a,X: a,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( ( less @ K @ X )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ L @ K ) ) )
% 2.45/1.48 & ( ~ ( less @ K @ X )
% 2.45/1.48 => ( ( ( less @ X @ K )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ R @ K ) ) )
% 2.45/1.48 & ( ~ ( less @ X @ K )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( some @ B @ Y ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_231_splice_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,X: product_prod @ ( list @ A ) @ ( list @ A )] :
% 2.45/1.48 ( ! [Ys2: list @ A] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( nil @ A ) @ Ys2 ) )
% 2.45/1.48 => ( ! [V2: A,Va: list @ A] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ V2 @ Va ) @ ( nil @ A ) ) )
% 2.45/1.48 => ~ ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_232_map__tailrec__rev_Ocases,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,X: product_prod @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) )] :
% 2.45/1.48 ( ! [F2: A > B,Bs: list @ B] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( nil @ A ) @ Bs ) ) )
% 2.45/1.48 => ~ ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.45/1.48 ( X
% 2.45/1.48 != ( product_Pair @ ( A > B ) @ ( product_prod @ ( list @ A ) @ ( list @ B ) ) @ F2 @ ( product_Pair @ ( list @ A ) @ ( list @ B ) @ ( cons @ A @ A4 @ As ) @ Bs ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_233_ord_Orbt__lookup_Osimps_I2_J,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,X: A,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( ( Less @ K @ X )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( rBT_Im35466040lookup @ A @ B @ Less @ L @ K ) ) )
% 2.45/1.48 & ( ~ ( Less @ K @ X )
% 2.45/1.48 => ( ( ( Less @ X @ K )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( rBT_Im35466040lookup @ A @ B @ Less @ R @ K ) ) )
% 2.45/1.48 & ( ~ ( Less @ X @ K )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.45/1.48 = ( some @ B @ Y ) ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_234_local_Omap__of__entries,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.45/1.48 => ( ( map_of @ a @ B @ ( rBT_Im954575269ntries @ a @ B @ T ) )
% 2.45/1.48 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_235_local_Orbt__lookup_Osimps_I1_J,axiom,
% 2.45/1.48 ! [B: $tType,K: a] :
% 2.45/1.48 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 2.45/1.48 = ( none @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_236_local_Orbt__lookup__Empty,axiom,
% 2.45/1.48 ! [B: $tType] :
% 2.45/1.48 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 2.45/1.48 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_237_local_Orbt__lookup__rbt__less,axiom,
% 2.45/1.48 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.45/1.48 = ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_238_local_Orbt__lookup__rbt__greater,axiom,
% 2.45/1.48 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.45/1.48 = ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_239_ord_Orbt__lookup__Empty,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType,Less: A > A > $o] :
% 2.45/1.48 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.45/1.48 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_240_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,Less: A > A > $o,K: A] :
% 2.45/1.48 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 2.45/1.48 = ( none @ B ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_241_ord_Orbt__lookup__rbt__less,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ T )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 2.45/1.48 = ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_242_ord_Orbt__lookup__rbt__greater,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.45/1.48 ( ( rBT_Im1259024060reater @ A @ B @ Less @ K @ T )
% 2.45/1.48 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 2.45/1.48 = ( none @ B ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_243_order__class_OacyclicI__order,axiom,
% 2.45/1.48 ! [A: $tType,B: $tType] :
% 2.45/1.48 ( ( order @ A @ ( type2 @ A ) )
% 2.45/1.48 => ! [R: set @ ( product_prod @ B @ B ),F: B > A] :
% 2.45/1.48 ( ! [A4: B,B4: B] :
% 2.45/1.48 ( ( member @ ( product_prod @ B @ B ) @ ( product_Pair @ B @ B @ A4 @ B4 ) @ R )
% 2.45/1.48 => ( ord_less @ A @ ( F @ B4 ) @ ( F @ A4 ) ) )
% 2.45/1.48 => ( transitive_acyclic @ B @ R ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_244_dom__def,axiom,
% 2.45/1.48 ! [B: $tType,A: $tType] :
% 2.45/1.48 ( ( dom @ A @ B )
% 2.45/1.48 = ( ^ [M: A > ( option @ B )] :
% 2.45/1.48 ( collect @ A
% 2.45/1.48 @ ^ [A5: A] :
% 2.45/1.48 ( ( M @ A5 )
% 2.45/1.48 != ( none @ B ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_245_extract__Some__iff,axiom,
% 2.45/1.48 ! [A: $tType,P: A > $o,Xs: list @ A,Ys: list @ A,Y: A,Zs: list @ A] :
% 2.45/1.48 ( ( ( extract @ A @ P @ Xs )
% 2.45/1.48 = ( some @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) @ ( product_Pair @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) @ Ys @ ( product_Pair @ A @ ( list @ A ) @ Y @ Zs ) ) ) )
% 2.45/1.48 = ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys @ ( cons @ A @ Y @ Zs ) ) )
% 2.45/1.48 & ( P @ Y )
% 2.45/1.48 & ~ ? [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 2.45/1.48 & ( P @ X2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_246_extract__SomeE,axiom,
% 2.45/1.48 ! [A: $tType,P: A > $o,Xs: list @ A,Ys: list @ A,Y: A,Zs: list @ A] :
% 2.45/1.48 ( ( ( extract @ A @ P @ Xs )
% 2.45/1.48 = ( some @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) @ ( product_Pair @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) @ Ys @ ( product_Pair @ A @ ( list @ A ) @ Y @ Zs ) ) ) )
% 2.45/1.48 => ( ( Xs
% 2.45/1.48 = ( append @ A @ Ys @ ( cons @ A @ Y @ Zs ) ) )
% 2.45/1.48 & ( P @ Y )
% 2.45/1.48 & ~ ? [X6: A] :
% 2.45/1.48 ( ( member @ A @ X6 @ ( set2 @ A @ Ys ) )
% 2.45/1.48 & ( P @ X6 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_247_extract__Nil__code,axiom,
% 2.45/1.48 ! [A: $tType,P: A > $o] :
% 2.45/1.48 ( ( extract @ A @ P @ ( nil @ A ) )
% 2.45/1.48 = ( none @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_248_extract__None__iff,axiom,
% 2.45/1.48 ! [A: $tType,P: A > $o,Xs: list @ A] :
% 2.45/1.48 ( ( ( extract @ A @ P @ Xs )
% 2.45/1.48 = ( none @ ( product_prod @ ( list @ A ) @ ( product_prod @ A @ ( list @ A ) ) ) ) )
% 2.45/1.48 = ( ~ ? [X2: A] :
% 2.45/1.48 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.45/1.48 & ( P @ X2 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_249_snoc__listrel1__snoc__iff,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A,R: set @ ( product_prod @ A @ A )] :
% 2.45/1.48 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ ( listrel1 @ A @ R ) )
% 2.45/1.48 = ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 2.45/1.48 & ( X = Y ) )
% 2.45/1.48 | ( ( Xs = Ys )
% 2.45/1.48 & ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_250_local_Ois__rbt__def,axiom,
% 2.45/1.48 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.45/1.48 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.45/1.48 = ( ( rBT_Im1040612427e_inv1 @ a @ B @ T )
% 2.45/1.48 & ( rBT_Im1040612428e_inv2 @ a @ B @ T )
% 2.45/1.48 & ( ( rBT_Im1805589839lor_of @ a @ B @ T )
% 2.45/1.48 = rBT_Impl_Mirabelle_B )
% 2.45/1.48 & ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_251_Cons__listrel1__Cons,axiom,
% 2.45/1.48 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.45/1.48 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) @ ( listrel1 @ A @ R ) )
% 2.45/1.48 = ( ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ R )
% 2.45/1.48 & ( Xs = Ys ) )
% 2.45/1.48 | ( ( X = Y )
% 2.45/1.48 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_252_listrel1I2,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),X: A] :
% 2.45/1.48 ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 2.45/1.48 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ X @ Ys ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_253_append__listrel1I,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,R: set @ ( product_prod @ A @ A ),Us2: list @ A,Vs2: list @ A] :
% 2.45/1.48 ( ( ( ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ Ys ) @ ( listrel1 @ A @ R ) )
% 2.45/1.48 & ( Us2 = Vs2 ) )
% 2.45/1.48 | ( ( Xs = Ys )
% 2.45/1.48 & ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Us2 @ Vs2 ) @ ( listrel1 @ A @ R ) ) ) )
% 2.45/1.48 => ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Ys @ Vs2 ) ) @ ( listrel1 @ A @ R ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(fact_254_not__listrel1__Nil,axiom,
% 2.45/1.48 ! [A: $tType,Xs: list @ A,R: set @ ( product_prod @ A @ A )] :
% 2.45/1.48 ~ ( member @ ( product_prod @ ( list @ A ) @ ( list @ A ) ) @ ( product_Pair @ ( list @ A ) @ ( list @ A ) @ Xs @ ( nil @ A ) ) @ ( listrel1 @ A @ R ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.45/1.48 ! [A6: $tType,A7: $tType] :
% 2.45/1.48 ( ( order @ A7 @ ( type2 @ A7 ) )
% 2.45/1.48 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 2.45/1.48 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.45/1.48
% 2.45/1.48 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 2.45/1.48 order @ $o @ ( type2 @ $o ) ).
% 2.45/1.48
% 2.45/1.48 thf(conj_0,conjecture,
% 2.45/1.48 ( ( less @ y @ z )
% 2.45/1.48 & ( rBT_Im1259024060reater @ a @ b @ less @ z @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf ) ) ) ).
% 2.45/1.48 ------------------------
% 2.65/1.50 % (30340)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_30182 for (2999ds/275Mi)
% 2.65/1.50 % (30337)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_30182 for (2999ds/27Mi)
% 2.65/1.50 % (30336)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_30182 for (2999ds/4Mi)
% 2.65/1.50 % (30338)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/2Mi)
% 2.65/1.50 % (30339)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_30182 for (2999ds/2Mi)
% 2.65/1.50 % (30335)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/183Mi)
% 2.65/1.50 % (30341)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/18Mi)
% 2.65/1.50 % (30339)Instruction limit reached!
% 2.65/1.50 % (30339)------------------------------
% 2.65/1.50 % (30339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.50 % (30339)Termination reason: Unknown
% 2.65/1.50 % (30339)Termination phase: shuffling
% 2.65/1.50
% 2.65/1.50 % (30339)Memory used [KB]: 1407
% 2.65/1.50 % (30339)Time elapsed: 0.002 s
% 2.65/1.50 % (30339)Instructions burned: 2 (million)
% 2.65/1.50 % (30339)------------------------------
% 2.65/1.50 % (30339)------------------------------
% 2.65/1.50 % (30336)Instruction limit reached!
% 2.65/1.50 % (30336)------------------------------
% 2.65/1.50 % (30336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.50 % (30336)Termination reason: Unknown
% 2.65/1.50 % (30336)Termination phase: shuffling
% 2.65/1.50
% 2.65/1.50 % (30336)Memory used [KB]: 1407
% 2.65/1.50 % (30336)Time elapsed: 0.003 s
% 2.65/1.50 % (30336)Instructions burned: 5 (million)
% 2.65/1.50 % (30336)------------------------------
% 2.65/1.50 % (30336)------------------------------
% 2.65/1.50 % (30338)Instruction limit reached!
% 2.65/1.50 % (30338)------------------------------
% 2.65/1.50 % (30338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.50 % (30338)Termination reason: Unknown
% 2.65/1.50 % (30338)Termination phase: shuffling
% 2.65/1.50
% 2.65/1.50 % (30338)Memory used [KB]: 1407
% 2.65/1.50 % (30338)Time elapsed: 0.003 s
% 2.65/1.50 % (30338)Instructions burned: 4 (million)
% 2.65/1.50 % (30338)------------------------------
% 2.65/1.50 % (30338)------------------------------
% 2.65/1.51 % (30341)Instruction limit reached!
% 2.65/1.51 % (30341)------------------------------
% 2.65/1.51 % (30341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.51 % (30341)Termination reason: Unknown
% 2.65/1.51 % (30341)Termination phase: shuffling
% 2.65/1.51
% 2.65/1.51 % (30341)Memory used [KB]: 1791
% 2.65/1.51 % (30341)Time elapsed: 0.008 s
% 2.65/1.51 % (30341)Instructions burned: 19 (million)
% 2.65/1.51 % (30341)------------------------------
% 2.65/1.51 % (30341)------------------------------
% 2.65/1.51 % (30337)Instruction limit reached!
% 2.65/1.51 % (30337)------------------------------
% 2.65/1.51 % (30337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.51 % (30337)Termination reason: Unknown
% 2.65/1.51 % (30337)Termination phase: shuffling
% 2.65/1.51
% 2.65/1.51 % (30337)Memory used [KB]: 1918
% 2.65/1.51 % (30337)Time elapsed: 0.011 s
% 2.65/1.51 % (30337)Instructions burned: 28 (million)
% 2.65/1.51 % (30337)------------------------------
% 2.65/1.51 % (30337)------------------------------
% 2.65/1.51 % (30347)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/3Mi)
% 2.65/1.51 % (30348)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_30182 for (2999ds/37Mi)
% 2.65/1.51 % (30349)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_30182 for (2999ds/15Mi)
% 2.65/1.51 % (30347)Instruction limit reached!
% 2.65/1.51 % (30347)------------------------------
% 2.65/1.51 % (30347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.51 % (30347)Termination reason: Unknown
% 2.65/1.51 % (30347)Termination phase: shuffling
% 2.65/1.51
% 2.65/1.51 % (30347)Memory used [KB]: 1535
% 2.65/1.51 % (30347)Time elapsed: 0.003 s
% 2.65/1.51 % (30347)Instructions burned: 6 (million)
% 2.65/1.51 % (30347)------------------------------
% 2.65/1.51 % (30347)------------------------------
% 2.65/1.52 % (30349)Instruction limit reached!
% 2.65/1.52 % (30349)------------------------------
% 2.65/1.52 % (30349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.52 % (30349)Termination reason: Unknown
% 2.65/1.52 % (30349)Termination phase: shuffling
% 2.65/1.52
% 2.65/1.52 % (30349)Memory used [KB]: 1663
% 2.65/1.52 % (30349)Time elapsed: 0.006 s
% 2.65/1.52 % (30349)Instructions burned: 15 (million)
% 2.65/1.52 % (30349)------------------------------
% 2.65/1.52 % (30349)------------------------------
% 2.65/1.52 % (30352)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_30182 for (2999ds/3Mi)
% 2.65/1.52 % (30352)Instruction limit reached!
% 2.65/1.52 % (30352)------------------------------
% 2.65/1.52 % (30352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.52 % (30352)Termination reason: Unknown
% 2.65/1.52 % (30352)Termination phase: shuffling
% 2.65/1.52
% 2.65/1.52 % (30352)Memory used [KB]: 1407
% 2.65/1.52 % (30352)Time elapsed: 0.002 s
% 2.65/1.52 % (30352)Instructions burned: 3 (million)
% 2.65/1.52 % (30352)------------------------------
% 2.65/1.52 % (30352)------------------------------
% 2.65/1.52 % (30354)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_30182 for (2999ds/1041Mi)
% 2.65/1.52 % (30356)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/7Mi)
% 2.65/1.52 % (30348)Instruction limit reached!
% 2.65/1.52 % (30348)------------------------------
% 2.65/1.52 % (30348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.52 % (30348)Termination reason: Unknown
% 2.65/1.52 % (30348)Termination phase: shuffling
% 2.65/1.52
% 2.65/1.52 % (30348)Memory used [KB]: 2174
% 2.65/1.52 % (30348)Time elapsed: 0.012 s
% 2.65/1.52 % (30348)Instructions burned: 39 (million)
% 2.65/1.52 % (30348)------------------------------
% 2.65/1.52 % (30348)------------------------------
% 2.65/1.53 % (30356)Instruction limit reached!
% 2.65/1.53 % (30356)------------------------------
% 2.65/1.53 % (30356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.53 % (30356)Termination reason: Unknown
% 2.65/1.53 % (30356)Termination phase: shuffling
% 2.65/1.53
% 2.65/1.53 % (30356)Memory used [KB]: 1535
% 2.65/1.53 % (30356)Time elapsed: 0.004 s
% 2.65/1.53 % (30356)Instructions burned: 9 (million)
% 2.65/1.53 % (30356)------------------------------
% 2.65/1.53 % (30356)------------------------------
% 2.65/1.53 % (30358)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/16Mi)
% 2.65/1.53 % (30359)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_30182 for (2999ds/3Mi)
% 2.65/1.53 % (30359)Instruction limit reached!
% 2.65/1.53 % (30359)------------------------------
% 2.65/1.53 % (30359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.53 % (30359)Termination reason: Unknown
% 2.65/1.53 % (30359)Termination phase: shuffling
% 2.65/1.53
% 2.65/1.53 % (30359)Memory used [KB]: 1407
% 2.65/1.53 % (30359)Time elapsed: 0.002 s
% 2.65/1.53 % (30359)Instructions burned: 3 (million)
% 2.65/1.53 % (30359)------------------------------
% 2.65/1.53 % (30359)------------------------------
% 2.65/1.53 % (30360)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_30182 for (2999ds/3Mi)
% 2.65/1.53 % (30358)Instruction limit reached!
% 2.65/1.53 % (30358)------------------------------
% 2.65/1.53 % (30358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.53 % (30358)Termination reason: Unknown
% 2.65/1.53 % (30358)Termination phase: shuffling
% 2.65/1.53
% 2.65/1.53 % (30358)Memory used [KB]: 1791
% 2.65/1.53 % (30358)Time elapsed: 0.007 s
% 2.65/1.53 % (30358)Instructions burned: 19 (million)
% 2.65/1.53 % (30358)------------------------------
% 2.65/1.53 % (30358)------------------------------
% 2.65/1.53 % (30360)Instruction limit reached!
% 2.65/1.53 % (30360)------------------------------
% 2.65/1.53 % (30360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.53 % (30360)Termination reason: Unknown
% 2.65/1.53 % (30360)Termination phase: shuffling
% 2.65/1.53
% 2.65/1.53 % (30360)Memory used [KB]: 1407
% 2.65/1.53 % (30360)Time elapsed: 0.002 s
% 2.65/1.53 % (30360)Instructions burned: 3 (million)
% 2.65/1.53 % (30360)------------------------------
% 2.65/1.53 % (30360)------------------------------
% 2.65/1.53 % (30362)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/7Mi)
% 2.65/1.54 % (30363)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/3Mi)
% 2.65/1.54 % (30362)Instruction limit reached!
% 2.65/1.54 % (30362)------------------------------
% 2.65/1.54 % (30362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.54 % (30362)Termination reason: Unknown
% 2.65/1.54 % (30362)Termination phase: shuffling
% 2.65/1.54
% 2.65/1.54 % (30362)Memory used [KB]: 1535
% 2.65/1.54 % (30362)Time elapsed: 0.004 s
% 2.65/1.54 % (30362)Instructions burned: 10 (million)
% 2.65/1.54 % (30362)------------------------------
% 2.65/1.54 % (30362)------------------------------
% 2.65/1.54 % (30363)Instruction limit reached!
% 2.65/1.54 % (30363)------------------------------
% 2.65/1.54 % (30363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.54 % (30363)Termination reason: Unknown
% 2.65/1.54 % (30363)Termination phase: shuffling
% 2.65/1.54
% 2.65/1.54 % (30363)Memory used [KB]: 1407
% 2.65/1.54 % (30363)Time elapsed: 0.002 s
% 2.65/1.54 % (30363)Instructions burned: 4 (million)
% 2.65/1.54 % (30363)------------------------------
% 2.65/1.54 % (30363)------------------------------
% 2.65/1.54 % (30367)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/4Mi)
% 2.65/1.54 % (30368)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/18Mi)
% 2.65/1.54 % (30367)Instruction limit reached!
% 2.65/1.54 % (30367)------------------------------
% 2.65/1.54 % (30367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.54 % (30367)Termination reason: Unknown
% 2.65/1.54 % (30367)Termination phase: shuffling
% 2.65/1.54
% 2.65/1.54 % (30367)Memory used [KB]: 1535
% 2.65/1.54 % (30367)Time elapsed: 0.003 s
% 2.65/1.54 % (30367)Instructions burned: 6 (million)
% 2.65/1.54 % (30367)------------------------------
% 2.65/1.54 % (30367)------------------------------
% 2.65/1.55 % (30372)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/710Mi)
% 2.65/1.55 % (30375)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/6Mi)
% 2.65/1.55 % (30368)Instruction limit reached!
% 2.65/1.55 % (30368)------------------------------
% 2.65/1.55 % (30368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.55 % (30368)Termination reason: Unknown
% 2.65/1.55 % (30368)Termination phase: shuffling
% 2.65/1.55
% 2.65/1.55 % (30368)Memory used [KB]: 1791
% 2.65/1.55 % (30368)Time elapsed: 0.007 s
% 2.65/1.55 % (30368)Instructions burned: 18 (million)
% 2.65/1.55 % (30368)------------------------------
% 2.65/1.55 % (30368)------------------------------
% 2.65/1.55 % (30375)Instruction limit reached!
% 2.65/1.55 % (30375)------------------------------
% 2.65/1.55 % (30375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.55 % (30375)Termination reason: Unknown
% 2.65/1.55 % (30375)Termination phase: shuffling
% 2.65/1.55
% 2.65/1.55 % (30375)Memory used [KB]: 1535
% 2.65/1.55 % (30375)Time elapsed: 0.004 s
% 2.65/1.55 % (30375)Instructions burned: 8 (million)
% 2.65/1.55 % (30375)------------------------------
% 2.65/1.55 % (30375)------------------------------
% 2.65/1.55 % (30376)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_30182 for (2999ds/902Mi)
% 2.65/1.55 % (30335)Instruction limit reached!
% 2.65/1.55 % (30335)------------------------------
% 2.65/1.55 % (30335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.55 % (30335)Termination reason: Unknown
% 2.65/1.55 % (30335)Termination phase: Saturation
% 2.65/1.55
% 2.65/1.55 % (30335)Memory used [KB]: 7419
% 2.65/1.55 % (30335)Time elapsed: 0.055 s
% 2.65/1.55 % (30335)Instructions burned: 186 (million)
% 2.65/1.55 % (30335)------------------------------
% 2.65/1.55 % (30335)------------------------------
% 2.65/1.56 % (30377)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_30182 for (2999ds/21Mi)
% 2.65/1.56 % (30378)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/5Mi)
% 2.65/1.56 % (30378)Instruction limit reached!
% 2.65/1.56 % (30378)------------------------------
% 2.65/1.56 % (30378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.56 % (30378)Termination reason: Unknown
% 2.65/1.56 % (30378)Termination phase: shuffling
% 2.65/1.56
% 2.65/1.56 % (30378)Memory used [KB]: 1535
% 2.65/1.56 % (30378)Time elapsed: 0.003 s
% 2.65/1.56 % (30378)Instructions burned: 6 (million)
% 2.65/1.56 % (30378)------------------------------
% 2.65/1.56 % (30378)------------------------------
% 2.65/1.56 % (30379)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_30182 for (2999ds/6Mi)
% 2.65/1.56 % (30377)Instruction limit reached!
% 2.65/1.56 % (30377)------------------------------
% 2.65/1.56 % (30377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.56 % (30377)Termination reason: Unknown
% 2.65/1.56 % (30377)Termination phase: shuffling
% 2.65/1.56
% 2.65/1.56 % (30377)Memory used [KB]: 1791
% 2.65/1.56 % (30377)Time elapsed: 0.008 s
% 2.65/1.56 % (30377)Instructions burned: 21 (million)
% 2.65/1.56 % (30377)------------------------------
% 2.65/1.56 % (30377)------------------------------
% 2.65/1.57 % (30379)Instruction limit reached!
% 2.65/1.57 % (30379)------------------------------
% 2.65/1.57 % (30379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.57 % (30379)Termination reason: Unknown
% 2.65/1.57 % (30379)Termination phase: shuffling
% 2.65/1.57
% 2.65/1.57 % (30379)Memory used [KB]: 1535
% 2.65/1.57 % (30379)Time elapsed: 0.003 s
% 2.65/1.57 % (30379)Instructions burned: 6 (million)
% 2.65/1.57 % (30379)------------------------------
% 2.65/1.57 % (30379)------------------------------
% 2.65/1.57 % (30388)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/377Mi)
% 2.65/1.57 % (30391)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_30182 for (2999ds/779Mi)
% 2.65/1.58 % (30393)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_30182 for (2999ds/19Mi)
% 2.65/1.58 % (30393)Instruction limit reached!
% 2.65/1.58 % (30393)------------------------------
% 2.65/1.58 % (30393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.58 % (30393)Termination reason: Unknown
% 2.65/1.58 % (30393)Termination phase: shuffling
% 2.65/1.58
% 2.65/1.58 % (30393)Memory used [KB]: 1791
% 2.65/1.58 % (30393)Time elapsed: 0.007 s
% 2.65/1.58 % (30393)Instructions burned: 22 (million)
% 2.65/1.58 % (30393)------------------------------
% 2.65/1.58 % (30393)------------------------------
% 2.65/1.58 % (30340)Instruction limit reached!
% 2.65/1.58 % (30340)------------------------------
% 2.65/1.58 % (30340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.58 % (30340)Termination reason: Unknown
% 2.65/1.58 % (30340)Termination phase: Saturation
% 2.65/1.58
% 2.65/1.58 % (30340)Memory used [KB]: 6908
% 2.65/1.58 % (30340)Time elapsed: 0.082 s
% 2.65/1.58 % (30340)Instructions burned: 276 (million)
% 2.65/1.58 % (30340)------------------------------
% 2.65/1.58 % (30340)------------------------------
% 2.65/1.59 % (30403)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/879Mi)
% 2.65/1.59 % (30404)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30182 for (2999ds/17Mi)
% 2.65/1.60 % (30404)Instruction limit reached!
% 2.65/1.60 % (30404)------------------------------
% 2.65/1.60 % (30404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (30404)Termination reason: Unknown
% 2.65/1.60 % (30404)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (30404)Memory used [KB]: 1791
% 2.65/1.60 % (30404)Time elapsed: 0.007 s
% 2.65/1.60 % (30404)Instructions burned: 19 (million)
% 2.65/1.60 % (30404)------------------------------
% 2.65/1.60 % (30404)------------------------------
% 2.65/1.61 % (30406)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30182 for (2998ds/3Mi)
% 2.65/1.61 % (30406)Instruction limit reached!
% 2.65/1.61 % (30406)------------------------------
% 2.65/1.61 % (30406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.61 % (30406)Termination reason: Unknown
% 2.65/1.61 % (30406)Termination phase: shuffling
% 2.65/1.61
% 2.65/1.61 % (30406)Memory used [KB]: 1407
% 2.65/1.61 % (30406)Time elapsed: 0.002 s
% 2.65/1.61 % (30406)Instructions burned: 3 (million)
% 2.65/1.61 % (30406)------------------------------
% 2.65/1.61 % (30406)------------------------------
% 2.65/1.62 % (30417)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30182 for (2998ds/30Mi)
% 2.65/1.63 % (30417)Instruction limit reached!
% 2.65/1.63 % (30417)------------------------------
% 2.65/1.63 % (30417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (30417)Termination reason: Unknown
% 2.65/1.63 % (30417)Termination phase: shuffling
% 2.65/1.63
% 2.65/1.63 % (30417)Memory used [KB]: 1918
% 2.65/1.63 % (30417)Time elapsed: 0.012 s
% 2.65/1.63 % (30417)Instructions burned: 32 (million)
% 2.65/1.63 % (30417)------------------------------
% 2.65/1.63 % (30417)------------------------------
% 2.65/1.64 % (30431)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30182 for (2998ds/127Mi)
% 2.65/1.67 % (30431)Instruction limit reached!
% 2.65/1.67 % (30431)------------------------------
% 2.65/1.67 % (30431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (30431)Termination reason: Unknown
% 2.65/1.67 % (30431)Termination phase: Property scanning
% 2.65/1.67
% 2.65/1.67 % (30431)Memory used [KB]: 2558
% 2.65/1.67 % (30431)Time elapsed: 0.038 s
% 2.65/1.67 % (30431)Instructions burned: 129 (million)
% 2.65/1.67 % (30431)------------------------------
% 2.65/1.67 % (30431)------------------------------
% 2.65/1.68 % (30388)Instruction limit reached!
% 2.65/1.68 % (30388)------------------------------
% 2.65/1.68 % (30388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.68 % (30388)Termination reason: Unknown
% 2.65/1.68 % (30388)Termination phase: Saturation
% 2.65/1.68
% 2.65/1.68 % (30388)Memory used [KB]: 8571
% 2.65/1.68 % (30388)Time elapsed: 0.113 s
% 2.65/1.68 % (30388)Instructions burned: 379 (million)
% 2.65/1.68 % (30388)------------------------------
% 2.65/1.68 % (30388)------------------------------
% 2.65/1.68 % (30450)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30182 for (2998ds/100Mi)
% 2.65/1.69 % (30456)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_30182 for (2997ds/3Mi)
% 2.65/1.69 % (30456)Instruction limit reached!
% 2.65/1.69 % (30456)------------------------------
% 2.65/1.69 % (30456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.69 % (30456)Termination reason: Unknown
% 2.65/1.69 % (30456)Termination phase: shuffling
% 2.65/1.69
% 2.65/1.69 % (30456)Memory used [KB]: 1407
% 2.65/1.69 % (30456)Time elapsed: 0.002 s
% 2.65/1.69 % (30456)Instructions burned: 3 (million)
% 2.65/1.69 % (30456)------------------------------
% 2.65/1.69 % (30456)------------------------------
% 2.65/1.70 % (30463)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_30182 for (2997ds/20Mi)
% 2.65/1.71 % (30463)Instruction limit reached!
% 2.65/1.71 % (30463)------------------------------
% 2.65/1.71 % (30463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.71 % (30463)Termination reason: Unknown
% 2.65/1.71 % (30463)Termination phase: shuffling
% 2.65/1.71
% 2.65/1.71 % (30463)Memory used [KB]: 1791
% 2.65/1.71 % (30463)Time elapsed: 0.008 s
% 2.65/1.71 % (30463)Instructions burned: 21 (million)
% 2.65/1.71 % (30463)------------------------------
% 2.65/1.71 % (30463)------------------------------
% 2.65/1.71 % (30450)Instruction limit reached!
% 2.65/1.71 % (30450)------------------------------
% 2.65/1.71 % (30450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.71 % (30450)Termination reason: Unknown
% 2.65/1.71 % (30450)Termination phase: Property scanning
% 2.65/1.71
% 2.65/1.71 % (30450)Memory used [KB]: 2558
% 2.65/1.71 % (30450)Time elapsed: 0.029 s
% 2.65/1.71 % (30450)Instructions burned: 103 (million)
% 2.65/1.71 % (30450)------------------------------
% 2.65/1.71 % (30450)------------------------------
% 2.65/1.72 % (30469)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_30182 for (2997ds/86Mi)
% 2.65/1.72 % (30471)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_30182 for (2997ds/107Mi)
% 2.65/1.75 % (30469)Instruction limit reached!
% 2.65/1.75 % (30469)------------------------------
% 2.65/1.75 % (30469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.75 % (30469)Termination reason: Unknown
% 2.65/1.75 % (30469)Termination phase: Property scanning
% 2.65/1.75
% 2.65/1.75 % (30469)Memory used [KB]: 2558
% 2.65/1.75 % (30469)Time elapsed: 0.027 s
% 2.65/1.75 % (30469)Instructions burned: 87 (million)
% 2.65/1.75 % (30469)------------------------------
% 2.65/1.75 % (30469)------------------------------
% 2.65/1.75 % (30372)Instruction limit reached!
% 2.65/1.75 % (30372)------------------------------
% 2.65/1.75 % (30372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.75 % (30372)Termination reason: Unknown
% 2.65/1.75 % (30372)Termination phase: Saturation
% 2.65/1.75
% 2.65/1.75 % (30372)Memory used [KB]: 8187
% 2.65/1.75 % (30372)Time elapsed: 0.206 s
% 2.65/1.75 % (30372)Instructions burned: 710 (million)
% 2.65/1.75 % (30372)------------------------------
% 2.65/1.75 % (30372)------------------------------
% 2.65/1.75 % (30471)Instruction limit reached!
% 2.65/1.75 % (30471)------------------------------
% 2.65/1.75 % (30471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.75 % (30471)Termination reason: Unknown
% 2.65/1.75 % (30471)Termination phase: Property scanning
% 2.65/1.75
% 2.65/1.75 % (30471)Memory used [KB]: 2686
% 2.65/1.75 % (30471)Time elapsed: 0.033 s
% 2.65/1.75 % (30471)Instructions burned: 109 (million)
% 2.65/1.75 % (30471)------------------------------
% 2.65/1.75 % (30471)------------------------------
% 2.65/1.76 % (30482)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_30182 for (2997ds/39Mi)
% 2.65/1.76 % (30486)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_30182 for (2997ds/448Mi)
% 2.65/1.76 % (30488)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_30182 for (2997ds/46Mi)
% 2.65/1.77 % (30482)Instruction limit reached!
% 2.65/1.77 % (30482)------------------------------
% 2.65/1.77 % (30482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.77 % (30482)Termination reason: Unknown
% 2.65/1.77 % (30482)Termination phase: shuffling
% 2.65/1.77
% 2.65/1.77 % (30482)Memory used [KB]: 2174
% 2.65/1.77 % (30482)Time elapsed: 0.012 s
% 2.65/1.77 % (30482)Instructions burned: 39 (million)
% 2.65/1.77 % (30482)------------------------------
% 2.65/1.77 % (30482)------------------------------
% 2.65/1.78 % (30494)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_30182 for (2997ds/98Mi)
% 2.65/1.78 % (30488)Instruction limit reached!
% 2.65/1.78 % (30488)------------------------------
% 2.65/1.78 % (30488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.78 % (30488)Termination reason: Unknown
% 2.65/1.78 % (30488)Termination phase: Property scanning
% 2.65/1.78
% 2.65/1.78 % (30488)Memory used [KB]: 1918
% 2.65/1.78 % (30488)Time elapsed: 0.015 s
% 2.65/1.78 % (30488)Instructions burned: 46 (million)
% 2.65/1.78 % (30488)------------------------------
% 2.65/1.78 % (30488)------------------------------
% 2.65/1.79 % (30498)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_30182 for (2997ds/507Mi)
% 2.65/1.80 % (30391)Instruction limit reached!
% 2.65/1.80 % (30391)------------------------------
% 2.65/1.80 % (30391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.80 % (30391)Termination reason: Unknown
% 2.65/1.80 % (30391)Termination phase: Saturation
% 2.65/1.80
% 2.65/1.80 % (30391)Memory used [KB]: 9466
% 2.65/1.80 % (30391)Time elapsed: 0.246 s
% 2.65/1.80 % (30391)Instructions burned: 780 (million)
% 2.65/1.80 % (30391)------------------------------
% 2.65/1.80 % (30391)------------------------------
% 2.65/1.80 % (30494)Instruction limit reached!
% 2.65/1.80 % (30494)------------------------------
% 2.65/1.80 % (30494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.80 % (30494)Termination reason: Unknown
% 2.65/1.80 % (30494)Termination phase: Preprocessing 3
% 2.65/1.80
% 2.65/1.80 % (30494)Memory used [KB]: 2430
% 2.65/1.80 % (30494)Time elapsed: 0.029 s
% 2.65/1.80 % (30494)Instructions burned: 99 (million)
% 2.65/1.80 % (30494)------------------------------
% 2.65/1.80 % (30494)------------------------------
% 2.65/1.81 % (30505)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_30182 for (2996ds/149Mi)
% 2.65/1.81 % (30508)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30182 for (2996ds/39Mi)
% 2.65/1.82 % (30376)Instruction limit reached!
% 2.65/1.82 % (30376)------------------------------
% 2.65/1.82 % (30376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.82 % (30376)Termination reason: Unknown
% 2.65/1.82 % (30376)Termination phase: Saturation
% 2.65/1.82
% 2.65/1.82 % (30376)Memory used [KB]: 9210
% 2.65/1.82 % (30376)Time elapsed: 0.273 s
% 2.65/1.82 % (30376)Instructions burned: 903 (million)
% 2.65/1.82 % (30376)------------------------------
% 2.65/1.82 % (30376)------------------------------
% 2.65/1.83 % (30508)Instruction limit reached!
% 2.65/1.83 % (30508)------------------------------
% 2.65/1.83 % (30508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.83 % (30508)Termination reason: Unknown
% 2.65/1.83 % (30508)Termination phase: Property scanning
% 2.65/1.83
% 2.65/1.83 % (30508)Memory used [KB]: 2046
% 2.65/1.83 % (30508)Time elapsed: 0.014 s
% 2.65/1.83 % (30508)Instructions burned: 41 (million)
% 2.65/1.83 % (30508)------------------------------
% 2.65/1.83 % (30508)------------------------------
% 2.65/1.83 % (30515)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_30182 for (2996ds/6Mi)
% 2.65/1.83 % (30354)Instruction limit reached!
% 2.65/1.83 % (30354)------------------------------
% 2.65/1.83 % (30354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.83 % (30354)Termination reason: Unknown
% 2.65/1.83 % (30354)Termination phase: Saturation
% 2.65/1.83
% 2.65/1.83 % (30354)Memory used [KB]: 10106
% 2.65/1.83 % (30354)Time elapsed: 0.316 s
% 2.65/1.83 % (30354)Instructions burned: 1043 (million)
% 2.65/1.83 % (30354)------------------------------
% 2.65/1.83 % (30354)------------------------------
% 2.65/1.84 % (30517)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_30182 for (2996ds/1087Mi)
% 2.65/1.84 % (30515)Instruction limit reached!
% 2.65/1.84 % (30515)------------------------------
% 2.65/1.84 % (30515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.84 % (30515)Termination reason: Unknown
% 2.65/1.84 % (30515)Termination phase: shuffling
% 2.65/1.84
% 2.65/1.84 % (30515)Memory used [KB]: 1535
% 2.65/1.84 % (30515)Time elapsed: 0.003 s
% 2.65/1.84 % (30515)Instructions burned: 7 (million)
% 2.65/1.84 % (30515)------------------------------
% 2.65/1.84 % (30515)------------------------------
% 2.65/1.84 % (30521)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30182 for (2996ds/47Mi)
% 2.65/1.85 % (30522)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_30182 for (2996ds/44Mi)
% 2.65/1.85 % (30505)Instruction limit reached!
% 2.65/1.85 % (30505)------------------------------
% 2.65/1.85 % (30505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.85 % (30505)Termination reason: Unknown
% 2.65/1.85 % (30505)Termination phase: Property scanning
% 2.65/1.85
% 2.65/1.85 % (30505)Memory used [KB]: 2558
% 2.65/1.85 % (30505)Time elapsed: 0.043 s
% 2.65/1.85 % (30505)Instructions burned: 149 (million)
% 2.65/1.85 % (30505)------------------------------
% 2.65/1.85 % (30505)------------------------------
% 2.65/1.85 % (30403)Instruction limit reached!
% 2.65/1.85 % (30403)------------------------------
% 2.65/1.85 % (30403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.85 % (30403)Termination reason: Unknown
% 2.65/1.85 % (30403)Termination phase: Saturation
% 2.65/1.85
% 2.65/1.85 % (30403)Memory used [KB]: 7803
% 2.65/1.85 % (30403)Time elapsed: 0.285 s
% 2.65/1.85 % (30403)Instructions burned: 879 (million)
% 2.65/1.85 % (30403)------------------------------
% 2.65/1.85 % (30403)------------------------------
% 2.65/1.86 % (30522)Instruction limit reached!
% 2.65/1.86 % (30522)------------------------------
% 2.65/1.86 % (30522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.86 % (30522)Termination reason: Unknown
% 2.65/1.86 % (30522)Termination phase: shuffling
% 2.65/1.86
% 2.65/1.86 % (30522)Memory used [KB]: 2302
% 2.65/1.86 % (30522)Time elapsed: 0.014 s
% 2.65/1.86 % (30522)Instructions burned: 46 (million)
% 2.65/1.86 % (30522)------------------------------
% 2.65/1.86 % (30522)------------------------------
% 2.65/1.86 % (30529)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_30182 for (2996ds/432Mi)
% 2.65/1.86 % (30521)Instruction limit reached!
% 2.65/1.86 % (30521)------------------------------
% 2.65/1.86 % (30521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.86 % (30521)Termination reason: Unknown
% 2.65/1.86 % (30521)Termination phase: Property scanning
% 2.65/1.86
% 2.65/1.86 % (30521)Memory used [KB]: 1918
% 2.65/1.86 % (30521)Time elapsed: 0.016 s
% 2.65/1.86 % (30521)Instructions burned: 48 (million)
% 2.65/1.86 % (30521)------------------------------
% 2.65/1.86 % (30521)------------------------------
% 2.65/1.86 % (30530)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30182 for (2996ds/62Mi)
% 2.65/1.87 % (30534)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_30182 for (2996ds/31Mi)
% 2.65/1.87 % (30535)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30182 for (2996ds/96Mi)
% 2.65/1.88 % (30534)Instruction limit reached!
% 2.65/1.88 % (30534)------------------------------
% 2.65/1.88 % (30534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.88 % (30534)Termination reason: Unknown
% 2.65/1.88 % (30534)Termination phase: shuffling
% 2.65/1.88
% 2.65/1.88 % (30534)Memory used [KB]: 1918
% 2.65/1.88 % (30534)Time elapsed: 0.011 s
% 2.65/1.88 % (30534)Instructions burned: 31 (million)
% 2.65/1.88 % (30534)------------------------------
% 2.65/1.88 % (30534)------------------------------
% 2.65/1.88 % (30530)Instruction limit reached!
% 2.65/1.88 % (30530)------------------------------
% 2.65/1.88 % (30530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.88 % (30530)Termination reason: Unknown
% 2.65/1.88 % (30530)Termination phase: Property scanning
% 2.65/1.88
% 2.65/1.88 % (30530)Memory used [KB]: 2302
% 2.65/1.88 % (30530)Time elapsed: 0.018 s
% 2.65/1.88 % (30530)Instructions burned: 62 (million)
% 2.65/1.88 % (30530)------------------------------
% 2.65/1.88 % (30530)------------------------------
% 2.65/1.89 % (30486)Instruction limit reached!
% 2.65/1.89 % (30486)------------------------------
% 2.65/1.89 % (30486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.89 % (30486)Termination reason: Unknown
% 2.65/1.89 % (30486)Termination phase: Saturation
% 2.65/1.89
% 2.65/1.89 % (30486)Memory used [KB]: 8827
% 2.65/1.89 % (30486)Time elapsed: 0.127 s
% 2.65/1.89 % (30486)Instructions burned: 449 (million)
% 2.65/1.89 % (30486)------------------------------
% 2.65/1.89 % (30486)------------------------------
% 2.65/1.89 % (30544)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_30182 for (2996ds/453Mi)
% 2.65/1.89 % (30546)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_30182 for (2996ds/71Mi)
% 2.65/1.90 % (30553)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30182 for (2996ds/83Mi)
% 2.65/1.90 % (30535)Instruction limit reached!
% 2.65/1.90 % (30535)------------------------------
% 2.65/1.90 % (30535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.90 % (30535)Termination reason: Unknown
% 2.65/1.90 % (30535)Termination phase: Function definition elimination
% 2.65/1.90
% 2.65/1.90 % (30535)Memory used [KB]: 2558
% 2.65/1.90 % (30535)Time elapsed: 0.030 s
% 2.65/1.90 % (30535)Instructions burned: 98 (million)
% 2.65/1.90 % (30535)------------------------------
% 2.65/1.90 % (30535)------------------------------
% 2.65/1.91 % (30561)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30182 for (2995ds/11Mi)
% 2.65/1.91 % (30561)Instruction limit reached!
% 2.65/1.91 % (30561)------------------------------
% 2.65/1.91 % (30561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.91 % (30561)Termination reason: Unknown
% 2.65/1.91 % (30561)Termination phase: shuffling
% 2.65/1.91
% 2.65/1.91 % (30561)Memory used [KB]: 1663
% 2.65/1.91 % (30561)Time elapsed: 0.004 s
% 2.65/1.91 % (30561)Instructions burned: 11 (million)
% 2.65/1.91 % (30561)------------------------------
% 2.65/1.91 % (30561)------------------------------
% 2.65/1.91 % (30546)Instruction limit reached!
% 2.65/1.91 % (30546)------------------------------
% 2.65/1.91 % (30546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.91 % (30546)Termination reason: Unknown
% 2.65/1.91 % (30546)Termination phase: Preprocessing 3
% 2.65/1.91
% 2.65/1.91 % (30546)Memory used [KB]: 2430
% 2.65/1.91 % (30546)Time elapsed: 0.023 s
% 2.65/1.91 % (30546)Instructions burned: 72 (million)
% 2.65/1.91 % (30546)------------------------------
% 2.65/1.91 % (30546)------------------------------
% 2.65/1.92 % (30498)Instruction limit reached!
% 2.65/1.92 % (30498)------------------------------
% 2.65/1.92 % (30498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.92 % (30498)Termination reason: Unknown
% 2.65/1.92 % (30498)Termination phase: Saturation
% 2.65/1.92
% 2.65/1.92 % (30498)Memory used [KB]: 8443
% 2.65/1.92 % (30498)Time elapsed: 0.131 s
% 2.65/1.92 % (30498)Instructions burned: 509 (million)
% 2.65/1.92 % (30498)------------------------------
% 2.65/1.92 % (30498)------------------------------
% 2.65/1.92 % (30571)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_30182 for (2995ds/41Mi)
% 2.65/1.92 % (30572)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30182 for (2995ds/6Mi)
% 2.65/1.92 % (30553)Instruction limit reached!
% 2.65/1.92 % (30553)------------------------------
% 2.65/1.92 % (30553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.92 % (30553)Termination reason: Unknown
% 2.65/1.92 % (30553)Termination phase: Saturation
% 2.65/1.92
% 2.65/1.92 % (30553)Memory used [KB]: 6652
% 2.65/1.92 % (30553)Time elapsed: 0.026 s
% 2.65/1.92 % (30553)Instructions burned: 84 (million)
% 2.65/1.92 % (30553)------------------------------
% 2.65/1.92 % (30553)------------------------------
% 2.65/1.92 % (30572)Instruction limit reached!
% 2.65/1.92 % (30572)------------------------------
% 2.65/1.92 % (30572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.92 % (30572)Termination reason: Unknown
% 2.65/1.92 % (30572)Termination phase: shuffling
% 2.65/1.92
% 2.65/1.92 % (30572)Memory used [KB]: 1535
% 2.65/1.92 % (30572)Time elapsed: 0.003 s
% 2.65/1.92 % (30572)Instructions burned: 6 (million)
% 2.65/1.92 % (30572)------------------------------
% 2.65/1.92 % (30572)------------------------------
% 2.65/1.93 % (30575)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30182 for (2995ds/150Mi)
% 2.65/1.93 % (30578)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30182 for (2995ds/343Mi)
% 2.65/1.93 % (30571)Instruction limit reached!
% 2.65/1.93 % (30571)------------------------------
% 2.65/1.93 % (30571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.93 % (30571)Termination reason: Unknown
% 2.65/1.93 % (30571)Termination phase: shuffling
% 2.65/1.93
% 2.65/1.93 % (30571)Memory used [KB]: 2174
% 2.65/1.93 % (30571)Time elapsed: 0.013 s
% 2.65/1.93 % (30571)Instructions burned: 43 (million)
% 2.65/1.93 % (30571)------------------------------
% 2.65/1.93 % (30571)------------------------------
% 2.65/1.93 % (30579)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_30182 for (2995ds/109Mi)
% 2.65/1.94 % (30581)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_30182 for (2995ds/253Mi)
% 2.65/1.96 % (30579)Instruction limit reached!
% 2.65/1.96 % (30579)------------------------------
% 2.65/1.96 % (30579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.96 % (30579)Termination reason: Unknown
% 2.65/1.96 % (30579)Termination phase: Function definition elimination
% 2.65/1.96
% 2.65/1.96 % (30579)Memory used [KB]: 2558
% 2.65/1.96 % (30579)Time elapsed: 0.033 s
% 2.65/1.96 % (30579)Instructions burned: 110 (million)
% 2.65/1.96 % (30579)------------------------------
% 2.65/1.96 % (30579)------------------------------
% 2.65/1.97 % (30575)Instruction limit reached!
% 2.65/1.97 % (30575)------------------------------
% 2.65/1.97 % (30575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.97 % (30575)Termination reason: Unknown
% 2.65/1.97 % (30575)Termination phase: Property scanning
% 2.65/1.97
% 2.65/1.97 % (30575)Memory used [KB]: 2942
% 2.65/1.97 % (30575)Time elapsed: 0.043 s
% 2.65/1.97 % (30575)Instructions burned: 150 (million)
% 2.65/1.97 % (30575)------------------------------
% 2.65/1.97 % (30575)------------------------------
% 2.65/1.97 % (30586)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30182 for (2995ds/140Mi)
% 2.65/1.98 % (30587)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_30182 for (2995ds/614Mi)
% 2.65/1.99 % (30529)Instruction limit reached!
% 2.65/1.99 % (30529)------------------------------
% 2.65/1.99 % (30529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.99 % (30529)Termination reason: Unknown
% 2.65/1.99 % (30529)Termination phase: Saturation
% 2.65/1.99
% 2.65/1.99 % (30529)Memory used [KB]: 4733
% 2.65/1.99 % (30529)Time elapsed: 0.128 s
% 2.65/1.99 % (30529)Instructions burned: 433 (million)
% 2.65/1.99 % (30529)------------------------------
% 2.65/1.99 % (30529)------------------------------
% 2.65/2.00 % (30588)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_30182 for (2995ds/202Mi)
% 6.24/2.02 % (30586)Instruction limit reached!
% 6.24/2.02 % (30586)------------------------------
% 6.24/2.02 % (30586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.02 % (30586)Termination reason: Unknown
% 6.24/2.02 % (30586)Termination phase: Saturation
% 6.24/2.02
% 6.24/2.02 % (30586)Memory used [KB]: 7036
% 6.24/2.02 % (30586)Time elapsed: 0.044 s
% 6.24/2.02 % (30586)Instructions burned: 140 (million)
% 6.24/2.02 % (30586)------------------------------
% 6.24/2.02 % (30586)------------------------------
% 6.24/2.02 % (30581)Instruction limit reached!
% 6.24/2.02 % (30581)------------------------------
% 6.24/2.02 % (30581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.02 % (30581)Termination reason: Unknown
% 6.24/2.02 % (30581)Termination phase: Saturation
% 6.24/2.02
% 6.24/2.02 % (30581)Memory used [KB]: 7036
% 6.24/2.02 % (30581)Time elapsed: 0.078 s
% 6.24/2.02 % (30581)Instructions burned: 254 (million)
% 6.24/2.02 % (30581)------------------------------
% 6.24/2.02 % (30581)------------------------------
% 6.24/2.02 % (30544)Instruction limit reached!
% 6.24/2.02 % (30544)------------------------------
% 6.24/2.02 % (30544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.02 % (30544)Termination reason: Unknown
% 6.24/2.02 % (30544)Termination phase: Saturation
% 6.24/2.02
% 6.24/2.02 % (30544)Memory used [KB]: 8059
% 6.24/2.02 % (30544)Time elapsed: 0.132 s
% 6.24/2.02 % (30544)Instructions burned: 453 (million)
% 6.24/2.02 % (30544)------------------------------
% 6.24/2.02 % (30544)------------------------------
% 6.24/2.03 % (30589)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_30182 for (2994ds/339Mi)
% 6.24/2.03 % (30590)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_30182 for (2994ds/283Mi)
% 6.24/2.03 % (30591)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30182 for (2994ds/134Mi)
% 6.24/2.04 % (30578)Instruction limit reached!
% 6.24/2.04 % (30578)------------------------------
% 6.24/2.04 % (30578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.04 % (30578)Termination reason: Unknown
% 6.24/2.04 % (30578)Termination phase: Saturation
% 6.24/2.04
% 6.24/2.04 % (30578)Memory used [KB]: 7931
% 6.24/2.04 % (30578)Time elapsed: 0.105 s
% 6.24/2.04 % (30578)Instructions burned: 345 (million)
% 6.24/2.04 % (30578)------------------------------
% 6.24/2.04 % (30578)------------------------------
% 6.24/2.05 % (30592)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30182 for (2994ds/298Mi)
% 6.24/2.06 % (30588)Instruction limit reached!
% 6.24/2.06 % (30588)------------------------------
% 6.24/2.06 % (30588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.06 % (30588)Termination reason: Unknown
% 6.24/2.06 % (30588)Termination phase: Saturation
% 6.24/2.06
% 6.24/2.06 % (30588)Memory used [KB]: 7036
% 6.24/2.06 % (30588)Time elapsed: 0.084 s
% 6.24/2.06 % (30588)Instructions burned: 205 (million)
% 6.24/2.06 % (30588)------------------------------
% 6.24/2.06 % (30588)------------------------------
% 6.24/2.07 % (30591)Instruction limit reached!
% 6.24/2.07 % (30591)------------------------------
% 6.24/2.07 % (30591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.24/2.07 % (30591)Termination reason: Unknown
% 6.24/2.07 % (30591)Termination phase: Saturation
% 6.24/2.07
% 6.24/2.07 % (30591)Memory used [KB]: 7164
% 6.24/2.07 % (30591)Time elapsed: 0.040 s
% 6.24/2.07 % (30591)Instructions burned: 137 (million)
% 6.24/2.07 % (30591)------------------------------
% 6.24/2.07 % (30591)------------------------------
% 6.24/2.07 % (30593)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30182 for (2994ds/192Mi)
% 6.24/2.08 % (30594)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_30182 for (2994ds/258Mi)
% 6.62/2.11 % (30590)Instruction limit reached!
% 6.62/2.11 % (30590)------------------------------
% 6.62/2.11 % (30590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.11 % (30590)Termination reason: Unknown
% 6.62/2.11 % (30590)Termination phase: Saturation
% 6.62/2.11
% 6.62/2.11 % (30590)Memory used [KB]: 7675
% 6.62/2.11 % (30590)Time elapsed: 0.087 s
% 6.62/2.11 % (30590)Instructions burned: 285 (million)
% 6.62/2.11 % (30590)------------------------------
% 6.62/2.11 % (30590)------------------------------
% 6.62/2.12 % (30595)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_30182 for (2993ds/90Mi)
% 6.62/2.12 % (30589)Instruction limit reached!
% 6.62/2.12 % (30589)------------------------------
% 6.62/2.12 % (30589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.12 % (30589)Termination reason: Unknown
% 6.62/2.12 % (30589)Termination phase: Saturation
% 6.62/2.12
% 6.62/2.12 % (30589)Memory used [KB]: 7803
% 6.62/2.12 % (30589)Time elapsed: 0.099 s
% 6.62/2.12 % (30589)Instructions burned: 339 (million)
% 6.62/2.12 % (30589)------------------------------
% 6.62/2.12 % (30589)------------------------------
% 6.62/2.13 % (30593)Instruction limit reached!
% 6.62/2.13 % (30593)------------------------------
% 6.62/2.13 % (30593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.13 % (30593)Termination reason: Unknown
% 6.62/2.13 % (30593)Termination phase: Saturation
% 6.62/2.13
% 6.62/2.13 % (30593)Memory used [KB]: 3582
% 6.62/2.13 % (30593)Time elapsed: 0.059 s
% 6.62/2.13 % (30593)Instructions burned: 192 (million)
% 6.62/2.13 % (30593)------------------------------
% 6.62/2.13 % (30593)------------------------------
% 6.62/2.13 % (30592)Instruction limit reached!
% 6.62/2.13 % (30592)------------------------------
% 6.62/2.13 % (30592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.13 % (30592)Termination reason: Unknown
% 6.62/2.13 % (30592)Termination phase: Saturation
% 6.62/2.13
% 6.62/2.13 % (30592)Memory used [KB]: 7803
% 6.62/2.13 % (30592)Time elapsed: 0.084 s
% 6.62/2.13 % (30592)Instructions burned: 298 (million)
% 6.62/2.13 % (30592)------------------------------
% 6.62/2.13 % (30592)------------------------------
% 6.62/2.13 % (30596)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_30182 for (2993ds/231Mi)
% 6.62/2.14 % (30597)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_30182 for (2993ds/458Mi)
% 6.62/2.14 % (30598)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_30182 for (2993ds/31Mi)
% 6.62/2.15 % (30598)Instruction limit reached!
% 6.62/2.15 % (30598)------------------------------
% 6.62/2.15 % (30598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.15 % (30598)Termination reason: Unknown
% 6.62/2.15 % (30598)Termination phase: shuffling
% 6.62/2.15
% 6.62/2.15 % (30598)Memory used [KB]: 1918
% 6.62/2.15 % (30598)Time elapsed: 0.012 s
% 6.62/2.15 % (30598)Instructions burned: 32 (million)
% 6.62/2.15 % (30598)------------------------------
% 6.62/2.15 % (30598)------------------------------
% 6.62/2.15 % (30595)Instruction limit reached!
% 6.62/2.15 % (30595)------------------------------
% 6.62/2.15 % (30595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.15 % (30595)Termination reason: Unknown
% 6.62/2.15 % (30595)Termination phase: Property scanning
% 6.62/2.15
% 6.62/2.15 % (30595)Memory used [KB]: 2558
% 6.62/2.15 % (30595)Time elapsed: 0.029 s
% 6.62/2.15 % (30595)Instructions burned: 93 (million)
% 6.62/2.15 % (30595)------------------------------
% 6.62/2.15 % (30595)------------------------------
% 6.62/2.16 % (30594)Instruction limit reached!
% 6.62/2.16 % (30594)------------------------------
% 6.62/2.16 % (30594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.16 % (30594)Termination reason: Unknown
% 6.62/2.16 % (30594)Termination phase: Saturation
% 6.62/2.16
% 6.62/2.16 % (30594)Memory used [KB]: 7803
% 6.62/2.16 % (30594)Time elapsed: 0.081 s
% 6.62/2.16 % (30594)Instructions burned: 258 (million)
% 6.62/2.16 % (30594)------------------------------
% 6.62/2.16 % (30594)------------------------------
% 6.62/2.16 % (30599)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_30182 for (2993ds/297Mi)
% 6.62/2.16 % (30600)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_30182 for (2993ds/987Mi)
% 6.62/2.16 % (30587)Instruction limit reached!
% 6.62/2.16 % (30587)------------------------------
% 6.62/2.16 % (30587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.16 % (30587)Termination reason: Unknown
% 6.62/2.16 % (30587)Termination phase: Saturation
% 6.62/2.16
% 6.62/2.16 % (30587)Memory used [KB]: 8827
% 6.62/2.16 % (30587)Time elapsed: 0.187 s
% 6.62/2.16 % (30587)Instructions burned: 615 (million)
% 6.62/2.16 % (30587)------------------------------
% 6.62/2.16 % (30587)------------------------------
% 6.62/2.17 % (30601)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_30182 for (2993ds/182Mi)
% 6.62/2.17 % (30602)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_30182 for (2993ds/182Mi)
% 7.27/2.20 % (30596)Instruction limit reached!
% 7.27/2.20 % (30596)------------------------------
% 7.27/2.20 % (30596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.20 % (30596)Termination reason: Unknown
% 7.27/2.20 % (30596)Termination phase: Saturation
% 7.27/2.20
% 7.27/2.20 % (30596)Memory used [KB]: 7419
% 7.27/2.20 % (30596)Time elapsed: 0.064 s
% 7.27/2.20 % (30596)Instructions burned: 233 (million)
% 7.27/2.20 % (30596)------------------------------
% 7.27/2.20 % (30596)------------------------------
% 7.27/2.21 % (30603)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_30182 for (2992ds/154Mi)
% 7.27/2.22 % (30601)Instruction limit reached!
% 7.27/2.22 % (30601)------------------------------
% 7.27/2.22 % (30601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.22 % (30601)Termination reason: Unknown
% 7.27/2.22 % (30601)Termination phase: Saturation
% 7.27/2.22
% 7.27/2.22 % (30601)Memory used [KB]: 7164
% 7.27/2.22 % (30601)Time elapsed: 0.052 s
% 7.27/2.22 % (30601)Instructions burned: 184 (million)
% 7.27/2.22 % (30601)------------------------------
% 7.27/2.22 % (30601)------------------------------
% 7.27/2.23 % (30602)Instruction limit reached!
% 7.27/2.23 % (30602)------------------------------
% 7.27/2.23 % (30602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.23 % (30602)Termination reason: Unknown
% 7.27/2.23 % (30602)Termination phase: Saturation
% 7.27/2.23
% 7.27/2.23 % (30602)Memory used [KB]: 7419
% 7.27/2.23 % (30602)Time elapsed: 0.054 s
% 7.27/2.23 % (30602)Instructions burned: 182 (million)
% 7.27/2.23 % (30602)------------------------------
% 7.27/2.23 % (30602)------------------------------
% 7.27/2.23 % (30604)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_30182 for (2992ds/79Mi)
% 7.27/2.23 % (30517)Instruction limit reached!
% 7.27/2.23 % (30517)------------------------------
% 7.27/2.23 % (30517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.23 % (30517)Termination reason: Unknown
% 7.27/2.23 % (30517)Termination phase: Saturation
% 7.27/2.23
% 7.27/2.23 % (30517)Memory used [KB]: 8187
% 7.27/2.23 % (30517)Time elapsed: 0.398 s
% 7.27/2.23 % (30517)Instructions burned: 1089 (million)
% 7.27/2.23 % (30517)------------------------------
% 7.27/2.23 % (30517)------------------------------
% 7.27/2.24 % (30605)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_30182 for (2992ds/216Mi)
% 7.27/2.24 % (30606)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30182 for (2992ds/114Mi)
% 7.27/2.24 % (30599)Instruction limit reached!
% 7.27/2.24 % (30599)------------------------------
% 7.27/2.24 % (30599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.24 % (30599)Termination reason: Unknown
% 7.27/2.24 % (30599)Termination phase: Saturation
% 7.27/2.24
% 7.27/2.24 % (30599)Memory used [KB]: 7675
% 7.27/2.24 % (30599)Time elapsed: 0.086 s
% 7.27/2.24 % (30599)Instructions burned: 299 (million)
% 7.27/2.24 % (30599)------------------------------
% 7.27/2.24 % (30599)------------------------------
% 7.27/2.25 % (30603)Instruction limit reached!
% 7.27/2.25 % (30603)------------------------------
% 7.27/2.25 % (30603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.25 % (30603)Termination reason: Unknown
% 7.27/2.25 % (30603)Termination phase: Saturation
% 7.27/2.25
% 7.27/2.25 % (30603)Memory used [KB]: 2814
% 7.27/2.25 % (30603)Time elapsed: 0.044 s
% 7.27/2.25 % (30603)Instructions burned: 157 (million)
% 7.27/2.25 % (30603)------------------------------
% 7.27/2.25 % (30603)------------------------------
% 7.27/2.25 % (30604)Instruction limit reached!
% 7.27/2.25 % (30604)------------------------------
% 7.27/2.25 % (30604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.25 % (30604)Termination reason: Unknown
% 7.27/2.25 % (30604)Termination phase: Property scanning
% 7.27/2.25
% 7.27/2.25 % (30604)Memory used [KB]: 2558
% 7.27/2.25 % (30604)Time elapsed: 0.026 s
% 7.27/2.25 % (30604)Instructions burned: 80 (million)
% 7.27/2.25 % (30604)------------------------------
% 7.27/2.25 % (30604)------------------------------
% 7.27/2.25 % (30607)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_30182 for (2992ds/922Mi)
% 7.27/2.26 % (30608)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_30182 for (2992ds/182Mi)
% 7.27/2.26 % (30609)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_30182 for (2992ds/164Mi)
% 7.27/2.27 % (30597)Instruction limit reached!
% 7.27/2.27 % (30597)------------------------------
% 7.27/2.27 % (30597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.27 % (30597)Termination reason: Unknown
% 7.27/2.27 % (30597)Termination phase: Saturation
% 7.27/2.27
% 7.27/2.27 % (30597)Memory used [KB]: 8571
% 7.27/2.27 % (30597)Time elapsed: 0.139 s
% 7.27/2.27 % (30597)Instructions burned: 460 (million)
% 7.27/2.27 % (30597)------------------------------
% 7.27/2.27 % (30597)------------------------------
% 7.27/2.28 % (30606)Instruction limit reached!
% 7.27/2.28 % (30606)------------------------------
% 7.27/2.28 % (30606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.28 % (30606)Termination reason: Unknown
% 7.27/2.28 % (30606)Termination phase: Property scanning
% 7.27/2.28
% 7.27/2.28 % (30606)Memory used [KB]: 2686
% 7.27/2.28 % (30606)Time elapsed: 0.034 s
% 7.27/2.28 % (30606)Instructions burned: 114 (million)
% 7.27/2.28 % (30606)------------------------------
% 7.27/2.28 % (30606)------------------------------
% 7.27/2.28 % (30610)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_30182 for (2992ds/50Mi)
% 7.27/2.28 % (30611)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30182 for (2992ds/368Mi)
% 7.27/2.29 % (30605)Instruction limit reached!
% 7.27/2.29 % (30605)------------------------------
% 7.27/2.29 % (30605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.27/2.29 % (30605)Termination reason: Unknown
% 7.27/2.29 % (30605)Termination phase: Saturation
% 7.27/2.29
% 7.27/2.29 % (30605)Memory used [KB]: 7419
% 7.27/2.29 % (30605)Time elapsed: 0.060 s
% 7.27/2.29 % (30605)Instructions burned: 218 (million)
% 7.27/2.29 % (30605)------------------------------
% 7.27/2.29 % (30605)------------------------------
% 7.96/2.30 % (30610)Instruction limit reached!
% 7.96/2.30 % (30610)------------------------------
% 7.96/2.30 % (30610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.30 % (30610)Termination reason: Unknown
% 7.96/2.30 % (30610)Termination phase: shuffling
% 7.96/2.30
% 7.96/2.30 % (30610)Memory used [KB]: 2302
% 7.96/2.30 % (30610)Time elapsed: 0.015 s
% 7.96/2.30 % (30610)Instructions burned: 50 (million)
% 7.96/2.30 % (30610)------------------------------
% 7.96/2.30 % (30610)------------------------------
% 7.96/2.30 % (30612)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_30182 for (2991ds/1021Mi)
% 7.96/2.31 % (30613)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_30182 for (2991ds/267Mi)
% 7.96/2.31 % (30609)Instruction limit reached!
% 7.96/2.31 % (30609)------------------------------
% 7.96/2.31 % (30609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.31 % (30609)Termination reason: Unknown
% 7.96/2.31 % (30609)Termination phase: Saturation
% 7.96/2.31
% 7.96/2.31 % (30609)Memory used [KB]: 2814
% 7.96/2.31 % (30609)Time elapsed: 0.046 s
% 7.96/2.31 % (30609)Instructions burned: 164 (million)
% 7.96/2.31 % (30609)------------------------------
% 7.96/2.31 % (30609)------------------------------
% 7.96/2.31 % (30608)Instruction limit reached!
% 7.96/2.31 % (30608)------------------------------
% 7.96/2.31 % (30608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.31 % (30608)Termination reason: Unknown
% 7.96/2.31 % (30608)Termination phase: Saturation
% 7.96/2.31
% 7.96/2.31 % (30608)Memory used [KB]: 7291
% 7.96/2.31 % (30608)Time elapsed: 0.051 s
% 7.96/2.31 % (30608)Instructions burned: 184 (million)
% 7.96/2.31 % (30608)------------------------------
% 7.96/2.31 % (30608)------------------------------
% 7.96/2.32 % (30614)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_30182 for (2991ds/204Mi)
% 7.96/2.32 % (30615)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_30182 for (2991ds/26Mi)
% 7.96/2.33 % (30615)Instruction limit reached!
% 7.96/2.33 % (30615)------------------------------
% 7.96/2.33 % (30615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.33 % (30615)Termination reason: Unknown
% 7.96/2.33 % (30615)Termination phase: shuffling
% 7.96/2.33
% 7.96/2.33 % (30615)Memory used [KB]: 2046
% 7.96/2.33 % (30615)Time elapsed: 0.009 s
% 7.96/2.33 % (30615)Instructions burned: 29 (million)
% 7.96/2.33 % (30615)------------------------------
% 7.96/2.33 % (30615)------------------------------
% 7.96/2.34 % (30616)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_30182 for (2991ds/53Mi)
% 7.96/2.35 % (30616)Instruction limit reached!
% 7.96/2.35 % (30616)------------------------------
% 7.96/2.35 % (30616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.35 % (30616)Termination reason: Unknown
% 7.96/2.35 % (30616)Termination phase: Property scanning
% 7.96/2.35
% 7.96/2.35 % (30616)Memory used [KB]: 2302
% 7.96/2.35 % (30616)Time elapsed: 0.017 s
% 7.96/2.35 % (30616)Instructions burned: 55 (million)
% 7.96/2.35 % (30616)------------------------------
% 7.96/2.35 % (30616)------------------------------
% 7.96/2.36 % (30617)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_30182 for (2991ds/4436Mi)
% 7.96/2.37 % (30614)Instruction limit reached!
% 7.96/2.37 % (30614)------------------------------
% 7.96/2.37 % (30614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.37 % (30614)Termination reason: Unknown
% 7.96/2.37 % (30614)Termination phase: Saturation
% 7.96/2.37
% 7.96/2.37 % (30614)Memory used [KB]: 7419
% 7.96/2.37 % (30614)Time elapsed: 0.060 s
% 7.96/2.37 % (30614)Instructions burned: 205 (million)
% 7.96/2.37 % (30614)------------------------------
% 7.96/2.37 % (30614)------------------------------
% 7.96/2.38 % (30618)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_30182 for (2991ds/1539Mi)
% 7.96/2.39 % (30613)Instruction limit reached!
% 7.96/2.39 % (30613)------------------------------
% 7.96/2.39 % (30613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.39 % (30613)Termination reason: Unknown
% 7.96/2.39 % (30613)Termination phase: Saturation
% 7.96/2.39
% 7.96/2.39 % (30613)Memory used [KB]: 7675
% 7.96/2.39 % (30613)Time elapsed: 0.081 s
% 7.96/2.39 % (30613)Instructions burned: 269 (million)
% 7.96/2.39 % (30613)------------------------------
% 7.96/2.39 % (30613)------------------------------
% 7.96/2.39 % (30611)Instruction limit reached!
% 7.96/2.39 % (30611)------------------------------
% 7.96/2.39 % (30611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.39 % (30611)Termination reason: Unknown
% 7.96/2.39 % (30611)Termination phase: Saturation
% 7.96/2.39
% 7.96/2.39 % (30611)Memory used [KB]: 8443
% 7.96/2.39 % (30611)Time elapsed: 0.110 s
% 7.96/2.39 % (30611)Instructions burned: 368 (million)
% 7.96/2.39 % (30611)------------------------------
% 7.96/2.39 % (30611)------------------------------
% 7.96/2.40 % (30619)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_30182 for (2991ds/408Mi)
% 8.41/2.40 % (30620)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_30182 for (2990ds/5205Mi)
% 8.41/2.46 % (30600)Instruction limit reached!
% 8.41/2.46 % (30600)------------------------------
% 8.41/2.46 % (30600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.41/2.46 % (30600)Termination reason: Unknown
% 8.41/2.46 % (30600)Termination phase: Saturation
% 8.41/2.46
% 8.41/2.46 % (30600)Memory used [KB]: 8699
% 8.41/2.46 % (30600)Time elapsed: 0.298 s
% 8.41/2.46 % (30600)Instructions burned: 990 (million)
% 8.41/2.46 % (30600)------------------------------
% 8.41/2.46 % (30600)------------------------------
% 8.41/2.47 % (30621)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_30182 for (2990ds/1913Mi)
% 8.73/2.51 % (30619)Instruction limit reached!
% 8.73/2.51 % (30619)------------------------------
% 8.73/2.51 % (30619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.51 % (30619)Termination reason: Unknown
% 8.73/2.51 % (30619)Termination phase: Saturation
% 8.73/2.51
% 8.73/2.51 % (30619)Memory used [KB]: 8699
% 8.73/2.51 % (30619)Time elapsed: 0.119 s
% 8.73/2.51 % (30619)Instructions burned: 409 (million)
% 8.73/2.51 % (30619)------------------------------
% 8.73/2.51 % (30619)------------------------------
% 8.73/2.52 % (30622)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_30182 for (2989ds/4350Mi)
% 8.73/2.54 % (30607)Instruction limit reached!
% 8.73/2.54 % (30607)------------------------------
% 8.73/2.54 % (30607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.54 % (30607)Termination reason: Unknown
% 8.73/2.54 % (30607)Termination phase: Saturation
% 8.73/2.54
% 8.73/2.54 % (30607)Memory used [KB]: 7675
% 8.73/2.54 % (30607)Time elapsed: 0.285 s
% 8.73/2.54 % (30607)Instructions burned: 924 (million)
% 8.73/2.54 % (30607)------------------------------
% 8.73/2.54 % (30607)------------------------------
% 8.73/2.55 % (30623)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_30182 for (2989ds/68Mi)
% 8.73/2.57 % (30623)Instruction limit reached!
% 8.73/2.57 % (30623)------------------------------
% 8.73/2.57 % (30623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.57 % (30623)Termination reason: Unknown
% 8.73/2.57 % (30623)Termination phase: Preprocessing 3
% 8.73/2.57
% 8.73/2.57 % (30623)Memory used [KB]: 2174
% 8.73/2.57 % (30623)Time elapsed: 0.022 s
% 8.73/2.57 % (30623)Instructions burned: 70 (million)
% 8.73/2.57 % (30623)------------------------------
% 8.73/2.57 % (30623)------------------------------
% 8.73/2.58 % (30624)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_30182 for (2989ds/358Mi)
% 9.18/2.61 % (30612)Instruction limit reached!
% 9.18/2.61 % (30612)------------------------------
% 9.18/2.61 % (30612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.61 % (30612)Termination reason: Unknown
% 9.18/2.61 % (30612)Termination phase: Saturation
% 9.18/2.61
% 9.18/2.61 % (30612)Memory used [KB]: 8827
% 9.18/2.61 % (30612)Time elapsed: 0.308 s
% 9.18/2.61 % (30612)Instructions burned: 1022 (million)
% 9.18/2.61 % (30612)------------------------------
% 9.18/2.61 % (30612)------------------------------
% 9.18/2.62 % (30625)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_30182 for (2988ds/31Mi)
% 9.18/2.63 % (30625)Instruction limit reached!
% 9.18/2.63 % (30625)------------------------------
% 9.18/2.63 % (30625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.63 % (30625)Termination reason: Unknown
% 9.18/2.63 % (30625)Termination phase: shuffling
% 9.18/2.63
% 9.18/2.63 % (30625)Memory used [KB]: 1918
% 9.18/2.63 % (30625)Time elapsed: 0.011 s
% 9.18/2.63 % (30625)Instructions burned: 31 (million)
% 9.18/2.63 % (30625)------------------------------
% 9.18/2.63 % (30625)------------------------------
% 9.18/2.64 % (30626)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30182 for (2988ds/279Mi)
% 9.18/2.68 % (30624)Instruction limit reached!
% 9.18/2.68 % (30624)------------------------------
% 9.18/2.68 % (30624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.68 % (30624)Termination reason: Unknown
% 9.18/2.68 % (30624)Termination phase: Saturation
% 9.18/2.68
% 9.18/2.68 % (30624)Memory used [KB]: 7675
% 9.18/2.68 % (30624)Time elapsed: 0.132 s
% 9.18/2.68 % (30624)Instructions burned: 358 (million)
% 9.18/2.68 % (30624)------------------------------
% 9.18/2.68 % (30624)------------------------------
% 9.18/2.69 % (30626)Refutation not found, incomplete strategy
% 9.18/2.69 % (30626)------------------------------
% 9.18/2.69 % (30626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.18/2.69 % (30626)Termination reason: Refutation not found, incomplete strategy
% 9.18/2.69
% 9.18/2.69
% 9.18/2.69 % (30626)Memory used [KB]: 7419
% 9.18/2.69 % (30626)Time elapsed: 0.048 s
% 9.18/2.69 % (30626)Instructions burned: 167 (million)
% 9.18/2.69 % (30626)------------------------------
% 9.18/2.69 % (30626)------------------------------
% 9.18/2.69 % (30627)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30182 for (2987ds/258Mi)
% 9.69/2.70 % (30628)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_30182 for (2987ds/26Mi)
% 9.69/2.70 % (30628)Instruction limit reached!
% 9.69/2.70 % (30628)------------------------------
% 9.69/2.70 % (30628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.69/2.70 % (30628)Termination reason: Unknown
% 9.69/2.70 % (30628)Termination phase: shuffling
% 9.69/2.70
% 9.69/2.70 % (30628)Memory used [KB]: 2046
% 9.69/2.70 % (30628)Time elapsed: 0.008 s
% 9.69/2.70 % (30628)Instructions burned: 26 (million)
% 9.69/2.70 % (30628)------------------------------
% 9.69/2.70 % (30628)------------------------------
% 9.69/2.71 % (30629)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_30182 for (2987ds/995Mi)
% 9.69/2.77 % (30627)Instruction limit reached!
% 9.69/2.77 % (30627)------------------------------
% 9.69/2.77 % (30627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.69/2.77 % (30627)Termination reason: Unknown
% 9.69/2.77 % (30627)Termination phase: Saturation
% 9.69/2.77
% 9.69/2.77 % (30627)Memory used [KB]: 7931
% 9.69/2.77 % (30627)Time elapsed: 0.076 s
% 9.69/2.77 % (30627)Instructions burned: 259 (million)
% 9.69/2.77 % (30627)------------------------------
% 9.69/2.77 % (30627)------------------------------
% 9.69/2.78 % (30630)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_30182 for (2987ds/373Mi)
% 9.80/2.85 % (30618)Instruction limit reached!
% 9.80/2.85 % (30618)------------------------------
% 9.80/2.85 % (30618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.85 % (30618)Termination reason: Unknown
% 9.80/2.85 % (30618)Termination phase: Saturation
% 9.80/2.85
% 9.80/2.85 % (30618)Memory used [KB]: 9210
% 9.80/2.85 % (30618)Time elapsed: 0.464 s
% 9.80/2.85 % (30618)Instructions burned: 1539 (million)
% 9.80/2.85 % (30618)------------------------------
% 9.80/2.85 % (30618)------------------------------
% 9.80/2.86 % (30631)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_30182 for (2986ds/253Mi)
% 9.80/2.89 % (30630)Instruction limit reached!
% 9.80/2.89 % (30630)------------------------------
% 9.80/2.89 % (30630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.89 % (30630)Termination reason: Unknown
% 9.80/2.89 % (30630)Termination phase: Saturation
% 9.80/2.89
% 9.80/2.89 % (30630)Memory used [KB]: 8443
% 9.80/2.89 % (30630)Time elapsed: 0.111 s
% 9.80/2.89 % (30630)Instructions burned: 376 (million)
% 9.80/2.89 % (30630)------------------------------
% 9.80/2.89 % (30630)------------------------------
% 10.39/2.90 % (30632)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_30182 for (2985ds/832Mi)
% 10.39/2.93 % (30631)Instruction limit reached!
% 10.39/2.93 % (30631)------------------------------
% 10.39/2.93 % (30631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.93 % (30631)Termination reason: Unknown
% 10.39/2.93 % (30631)Termination phase: Saturation
% 10.39/2.93
% 10.39/2.93 % (30631)Memory used [KB]: 7803
% 10.39/2.93 % (30631)Time elapsed: 0.071 s
% 10.39/2.93 % (30631)Instructions burned: 255 (million)
% 10.39/2.93 % (30631)------------------------------
% 10.39/2.93 % (30631)------------------------------
% 10.39/2.94 % (30633)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_30182 for (2985ds/668Mi)
% 10.39/3.00 % (30621)Instruction limit reached!
% 10.39/3.00 % (30621)------------------------------
% 10.39/3.00 % (30621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/3.00 % (30621)Termination reason: Unknown
% 10.39/3.00 % (30621)Termination phase: Saturation
% 10.39/3.00
% 10.39/3.00 % (30621)Memory used [KB]: 3837
% 10.39/3.00 % (30621)Time elapsed: 0.551 s
% 10.39/3.00 % (30621)Instructions burned: 1914 (million)
% 10.39/3.00 % (30621)------------------------------
% 10.39/3.00 % (30621)------------------------------
% 10.39/3.00 % (30629)Instruction limit reached!
% 10.39/3.00 % (30629)------------------------------
% 10.39/3.00 % (30629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/3.00 % (30629)Termination reason: Unknown
% 10.39/3.00 % (30629)Termination phase: Saturation
% 10.39/3.00
% 10.39/3.00 % (30629)Memory used [KB]: 9466
% 10.39/3.00 % (30629)Time elapsed: 0.291 s
% 10.39/3.00 % (30629)Instructions burned: 997 (million)
% 10.39/3.00 % (30629)------------------------------
% 10.39/3.00 % (30629)------------------------------
% 10.39/3.01 % (30634)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_30182 for (2984ds/40Mi)
% 10.39/3.01 % (30635)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_30182 for (2984ds/294Mi)
% 10.39/3.02 % (30634)Instruction limit reached!
% 10.39/3.02 % (30634)------------------------------
% 10.39/3.02 % (30634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/3.02 % (30634)Termination reason: Unknown
% 10.39/3.02 % (30634)Termination phase: shuffling
% 10.39/3.02
% 10.39/3.02 % (30634)Memory used [KB]: 2174
% 10.39/3.02 % (30634)Time elapsed: 0.013 s
% 10.39/3.02 % (30634)Instructions burned: 42 (million)
% 10.39/3.02 % (30634)------------------------------
% 10.39/3.02 % (30634)------------------------------
% 13.32/3.03 % (30636)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_30182 for (2984ds/187Mi)
% 13.32/3.05 % (30635)Refutation not found, incomplete strategy
% 13.32/3.05 % (30635)------------------------------
% 13.32/3.05 % (30635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.05 % (30635)Termination reason: Refutation not found, incomplete strategy
% 13.32/3.05
% 13.32/3.05
% 13.32/3.05 % (30635)Memory used [KB]: 7291
% 13.32/3.05 % (30635)Time elapsed: 0.035 s
% 13.32/3.05 % (30635)Instructions burned: 124 (million)
% 13.32/3.05 % (30635)------------------------------
% 13.32/3.05 % (30635)------------------------------
% 13.32/3.06 % (30637)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30182 for (2984ds/371Mi)
% 13.32/3.08 % (30636)Instruction limit reached!
% 13.32/3.08 % (30636)------------------------------
% 13.32/3.08 % (30636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.32/3.08 % (30636)Termination reason: Unknown
% 13.32/3.08 % (30636)Termination phase: Saturation
% 13.32/3.08
% 13.32/3.08 % (30636)Memory used [KB]: 7419
% 13.32/3.08 % (30636)Time elapsed: 0.054 s
% 13.32/3.08 % (30636)Instructions burned: 188 (million)
% 13.32/3.08 % (30636)------------------------------
% 13.32/3.08 % (30636)------------------------------
% 13.32/3.09 % (30638)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30182 for (2983ds/1827Mi)
% 13.93/3.13 % (30633)Instruction limit reached!
% 13.93/3.13 % (30633)------------------------------
% 13.93/3.13 % (30633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.13 % (30633)Termination reason: Unknown
% 13.93/3.13 % (30633)Termination phase: Saturation
% 13.93/3.13
% 13.93/3.13 % (30633)Memory used [KB]: 13944
% 13.93/3.13 % (30633)Time elapsed: 0.195 s
% 13.93/3.13 % (30633)Instructions burned: 669 (million)
% 13.93/3.13 % (30633)------------------------------
% 13.93/3.13 % (30633)------------------------------
% 13.93/3.14 % (30639)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_30182 for (2983ds/70Mi)
% 13.93/3.14 % (30632)Instruction limit reached!
% 13.93/3.14 % (30632)------------------------------
% 13.93/3.14 % (30632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.14 % (30632)Termination reason: Unknown
% 13.93/3.14 % (30632)Termination phase: Saturation
% 13.93/3.14
% 13.93/3.14 % (30632)Memory used [KB]: 9083
% 13.93/3.14 % (30632)Time elapsed: 0.247 s
% 13.93/3.14 % (30632)Instructions burned: 832 (million)
% 13.93/3.14 % (30632)------------------------------
% 13.93/3.14 % (30632)------------------------------
% 13.93/3.15 % (30640)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_30182 for (2983ds/316Mi)
% 13.93/3.16 % (30639)Instruction limit reached!
% 13.93/3.16 % (30639)------------------------------
% 13.93/3.16 % (30639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.16 % (30639)Termination reason: Unknown
% 13.93/3.16 % (30639)Termination phase: Property scanning
% 13.93/3.16
% 13.93/3.16 % (30639)Memory used [KB]: 2302
% 13.93/3.16 % (30639)Time elapsed: 0.020 s
% 13.93/3.16 % (30639)Instructions burned: 70 (million)
% 13.93/3.16 % (30639)------------------------------
% 13.93/3.16 % (30639)------------------------------
% 13.93/3.17 % (30641)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_30182 for (2983ds/932Mi)
% 13.93/3.17 % (30637)Instruction limit reached!
% 13.93/3.17 % (30637)------------------------------
% 13.93/3.17 % (30637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.93/3.17 % (30637)Termination reason: Unknown
% 13.93/3.17 % (30637)Termination phase: Saturation
% 13.93/3.17
% 13.93/3.17 % (30637)Memory used [KB]: 8059
% 13.93/3.17 % (30637)Time elapsed: 0.114 s
% 13.93/3.17 % (30637)Instructions burned: 372 (million)
% 13.93/3.17 % (30637)------------------------------
% 13.93/3.17 % (30637)------------------------------
% 13.93/3.18 % (30642)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_30182 for (2983ds/4714Mi)
% 14.35/3.22 % (30640)Refutation not found, incomplete strategy
% 14.35/3.22 % (30640)------------------------------
% 14.35/3.22 % (30640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.22 % (30640)Termination reason: Refutation not found, incomplete strategy
% 14.35/3.22
% 14.35/3.22
% 14.35/3.22 % (30640)Memory used [KB]: 7675
% 14.35/3.22 % (30640)Time elapsed: 0.068 s
% 14.35/3.22 % (30640)Instructions burned: 241 (million)
% 14.35/3.22 % (30640)------------------------------
% 14.35/3.22 % (30640)------------------------------
% 14.35/3.23 % (30643)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_30182 for (2982ds/8250Mi)
% 14.35/3.25 % (30642)Refutation not found, incomplete strategy
% 14.35/3.25 % (30642)------------------------------
% 14.35/3.25 % (30642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.25 % (30642)Termination reason: Refutation not found, incomplete strategy
% 14.35/3.25
% 14.35/3.25
% 14.35/3.25 % (30642)Memory used [KB]: 7803
% 14.35/3.25 % (30642)Time elapsed: 0.068 s
% 14.35/3.25 % (30642)Instructions burned: 236 (million)
% 14.35/3.25 % (30642)------------------------------
% 14.35/3.25 % (30642)------------------------------
% 14.35/3.26 % (30644)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_30182 for (2982ds/770Mi)
% 15.10/3.44 % (30641)Instruction limit reached!
% 15.10/3.44 % (30641)------------------------------
% 15.10/3.44 % (30641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.10/3.44 % (30641)Termination reason: Unknown
% 15.10/3.44 % (30641)Termination phase: Saturation
% 15.10/3.44
% 15.10/3.44 % (30641)Memory used [KB]: 9978
% 15.10/3.44 % (30641)Time elapsed: 0.274 s
% 15.10/3.44 % (30641)Instructions burned: 932 (million)
% 15.10/3.44 % (30641)------------------------------
% 15.10/3.44 % (30641)------------------------------
% 15.10/3.45 % (30645)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30182 for (2980ds/794Mi)
% 15.10/3.49 % (30644)Instruction limit reached!
% 15.10/3.49 % (30644)------------------------------
% 15.10/3.49 % (30644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.10/3.49 % (30644)Termination reason: Unknown
% 15.10/3.49 % (30644)Termination phase: Saturation
% 15.10/3.49
% 15.10/3.49 % (30644)Memory used [KB]: 8699
% 15.10/3.49 % (30644)Time elapsed: 0.229 s
% 15.10/3.49 % (30644)Instructions burned: 773 (million)
% 15.10/3.49 % (30644)------------------------------
% 15.10/3.49 % (30644)------------------------------
% 15.10/3.50 % (30646)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30182 for (2979ds/464Mi)
% 16.23/3.64 % (30646)Instruction limit reached!
% 16.23/3.64 % (30646)------------------------------
% 16.23/3.64 % (30646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.23/3.64 % (30646)Termination reason: Unknown
% 16.23/3.64 % (30646)Termination phase: Saturation
% 16.23/3.64
% 16.23/3.64 % (30646)Memory used [KB]: 8187
% 16.23/3.64 % (30646)Time elapsed: 0.144 s
% 16.23/3.64 % (30646)Instructions burned: 464 (million)
% 16.23/3.64 % (30646)------------------------------
% 16.23/3.64 % (30646)------------------------------
% 16.23/3.65 % (30638)Instruction limit reached!
% 16.23/3.65 % (30638)------------------------------
% 16.23/3.65 % (30638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.23/3.65 % (30638)Termination reason: Unknown
% 16.23/3.65 % (30638)Termination phase: Saturation
% 16.23/3.65
% 16.23/3.65 % (30638)Memory used [KB]: 9083
% 16.23/3.65 % (30638)Time elapsed: 0.556 s
% 16.23/3.65 % (30638)Instructions burned: 1830 (million)
% 16.23/3.65 % (30638)------------------------------
% 16.23/3.65 % (30638)------------------------------
% 16.23/3.65 % (30647)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_30182 for (2978ds/1376Mi)
% 16.23/3.66 % (30648)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30182 for (2978ds/906Mi)
% 17.25/3.70 % (30645)Instruction limit reached!
% 17.25/3.70 % (30645)------------------------------
% 17.25/3.70 % (30645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.70 % (30645)Termination reason: Unknown
% 17.25/3.70 % (30645)Termination phase: Saturation
% 17.25/3.70
% 17.25/3.70 % (30645)Memory used [KB]: 6140
% 17.25/3.70 % (30645)Time elapsed: 0.251 s
% 17.25/3.70 % (30645)Instructions burned: 796 (million)
% 17.25/3.70 % (30645)------------------------------
% 17.25/3.70 % (30645)------------------------------
% 17.25/3.71 % (30649)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_30182 for (2977ds/434Mi)
% 17.25/3.71 % (30617)Instruction limit reached!
% 17.25/3.71 % (30617)------------------------------
% 17.25/3.71 % (30617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.71 % (30617)Termination reason: Unknown
% 17.25/3.71 % (30617)Termination phase: Saturation
% 17.25/3.71
% 17.25/3.71 % (30617)Memory used [KB]: 10234
% 17.25/3.71 % (30617)Time elapsed: 1.354 s
% 17.25/3.71 % (30617)Instructions burned: 4439 (million)
% 17.25/3.71 % (30617)------------------------------
% 17.25/3.71 % (30617)------------------------------
% 17.25/3.72 % (30650)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_30182 for (2977ds/865Mi)
% 17.75/3.80 % (30622)Instruction limit reached!
% 17.75/3.80 % (30622)------------------------------
% 17.75/3.80 % (30622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.75/3.80 % (30622)Termination reason: Unknown
% 17.75/3.80 % (30622)Termination phase: Saturation
% 17.75/3.80
% 17.75/3.80 % (30622)Memory used [KB]: 10618
% 17.75/3.80 % (30622)Time elapsed: 1.299 s
% 17.75/3.80 % (30622)Instructions burned: 4353 (million)
% 17.75/3.80 % (30622)------------------------------
% 17.75/3.80 % (30622)------------------------------
% 17.75/3.81 % (30651)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_30182 for (2976ds/593Mi)
% 17.75/3.83 % (30649)Instruction limit reached!
% 17.75/3.83 % (30649)------------------------------
% 17.75/3.83 % (30649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.75/3.83 % (30649)Termination reason: Unknown
% 17.75/3.83 % (30649)Termination phase: Saturation
% 17.75/3.83
% 17.75/3.83 % (30649)Memory used [KB]: 7164
% 17.75/3.83 % (30649)Time elapsed: 0.124 s
% 17.75/3.83 % (30649)Instructions burned: 437 (million)
% 17.75/3.83 % (30649)------------------------------
% 17.75/3.83 % (30649)------------------------------
% 17.75/3.84 % (30652)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_30182 for (2976ds/443Mi)
% 18.00/3.96 % (30648)Instruction limit reached!
% 18.00/3.96 % (30648)------------------------------
% 18.00/3.96 % (30648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.96 % (30648)Termination reason: Unknown
% 18.00/3.96 % (30648)Termination phase: Saturation
% 18.00/3.96
% 18.00/3.96 % (30648)Memory used [KB]: 13944
% 18.00/3.96 % (30648)Time elapsed: 0.310 s
% 18.00/3.96 % (30648)Instructions burned: 907 (million)
% 18.00/3.96 % (30648)------------------------------
% 18.00/3.96 % (30648)------------------------------
% 18.00/3.97 % (30653)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_30182 for (2975ds/594Mi)
% 18.00/3.98 % (30651)Instruction limit reached!
% 18.00/3.98 % (30651)------------------------------
% 18.00/3.98 % (30651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.98 % (30651)Termination reason: Unknown
% 18.00/3.98 % (30651)Termination phase: Saturation
% 18.00/3.98
% 18.00/3.98 % (30651)Memory used [KB]: 9594
% 18.00/3.98 % (30651)Time elapsed: 0.166 s
% 18.00/3.98 % (30651)Instructions burned: 593 (million)
% 18.00/3.98 % (30651)------------------------------
% 18.00/3.98 % (30651)------------------------------
% 18.00/3.98 % (30652)Instruction limit reached!
% 18.00/3.98 % (30652)------------------------------
% 18.00/3.98 % (30652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.98 % (30652)Termination reason: Unknown
% 18.00/3.98 % (30652)Termination phase: Saturation
% 18.00/3.98
% 18.00/3.98 % (30652)Memory used [KB]: 8187
% 18.00/3.98 % (30652)Time elapsed: 0.134 s
% 18.00/3.98 % (30652)Instructions burned: 445 (million)
% 18.00/3.98 % (30652)------------------------------
% 18.00/3.98 % (30652)------------------------------
% 18.00/3.98 % (30650)Instruction limit reached!
% 18.00/3.98 % (30650)------------------------------
% 18.00/3.98 % (30650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.98 % (30650)Termination reason: Unknown
% 18.00/3.98 % (30650)Termination phase: Saturation
% 18.00/3.98
% 18.00/3.98 % (30650)Memory used [KB]: 8955
% 18.00/3.98 % (30650)Time elapsed: 0.257 s
% 18.00/3.98 % (30650)Instructions burned: 865 (million)
% 18.00/3.98 % (30650)------------------------------
% 18.00/3.98 % (30650)------------------------------
% 18.00/3.99 % (30654)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_30182 for (2975ds/327Mi)
% 18.00/3.99 % (30655)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_30182 for (2975ds/5411Mi)
% 18.00/3.99 % (30656)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_30182 for (2975ds/1762Mi)
% 18.00/4.01 % (30620)Instruction limit reached!
% 18.00/4.01 % (30620)------------------------------
% 18.00/4.01 % (30620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/4.01 % (30620)Termination reason: Unknown
% 18.00/4.01 % (30620)Termination phase: Saturation
% 18.00/4.01
% 18.00/4.01 % (30620)Memory used [KB]: 15863
% 18.00/4.01 % (30620)Time elapsed: 1.604 s
% 18.00/4.01 % (30620)Instructions burned: 5205 (million)
% 18.00/4.01 % (30620)------------------------------
% 18.00/4.01 % (30620)------------------------------
% 18.00/4.02 % (30657)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_30182 for (2974ds/96Mi)
% 20.34/4.04 % (30657)Instruction limit reached!
% 20.34/4.04 % (30657)------------------------------
% 20.34/4.04 % (30657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.04 % (30657)Termination reason: Unknown
% 20.34/4.04 % (30657)Termination phase: Preprocessing 3
% 20.34/4.04
% 20.34/4.04 % (30657)Memory used [KB]: 2430
% 20.34/4.04 % (30657)Time elapsed: 0.028 s
% 20.34/4.04 % (30657)Instructions burned: 98 (million)
% 20.34/4.04 % (30657)------------------------------
% 20.34/4.04 % (30657)------------------------------
% 20.34/4.05 % (30658)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_30182 for (2974ds/503Mi)
% 20.34/4.06 % (30647)Instruction limit reached!
% 20.34/4.06 % (30647)------------------------------
% 20.34/4.06 % (30647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.06 % (30647)Termination reason: Unknown
% 20.34/4.06 % (30647)Termination phase: Saturation
% 20.34/4.06
% 20.34/4.06 % (30647)Memory used [KB]: 14200
% 20.34/4.06 % (30647)Time elapsed: 0.409 s
% 20.34/4.06 % (30647)Instructions burned: 1378 (million)
% 20.34/4.06 % (30647)------------------------------
% 20.34/4.06 % (30647)------------------------------
% 20.34/4.07 % (30659)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_30182 for (2974ds/90Mi)
% 20.34/4.08 % (30658)Refutation not found, incomplete strategy
% 20.34/4.08 % (30658)------------------------------
% 20.34/4.08 % (30658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.08 % (30658)Termination reason: Refutation not found, incomplete strategy
% 20.34/4.08
% 20.34/4.08
% 20.34/4.08 % (30658)Memory used [KB]: 7164
% 20.34/4.08 % (30658)Time elapsed: 0.030 s
% 20.34/4.08 % (30658)Instructions burned: 94 (million)
% 20.34/4.08 % (30658)------------------------------
% 20.34/4.08 % (30658)------------------------------
% 20.34/4.09 % (30654)Instruction limit reached!
% 20.34/4.09 % (30654)------------------------------
% 20.34/4.09 % (30654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.09 % (30654)Termination reason: Unknown
% 20.34/4.09 % (30654)Termination phase: Saturation
% 20.34/4.09
% 20.34/4.09 % (30654)Memory used [KB]: 8187
% 20.34/4.09 % (30654)Time elapsed: 0.101 s
% 20.34/4.09 % (30654)Instructions burned: 328 (million)
% 20.34/4.09 % (30654)------------------------------
% 20.34/4.09 % (30654)------------------------------
% 20.34/4.09 % (30660)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_30182 for (2973ds/593Mi)
% 20.34/4.09 % (30659)Instruction limit reached!
% 20.34/4.09 % (30659)------------------------------
% 20.34/4.09 % (30659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.34/4.09 % (30659)Termination reason: Unknown
% 20.34/4.09 % (30659)Termination phase: Property scanning
% 20.34/4.09
% 20.34/4.09 % (30659)Memory used [KB]: 2558
% 20.34/4.09 % (30659)Time elapsed: 0.029 s
% 20.34/4.09 % (30659)Instructions burned: 91 (million)
% 20.34/4.09 % (30659)------------------------------
% 20.34/4.09 % (30659)------------------------------
% 20.34/4.10 % (30661)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_30182 for (2973ds/1512Mi)
% 20.34/4.10 % (30662)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_30182 for (2973ds/569Mi)
% 20.97/4.15 % (30653)Instruction limit reached!
% 20.97/4.15 % (30653)------------------------------
% 20.97/4.15 % (30653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.15 % (30653)Termination reason: Unknown
% 20.97/4.15 % (30653)Termination phase: Saturation
% 20.97/4.15
% 20.97/4.15 % (30653)Memory used [KB]: 8059
% 20.97/4.15 % (30653)Time elapsed: 0.181 s
% 20.97/4.15 % (30653)Instructions burned: 594 (million)
% 20.97/4.15 % (30653)------------------------------
% 20.97/4.15 % (30653)------------------------------
% 20.97/4.16 % (30663)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_30182 for (2973ds/501Mi)
% 21.24/4.24 % (30663)Refutation not found, incomplete strategy
% 21.24/4.24 % (30663)------------------------------
% 21.24/4.24 % (30663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.24/4.24 % (30663)Termination reason: Refutation not found, incomplete strategy
% 21.24/4.24
% 21.24/4.24
% 21.24/4.24 % (30663)Memory used [KB]: 8699
% 21.24/4.24 % (30663)Time elapsed: 0.081 s
% 21.24/4.24 % (30663)Instructions burned: 259 (million)
% 21.24/4.24 % (30663)------------------------------
% 21.24/4.24 % (30663)------------------------------
% 21.24/4.25 % (30664)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_30182 for (2972ds/562Mi)
% 21.24/4.27 % (30662)Instruction limit reached!
% 21.24/4.27 % (30662)------------------------------
% 21.24/4.27 % (30662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.24/4.27 % (30662)Termination reason: Unknown
% 21.24/4.27 % (30662)Termination phase: Saturation
% 21.24/4.27
% 21.24/4.27 % (30662)Memory used [KB]: 8827
% 21.24/4.27 % (30662)Time elapsed: 0.165 s
% 21.24/4.27 % (30662)Instructions burned: 571 (million)
% 21.24/4.27 % (30662)------------------------------
% 21.24/4.27 % (30662)------------------------------
% 21.24/4.27 % (30660)Instruction limit reached!
% 21.24/4.27 % (30660)------------------------------
% 21.24/4.27 % (30660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.24/4.27 % (30660)Termination reason: Unknown
% 21.24/4.27 % (30660)Termination phase: Saturation
% 21.24/4.27
% 21.24/4.27 % (30660)Memory used [KB]: 8955
% 21.24/4.27 % (30660)Time elapsed: 0.181 s
% 21.24/4.27 % (30660)Instructions burned: 595 (million)
% 21.24/4.27 % (30660)------------------------------
% 21.24/4.27 % (30660)------------------------------
% 21.24/4.28 % (30665)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30182 for (2972ds/406Mi)
% 21.24/4.28 % (30666)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_30182 for (2972ds/582Mi)
% 22.31/4.40 % (30665)Instruction limit reached!
% 22.31/4.40 % (30665)------------------------------
% 22.31/4.40 % (30665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.31/4.40 % (30665)Termination reason: Unknown
% 22.31/4.40 % (30665)Termination phase: Saturation
% 22.31/4.40
% 22.31/4.40 % (30665)Memory used [KB]: 8571
% 22.31/4.40 % (30665)Time elapsed: 0.125 s
% 22.31/4.40 % (30665)Instructions burned: 406 (million)
% 22.31/4.40 % (30665)------------------------------
% 22.31/4.40 % (30665)------------------------------
% 22.31/4.41 % (30667)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_30182 for (2970ds/456Mi)
% 22.31/4.42 % (30664)Instruction limit reached!
% 22.31/4.42 % (30664)------------------------------
% 22.31/4.42 % (30664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.31/4.42 % (30664)Termination reason: Unknown
% 22.31/4.42 % (30664)Termination phase: Saturation
% 22.31/4.42
% 22.31/4.42 % (30664)Memory used [KB]: 8699
% 22.31/4.42 % (30664)Time elapsed: 0.166 s
% 22.31/4.42 % (30664)Instructions burned: 564 (million)
% 22.31/4.42 % (30664)------------------------------
% 22.31/4.42 % (30664)------------------------------
% 22.31/4.43 % (30668)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_30182 for (2970ds/393Mi)
% 22.31/4.46 % (30666)Instruction limit reached!
% 22.31/4.46 % (30666)------------------------------
% 22.31/4.46 % (30666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.31/4.46 % (30666)Termination reason: Unknown
% 22.31/4.46 % (30666)Termination phase: Saturation
% 22.31/4.46
% 22.31/4.46 % (30666)Memory used [KB]: 7803
% 22.31/4.46 % (30666)Time elapsed: 0.173 s
% 22.31/4.46 % (30666)Instructions burned: 584 (million)
% 22.31/4.46 % (30666)------------------------------
% 22.31/4.46 % (30666)------------------------------
% 22.31/4.47 % (30669)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_30182 for (2970ds/1335Mi)
% 23.10/4.51 % (30656)Instruction limit reached!
% 23.10/4.51 % (30656)------------------------------
% 23.10/4.51 % (30656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.51 % (30656)Termination reason: Unknown
% 23.10/4.51 % (30656)Termination phase: Saturation
% 23.10/4.51
% 23.10/4.51 % (30656)Memory used [KB]: 9594
% 23.10/4.51 % (30656)Time elapsed: 0.521 s
% 23.10/4.51 % (30656)Instructions burned: 1763 (million)
% 23.10/4.51 % (30656)------------------------------
% 23.10/4.51 % (30656)------------------------------
% 23.10/4.52 % (30670)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_30182 for (2969ds/3373Mi)
% 23.10/4.54 % (30668)Instruction limit reached!
% 23.10/4.54 % (30668)------------------------------
% 23.10/4.54 % (30668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.54 % (30668)Termination reason: Unknown
% 23.10/4.54 % (30668)Termination phase: Saturation
% 23.10/4.54
% 23.10/4.54 % (30668)Memory used [KB]: 7547
% 23.10/4.54 % (30668)Time elapsed: 0.112 s
% 23.10/4.54 % (30668)Instructions burned: 395 (million)
% 23.10/4.54 % (30668)------------------------------
% 23.10/4.54 % (30668)------------------------------
% 23.10/4.54 % (30661)Instruction limit reached!
% 23.10/4.54 % (30661)------------------------------
% 23.10/4.54 % (30661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.54 % (30661)Termination reason: Unknown
% 23.10/4.54 % (30661)Termination phase: Saturation
% 23.10/4.54
% 23.10/4.54 % (30661)Memory used [KB]: 9210
% 23.10/4.54 % (30661)Time elapsed: 0.449 s
% 23.10/4.54 % (30661)Instructions burned: 1512 (million)
% 23.10/4.54 % (30661)------------------------------
% 23.10/4.54 % (30661)------------------------------
% 23.10/4.55 % (30671)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_30182 for (2969ds/474Mi)
% 23.10/4.55 % (30667)Instruction limit reached!
% 23.10/4.55 % (30667)------------------------------
% 23.10/4.55 % (30667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.55 % (30667)Termination reason: Unknown
% 23.10/4.55 % (30667)Termination phase: Saturation
% 23.10/4.55
% 23.10/4.55 % (30667)Memory used [KB]: 8315
% 23.10/4.55 % (30667)Time elapsed: 0.141 s
% 23.10/4.55 % (30667)Instructions burned: 457 (million)
% 23.10/4.55 % (30667)------------------------------
% 23.10/4.55 % (30667)------------------------------
% 23.10/4.55 % (30672)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_30182 for (2969ds/157Mi)
% 23.10/4.56 % (30673)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_30182 for (2969ds/590Mi)
% 23.10/4.59 % (30672)Instruction limit reached!
% 23.10/4.59 % (30672)------------------------------
% 23.10/4.59 % (30672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.59 % (30672)Termination reason: Unknown
% 23.10/4.59 % (30672)Termination phase: Saturation
% 23.10/4.59
% 23.10/4.59 % (30672)Memory used [KB]: 7036
% 23.10/4.59 % (30672)Time elapsed: 0.043 s
% 23.10/4.59 % (30672)Instructions burned: 157 (million)
% 23.10/4.59 % (30672)------------------------------
% 23.10/4.59 % (30672)------------------------------
% 24.08/4.60 % (30674)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_30182 for (2968ds/104Mi)
% 24.08/4.64 % (30674)Instruction limit reached!
% 24.08/4.64 % (30674)------------------------------
% 24.08/4.64 % (30674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.08/4.64 % (30674)Termination reason: Unknown
% 24.08/4.64 % (30674)Termination phase: Property scanning
% 24.08/4.64
% 24.08/4.64 % (30674)Memory used [KB]: 2558
% 24.08/4.64 % (30674)Time elapsed: 0.033 s
% 24.08/4.64 % (30674)Instructions burned: 105 (million)
% 24.08/4.64 % (30674)------------------------------
% 24.08/4.64 % (30674)------------------------------
% 24.08/4.65 % (30675)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_30182 for (2968ds/414Mi)
% 24.08/4.69 % (30671)Instruction limit reached!
% 24.08/4.69 % (30671)------------------------------
% 24.08/4.69 % (30671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.08/4.69 % (30671)Termination reason: Unknown
% 24.08/4.69 % (30671)Termination phase: Saturation
% 24.08/4.69
% 24.08/4.69 % (30671)Memory used [KB]: 8187
% 24.08/4.69 % (30671)Time elapsed: 0.144 s
% 24.08/4.69 % (30671)Instructions burned: 475 (million)
% 24.08/4.69 % (30671)------------------------------
% 24.08/4.69 % (30671)------------------------------
% 24.47/4.70 % (30676)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_30182 for (2967ds/715Mi)
% 24.47/4.73 % (30673)Instruction limit reached!
% 24.47/4.73 % (30673)------------------------------
% 24.47/4.73 % (30673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.47/4.73 % (30673)Termination reason: Unknown
% 24.47/4.73 % (30673)Termination phase: Saturation
% 24.47/4.73
% 24.47/4.73 % (30673)Memory used [KB]: 9083
% 24.47/4.73 % (30673)Time elapsed: 0.171 s
% 24.47/4.73 % (30673)Instructions burned: 590 (million)
% 24.47/4.73 % (30673)------------------------------
% 24.47/4.73 % (30673)------------------------------
% 24.47/4.74 % (30677)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_30182 for (2967ds/961Mi)
% 24.47/4.76 % (30675)Instruction limit reached!
% 24.47/4.76 % (30675)------------------------------
% 24.47/4.76 % (30675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.47/4.76 % (30675)Termination reason: Unknown
% 24.47/4.76 % (30675)Termination phase: Saturation
% 24.47/4.76
% 24.47/4.76 % (30675)Memory used [KB]: 7931
% 24.47/4.76 % (30675)Time elapsed: 0.119 s
% 24.47/4.76 % (30675)Instructions burned: 414 (million)
% 24.47/4.76 % (30675)------------------------------
% 24.47/4.76 % (30675)------------------------------
% 24.47/4.77 % (30678)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_30182 for (2967ds/1213Mi)
% 24.99/4.87 % (30669)Instruction limit reached!
% 24.99/4.87 % (30669)------------------------------
% 24.99/4.87 % (30669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.87 % (30669)Termination reason: Unknown
% 24.99/4.87 % (30669)Termination phase: Saturation
% 24.99/4.87
% 24.99/4.87 % (30669)Memory used [KB]: 9594
% 24.99/4.87 % (30669)Time elapsed: 0.402 s
% 24.99/4.87 % (30669)Instructions burned: 1337 (million)
% 24.99/4.87 % (30669)------------------------------
% 24.99/4.87 % (30669)------------------------------
% 24.99/4.88 % (30679)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_30182 for (2966ds/1979Mi)
% 24.99/4.88 % (30655)Instruction limit reached!
% 24.99/4.88 % (30655)------------------------------
% 24.99/4.88 % (30655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.88 % (30655)Termination reason: Unknown
% 24.99/4.88 % (30655)Termination phase: Saturation
% 24.99/4.88
% 24.99/4.88 % (30655)Memory used [KB]: 7164
% 24.99/4.88 % (30655)Time elapsed: 0.899 s
% 24.99/4.88 % (30655)Instructions burned: 5411 (million)
% 24.99/4.88 % (30655)------------------------------
% 24.99/4.88 % (30655)------------------------------
% 24.99/4.89 % (30680)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_30182 for (2966ds/481Mi)
% 25.60/4.92 % (30676)Instruction limit reached!
% 25.60/4.92 % (30676)------------------------------
% 25.60/4.92 % (30676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.60/4.92 % (30676)Termination reason: Unknown
% 25.60/4.92 % (30676)Termination phase: Saturation
% 25.60/4.92
% 25.60/4.92 % (30676)Memory used [KB]: 4349
% 25.60/4.92 % (30676)Time elapsed: 0.223 s
% 25.60/4.92 % (30676)Instructions burned: 716 (million)
% 25.60/4.92 % (30676)------------------------------
% 25.60/4.92 % (30676)------------------------------
% 25.60/4.93 % (30681)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_30182 for (2965ds/783Mi)
% 27.37/5.04 % (30677)Instruction limit reached!
% 27.37/5.04 % (30677)------------------------------
% 27.37/5.04 % (30677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.04 % (30677)Termination reason: Unknown
% 27.37/5.04 % (30677)Termination phase: Saturation
% 27.37/5.04
% 27.37/5.04 % (30677)Memory used [KB]: 8827
% 27.37/5.04 % (30677)Time elapsed: 0.297 s
% 27.37/5.04 % (30677)Instructions burned: 963 (million)
% 27.37/5.04 % (30677)------------------------------
% 27.37/5.04 % (30677)------------------------------
% 27.37/5.04 % (30680)Instruction limit reached!
% 27.37/5.04 % (30680)------------------------------
% 27.37/5.04 % (30680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.37/5.04 % (30680)Termination reason: Unknown
% 27.37/5.04 % (30680)Termination phase: Saturation
% 27.37/5.04
% 27.37/5.04 % (30680)Memory used [KB]: 7803
% 27.37/5.04 % (30680)Time elapsed: 0.148 s
% 27.37/5.04 % (30680)Instructions burned: 483 (million)
% 27.37/5.04 % (30680)------------------------------
% 27.37/5.04 % (30680)------------------------------
% 27.37/5.05 % (30682)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_30182 for (2964ds/432Mi)
% 27.37/5.05 % (30683)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_30182 for (2964ds/1670Mi)
% 27.93/5.15 % (30678)Instruction limit reached!
% 27.93/5.15 % (30678)------------------------------
% 27.93/5.15 % (30678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.15 % (30678)Termination reason: Unknown
% 27.93/5.15 % (30678)Termination phase: Saturation
% 27.93/5.15
% 27.93/5.15 % (30678)Memory used [KB]: 8955
% 27.93/5.15 % (30678)Time elapsed: 0.376 s
% 27.93/5.15 % (30678)Instructions burned: 1215 (million)
% 27.93/5.15 % (30678)------------------------------
% 27.93/5.15 % (30678)------------------------------
% 27.93/5.16 % (30684)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_30182 for (2963ds/90Mi)
% 27.93/5.16 % (30681)Instruction limit reached!
% 27.93/5.16 % (30681)------------------------------
% 27.93/5.16 % (30681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.16 % (30681)Termination reason: Unknown
% 27.93/5.16 % (30681)Termination phase: Saturation
% 27.93/5.16
% 27.93/5.16 % (30681)Memory used [KB]: 7931
% 27.93/5.16 % (30681)Time elapsed: 0.230 s
% 27.93/5.16 % (30681)Instructions burned: 785 (million)
% 27.93/5.16 % (30681)------------------------------
% 27.93/5.16 % (30681)------------------------------
% 27.93/5.17 % (30685)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_30182 for (2963ds/346Mi)
% 27.93/5.18 % (30682)Instruction limit reached!
% 27.93/5.18 % (30682)------------------------------
% 27.93/5.18 % (30682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.18 % (30682)Termination reason: Unknown
% 27.93/5.18 % (30682)Termination phase: Saturation
% 27.93/5.18
% 27.93/5.18 % (30682)Memory used [KB]: 7675
% 27.93/5.18 % (30682)Time elapsed: 0.132 s
% 27.93/5.18 % (30682)Instructions burned: 435 (million)
% 27.93/5.18 % (30682)------------------------------
% 27.93/5.18 % (30682)------------------------------
% 27.93/5.18 % (30684)Instruction limit reached!
% 27.93/5.18 % (30684)------------------------------
% 27.93/5.18 % (30684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.18 % (30684)Termination reason: Unknown
% 27.93/5.18 % (30684)Termination phase: Property scanning
% 27.93/5.18
% 27.93/5.18 % (30684)Memory used [KB]: 2558
% 27.93/5.18 % (30684)Time elapsed: 0.028 s
% 27.93/5.18 % (30684)Instructions burned: 90 (million)
% 27.93/5.18 % (30684)------------------------------
% 27.93/5.18 % (30684)------------------------------
% 27.93/5.19 % (30686)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_30182 for (2963ds/401Mi)
% 27.93/5.19 % (30687)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_30182 for (2962ds/6454Mi)
% 28.41/5.28 % (30685)Instruction limit reached!
% 28.41/5.28 % (30685)------------------------------
% 28.41/5.28 % (30685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.41/5.28 % (30685)Termination reason: Unknown
% 28.41/5.28 % (30685)Termination phase: Saturation
% 28.41/5.28
% 28.41/5.28 % (30685)Memory used [KB]: 7931
% 28.41/5.28 % (30685)Time elapsed: 0.104 s
% 28.41/5.28 % (30685)Instructions burned: 346 (million)
% 28.41/5.28 % (30685)------------------------------
% 28.41/5.28 % (30685)------------------------------
% 28.41/5.29 % (30688)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_30182 for (2962ds/283Mi)
% 28.82/5.30 % (30686)Instruction limit reached!
% 28.82/5.30 % (30686)------------------------------
% 28.82/5.30 % (30686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.82/5.30 % (30686)Termination reason: Unknown
% 28.82/5.30 % (30686)Termination phase: Saturation
% 28.82/5.30
% 28.82/5.30 % (30686)Memory used [KB]: 8699
% 28.82/5.30 % (30686)Time elapsed: 0.112 s
% 28.82/5.30 % (30686)Instructions burned: 401 (million)
% 28.82/5.30 % (30686)------------------------------
% 28.82/5.30 % (30686)------------------------------
% 28.82/5.31 % (30689)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_30182 for (2961ds/865Mi)
% 28.82/5.37 % (30688)Instruction limit reached!
% 28.82/5.37 % (30688)------------------------------
% 28.82/5.37 % (30688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.82/5.37 % (30688)Termination reason: Unknown
% 28.82/5.37 % (30688)Termination phase: Saturation
% 28.82/5.37
% 28.82/5.37 % (30688)Memory used [KB]: 8059
% 28.82/5.37 % (30688)Time elapsed: 0.087 s
% 28.82/5.37 % (30688)Instructions burned: 283 (million)
% 28.82/5.37 % (30688)------------------------------
% 28.82/5.37 % (30688)------------------------------
% 28.82/5.38 % (30690)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_30182 for (2961ds/4528Mi)
% 29.33/5.47 % (30679)Instruction limit reached!
% 29.33/5.47 % (30679)------------------------------
% 29.33/5.47 % (30679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.47 % (30679)Termination reason: Unknown
% 29.33/5.47 % (30679)Termination phase: Saturation
% 29.33/5.47
% 29.33/5.47 % (30679)Memory used [KB]: 8827
% 29.33/5.47 % (30679)Time elapsed: 0.598 s
% 29.33/5.47 % (30679)Instructions burned: 1981 (million)
% 29.33/5.47 % (30679)------------------------------
% 29.33/5.47 % (30679)------------------------------
% 29.33/5.48 % (30691)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_30182 for (2960ds/1001Mi)
% 29.62/5.55 % (30683)Instruction limit reached!
% 29.62/5.55 % (30683)------------------------------
% 29.62/5.55 % (30683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.62/5.55 % (30683)Termination reason: Unknown
% 29.62/5.55 % (30683)Termination phase: Saturation
% 29.62/5.55
% 29.62/5.55 % (30683)Memory used [KB]: 11769
% 29.62/5.55 % (30683)Time elapsed: 0.496 s
% 29.62/5.55 % (30683)Instructions burned: 1671 (million)
% 29.62/5.55 % (30683)------------------------------
% 29.62/5.55 % (30683)------------------------------
% 29.62/5.56 % (30692)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_30182 for (2959ds/102Mi)
% 29.62/5.57 % (30689)Instruction limit reached!
% 29.62/5.57 % (30689)------------------------------
% 29.62/5.57 % (30689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.62/5.57 % (30689)Termination reason: Unknown
% 29.62/5.57 % (30689)Termination phase: Saturation
% 29.62/5.57
% 29.62/5.57 % (30689)Memory used [KB]: 9978
% 29.62/5.57 % (30689)Time elapsed: 0.260 s
% 29.62/5.57 % (30689)Instructions burned: 866 (million)
% 29.62/5.57 % (30689)------------------------------
% 29.62/5.57 % (30689)------------------------------
% 29.62/5.57 % (30670)Instruction limit reached!
% 29.62/5.57 % (30670)------------------------------
% 29.62/5.57 % (30670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.62/5.57 % (30670)Termination reason: Unknown
% 29.62/5.57 % (30670)Termination phase: Saturation
% 29.62/5.57
% 29.62/5.57 % (30670)Memory used [KB]: 11769
% 29.62/5.57 % (30670)Time elapsed: 1.055 s
% 29.62/5.57 % (30670)Instructions burned: 3375 (million)
% 29.62/5.57 % (30670)------------------------------
% 29.62/5.57 % (30670)------------------------------
% 29.62/5.58 % (30693)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_30182 for (2959ds/952Mi)
% 29.62/5.58 % (30694)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_30182 for (2959ds/578Mi)
% 29.62/5.58 % (30692)Instruction limit reached!
% 29.62/5.58 % (30692)------------------------------
% 29.62/5.58 % (30692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.62/5.58 % (30692)Termination reason: Unknown
% 29.62/5.58 % (30692)Termination phase: Property scanning
% 29.62/5.58
% 29.62/5.58 % (30692)Memory used [KB]: 2558
% 29.62/5.58 % (30692)Time elapsed: 0.030 s
% 29.62/5.58 % (30692)Instructions burned: 102 (million)
% 29.62/5.58 % (30692)------------------------------
% 29.62/5.58 % (30692)------------------------------
% 29.62/5.59 % (30695)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_30182 for (2959ds/643Mi)
% 30.72/5.75 % (30694)Instruction limit reached!
% 30.72/5.75 % (30694)------------------------------
% 30.72/5.75 % (30694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.75 % (30694)Termination reason: Unknown
% 30.72/5.75 % (30694)Termination phase: Saturation
% 30.72/5.75
% 30.72/5.75 % (30694)Memory used [KB]: 8827
% 30.72/5.75 % (30694)Time elapsed: 0.167 s
% 30.72/5.75 % (30694)Instructions burned: 580 (million)
% 30.72/5.75 % (30694)------------------------------
% 30.72/5.75 % (30694)------------------------------
% 30.72/5.76 % (30696)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_30182 for (2957ds/865Mi)
% 30.72/5.76 % (30643)Instruction limit reached!
% 30.72/5.76 % (30643)------------------------------
% 30.72/5.76 % (30643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.76 % (30643)Termination reason: Unknown
% 30.72/5.76 % (30643)Termination phase: Saturation
% 30.72/5.76
% 30.72/5.76 % (30643)Memory used [KB]: 14200
% 30.72/5.76 % (30643)Time elapsed: 2.532 s
% 30.72/5.76 % (30643)Instructions burned: 8250 (million)
% 30.72/5.76 % (30643)------------------------------
% 30.72/5.76 % (30643)------------------------------
% 30.72/5.77 % (30697)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_30182 for (2957ds/1174Mi)
% 30.72/5.78 % (30695)Instruction limit reached!
% 30.72/5.78 % (30695)------------------------------
% 30.72/5.78 % (30695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.78 % (30695)Termination reason: Unknown
% 30.72/5.78 % (30695)Termination phase: Saturation
% 30.72/5.78
% 30.72/5.78 % (30695)Memory used [KB]: 9466
% 30.72/5.78 % (30695)Time elapsed: 0.188 s
% 30.72/5.78 % (30695)Instructions burned: 646 (million)
% 30.72/5.78 % (30695)------------------------------
% 30.72/5.78 % (30695)------------------------------
% 30.72/5.79 % (30691)Instruction limit reached!
% 30.72/5.79 % (30691)------------------------------
% 30.72/5.79 % (30691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.79 % (30691)Termination reason: Unknown
% 30.72/5.79 % (30691)Termination phase: Saturation
% 30.72/5.79
% 30.72/5.79 % (30691)Memory used [KB]: 10490
% 30.72/5.79 % (30691)Time elapsed: 0.307 s
% 30.72/5.79 % (30691)Instructions burned: 1003 (million)
% 30.72/5.79 % (30691)------------------------------
% 30.72/5.79 % (30691)------------------------------
% 30.72/5.79 % (30698)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_30182 for (2957ds/644Mi)
% 31.49/5.80 % (30699)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_30182 for (2956ds/1201Mi)
% 31.49/5.87 % (30693)Instruction limit reached!
% 31.49/5.87 % (30693)------------------------------
% 31.49/5.87 % (30693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.49/5.87 % (30693)Termination reason: Unknown
% 31.49/5.87 % (30693)Termination phase: Saturation
% 31.49/5.87
% 31.49/5.87 % (30693)Memory used [KB]: 10106
% 31.49/5.87 % (30693)Time elapsed: 0.292 s
% 31.49/5.87 % (30693)Instructions burned: 953 (million)
% 31.49/5.87 % (30693)------------------------------
% 31.49/5.87 % (30693)------------------------------
% 31.49/5.88 % (30700)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_30182 for (2956ds/1046Mi)
% 31.80/5.99 % (30698)Instruction limit reached!
% 31.80/5.99 % (30698)------------------------------
% 31.80/5.99 % (30698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.80/5.99 % (30698)Termination reason: Unknown
% 31.80/5.99 % (30698)Termination phase: Saturation
% 31.80/5.99
% 31.80/5.99 % (30698)Memory used [KB]: 10746
% 31.80/5.99 % (30698)Time elapsed: 0.198 s
% 31.80/5.99 % (30698)Instructions burned: 644 (million)
% 31.80/5.99 % (30698)------------------------------
% 31.80/5.99 % (30698)------------------------------
% 31.80/6.00 % (30701)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_30182 for (2955ds/222Mi)
% 31.80/6.02 % (30696)Instruction limit reached!
% 31.80/6.02 % (30696)------------------------------
% 31.80/6.02 % (30696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.80/6.02 % (30696)Termination reason: Unknown
% 31.80/6.02 % (30696)Termination phase: Saturation
% 31.80/6.02
% 31.80/6.02 % (30696)Memory used [KB]: 10490
% 31.80/6.02 % (30696)Time elapsed: 0.263 s
% 31.80/6.02 % (30696)Instructions burned: 868 (million)
% 31.80/6.02 % (30696)------------------------------
% 31.80/6.02 % (30696)------------------------------
% 34.13/6.03 % (30702)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_30182 for (2954ds/68Mi)
% 34.13/6.05 % (30702)Instruction limit reached!
% 34.13/6.05 % (30702)------------------------------
% 34.13/6.05 % (30702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.13/6.05 % (30702)Termination reason: Unknown
% 34.13/6.05 % (30702)Termination phase: Preprocessing 3
% 34.13/6.05
% 34.13/6.05 % (30702)Memory used [KB]: 2174
% 34.13/6.05 % (30702)Time elapsed: 0.022 s
% 34.13/6.05 % (30702)Instructions burned: 69 (million)
% 34.13/6.05 % (30702)------------------------------
% 34.13/6.05 % (30702)------------------------------
% 34.13/6.06 % (30701)Instruction limit reached!
% 34.13/6.06 % (30701)------------------------------
% 34.13/6.06 % (30701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.13/6.06 % (30701)Termination reason: Unknown
% 34.13/6.06 % (30701)Termination phase: Saturation
% 34.13/6.06
% 34.13/6.06 % (30701)Memory used [KB]: 7291
% 34.13/6.06 % (30701)Time elapsed: 0.062 s
% 34.13/6.06 % (30701)Instructions burned: 224 (million)
% 34.13/6.06 % (30701)------------------------------
% 34.13/6.06 % (30701)------------------------------
% 34.13/6.06 % (30703)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_30182 for (2954ds/454Mi)
% 34.13/6.08 % (30704)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_30182 for (2954ds/360Mi)
% 34.97/6.13 % (30697)Instruction limit reached!
% 34.97/6.13 % (30697)------------------------------
% 34.97/6.13 % (30697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.13 % (30697)Termination reason: Unknown
% 34.97/6.13 % (30697)Termination phase: Saturation
% 34.97/6.13
% 34.97/6.13 % (30697)Memory used [KB]: 9850
% 34.97/6.13 % (30697)Time elapsed: 0.354 s
% 34.97/6.13 % (30697)Instructions burned: 1175 (million)
% 34.97/6.13 % (30697)------------------------------
% 34.97/6.13 % (30697)------------------------------
% 34.97/6.14 % (30705)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_30182 for (2953ds/157Mi)
% 34.97/6.14 % (30699)Instruction limit reached!
% 34.97/6.14 % (30699)------------------------------
% 34.97/6.14 % (30699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.14 % (30699)Termination reason: Unknown
% 34.97/6.14 % (30699)Termination phase: Saturation
% 34.97/6.14
% 34.97/6.14 % (30699)Memory used [KB]: 10618
% 34.97/6.14 % (30699)Time elapsed: 0.343 s
% 34.97/6.14 % (30699)Instructions burned: 1201 (million)
% 34.97/6.14 % (30699)------------------------------
% 34.97/6.14 % (30699)------------------------------
% 34.97/6.15 % (30706)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_30182 for (2953ds/5061Mi)
% 34.97/6.18 % (30705)Instruction limit reached!
% 34.97/6.18 % (30705)------------------------------
% 34.97/6.18 % (30705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.18 % (30705)Termination reason: Unknown
% 34.97/6.18 % (30705)Termination phase: Saturation
% 34.97/6.18
% 34.97/6.18 % (30705)Memory used [KB]: 7036
% 34.97/6.18 % (30705)Time elapsed: 0.043 s
% 34.97/6.18 % (30705)Instructions burned: 157 (million)
% 34.97/6.18 % (30705)------------------------------
% 34.97/6.18 % (30705)------------------------------
% 34.97/6.18 % (30700)Instruction limit reached!
% 34.97/6.18 % (30700)------------------------------
% 34.97/6.18 % (30700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.18 % (30700)Termination reason: Unknown
% 34.97/6.18 % (30700)Termination phase: Saturation
% 34.97/6.18
% 34.97/6.18 % (30700)Memory used [KB]: 9210
% 34.97/6.18 % (30700)Time elapsed: 0.305 s
% 34.97/6.18 % (30700)Instructions burned: 1047 (million)
% 34.97/6.18 % (30700)------------------------------
% 34.97/6.18 % (30700)------------------------------
% 34.97/6.19 % (30707)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_30182 for (2953ds/2401Mi)
% 34.97/6.19 % (30708)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_30182 for (2953ds/5798Mi)
% 34.97/6.19 % (30703)Instruction limit reached!
% 34.97/6.19 % (30703)------------------------------
% 34.97/6.19 % (30703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.19 % (30703)Termination reason: Unknown
% 34.97/6.19 % (30703)Termination phase: Saturation
% 34.97/6.19
% 34.97/6.19 % (30703)Memory used [KB]: 13304
% 34.97/6.19 % (30703)Time elapsed: 0.131 s
% 34.97/6.19 % (30703)Instructions burned: 454 (million)
% 34.97/6.19 % (30703)------------------------------
% 34.97/6.19 % (30703)------------------------------
% 35.42/6.20 % (30709)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_30182 for (2952ds/346Mi)
% 35.42/6.22 % (30704)Instruction limit reached!
% 35.42/6.22 % (30704)------------------------------
% 35.42/6.22 % (30704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.42/6.22 % (30704)Termination reason: Unknown
% 35.42/6.22 % (30704)Termination phase: Saturation
% 35.42/6.22
% 35.42/6.22 % (30704)Memory used [KB]: 8571
% 35.42/6.22 % (30704)Time elapsed: 0.144 s
% 35.42/6.22 % (30704)Instructions burned: 362 (million)
% 35.42/6.22 % (30704)------------------------------
% 35.42/6.22 % (30704)------------------------------
% 35.42/6.23 % (30710)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_30182 for (2952ds/1321Mi)
% 35.78/6.30 % (30709)Instruction limit reached!
% 35.78/6.30 % (30709)------------------------------
% 35.78/6.30 % (30709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.78/6.30 % (30709)Termination reason: Unknown
% 35.78/6.30 % (30709)Termination phase: Saturation
% 35.78/6.30
% 35.78/6.30 % (30709)Memory used [KB]: 7931
% 35.78/6.30 % (30709)Time elapsed: 0.104 s
% 35.78/6.30 % (30709)Instructions burned: 348 (million)
% 35.78/6.30 % (30709)------------------------------
% 35.78/6.30 % (30709)------------------------------
% 35.78/6.31 % (30711)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_30182 for (2951ds/1312Mi)
% 36.50/6.63 % (30710)Instruction limit reached!
% 36.50/6.63 % (30710)------------------------------
% 36.50/6.63 % (30710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.50/6.63 % (30710)Termination reason: Unknown
% 36.50/6.63 % (30710)Termination phase: Saturation
% 36.50/6.63
% 36.50/6.63 % (30710)Memory used [KB]: 4477
% 36.50/6.63 % (30710)Time elapsed: 0.401 s
% 36.50/6.63 % (30710)Instructions burned: 1323 (million)
% 36.50/6.63 % (30710)------------------------------
% 36.50/6.63 % (30710)------------------------------
% 36.50/6.63 % (30690)Instruction limit reached!
% 36.50/6.63 % (30690)------------------------------
% 36.50/6.63 % (30690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.50/6.63 % (30690)Termination reason: Unknown
% 36.50/6.63 % (30690)Termination phase: Saturation
% 36.50/6.63
% 36.50/6.63 % (30690)Memory used [KB]: 5884
% 36.50/6.63 % (30690)Time elapsed: 1.254 s
% 36.50/6.63 % (30690)Instructions burned: 4529 (million)
% 36.50/6.63 % (30690)------------------------------
% 36.50/6.63 % (30690)------------------------------
% 36.50/6.64 % (30712)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_30182 for (2948ds/672Mi)
% 36.50/6.64 % (30713)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_30182 for (2948ds/1897Mi)
% 37.05/6.70 % (30711)Instruction limit reached!
% 37.05/6.70 % (30711)------------------------------
% 37.05/6.70 % (30711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.05/6.70 % (30711)Termination reason: Unknown
% 37.05/6.70 % (30711)Termination phase: Saturation
% 37.05/6.70
% 37.05/6.70 % (30711)Memory used [KB]: 9338
% 37.05/6.70 % (30711)Time elapsed: 0.388 s
% 37.05/6.70 % (30711)Instructions burned: 1313 (million)
% 37.05/6.70 % (30711)------------------------------
% 37.05/6.70 % (30711)------------------------------
% 37.05/6.71 % (30714)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_30182 for (2947ds/1202Mi)
% 37.55/6.83 % (30712)Instruction limit reached!
% 37.55/6.83 % (30712)------------------------------
% 37.55/6.83 % (30712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.83 % (30712)Termination reason: Unknown
% 37.55/6.83 % (30712)Termination phase: Saturation
% 37.55/6.83
% 37.55/6.83 % (30712)Memory used [KB]: 8059
% 37.55/6.83 % (30712)Time elapsed: 0.197 s
% 37.55/6.83 % (30712)Instructions burned: 674 (million)
% 37.55/6.83 % (30712)------------------------------
% 37.55/6.83 % (30712)------------------------------
% 37.55/6.84 % (30715)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_30182 for (2946ds/1493Mi)
% 37.55/6.89 % (30715)Refutation not found, incomplete strategy
% 37.55/6.89 % (30715)------------------------------
% 37.55/6.89 % (30715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.89 % (30715)Termination reason: Refutation not found, incomplete strategy
% 37.55/6.89
% 37.55/6.89
% 37.55/6.89 % (30715)Memory used [KB]: 7291
% 37.55/6.89 % (30715)Time elapsed: 0.046 s
% 37.55/6.89 % (30715)Instructions burned: 162 (million)
% 37.55/6.89 % (30715)------------------------------
% 37.55/6.89 % (30715)------------------------------
% 37.91/6.90 % (30716)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_30182 for (2946ds/7679Mi)
% 37.91/6.90 % (30707)Instruction limit reached!
% 37.91/6.90 % (30707)------------------------------
% 37.91/6.90 % (30707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.91/6.90 % (30707)Termination reason: Unknown
% 37.91/6.90 % (30707)Termination phase: Saturation
% 37.91/6.90
% 37.91/6.90 % (30707)Memory used [KB]: 6140
% 37.91/6.90 % (30707)Time elapsed: 0.713 s
% 37.91/6.90 % (30707)Instructions burned: 2403 (million)
% 37.91/6.90 % (30707)------------------------------
% 37.91/6.90 % (30707)------------------------------
% 37.91/6.91 % (30717)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_30182 for (2945ds/340Mi)
% 37.91/7.01 % (30717)Instruction limit reached!
% 37.91/7.01 % (30717)------------------------------
% 37.91/7.01 % (30717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.91/7.01 % (30717)Termination reason: Unknown
% 37.91/7.01 % (30717)Termination phase: Saturation
% 37.91/7.01
% 37.91/7.01 % (30717)Memory used [KB]: 9338
% 37.91/7.01 % (30717)Time elapsed: 0.101 s
% 37.91/7.01 % (30717)Instructions burned: 341 (million)
% 37.91/7.01 % (30717)------------------------------
% 37.91/7.01 % (30717)------------------------------
% 41.20/7.02 % (30718)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_30182 for (2944ds/3672Mi)
% 41.20/7.02 % (30687)Instruction limit reached!
% 41.20/7.02 % (30687)------------------------------
% 41.20/7.02 % (30687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.20/7.02 % (30687)Termination reason: Unknown
% 41.20/7.02 % (30687)Termination phase: Saturation
% 41.20/7.02
% 41.20/7.02 % (30687)Memory used [KB]: 9338
% 41.20/7.02 % (30687)Time elapsed: 1.831 s
% 41.20/7.02 % (30687)Instructions burned: 6456 (million)
% 41.20/7.02 % (30687)------------------------------
% 41.20/7.02 % (30687)------------------------------
% 41.20/7.03 % (30719)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_30182 for (2944ds/1535Mi)
% 41.20/7.08 % (30714)Instruction limit reached!
% 41.20/7.08 % (30714)------------------------------
% 41.20/7.08 % (30714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.20/7.08 % (30714)Termination reason: Unknown
% 41.20/7.08 % (30714)Termination phase: Saturation
% 41.20/7.08
% 41.20/7.08 % (30714)Memory used [KB]: 4733
% 41.20/7.08 % (30714)Time elapsed: 0.366 s
% 41.20/7.08 % (30714)Instructions burned: 1205 (million)
% 41.20/7.08 % (30714)------------------------------
% 41.20/7.08 % (30714)------------------------------
% 41.20/7.09 % (30720)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_30182 for (2944ds/4637Mi)
% 42.17/7.22 % (30713)Instruction limit reached!
% 42.17/7.22 % (30713)------------------------------
% 42.17/7.22 % (30713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.17/7.22 % (30713)Termination reason: Unknown
% 42.17/7.22 % (30713)Termination phase: Saturation
% 42.17/7.22
% 42.17/7.22 % (30713)Memory used [KB]: 8699
% 42.17/7.22 % (30713)Time elapsed: 0.580 s
% 42.17/7.22 % (30713)Instructions burned: 1898 (million)
% 42.17/7.22 % (30713)------------------------------
% 42.17/7.22 % (30713)------------------------------
% 42.17/7.23 % (30721)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_30182 for (2942ds/3174Mi)
% 43.12/7.50 % (30719)Instruction limit reached!
% 43.12/7.50 % (30719)------------------------------
% 43.12/7.50 % (30719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.12/7.50 % (30719)Termination reason: Unknown
% 43.12/7.50 % (30719)Termination phase: Saturation
% 43.12/7.50
% 43.12/7.50 % (30719)Memory used [KB]: 12409
% 43.12/7.50 % (30719)Time elapsed: 0.464 s
% 43.12/7.50 % (30719)Instructions burned: 1538 (million)
% 43.12/7.50 % (30719)------------------------------
% 43.12/7.50 % (30719)------------------------------
% 43.12/7.51 % (30722)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_30182 for (2939ds/307Mi)
% 43.12/7.59 % (30722)Instruction limit reached!
% 43.12/7.59 % (30722)------------------------------
% 43.12/7.59 % (30722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.12/7.59 % (30722)Termination reason: Unknown
% 43.12/7.59 % (30722)Termination phase: Saturation
% 43.12/7.59
% 43.12/7.59 % (30722)Memory used [KB]: 7803
% 43.12/7.59 % (30722)Time elapsed: 0.088 s
% 43.12/7.59 % (30722)Instructions burned: 309 (million)
% 43.12/7.59 % (30722)------------------------------
% 43.12/7.59 % (30722)------------------------------
% 43.97/7.60 % (30723)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_30182 for (2938ds/3619Mi)
% 43.97/7.64 % (30706)Instruction limit reached!
% 43.97/7.64 % (30706)------------------------------
% 43.97/7.64 % (30706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.97/7.64 % (30706)Termination reason: Unknown
% 43.97/7.64 % (30706)Termination phase: Saturation
% 43.97/7.64
% 43.97/7.64 % (30706)Memory used [KB]: 12792
% 43.97/7.64 % (30706)Time elapsed: 1.488 s
% 43.97/7.64 % (30706)Instructions burned: 5061 (million)
% 43.97/7.64 % (30706)------------------------------
% 43.97/7.64 % (30706)------------------------------
% 43.97/7.65 % (30724)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_30182 for (2938ds/2325Mi)
% 44.44/7.86 % (30708)Instruction limit reached!
% 44.44/7.86 % (30708)------------------------------
% 44.44/7.86 % (30708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.44/7.86 % (30708)Termination reason: Unknown
% 44.44/7.86 % (30708)Termination phase: Saturation
% 44.44/7.86
% 44.44/7.86 % (30708)Memory used [KB]: 8699
% 44.44/7.86 % (30708)Time elapsed: 1.672 s
% 44.44/7.86 % (30708)Instructions burned: 5799 (million)
% 44.44/7.86 % (30708)------------------------------
% 44.44/7.86 % (30708)------------------------------
% 44.44/7.87 % (30725)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_30182 for (2936ds/2341Mi)
% 48.42/8.12 % (30718)Instruction limit reached!
% 48.42/8.12 % (30718)------------------------------
% 48.42/8.12 % (30718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.42/8.12 % (30718)Termination reason: Unknown
% 48.42/8.12 % (30718)Termination phase: Saturation
% 48.42/8.12
% 48.42/8.12 % (30718)Memory used [KB]: 10874
% 48.42/8.12 % (30718)Time elapsed: 1.104 s
% 48.42/8.12 % (30718)Instructions burned: 3672 (million)
% 48.42/8.12 % (30718)------------------------------
% 48.42/8.12 % (30718)------------------------------
% 48.02/8.13 % (30726)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_30182 for (2933ds/7257Mi)
% 48.02/8.16 % (30721)Instruction limit reached!
% 48.02/8.16 % (30721)------------------------------
% 48.02/8.16 % (30721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.02/8.16 % (30721)Termination reason: Unknown
% 48.02/8.16 % (30721)Termination phase: Saturation
% 48.02/8.16
% 48.02/8.16 % (30721)Memory used [KB]: 10490
% 48.02/8.16 % (30721)Time elapsed: 0.931 s
% 48.02/8.16 % (30721)Instructions burned: 3174 (million)
% 48.02/8.16 % (30721)------------------------------
% 48.02/8.16 % (30721)------------------------------
% 48.02/8.17 % (30727)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_30182 for (2933ds/3710Mi)
% 50.06/8.35 % (30724)Refutation not found, non-redundant clauses discarded% (30724)------------------------------
% 50.06/8.35 % (30724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.06/8.35 % (30724)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.06/8.35
% 50.06/8.35 % (30724)Memory used [KB]: 11129
% 50.06/8.35 % (30724)Time elapsed: 0.701 s
% 50.06/8.35 % (30724)Instructions burned: 2311 (million)
% 50.06/8.35 % (30724)------------------------------
% 50.06/8.35 % (30724)------------------------------
% 50.06/8.36 % (30728)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_30182 for (2931ds/326Mi)
% 50.51/8.45 % (30720)Instruction limit reached!
% 50.51/8.45 % (30720)------------------------------
% 50.51/8.45 % (30720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.51/8.45 % (30720)Termination reason: Unknown
% 50.51/8.45 % (30720)Termination phase: Saturation
% 50.51/8.45
% 50.51/8.45 % (30720)Memory used [KB]: 13688
% 50.51/8.45 % (30720)Time elapsed: 1.366 s
% 50.51/8.45 % (30720)Instructions burned: 4637 (million)
% 50.51/8.45 % (30720)------------------------------
% 50.51/8.45 % (30720)------------------------------
% 50.51/8.45 % (30728)Instruction limit reached!
% 50.51/8.45 % (30728)------------------------------
% 50.51/8.45 % (30728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.51/8.45 % (30728)Termination reason: Unknown
% 50.51/8.45 % (30728)Termination phase: Saturation
% 50.51/8.45
% 50.51/8.45 % (30728)Memory used [KB]: 7291
% 50.51/8.45 % (30728)Time elapsed: 0.097 s
% 50.51/8.45 % (30728)Instructions burned: 329 (million)
% 50.51/8.45 % (30728)------------------------------
% 50.51/8.45 % (30728)------------------------------
% 50.51/8.46 % (30729)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_30182 for (2930ds/1100Mi)
% 50.51/8.46 % (30730)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30182 for (2930ds/406Mi)
% 50.99/8.57 % (30725)Instruction limit reached!
% 50.99/8.57 % (30725)------------------------------
% 50.99/8.57 % (30725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.99/8.57 % (30725)Termination reason: Unknown
% 50.99/8.57 % (30725)Termination phase: Saturation
% 50.99/8.57
% 50.99/8.57 % (30725)Memory used [KB]: 8955
% 50.99/8.57 % (30725)Time elapsed: 0.694 s
% 50.99/8.57 % (30725)Instructions burned: 2346 (million)
% 50.99/8.57 % (30725)------------------------------
% 50.99/8.57 % (30725)------------------------------
% 50.99/8.58 % (30731)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_30182 for (2929ds/1871Mi)
% 50.99/8.59 % (30730)Instruction limit reached!
% 50.99/8.59 % (30730)------------------------------
% 50.99/8.59 % (30730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.99/8.59 % (30730)Termination reason: Unknown
% 50.99/8.59 % (30730)Termination phase: Saturation
% 50.99/8.59
% 50.99/8.59 % (30730)Memory used [KB]: 8571
% 50.99/8.59 % (30730)Time elapsed: 0.125 s
% 50.99/8.59 % (30730)Instructions burned: 408 (million)
% 50.99/8.59 % (30730)------------------------------
% 50.99/8.59 % (30730)------------------------------
% 51.40/8.60 % (30732)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_30182 for (2928ds/1194Mi)
% 51.40/8.66 % (30723)Instruction limit reached!
% 51.40/8.66 % (30723)------------------------------
% 51.40/8.66 % (30723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.40/8.66 % (30723)Termination reason: Unknown
% 51.40/8.66 % (30723)Termination phase: Saturation
% 51.40/8.66
% 51.40/8.66 % (30723)Memory used [KB]: 13304
% 51.40/8.66 % (30723)Time elapsed: 1.054 s
% 51.40/8.66 % (30723)Instructions burned: 3619 (million)
% 51.40/8.66 % (30723)------------------------------
% 51.40/8.66 % (30723)------------------------------
% 51.40/8.67 % (30733)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_30182 for (2928ds/474Mi)
% 51.69/8.80 % (30729)Instruction limit reached!
% 51.69/8.80 % (30729)------------------------------
% 51.69/8.80 % (30729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.69/8.80 % (30729)Termination reason: Unknown
% 51.69/8.80 % (30729)Termination phase: Saturation
% 51.69/8.80
% 51.69/8.80 % (30729)Memory used [KB]: 10618
% 51.69/8.80 % (30729)Time elapsed: 0.343 s
% 51.69/8.80 % (30729)Instructions burned: 1102 (million)
% 51.69/8.80 % (30729)------------------------------
% 51.69/8.80 % (30729)------------------------------
% 51.69/8.81 % (30733)Instruction limit reached!
% 51.69/8.81 % (30733)------------------------------
% 51.69/8.81 % (30733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.69/8.81 % (30733)Termination reason: Unknown
% 51.69/8.81 % (30733)Termination phase: Saturation
% 51.69/8.81
% 51.69/8.81 % (30733)Memory used [KB]: 8187
% 51.69/8.81 % (30733)Time elapsed: 0.144 s
% 51.69/8.81 % (30733)Instructions burned: 475 (million)
% 51.69/8.81 % (30733)------------------------------
% 51.69/8.81 % (30733)------------------------------
% 51.69/8.81 % (30734)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_30182 for (2926ds/3115Mi)
% 51.69/8.82 % (30735)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_30182 for (2926ds/831Mi)
% 52.28/8.96 % (30732)Instruction limit reached!
% 52.28/8.96 % (30732)------------------------------
% 52.28/8.96 % (30732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.28/8.96 % (30732)Termination reason: Unknown
% 52.28/8.96 % (30732)Termination phase: Saturation
% 52.28/8.96
% 52.28/8.96 % (30732)Memory used [KB]: 9083
% 52.28/8.96 % (30732)Time elapsed: 0.359 s
% 52.28/8.96 % (30732)Instructions burned: 1195 (million)
% 52.28/8.96 % (30732)------------------------------
% 52.28/8.96 % (30732)------------------------------
% 52.28/8.97 % (30736)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_30182 for (2925ds/1188Mi)
% 55.44/9.06 % (30735)Instruction limit reached!
% 55.44/9.06 % (30735)------------------------------
% 55.44/9.06 % (30735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.44/9.06 % (30735)Termination reason: Unknown
% 55.44/9.06 % (30735)Termination phase: Saturation
% 55.44/9.06
% 55.44/9.06 % (30735)Memory used [KB]: 10618
% 55.44/9.06 % (30735)Time elapsed: 0.244 s
% 55.44/9.06 % (30735)Instructions burned: 834 (million)
% 55.44/9.06 % (30735)------------------------------
% 55.44/9.06 % (30735)------------------------------
% 55.44/9.07 % (30737)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_30182 for (2924ds/2868Mi)
% 56.10/9.13 % (30731)Instruction limit reached!
% 56.10/9.13 % (30731)------------------------------
% 56.10/9.13 % (30731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.10/9.13 % (30731)Termination reason: Unknown
% 56.10/9.13 % (30731)Termination phase: Saturation
% 56.10/9.13
% 56.10/9.13 % (30731)Memory used [KB]: 8827
% 56.10/9.13 % (30731)Time elapsed: 0.557 s
% 56.10/9.13 % (30731)Instructions burned: 1871 (million)
% 56.10/9.13 % (30731)------------------------------
% 56.10/9.13 % (30731)------------------------------
% 56.10/9.14 % (30737)Refutation not found, incomplete strategy
% 56.10/9.14 % (30737)------------------------------
% 56.10/9.14 % (30737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.10/9.14 % (30737)Termination reason: Refutation not found, incomplete strategy
% 56.10/9.14
% 56.10/9.14
% 56.10/9.14 % (30737)Memory used [KB]: 7803
% 56.10/9.14 % (30737)Time elapsed: 0.065 s
% 56.10/9.14 % (30737)Instructions burned: 235 (million)
% 56.10/9.14 % (30737)------------------------------
% 56.10/9.14 % (30737)------------------------------
% 56.10/9.14 % (30738)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_30182 for (2923ds/1516Mi)
% 56.10/9.15 % (30739)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_30182 for (2923ds/2321Mi)
% 56.10/9.16 % (30716)Instruction limit reached!
% 56.10/9.16 % (30716)------------------------------
% 56.10/9.16 % (30716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.10/9.16 % (30716)Termination reason: Unknown
% 56.10/9.16 % (30716)Termination phase: Saturation
% 56.10/9.16
% 56.10/9.16 % (30716)Memory used [KB]: 13560
% 56.10/9.16 % (30716)Time elapsed: 2.266 s
% 56.10/9.16 % (30716)Instructions burned: 7680 (million)
% 56.10/9.16 % (30716)------------------------------
% 56.10/9.16 % (30716)------------------------------
% 56.10/9.17 % (30740)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_30182 for (2923ds/2812Mi)
% 56.53/9.22 % (30739)Refutation not found, incomplete strategy
% 56.53/9.22 % (30739)------------------------------
% 56.53/9.22 % (30739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.53/9.22 % (30739)Termination reason: Refutation not found, incomplete strategy
% 56.53/9.22
% 56.53/9.22
% 56.53/9.22 % (30739)Memory used [KB]: 7931
% 56.53/9.22 % (30739)Time elapsed: 0.069 s
% 56.53/9.22 % (30739)Instructions burned: 249 (million)
% 56.53/9.22 % (30739)------------------------------
% 56.53/9.22 % (30739)------------------------------
% 56.53/9.23 % (30741)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_30182 for (2922ds/4604Mi)
% 56.53/9.26 % (30727)Instruction limit reached!
% 56.53/9.26 % (30727)------------------------------
% 56.53/9.26 % (30727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.53/9.26 % (30727)Termination reason: Unknown
% 56.53/9.26 % (30727)Termination phase: Saturation
% 56.53/9.26
% 56.53/9.26 % (30727)Memory used [KB]: 14456
% 56.53/9.26 % (30727)Time elapsed: 1.088 s
% 56.53/9.26 % (30727)Instructions burned: 3710 (million)
% 56.53/9.26 % (30727)------------------------------
% 56.53/9.26 % (30727)------------------------------
% 56.53/9.27 % (30742)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_30182 for (2922ds/2678Mi)
% 56.99/9.31 % (30736)Instruction limit reached!
% 56.99/9.31 % (30736)------------------------------
% 56.99/9.31 % (30736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.99/9.31 % (30736)Termination reason: Unknown
% 56.99/9.31 % (30736)Termination phase: Saturation
% 56.99/9.31
% 56.99/9.31 % (30736)Memory used [KB]: 10874
% 56.99/9.31 % (30736)Time elapsed: 0.346 s
% 56.99/9.31 % (30736)Instructions burned: 1189 (million)
% 56.99/9.31 % (30736)------------------------------
% 56.99/9.31 % (30736)------------------------------
% 56.99/9.32 % (30743)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_30182 for (2921ds/643Mi)
% 57.42/9.51 % (30743)Instruction limit reached!
% 57.42/9.51 % (30743)------------------------------
% 57.42/9.51 % (30743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.42/9.51 % (30743)Termination reason: Unknown
% 57.42/9.51 % (30743)Termination phase: Saturation
% 57.42/9.51
% 57.42/9.51 % (30743)Memory used [KB]: 9466
% 57.42/9.51 % (30743)Time elapsed: 0.186 s
% 57.42/9.51 % (30743)Instructions burned: 643 (million)
% 57.42/9.51 % (30743)------------------------------
% 57.42/9.51 % (30743)------------------------------
% 57.42/9.52 % (30744)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_30182 for (2919ds/458Mi)
% 57.42/9.55 % (30738)Instruction limit reached!
% 57.42/9.55 % (30738)------------------------------
% 57.42/9.55 % (30738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.42/9.55 % (30738)Termination reason: Unknown
% 57.42/9.55 % (30738)Termination phase: Saturation
% 57.42/9.55
% 57.42/9.55 % (30738)Memory used [KB]: 7803
% 57.42/9.55 % (30738)Time elapsed: 0.414 s
% 57.42/9.55 % (30738)Instructions burned: 1518 (million)
% 57.42/9.55 % (30738)------------------------------
% 57.42/9.55 % (30738)------------------------------
% 57.42/9.56 % (30745)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_30182 for (2919ds/2546Mi)
% 58.24/9.65 % (30744)Instruction limit reached!
% 58.24/9.65 % (30744)------------------------------
% 58.24/9.65 % (30744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.24/9.65 % (30744)Termination reason: Unknown
% 58.24/9.65 % (30744)Termination phase: Saturation
% 58.24/9.65
% 58.24/9.65 % (30744)Memory used [KB]: 8699
% 58.24/9.65 % (30744)Time elapsed: 0.134 s
% 58.24/9.65 % (30744)Instructions burned: 458 (million)
% 58.24/9.65 % (30744)------------------------------
% 58.24/9.65 % (30744)------------------------------
% 58.24/9.66 % (30746)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_30182 for (2918ds/1432Mi)
% 58.58/9.75 % (30734)Instruction limit reached!
% 58.58/9.75 % (30734)------------------------------
% 58.58/9.75 % (30734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.58/9.75 % (30734)Termination reason: Unknown
% 58.58/9.75 % (30734)Termination phase: Saturation
% 58.58/9.75
% 58.58/9.75 % (30734)Memory used [KB]: 12153
% 58.58/9.75 % (30734)Time elapsed: 0.937 s
% 58.58/9.75 % (30734)Instructions burned: 3117 (million)
% 58.58/9.75 % (30734)------------------------------
% 58.58/9.75 % (30734)------------------------------
% 58.58/9.76 % (30747)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_30182 for (2917ds/386Mi)
% 58.75/9.87 % (30747)Instruction limit reached!
% 58.75/9.87 % (30747)------------------------------
% 58.75/9.87 % (30747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.75/9.87 % (30747)Termination reason: Unknown
% 58.75/9.87 % (30747)Termination phase: Saturation
% 58.75/9.87
% 58.75/9.87 % (30747)Memory used [KB]: 8699
% 58.75/9.87 % (30747)Time elapsed: 0.109 s
% 58.75/9.87 % (30747)Instructions burned: 388 (million)
% 58.75/9.87 % (30747)------------------------------
% 58.75/9.87 % (30747)------------------------------
% 58.75/9.88 % (30748)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_30182 for (2916ds/360Mi)
% 58.97/9.98 % (30748)Instruction limit reached!
% 58.97/9.98 % (30748)------------------------------
% 58.97/9.98 % (30748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.97/9.98 % (30748)Termination reason: Unknown
% 58.97/9.98 % (30748)Termination phase: Saturation
% 58.97/9.98
% 58.97/9.98 % (30748)Memory used [KB]: 8571
% 58.97/9.98 % (30748)Time elapsed: 0.100 s
% 58.97/9.98 % (30748)Instructions burned: 362 (million)
% 58.97/9.98 % (30748)------------------------------
% 58.97/9.98 % (30748)------------------------------
% 58.97/9.99 % (30749)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_30182 for (2915ds/5446Mi)
% 58.97/10.02 % (30740)Instruction limit reached!
% 58.97/10.02 % (30740)------------------------------
% 58.97/10.02 % (30740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.97/10.02 % (30740)Termination reason: Unknown
% 58.97/10.02 % (30740)Termination phase: Saturation
% 58.97/10.02
% 58.97/10.02 % (30740)Memory used [KB]: 9466
% 58.97/10.02 % (30740)Time elapsed: 0.844 s
% 58.97/10.02 % (30740)Instructions burned: 2813 (million)
% 58.97/10.02 % (30740)------------------------------
% 58.97/10.02 % (30740)------------------------------
% 62.47/10.03 % (30750)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_30182 for (2914ds/2573Mi)
% 62.47/10.03 % (30746)Instruction limit reached!
% 62.47/10.03 % (30746)------------------------------
% 62.47/10.03 % (30746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.47/10.03 % (30746)Termination reason: Unknown
% 62.47/10.03 % (30746)Termination phase: Saturation
% 62.47/10.03
% 62.47/10.03 % (30746)Memory used [KB]: 10106
% 62.47/10.03 % (30746)Time elapsed: 0.392 s
% 62.47/10.03 % (30746)Instructions burned: 1432 (million)
% 62.47/10.03 % (30746)------------------------------
% 62.47/10.03 % (30746)------------------------------
% 62.47/10.04 % (30751)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_30182 for (2914ds/2655Mi)
% 62.47/10.05 % (30742)Instruction limit reached!
% 62.47/10.05 % (30742)------------------------------
% 62.47/10.05 % (30742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.47/10.05 % (30742)Termination reason: Unknown
% 62.47/10.05 % (30742)Termination phase: Saturation
% 62.47/10.05
% 62.47/10.05 % (30742)Memory used [KB]: 12153
% 62.47/10.05 % (30742)Time elapsed: 0.783 s
% 62.47/10.05 % (30742)Instructions burned: 2679 (million)
% 62.47/10.05 % (30742)------------------------------
% 62.47/10.05 % (30742)------------------------------
% 62.47/10.06 % (30752)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_30182 for (2914ds/2781Mi)
% 63.23/10.27 % (30726)Instruction limit reached!
% 63.23/10.27 % (30726)------------------------------
% 63.23/10.27 % (30726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.23/10.27 % (30726)Termination reason: Unknown
% 63.23/10.27 % (30726)Termination phase: Saturation
% 63.23/10.27
% 63.23/10.27 % (30726)Memory used [KB]: 11129
% 63.23/10.27 % (30726)Time elapsed: 2.143 s
% 63.23/10.27 % (30726)Instructions burned: 7258 (million)
% 63.23/10.27 % (30726)------------------------------
% 63.23/10.27 % (30726)------------------------------
% 63.23/10.29 % (30753)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_30182 for (2912ds/307Mi)
% 63.61/10.30 % (30745)Instruction limit reached!
% 63.61/10.30 % (30745)------------------------------
% 63.61/10.30 % (30745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.61/10.30 % (30745)Termination reason: Unknown
% 63.61/10.30 % (30745)Termination phase: Saturation
% 63.61/10.30
% 63.61/10.30 % (30745)Memory used [KB]: 8955
% 63.61/10.30 % (30745)Time elapsed: 0.758 s
% 63.61/10.30 % (30745)Instructions burned: 2546 (million)
% 63.61/10.30 % (30745)------------------------------
% 63.61/10.30 % (30745)------------------------------
% 63.61/10.31 % (30754)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_30182 for (2911ds/1548Mi)
% 63.61/10.37 % (30753)Instruction limit reached!
% 63.61/10.37 % (30753)------------------------------
% 63.61/10.37 % (30753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.61/10.37 % (30753)Termination reason: Unknown
% 63.61/10.37 % (30753)Termination phase: Saturation
% 63.61/10.37
% 63.61/10.37 % (30753)Memory used [KB]: 7803
% 63.61/10.37 % (30753)Time elapsed: 0.087 s
% 63.61/10.37 % (30753)Instructions burned: 307 (million)
% 63.61/10.37 % (30753)------------------------------
% 63.61/10.37 % (30753)------------------------------
% 63.61/10.38 % (30755)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_30182 for (2911ds/5214Mi)
% 64.32/10.61 % (30741)Instruction limit reached!
% 64.32/10.61 % (30741)------------------------------
% 64.32/10.61 % (30741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.32/10.61 % (30741)Termination reason: Unknown
% 64.32/10.61 % (30741)Termination phase: Saturation
% 64.32/10.61
% 64.32/10.61 % (30741)Memory used [KB]: 14839
% 64.32/10.61 % (30741)Time elapsed: 1.380 s
% 64.32/10.61 % (30741)Instructions burned: 4607 (million)
% 64.32/10.61 % (30741)------------------------------
% 64.32/10.61 % (30741)------------------------------
% 64.32/10.62 % (30756)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_30182 for (2908ds/3201Mi)
% 64.45/10.75 % (30754)Instruction limit reached!
% 64.45/10.75 % (30754)------------------------------
% 64.45/10.75 % (30754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.45/10.75 % (30754)Termination reason: Unknown
% 64.45/10.75 % (30754)Termination phase: Saturation
% 64.45/10.75
% 64.45/10.75 % (30754)Memory used [KB]: 8443
% 64.45/10.75 % (30754)Time elapsed: 0.439 s
% 64.45/10.75 % (30754)Instructions burned: 1548 (million)
% 64.45/10.75 % (30754)------------------------------
% 64.45/10.75 % (30754)------------------------------
% 64.45/10.76 % (30757)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_30182 for (2907ds/454Mi)
% 65.00/10.80 % (30750)Instruction limit reached!
% 65.00/10.80 % (30750)------------------------------
% 65.00/10.80 % (30750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.00/10.80 % (30750)Termination reason: Unknown
% 65.00/10.80 % (30750)Termination phase: Saturation
% 65.00/10.80
% 65.00/10.80 % (30750)Memory used [KB]: 12153
% 65.00/10.80 % (30750)Time elapsed: 0.777 s
% 65.00/10.80 % (30750)Instructions burned: 2575 (million)
% 65.00/10.80 % (30750)------------------------------
% 65.00/10.80 % (30750)------------------------------
% 65.00/10.81 % (30751)Instruction limit reached!
% 65.00/10.81 % (30751)------------------------------
% 65.00/10.81 % (30751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.00/10.81 % (30751)Termination reason: Unknown
% 65.00/10.81 % (30751)Termination phase: Saturation
% 65.00/10.81
% 65.00/10.81 % (30751)Memory used [KB]: 19061
% 65.00/10.81 % (30751)Time elapsed: 0.770 s
% 65.00/10.81 % (30751)Instructions burned: 2658 (million)
% 65.00/10.81 % (30751)------------------------------
% 65.00/10.81 % (30751)------------------------------
% 65.00/10.81 % (30758)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_30182 for (2906ds/3049Mi)
% 65.00/10.82 % (30759)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_30182 for (2906ds/7311Mi)
% 65.00/10.89 % (30757)Instruction limit reached!
% 65.00/10.89 % (30757)------------------------------
% 65.00/10.89 % (30757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.00/10.89 % (30757)Termination reason: Unknown
% 65.00/10.89 % (30757)Termination phase: Saturation
% 65.00/10.89
% 65.00/10.89 % (30757)Memory used [KB]: 12537
% 65.00/10.89 % (30757)Time elapsed: 0.131 s
% 65.00/10.89 % (30757)Instructions burned: 456 (million)
% 65.00/10.89 % (30757)------------------------------
% 65.00/10.89 % (30757)------------------------------
% 66.81/10.90 % (30760)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_30182 for (2905ds/6804Mi)
% 66.81/10.91 % (30752)Instruction limit reached!
% 66.81/10.91 % (30752)------------------------------
% 66.81/10.91 % (30752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.81/10.91 % (30752)Termination reason: Unknown
% 66.81/10.91 % (30752)Termination phase: Saturation
% 66.81/10.91
% 66.81/10.91 % (30752)Memory used [KB]: 6268
% 66.81/10.91 % (30752)Time elapsed: 0.853 s
% 66.81/10.91 % (30752)Instructions burned: 2784 (million)
% 66.81/10.91 % (30752)------------------------------
% 66.81/10.91 % (30752)------------------------------
% 66.81/10.92 % (30761)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_30182 for (2905ds/1683Mi)
% 72.11/11.42 % (30761)Instruction limit reached!
% 72.11/11.42 % (30761)------------------------------
% 72.11/11.42 % (30761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.11/11.42 % (30761)Termination reason: Unknown
% 72.11/11.42 % (30761)Termination phase: Saturation
% 72.11/11.42
% 72.11/11.42 % (30761)Memory used [KB]: 8699
% 72.11/11.42 % (30761)Time elapsed: 0.502 s
% 72.11/11.42 % (30761)Instructions burned: 1683 (million)
% 72.11/11.42 % (30761)------------------------------
% 72.11/11.42 % (30761)------------------------------
% 72.11/11.43 % (30762)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_30182 for (2900ds/4688Mi)
% 72.76/11.58 % (30756)Instruction limit reached!
% 72.76/11.58 % (30756)------------------------------
% 72.76/11.58 % (30756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.76/11.58 % (30756)Termination reason: Unknown
% 72.76/11.58 % (30756)Termination phase: Saturation
% 72.76/11.58
% 72.76/11.58 % (30756)Memory used [KB]: 11641
% 72.76/11.58 % (30756)Time elapsed: 0.968 s
% 72.76/11.58 % (30756)Instructions burned: 3202 (million)
% 72.76/11.58 % (30756)------------------------------
% 72.76/11.58 % (30756)------------------------------
% 72.76/11.59 % (30763)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_30182 for (2898ds/2207Mi)
% 73.36/11.67 % (30749)Instruction limit reached!
% 73.36/11.67 % (30749)------------------------------
% 73.36/11.67 % (30749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.36/11.67 % (30749)Termination reason: Unknown
% 73.36/11.67 % (30749)Termination phase: Saturation
% 73.36/11.67
% 73.36/11.67 % (30749)Memory used [KB]: 13816
% 73.36/11.67 % (30749)Time elapsed: 1.706 s
% 73.36/11.67 % (30749)Instructions burned: 5448 (million)
% 73.36/11.67 % (30749)------------------------------
% 73.36/11.67 % (30749)------------------------------
% 73.36/11.68 % (30764)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_30182 for (2898ds/8216Mi)
% 73.84/11.72 % (30758)Instruction limit reached!
% 73.84/11.72 % (30758)------------------------------
% 73.84/11.72 % (30758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.84/11.72 % (30758)Termination reason: Unknown
% 73.84/11.72 % (30758)Termination phase: Saturation
% 73.84/11.72
% 73.84/11.72 % (30758)Memory used [KB]: 9722
% 73.84/11.72 % (30758)Time elapsed: 0.906 s
% 73.84/11.72 % (30758)Instructions burned: 3049 (million)
% 73.84/11.72 % (30758)------------------------------
% 73.84/11.72 % (30758)------------------------------
% 73.84/11.73 % (30765)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_30182 for (2897ds/430Mi)
% 74.16/11.86 % (30765)Instruction limit reached!
% 74.16/11.86 % (30765)------------------------------
% 74.16/11.86 % (30765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.16/11.86 % (30765)Termination reason: Unknown
% 74.16/11.86 % (30765)Termination phase: Saturation
% 74.16/11.86
% 74.16/11.86 % (30765)Memory used [KB]: 8571
% 74.16/11.86 % (30765)Time elapsed: 0.129 s
% 74.16/11.86 % (30765)Instructions burned: 433 (million)
% 74.16/11.86 % (30765)------------------------------
% 74.16/11.86 % (30765)------------------------------
% 74.16/11.87 % (30766)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_30182 for (2896ds/2012Mi)
% 74.60/11.96 % (30755)Instruction limit reached!
% 74.60/11.96 % (30755)------------------------------
% 74.60/11.96 % (30755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.60/11.96 % (30755)Termination reason: Unknown
% 74.60/11.96 % (30755)Termination phase: Saturation
% 74.60/11.96
% 74.60/11.96 % (30755)Memory used [KB]: 14583
% 74.60/11.96 % (30755)Time elapsed: 1.578 s
% 74.60/11.96 % (30755)Instructions burned: 5215 (million)
% 74.60/11.96 % (30755)------------------------------
% 74.60/11.96 % (30755)------------------------------
% 74.60/11.97 % (30767)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_30182 for (2895ds/631Mi)
% 77.20/12.17 % (30767)Instruction limit reached!
% 77.20/12.17 % (30767)------------------------------
% 77.20/12.17 % (30767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.20/12.17 % (30767)Termination reason: Unknown
% 77.20/12.17 % (30767)Termination phase: Saturation
% 77.20/12.17
% 77.20/12.17 % (30767)Memory used [KB]: 10106
% 77.20/12.17 % (30767)Time elapsed: 0.199 s
% 77.20/12.17 % (30767)Instructions burned: 631 (million)
% 77.20/12.17 % (30767)------------------------------
% 77.20/12.17 % (30767)------------------------------
% 77.20/12.18 % (30768)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_30182 for (2893ds/8785Mi)
% 77.70/12.28 % (30763)Instruction limit reached!
% 77.70/12.28 % (30763)------------------------------
% 77.70/12.28 % (30763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.70/12.28 % (30763)Termination reason: Unknown
% 77.70/12.28 % (30763)Termination phase: Saturation
% 77.70/12.28
% 77.70/12.28 % (30763)Memory used [KB]: 9978
% 77.70/12.28 % (30763)Time elapsed: 0.687 s
% 77.70/12.28 % (30763)Instructions burned: 2210 (million)
% 77.70/12.28 % (30763)------------------------------
% 77.70/12.28 % (30763)------------------------------
% 77.70/12.29 % (30769)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_30182 for (2891ds/739Mi)
% 78.80/12.47 % (30766)Instruction limit reached!
% 78.80/12.47 % (30766)------------------------------
% 78.80/12.47 % (30766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.80/12.47 % (30766)Termination reason: Unknown
% 78.80/12.47 % (30766)Termination phase: Saturation
% 78.80/12.47
% 78.80/12.47 % (30766)Memory used [KB]: 15991
% 78.80/12.47 % (30766)Time elapsed: 0.601 s
% 78.80/12.47 % (30766)Instructions burned: 2013 (million)
% 78.80/12.47 % (30766)------------------------------
% 78.80/12.47 % (30766)------------------------------
% 78.80/12.48 % (30770)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_30182 for (2890ds/5473Mi)
% 79.28/12.51 % (30769)Instruction limit reached!
% 79.28/12.51 % (30769)------------------------------
% 79.28/12.51 % (30769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.28/12.51 % (30769)Termination reason: Unknown
% 79.28/12.51 % (30769)Termination phase: Saturation
% 79.28/12.51
% 79.28/12.51 % (30769)Memory used [KB]: 8955
% 79.28/12.51 % (30769)Time elapsed: 0.225 s
% 79.28/12.51 % (30769)Instructions burned: 740 (million)
% 79.28/12.51 % (30769)------------------------------
% 79.28/12.51 % (30769)------------------------------
% 79.28/12.52 % (30771)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_30182 for (2889ds/43570Mi)
% 80.71/12.82 % (30762)Instruction limit reached!
% 80.71/12.82 % (30762)------------------------------
% 80.71/12.82 % (30762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.71/12.82 % (30762)Termination reason: Unknown
% 80.71/12.82 % (30762)Termination phase: Saturation
% 80.71/12.82
% 80.71/12.82 % (30762)Memory used [KB]: 9978
% 80.71/12.82 % (30762)Time elapsed: 1.391 s
% 80.71/12.82 % (30762)Instructions burned: 4688 (million)
% 80.71/12.82 % (30762)------------------------------
% 80.71/12.82 % (30762)------------------------------
% 80.71/12.83 % (30772)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_30182 for (2886ds/8382Mi)
% 80.71/12.84 % (30760)Instruction limit reached!
% 80.71/12.84 % (30760)------------------------------
% 80.71/12.84 % (30760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.71/12.84 % (30760)Termination reason: Unknown
% 80.71/12.84 % (30760)Termination phase: Saturation
% 80.71/12.84
% 80.71/12.84 % (30760)Memory used [KB]: 11385
% 80.71/12.84 % (30760)Time elapsed: 1.946 s
% 80.71/12.84 % (30760)Instructions burned: 6805 (million)
% 80.71/12.84 % (30760)------------------------------
% 80.71/12.84 % (30760)------------------------------
% 80.71/12.85 % (30773)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_30182 for (2886ds/407Mi)
% 80.71/12.89 % (30759)Instruction limit reached!
% 80.71/12.89 % (30759)------------------------------
% 80.71/12.89 % (30759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.71/12.89 % (30759)Termination reason: Unknown
% 80.71/12.89 % (30759)Termination phase: Saturation
% 80.71/12.89
% 80.71/12.89 % (30759)Memory used [KB]: 13048
% 80.71/12.89 % (30759)Time elapsed: 2.076 s
% 80.71/12.89 % (30759)Instructions burned: 7312 (million)
% 80.71/12.89 % (30759)------------------------------
% 80.71/12.89 % (30759)------------------------------
% 81.03/12.90 % (30774)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_30182 for (2885ds/2971Mi)
% 81.03/12.97 % (30774)Refutation not found, incomplete strategy
% 81.03/12.97 % (30774)------------------------------
% 81.03/12.97 % (30774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.03/12.97 % (30774)Termination reason: Refutation not found, incomplete strategy
% 81.03/12.97
% 81.03/12.97
% 81.03/12.97 % (30774)Memory used [KB]: 7803
% 81.03/12.97 % (30774)Time elapsed: 0.067 s
% 81.03/12.97 % (30774)Instructions burned: 235 (million)
% 81.03/12.97 % (30774)------------------------------
% 81.03/12.97 % (30774)------------------------------
% 81.03/12.98 % (30773)Instruction limit reached!
% 81.03/12.98 % (30773)------------------------------
% 81.03/12.98 % (30773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.03/12.98 % (30773)Termination reason: Unknown
% 81.03/12.98 % (30773)Termination phase: Saturation
% 81.03/12.98
% 81.03/12.98 % (30773)Memory used [KB]: 8699
% 81.03/12.98 % (30773)Time elapsed: 0.125 s
% 81.03/12.98 % (30773)Instructions burned: 408 (million)
% 81.03/12.98 % (30773)------------------------------
% 81.03/12.98 % (30773)------------------------------
% 81.03/12.98 % (30775)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_30182 for (2885ds/9822Mi)
% 81.03/12.99 % (30776)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_30182 for (2885ds/8425Mi)
% 90.55/14.03 % (30764)Instruction limit reached!
% 90.55/14.03 % (30764)------------------------------
% 90.55/14.03 % (30764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.55/14.03 % (30764)Termination reason: Unknown
% 90.55/14.03 % (30764)Termination phase: Saturation
% 90.55/14.03
% 90.55/14.03 % (30764)Memory used [KB]: 11257
% 90.55/14.03 % (30764)Time elapsed: 2.352 s
% 90.55/14.03 % (30764)Instructions burned: 8217 (million)
% 90.55/14.03 % (30764)------------------------------
% 90.55/14.03 % (30764)------------------------------
% 90.55/14.04 % (30777)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_30182 for (2874ds/3107Mi)
% 90.55/14.07 % (30770)Instruction limit reached!
% 90.55/14.07 % (30770)------------------------------
% 90.55/14.07 % (30770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.55/14.07 % (30770)Termination reason: Unknown
% 90.55/14.07 % (30770)Termination phase: Saturation
% 90.55/14.07
% 90.55/14.07 % (30770)Memory used [KB]: 10234
% 90.55/14.07 % (30770)Time elapsed: 1.596 s
% 90.55/14.07 % (30770)Instructions burned: 5474 (million)
% 90.55/14.07 % (30770)------------------------------
% 90.55/14.07 % (30770)------------------------------
% 90.55/14.08 % (30778)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_30182 for (2874ds/7967Mi)
% 91.13/14.15 % (30778)Refutation not found, incomplete strategy
% 91.13/14.15 % (30778)------------------------------
% 91.13/14.15 % (30778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.13/14.15 % (30778)Termination reason: Refutation not found, incomplete strategy
% 91.13/14.15
% 91.13/14.15
% 91.13/14.15 % (30778)Memory used [KB]: 7803
% 91.13/14.15 % (30778)Time elapsed: 0.066 s
% 91.13/14.15 % (30778)Instructions burned: 235 (million)
% 91.13/14.15 % (30778)------------------------------
% 91.13/14.15 % (30778)------------------------------
% 91.13/14.16 % (30779)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_30182 for (2873ds/3629Mi)
% 94.08/14.76 % (30768)Instruction limit reached!
% 94.08/14.76 % (30768)------------------------------
% 94.08/14.76 % (30768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.08/14.76 % (30768)Termination reason: Unknown
% 94.08/14.76 % (30768)Termination phase: Saturation
% 94.08/14.76
% 94.08/14.76 % (30768)Memory used [KB]: 13944
% 94.08/14.76 % (30768)Time elapsed: 2.584 s
% 94.08/14.76 % (30768)Instructions burned: 8785 (million)
% 94.08/14.76 % (30768)------------------------------
% 94.08/14.76 % (30768)------------------------------
% 94.08/14.77 % (30937)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_30182 for (2867ds/939Mi)
% 94.56/14.89 % (30777)Instruction limit reached!
% 94.56/14.89 % (30777)------------------------------
% 94.56/14.89 % (30777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.56/14.89 % (30777)Termination reason: Unknown
% 94.56/14.89 % (30777)Termination phase: Saturation
% 94.56/14.89
% 94.56/14.89 % (30777)Memory used [KB]: 11129
% 94.56/14.89 % (30777)Time elapsed: 0.852 s
% 94.56/14.89 % (30777)Instructions burned: 3107 (million)
% 94.56/14.89 % (30777)------------------------------
% 94.56/14.89 % (30777)------------------------------
% 95.81/14.90 % (31006)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_30182 for (2865ds/1188Mi)
% 97.54/15.05 % (30937)Instruction limit reached!
% 97.54/15.05 % (30937)------------------------------
% 97.54/15.05 % (30937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.54/15.05 % (30937)Termination reason: Unknown
% 97.54/15.05 % (30937)Termination phase: Saturation
% 97.54/15.05
% 97.54/15.05 % (30937)Memory used [KB]: 9338
% 97.54/15.05 % (30937)Time elapsed: 0.285 s
% 97.54/15.05 % (30937)Instructions burned: 941 (million)
% 97.54/15.05 % (30937)------------------------------
% 97.54/15.05 % (30937)------------------------------
% 97.54/15.06 % (31051)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_30182 for (2864ds/3205Mi)
% 98.64/15.23 % (30779)Instruction limit reached!
% 98.64/15.23 % (30779)------------------------------
% 98.64/15.23 % (30779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.64/15.23 % (30779)Termination reason: Unknown
% 98.64/15.23 % (30779)Termination phase: Saturation
% 98.64/15.23
% 98.64/15.23 % (30779)Memory used [KB]: 12025
% 98.64/15.23 % (30779)Time elapsed: 1.077 s
% 98.64/15.23 % (30779)Instructions burned: 3630 (million)
% 98.64/15.23 % (30779)------------------------------
% 98.64/15.23 % (30779)------------------------------
% 98.64/15.24 % (31153)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_30182 for (2862ds/865Mi)
% 98.64/15.25 % (31006)Instruction limit reached!
% 98.64/15.25 % (31006)------------------------------
% 98.64/15.25 % (31006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.64/15.25 % (31006)Termination reason: Unknown
% 98.64/15.25 % (31006)Termination phase: Saturation
% 98.64/15.25
% 98.64/15.25 % (31006)Memory used [KB]: 10874
% 98.64/15.25 % (31006)Time elapsed: 0.356 s
% 98.64/15.25 % (31006)Instructions burned: 1189 (million)
% 98.64/15.25 % (31006)------------------------------
% 98.64/15.25 % (31006)------------------------------
% 98.64/15.26 % (30772)Instruction limit reached!
% 98.64/15.26 % (30772)------------------------------
% 98.64/15.26 % (30772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.64/15.26 % (30772)Termination reason: Unknown
% 98.64/15.26 % (30772)Termination phase: Saturation
% 98.64/15.26
% 98.64/15.26 % (30772)Memory used [KB]: 11257
% 98.64/15.26 % (30772)Time elapsed: 2.428 s
% 98.64/15.26 % (30772)Instructions burned: 8382 (million)
% 98.64/15.26 % (30772)------------------------------
% 98.64/15.26 % (30772)------------------------------
% 98.64/15.27 % (31161)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_30182 for (2862ds/7469Mi)
% 98.64/15.28 % (31162)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_30182 for (2862ds/4165Mi)
% 99.42/15.41 % (30776)Instruction limit reached!
% 99.42/15.41 % (30776)------------------------------
% 99.42/15.41 % (30776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.42/15.41 % (30776)Termination reason: Unknown
% 99.42/15.41 % (30776)Termination phase: Saturation
% 99.42/15.41
% 99.42/15.41 % (30776)Memory used [KB]: 15095
% 99.42/15.41 % (30776)Time elapsed: 2.429 s
% 99.42/15.41 % (30776)Instructions burned: 8428 (million)
% 99.42/15.41 % (30776)------------------------------
% 99.42/15.41 % (30776)------------------------------
% 99.42/15.42 % (31177)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_30182 for (2860ds/13468Mi)
% 99.66/15.52 % (31153)Instruction limit reached!
% 99.66/15.52 % (31153)------------------------------
% 99.66/15.52 % (31153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.66/15.52 % (31153)Termination reason: Unknown
% 99.66/15.52 % (31153)Termination phase: Saturation
% 99.66/15.52
% 99.66/15.52 % (31153)Memory used [KB]: 9978
% 99.66/15.52 % (31153)Time elapsed: 0.276 s
% 99.66/15.52 % (31153)Instructions burned: 866 (million)
% 99.66/15.52 % (31153)------------------------------
% 99.66/15.52 % (31153)------------------------------
% 99.66/15.53 % (31223)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_30182 for (2859ds/2635Mi)
% 100.57/15.85 % (30775)Instruction limit reached!
% 100.57/15.85 % (30775)------------------------------
% 100.57/15.85 % (30775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.57/15.85 % (30775)Termination reason: Unknown
% 100.57/15.85 % (30775)Termination phase: Saturation
% 100.57/15.85
% 100.57/15.85 % (30775)Memory used [KB]: 15607
% 100.57/15.85 % (30775)Time elapsed: 2.869 s
% 100.57/15.85 % (30775)Instructions burned: 9825 (million)
% 100.57/15.85 % (30775)------------------------------
% 100.57/15.85 % (30775)------------------------------
% 100.57/15.86 % (31353)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_30182 for (2856ds/631Mi)
% 104.57/16.04 % (31051)Instruction limit reached!
% 104.57/16.04 % (31051)------------------------------
% 104.57/16.04 % (31051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.57/16.04 % (31051)Termination reason: Unknown
% 104.57/16.04 % (31051)Termination phase: Saturation
% 104.57/16.04
% 104.57/16.04 % (31051)Memory used [KB]: 12537
% 104.57/16.04 % (31051)Time elapsed: 0.977 s
% 104.57/16.04 % (31051)Instructions burned: 3207 (million)
% 104.57/16.04 % (31051)------------------------------
% 104.57/16.04 % (31051)------------------------------
% 104.57/16.04 % (31353)Instruction limit reached!
% 104.57/16.04 % (31353)------------------------------
% 104.57/16.04 % (31353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.57/16.04 % (31353)Termination reason: Unknown
% 104.57/16.04 % (31353)Termination phase: Saturation
% 104.57/16.04
% 104.57/16.04 % (31353)Memory used [KB]: 9466
% 104.57/16.04 % (31353)Time elapsed: 0.185 s
% 104.57/16.04 % (31353)Instructions burned: 631 (million)
% 104.57/16.04 % (31353)------------------------------
% 104.57/16.04 % (31353)------------------------------
% 104.57/16.05 % (31397)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_30182 for (2854ds/15557Mi)
% 104.57/16.05 % (31398)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_30182 for (2854ds/2142Mi)
% 106.00/16.32 % (31223)Instruction limit reached!
% 106.00/16.32 % (31223)------------------------------
% 106.00/16.32 % (31223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.00/16.32 % (31223)Termination reason: Unknown
% 106.00/16.32 % (31223)Termination phase: Saturation
% 106.00/16.32
% 106.00/16.32 % (31223)Memory used [KB]: 12665
% 106.00/16.32 % (31223)Time elapsed: 0.797 s
% 106.00/16.32 % (31223)Instructions burned: 2637 (million)
% 106.00/16.32 % (31223)------------------------------
% 106.00/16.32 % (31223)------------------------------
% 106.00/16.33 % (31399)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_30182 for (2851ds/5624Mi)
% 106.85/16.52 % (31162)Instruction limit reached!
% 106.85/16.52 % (31162)------------------------------
% 106.85/16.52 % (31162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.85/16.52 % (31162)Termination reason: Unknown
% 106.85/16.52 % (31162)Termination phase: Saturation
% 106.85/16.52
% 106.85/16.52 % (31162)Memory used [KB]: 9978
% 106.85/16.52 % (31162)Time elapsed: 1.239 s
% 106.85/16.52 % (31162)Instructions burned: 4167 (million)
% 106.85/16.52 % (31162)------------------------------
% 106.85/16.52 % (31162)------------------------------
% 106.85/16.53 % (31400)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_30182 for (2849ds/1665Mi)
% 107.19/16.69 % (31398)Instruction limit reached!
% 107.19/16.69 % (31398)------------------------------
% 107.19/16.69 % (31398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.19/16.69 % (31398)Termination reason: Unknown
% 107.19/16.69 % (31398)Termination phase: Saturation
% 107.19/16.69
% 107.19/16.69 % (31398)Memory used [KB]: 8699
% 107.19/16.69 % (31398)Time elapsed: 0.661 s
% 107.19/16.69 % (31398)Instructions burned: 2144 (million)
% 107.19/16.69 % (31398)------------------------------
% 107.19/16.69 % (31398)------------------------------
% 108.13/16.70 % (31401)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_30182 for (2847ds/64912Mi)
% 108.73/17.01 % (31400)Instruction limit reached!
% 108.73/17.01 % (31400)------------------------------
% 108.73/17.01 % (31400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.73/17.01 % (31400)Termination reason: Unknown
% 108.73/17.01 % (31400)Termination phase: Saturation
% 108.73/17.01
% 108.73/17.01 % (31400)Memory used [KB]: 11769
% 108.73/17.01 % (31400)Time elapsed: 0.488 s
% 108.73/17.01 % (31400)Instructions burned: 1667 (million)
% 108.73/17.01 % (31400)------------------------------
% 108.73/17.01 % (31400)------------------------------
% 111.61/17.02 % (31402)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_30182 for (2844ds/7801Mi)
% 113.24/17.39 % (31161)Instruction limit reached!
% 113.24/17.39 % (31161)------------------------------
% 113.24/17.39 % (31161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.24/17.39 % (31161)Termination reason: Unknown
% 113.24/17.39 % (31161)Termination phase: Saturation
% 113.24/17.39
% 113.24/17.39 % (31161)Memory used [KB]: 8955
% 113.24/17.39 % (31161)Time elapsed: 2.124 s
% 113.24/17.39 % (31161)Instructions burned: 7471 (million)
% 113.24/17.39 % (31161)------------------------------
% 113.24/17.39 % (31161)------------------------------
% 113.86/17.41 % (31403)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_30182 for (2840ds/15194Mi)
% 118.63/18.04 % (31399)Instruction limit reached!
% 118.63/18.04 % (31399)------------------------------
% 118.63/18.04 % (31399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.63/18.04 % (31399)Termination reason: Unknown
% 118.63/18.04 % (31399)Termination phase: Saturation
% 118.63/18.04
% 118.63/18.04 % (31399)Memory used [KB]: 12665
% 118.63/18.04 % (31399)Time elapsed: 1.710 s
% 118.63/18.04 % (31399)Instructions burned: 5626 (million)
% 118.63/18.04 % (31399)------------------------------
% 118.63/18.04 % (31399)------------------------------
% 118.63/18.05 % (31404)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_30182 for (2834ds/6753Mi)
% 127.58/19.35 % (31402)Instruction limit reached!
% 127.58/19.35 % (31402)------------------------------
% 127.58/19.35 % (31402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.58/19.35 % (31402)Termination reason: Unknown
% 127.58/19.35 % (31402)Termination phase: Saturation
% 127.58/19.35
% 127.58/19.35 % (31402)Memory used [KB]: 11385
% 127.58/19.35 % (31402)Time elapsed: 2.323 s
% 127.58/19.35 % (31402)Instructions burned: 7803 (million)
% 127.58/19.35 % (31402)------------------------------
% 127.58/19.35 % (31402)------------------------------
% 127.58/19.36 % (31405)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_30182 for (2821ds/1003Mi)
% 128.83/19.54 % (30771)Instruction limit reached!
% 128.83/19.54 % (30771)------------------------------
% 128.83/19.54 % (30771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.83/19.54 % (30771)Termination reason: Unknown
% 128.83/19.54 % (30771)Termination phase: Saturation
% 128.83/19.54
% 128.83/19.54 % (30771)Memory used [KB]: 8443
% 128.83/19.54 % (30771)Time elapsed: 7.022 s
% 128.83/19.54 % (30771)Instructions burned: 43570 (million)
% 128.83/19.54 % (30771)------------------------------
% 128.83/19.54 % (30771)------------------------------
% 128.83/19.55 % (31406)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_30182 for (2819ds/13018Mi)
% 128.83/19.59 % (31177)Instruction limit reached!
% 128.83/19.59 % (31177)------------------------------
% 128.83/19.59 % (31177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.83/19.59 % (31177)Termination reason: Unknown
% 128.83/19.59 % (31177)Termination phase: Saturation
% 128.83/19.59
% 128.83/19.59 % (31177)Memory used [KB]: 18421
% 128.83/19.59 % (31177)Time elapsed: 4.171 s
% 128.83/19.59 % (31177)Instructions burned: 13468 (million)
% 128.83/19.59 % (31177)------------------------------
% 128.83/19.59 % (31177)------------------------------
% 129.39/19.61 % (31407)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_30182 for (2818ds/1267Mi)
% 129.39/19.65 % (31405)Instruction limit reached!
% 129.39/19.65 % (31405)------------------------------
% 129.39/19.65 % (31405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 129.39/19.65 % (31405)Termination reason: Unknown
% 129.39/19.65 % (31405)Termination phase: Saturation
% 129.39/19.65
% 129.39/19.65 % (31405)Memory used [KB]: 8699
% 129.39/19.65 % (31405)Time elapsed: 0.294 s
% 129.39/19.65 % (31405)Instructions burned: 1005 (million)
% 129.39/19.65 % (31405)------------------------------
% 129.39/19.65 % (31405)------------------------------
% 129.39/19.66 % (31408)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_30182 for (2818ds/2570Mi)
% 130.49/19.83 % (31404)Instruction limit reached!
% 130.49/19.83 % (31404)------------------------------
% 130.49/19.83 % (31404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 130.49/19.83 % (31404)Termination reason: Unknown
% 130.49/19.83 % (31404)Termination phase: Saturation
% 130.49/19.83
% 130.49/19.83 % (31404)Memory used [KB]: 10362
% 130.49/19.83 % (31404)Time elapsed: 1.783 s
% 130.49/19.83 % (31404)Instructions burned: 6755 (million)
% 130.49/19.83 % (31404)------------------------------
% 130.49/19.83 % (31404)------------------------------
% 130.49/19.84 % (31409)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_30182 for (2816ds/13163Mi)
% 130.85/19.96 % (31407)Instruction limit reached!
% 130.85/19.96 % (31407)------------------------------
% 130.85/19.96 % (31407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 130.85/19.96 % (31407)Termination reason: Unknown
% 130.85/19.96 % (31407)Termination phase: Saturation
% 130.85/19.96
% 130.85/19.96 % (31407)Memory used [KB]: 7675
% 130.85/19.96 % (31407)Time elapsed: 0.351 s
% 130.85/19.96 % (31407)Instructions burned: 1267 (million)
% 130.85/19.96 % (31407)------------------------------
% 130.85/19.96 % (31407)------------------------------
% 130.85/19.97 % (31410)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_30182 for (2815ds/5087Mi)
% 135.29/20.40 % (31408)Instruction limit reached!
% 135.29/20.40 % (31408)------------------------------
% 135.29/20.40 % (31408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.29/20.40 % (31408)Termination reason: Unknown
% 135.29/20.40 % (31408)Termination phase: Saturation
% 135.29/20.40
% 135.29/20.40 % (31408)Memory used [KB]: 9850
% 135.29/20.40 % (31408)Time elapsed: 0.744 s
% 135.29/20.40 % (31408)Instructions burned: 2570 (million)
% 135.29/20.40 % (31408)------------------------------
% 135.29/20.40 % (31408)------------------------------
% 135.29/20.41 % (31411)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_30182 for (2810ds/10380Mi)
% 137.11/20.77 % (31397)Instruction limit reached!
% 137.11/20.77 % (31397)------------------------------
% 137.11/20.77 % (31397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.11/20.77 % (31397)Termination reason: Unknown
% 137.11/20.77 % (31397)Termination phase: Saturation
% 137.11/20.77
% 137.11/20.77 % (31397)Memory used [KB]: 28656
% 137.11/20.77 % (31397)Time elapsed: 4.744 s
% 137.11/20.77 % (31397)Instructions burned: 15560 (million)
% 137.11/20.77 % (31397)------------------------------
% 137.11/20.77 % (31397)------------------------------
% 137.11/20.78 % (31412)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_30182 for (2807ds/4218Mi)
% 143.03/21.51 % (31410)Instruction limit reached!
% 143.03/21.51 % (31410)------------------------------
% 143.03/21.51 % (31410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.03/21.51 % (31410)Termination reason: Unknown
% 143.03/21.51 % (31410)Termination phase: Saturation
% 143.03/21.51
% 143.03/21.51 % (31410)Memory used [KB]: 11257
% 143.03/21.51 % (31410)Time elapsed: 1.545 s
% 143.03/21.51 % (31410)Instructions burned: 5090 (million)
% 143.03/21.51 % (31410)------------------------------
% 143.03/21.51 % (31410)------------------------------
% 143.03/21.52 % (31413)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_30182 for (2799ds/3971Mi)
% 144.84/21.80 % (31403)Instruction limit reached!
% 144.84/21.80 % (31403)------------------------------
% 144.84/21.80 % (31403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 144.84/21.80 % (31403)Termination reason: Unknown
% 144.84/21.80 % (31403)Termination phase: Saturation
% 144.84/21.80
% 144.84/21.80 % (31403)Memory used [KB]: 14328
% 144.84/21.80 % (31403)Time elapsed: 4.415 s
% 144.84/21.80 % (31403)Instructions burned: 15195 (million)
% 144.84/21.80 % (31403)------------------------------
% 144.84/21.80 % (31403)------------------------------
% 144.84/21.81 % (31414)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_30182 for (2796ds/14014Mi)
% 146.72/22.03 % (31412)Instruction limit reached!
% 146.72/22.03 % (31412)------------------------------
% 146.72/22.03 % (31412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.72/22.03 % (31412)Termination reason: Unknown
% 146.72/22.03 % (31412)Termination phase: Saturation
% 146.72/22.03
% 146.72/22.03 % (31412)Memory used [KB]: 11001
% 146.72/22.03 % (31412)Time elapsed: 1.253 s
% 146.72/22.03 % (31412)Instructions burned: 4220 (million)
% 146.72/22.03 % (31412)------------------------------
% 146.72/22.03 % (31412)------------------------------
% 146.72/22.04 % (31415)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_30182 for (2794ds/8517Mi)
% 150.79/22.72 % (31413)Instruction limit reached!
% 150.79/22.72 % (31413)------------------------------
% 150.79/22.72 % (31413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 150.79/22.72 % (31413)Termination reason: Unknown
% 150.79/22.72 % (31413)Termination phase: Saturation
% 150.79/22.72
% 150.79/22.72 % (31413)Memory used [KB]: 19445
% 150.79/22.72 % (31413)Time elapsed: 1.199 s
% 150.79/22.72 % (31413)Instructions burned: 3972 (million)
% 150.79/22.72 % (31413)------------------------------
% 150.79/22.72 % (31413)------------------------------
% 150.79/22.73 % (31416)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_30182 for (2787ds/10148Mi)
% 155.67/23.33 % (31411)Instruction limit reached!
% 155.67/23.33 % (31411)------------------------------
% 155.67/23.33 % (31411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.67/23.33 % (31411)Termination reason: Unknown
% 155.67/23.33 % (31411)Termination phase: Saturation
% 155.67/23.33
% 155.67/23.33 % (31411)Memory used [KB]: 8187
% 155.67/23.33 % (31411)Time elapsed: 2.918 s
% 155.67/23.33 % (31411)Instructions burned: 10382 (million)
% 155.67/23.33 % (31411)------------------------------
% 155.67/23.33 % (31411)------------------------------
% 155.67/23.34 % (31417)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_30182 for (2781ds/9078Mi)
% 156.90/23.56 % (31406)Instruction limit reached!
% 156.90/23.56 % (31406)------------------------------
% 156.90/23.56 % (31406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.90/23.56 % (31406)Termination reason: Unknown
% 156.90/23.56 % (31406)Termination phase: Saturation
% 156.90/23.56
% 156.90/23.56 % (31406)Memory used [KB]: 31342
% 156.90/23.56 % (31406)Time elapsed: 4.006 s
% 156.90/23.56 % (31406)Instructions burned: 13019 (million)
% 156.90/23.56 % (31406)------------------------------
% 156.90/23.56 % (31406)------------------------------
% 156.90/23.57 % (31418)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_30182 for (2779ds/16164Mi)
% 156.90/23.59 % (31409)Instruction limit reached!
% 156.90/23.59 % (31409)------------------------------
% 156.90/23.59 % (31409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.90/23.59 % (31409)Termination reason: Unknown
% 156.90/23.59 % (31409)Termination phase: Saturation
% 156.90/23.59
% 156.90/23.59 % (31409)Memory used [KB]: 10490
% 156.90/23.59 % (31409)Time elapsed: 3.744 s
% 156.90/23.59 % (31409)Instructions burned: 13164 (million)
% 156.90/23.59 % (31409)------------------------------
% 156.90/23.59 % (31409)------------------------------
% 156.90/23.60 % (31419)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_30182 for (2778ds/6102Mi)
% 164.07/24.58 % (31415)Instruction limit reached!
% 164.07/24.58 % (31415)------------------------------
% 164.07/24.58 % (31415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.07/24.58 % (31415)Termination reason: Unknown
% 164.07/24.58 % (31415)Termination phase: Saturation
% 164.07/24.58
% 164.07/24.58 % (31415)Memory used [KB]: 15607
% 164.07/24.58 % (31415)Time elapsed: 2.539 s
% 164.07/24.58 % (31415)Instructions burned: 8519 (million)
% 164.07/24.58 % (31415)------------------------------
% 164.07/24.58 % (31415)------------------------------
% 164.07/24.59 % (31420)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_30182 for (2769ds/10308Mi)
% 169.67/25.33 % (31419)Instruction limit reached!
% 169.67/25.33 % (31419)------------------------------
% 169.67/25.33 % (31419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.67/25.33 % (31419)Termination reason: Unknown
% 169.67/25.33 % (31419)Termination phase: Saturation
% 169.67/25.33
% 169.67/25.33 % (31419)Memory used [KB]: 20724
% 169.67/25.33 % (31419)Time elapsed: 1.730 s
% 169.67/25.33 % (31419)Instructions burned: 6103 (million)
% 169.67/25.33 % (31419)------------------------------
% 169.67/25.33 % (31419)------------------------------
% 169.67/25.34 % (31421)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_30182 for (2761ds/4041Mi)
% 171.52/25.65 % (31416)Instruction limit reached!
% 171.52/25.65 % (31416)------------------------------
% 171.52/25.65 % (31416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 171.52/25.65 % (31416)Termination reason: Unknown
% 171.52/25.65 % (31416)Termination phase: Saturation
% 171.52/25.65
% 171.52/25.65 % (31416)Memory used [KB]: 10618
% 171.52/25.65 % (31416)Time elapsed: 2.923 s
% 171.52/25.65 % (31416)Instructions burned: 10149 (million)
% 171.52/25.65 % (31416)------------------------------
% 171.52/25.65 % (31416)------------------------------
% 171.52/25.66 % (31422)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_30182 for (2758ds/6901Mi)
% 173.10/25.90 % (31414)Instruction limit reached!
% 173.10/25.90 % (31414)------------------------------
% 173.10/25.90 % (31414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 173.10/25.90 % (31414)Termination reason: Unknown
% 173.10/25.90 % (31414)Termination phase: Saturation
% 173.10/25.90
% 173.10/25.90 % (31414)Memory used [KB]: 12665
% 173.10/25.90 % (31414)Time elapsed: 4.093 s
% 173.10/25.90 % (31414)Instructions burned: 14015 (million)
% 173.10/25.90 % (31414)------------------------------
% 173.10/25.90 % (31414)------------------------------
% 173.10/25.91 % (31423)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_30182 for (2755ds/5576Mi)
% 173.10/25.92 % (31417)Instruction limit reached!
% 173.10/25.92 % (31417)------------------------------
% 173.10/25.92 % (31417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 173.10/25.92 % (31417)Termination reason: Unknown
% 173.10/25.92 % (31417)Termination phase: Saturation
% 173.10/25.92
% 173.10/25.92 % (31417)Memory used [KB]: 20724
% 173.10/25.92 % (31417)Time elapsed: 2.583 s
% 173.10/25.92 % (31417)Instructions burned: 9079 (million)
% 173.10/25.92 % (31417)------------------------------
% 173.10/25.92 % (31417)------------------------------
% 173.10/25.93 % (31424)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_30182 for (2755ds/2014Mi)
% 178.12/26.53 % (31424)Instruction limit reached!
% 178.12/26.53 % (31424)------------------------------
% 178.12/26.53 % (31424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.12/26.53 % (31424)Termination reason: Unknown
% 178.12/26.53 % (31424)Termination phase: Saturation
% 178.12/26.53
% 178.12/26.53 % (31424)Memory used [KB]: 9850
% 178.12/26.53 % (31424)Time elapsed: 0.599 s
% 178.12/26.53 % (31424)Instructions burned: 2016 (million)
% 178.12/26.53 % (31424)------------------------------
% 178.12/26.53 % (31424)------------------------------
% 178.12/26.54 % (31425)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_30182 for (2749ds/5115Mi)
% 178.12/26.55 % (31421)Instruction limit reached!
% 178.12/26.55 % (31421)------------------------------
% 178.12/26.55 % (31421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.12/26.55 % (31421)Termination reason: Unknown
% 178.12/26.55 % (31421)Termination phase: Saturation
% 178.12/26.55
% 178.12/26.55 % (31421)Memory used [KB]: 10362
% 178.12/26.55 % (31421)Time elapsed: 1.213 s
% 178.12/26.55 % (31421)Instructions burned: 4042 (million)
% 178.12/26.55 % (31421)------------------------------
% 178.12/26.55 % (31421)------------------------------
% 178.12/26.56 % (31426)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_30182 for (2749ds/13001Mi)
% 178.72/26.60 % (31426)Refutation not found, incomplete strategy
% 178.72/26.60 % (31426)------------------------------
% 178.72/26.60 % (31426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.72/26.60 % (31426)Termination reason: Refutation not found, incomplete strategy
% 178.72/26.60
% 178.72/26.60
% 178.72/26.60 % (31426)Memory used [KB]: 7291
% 178.72/26.60 % (31426)Time elapsed: 0.045 s
% 178.72/26.60 % (31426)Instructions burned: 163 (million)
% 178.72/26.60 % (31426)------------------------------
% 178.72/26.60 % (31426)------------------------------
% 178.72/26.61 % (31427)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_30182 for (2748ds/11105Mi)
% 185.13/27.54 % (31423)Instruction limit reached!
% 185.13/27.54 % (31423)------------------------------
% 185.13/27.54 % (31423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 185.13/27.54 % (31423)Termination reason: Unknown
% 185.13/27.54 % (31423)Termination phase: Saturation
% 185.13/27.54
% 185.13/27.54 % (31423)Memory used [KB]: 11385
% 185.13/27.54 % (31423)Time elapsed: 1.633 s
% 185.13/27.54 % (31423)Instructions burned: 5578 (million)
% 185.13/27.54 % (31423)------------------------------
% 185.13/27.54 % (31423)------------------------------
% 185.13/27.55 % (31428)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_30182 for (2739ds/13832Mi)
% 185.79/27.61 % (31420)First to succeed.
% 185.79/27.61 % (31420)Refutation found. Thanks to Tanya!
% 185.79/27.61 % SZS status Theorem for DTF2THF_30182
% 185.79/27.61 % SZS output start Proof for DTF2THF_30182
% 185.79/27.61 thf(type_def_5, type, itself: ($tType) > $tType).
% 185.79/27.61 thf(type_def_7, type, set: ($tType) > $tType).
% 185.79/27.61 thf(type_def_8, type, list: ($tType) > $tType).
% 185.79/27.61 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 185.79/27.61 thf(type_def_10, type, option: ($tType) > $tType).
% 185.79/27.61 thf(type_def_11, type, rBT_Im1923302023_color: $tType).
% 185.79/27.61 thf(type_def_12, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 185.79/27.61 thf(type_def_13, type, a: $tType).
% 185.79/27.61 thf(type_def_14, type, b: $tType).
% 185.79/27.61 thf(func_def_0, type, rBT_Im1923302023_color: $tType).
% 185.79/27.61 thf(func_def_1, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 185.79/27.61 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 185.79/27.61 thf(func_def_3, type, option: ($tType) > $tType).
% 185.79/27.61 thf(func_def_4, type, list: ($tType) > $tType).
% 185.79/27.61 thf(func_def_5, type, set: ($tType) > $tType).
% 185.79/27.61 thf(func_def_6, type, itself: ($tType) > $tType).
% 185.79/27.61 thf(func_def_7, type, b: $tType).
% 185.79/27.61 thf(func_def_8, type, a: $tType).
% 185.79/27.61 thf(func_def_9, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 185.79/27.61 thf(func_def_10, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 185.79/27.61 thf(func_def_11, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 185.79/27.61 thf(func_def_12, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_13, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 185.79/27.61 thf(func_def_14, type, distinct: !>[X0: $tType]:(list @ X0 > $o)).
% 185.79/27.61 thf(func_def_15, type, extract: !>[X0: $tType]:((X0 > $o) > list @ X0 > option @ product_prod @ list @ X0 @ product_prod @ X0 @ list @ X0)).
% 185.79/27.61 thf(func_def_16, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_17, type, nil: !>[X0: $tType]:(list @ X0)).
% 185.79/27.61 thf(func_def_18, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 185.79/27.61 thf(func_def_19, type, listrel1: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0)).
% 185.79/27.61 thf(func_def_20, type, lexordp: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_21, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_22, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 185.79/27.61 thf(func_def_23, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 185.79/27.61 thf(func_def_24, type, union: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_25, type, dom: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > set @ X0)).
% 185.79/27.61 thf(func_def_26, type, map_of: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > X0 > option @ X1)).
% 185.79/27.61 thf(func_def_27, type, none: !>[X0: $tType]:(option @ X0)).
% 185.79/27.61 thf(func_def_28, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 185.79/27.61 thf(func_def_29, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 185.79/27.61 thf(func_def_30, type, strict_mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 185.79/27.61 thf(func_def_31, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 185.79/27.61 thf(func_def_32, type, type2: !>[X0: $tType]:(itself @ X0)).
% 185.79/27.61 thf(func_def_33, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 185.79/27.61 thf(func_def_34, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 185.79/27.61 thf(func_def_35, type, rBT_Im1805589839lor_of: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im1923302023_color)).
% 185.79/27.61 thf(func_def_36, type, rBT_Im954575269ntries: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > list @ product_prod @ X0 @ X1)).
% 185.79/27.61 thf(func_def_37, type, rBT_Im1040612427e_inv1: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_38, type, rBT_Im1040612428e_inv2: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_39, type, rBT_Im380146495e_keys: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > list @ X0)).
% 185.79/27.61 thf(func_def_40, type, rBT_Im862805236is_rbt: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_41, type, rBT_Im1259024060reater: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_42, type, rBT_Im2075124343t_less: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_43, type, rBT_Im35466040lookup: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > X0 > option @ X1)).
% 185.79/27.61 thf(func_def_44, type, rBT_Im759614907sorted: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 185.79/27.61 thf(func_def_45, type, rBT_Im480247531Branch: !>[X0: $tType, X1: $tType]:(rBT_Im1923302023_color > rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 185.79/27.61 thf(func_def_46, type, rBT_Im418718756_Empty: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1)).
% 185.79/27.61 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 185.79/27.61 thf(func_def_48, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 185.79/27.61 thf(func_def_49, type, set_greaterThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 185.79/27.61 thf(func_def_50, type, set_lessThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 185.79/27.61 thf(func_def_51, type, transitive_acyclic: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 185.79/27.61 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 185.79/27.61 thf(func_def_53, type, b2: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_54, type, c: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_55, type, k: a).
% 185.79/27.61 thf(func_def_56, type, l: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_57, type, less: a > a > $o).
% 185.79/27.61 thf(func_def_58, type, r: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_59, type, s: b).
% 185.79/27.61 thf(func_def_60, type, t: b).
% 185.79/27.61 thf(func_def_61, type, va: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_62, type, vb: a).
% 185.79/27.61 thf(func_def_63, type, vc: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_64, type, vd: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_65, type, ve: a).
% 185.79/27.61 thf(func_def_66, type, vf: rBT_Im246033960le_rbt @ a @ b).
% 185.79/27.61 thf(func_def_67, type, vg: b).
% 185.79/27.61 thf(func_def_68, type, vii: b).
% 185.79/27.61 thf(func_def_69, type, x: a).
% 185.79/27.61 thf(func_def_70, type, y: a).
% 185.79/27.61 thf(func_def_71, type, z: a).
% 185.79/27.61 thf(func_def_90, type, sP0: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_91, type, sP1: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_92, type, sP2: (list @ a > list @ a > $o) > $o).
% 185.79/27.61 thf(func_def_93, type, sP3: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > (X0 > $o) > X0 > $o)).
% 185.79/27.61 thf(func_def_94, type, sP4: list @ a > a > a > list @ a > $o).
% 185.79/27.61 thf(func_def_95, type, sP5: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_96, type, sP6: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_97, type, sP7: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_98, type, sP8: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_99, type, sP9: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0 > X0 > $o)).
% 185.79/27.61 thf(func_def_100, type, sP10: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_101, type, sP11: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_102, type, sP12: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_103, type, sP13: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_104, type, sP14: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_105, type, sP15: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > $o)).
% 185.79/27.61 thf(func_def_106, type, sP16: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0 > X0 > $o)).
% 185.79/27.61 thf(func_def_107, type, sP17: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_108, type, sP18: (list @ a > list @ a > $o) > $o).
% 185.79/27.61 thf(func_def_109, type, sP19: !>[X0: $tType]:(X0 > X0 > list @ X0 > list @ X0 > set @ product_prod @ X0 @ X0 > $o)).
% 185.79/27.61 thf(func_def_110, type, sP20: !>[X0: $tType]:(X0 > X0 > list @ X0 > list @ X0 > set @ product_prod @ X0 @ X0 > $o)).
% 185.79/27.61 thf(func_def_111, type, sP21: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_112, type, sP22: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_113, type, sP23: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_114, type, sP24: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 185.79/27.61 thf(func_def_115, type, sP25: !>[X0: $tType]:(list @ X0 > (X0 > $o) > $o)).
% 185.79/27.61 thf(func_def_116, type, sP26: (list @ a > list @ a > $o) > $o).
% 185.79/27.61 thf(func_def_117, type, sP27: list @ a > a > a > list @ a > $o).
% 185.79/27.61 thf(func_def_118, type, sP28: list @ a > list @ a > $o).
% 185.79/27.61 thf(func_def_119, type, sP29: !>[X0: $tType]:(list @ X0 > (X0 > $o) > $o)).
% 185.79/27.61 thf(func_def_120, type, sP30: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > $o)).
% 185.79/27.61 thf(func_def_121, type, sK31: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_122, type, sK32: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 185.79/27.61 thf(func_def_123, type, sK33: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 185.79/27.61 thf(func_def_124, type, sK34: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_125, type, sK35: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_126, type, sK36: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 185.79/27.61 thf(func_def_127, type, sK37: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 185.79/27.61 thf(func_def_128, type, sK38: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_129, type, sK39: !>[X0: $tType]:(rBT_Im246033960le_rbt @ a @ X0 > a > a)).
% 185.79/27.61 thf(func_def_130, type, sK40: !>[X0: $tType]:((a > X0) > a)).
% 185.79/27.61 thf(func_def_131, type, sK41: !>[X0: $tType]:((a > X0) > a)).
% 185.79/27.61 thf(func_def_132, type, sK42: !>[X0: $tType]:((X0 > a) > set @ product_prod @ X0 @ X0 > X0)).
% 185.79/27.61 thf(func_def_133, type, sK43: !>[X0: $tType]:((X0 > a) > set @ product_prod @ X0 @ X0 > X0)).
% 185.79/27.61 thf(func_def_134, type, sK44: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_135, type, sK45: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_136, type, sK46: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_137, type, sK47: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_138, type, sK48: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_139, type, sK49: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_140, type, sK50: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_141, type, sK51: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_142, type, sK52: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_143, type, sK53: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_144, type, sK54: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_145, type, sK55: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_146, type, sK56: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_147, type, sK57: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_148, type, sK58: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_149, type, sK59: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_150, type, sK60: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_151, type, sK61: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_152, type, sK62: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_153, type, sK63: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_154, type, sK64: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ product_prod @ X1 @ X1 > X1)).
% 185.79/27.61 thf(func_def_155, type, sK65: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ product_prod @ X1 @ X1 > X1)).
% 185.79/27.61 thf(func_def_156, type, sK66: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_157, type, sK67: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_158, type, sK68: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_159, type, sK69: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 185.79/27.61 thf(func_def_160, type, sK70: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_161, type, sK71: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 185.79/27.61 thf(func_def_162, type, sK72: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_163, type, sK73: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 185.79/27.61 thf(func_def_164, type, sK74: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 185.79/27.61 thf(func_def_165, type, sK75: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 185.79/27.61 thf(func_def_166, type, sK76: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 185.79/27.61 thf(func_def_167, type, sK77: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_168, type, sK78: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_169, type, sK79: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_170, type, sK80: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_171, type, sK81: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_172, type, sK82: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_173, type, sK83: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_174, type, sK84: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_175, type, sK85: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_176, type, sK86: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_177, type, sK87: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_178, type, sK88: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_179, type, sK89: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_180, type, sK90: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1)).
% 185.79/27.61 thf(func_def_181, type, sK91: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_182, type, sK92: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_183, type, sK93: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_184, type, sK94: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_185, type, sK95: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_186, type, sK96: list @ a > a > a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_187, type, sK97: list @ a > a).
% 185.79/27.61 thf(func_def_188, type, sK98: list @ a > list @ a).
% 185.79/27.61 thf(func_def_189, type, sK99: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_190, type, sK100: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_191, type, sK101: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_192, type, sK102: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_193, type, sK103: !>[X0: $tType]:(a > rBT_Im246033960le_rbt @ a @ X0 > rBT_Im246033960le_rbt @ a @ X0 > X0)).
% 185.79/27.61 thf(func_def_194, type, sK104: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_195, type, sK105: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_196, type, sK106: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_197, type, sK107: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_198, type, sK108: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_199, type, sK109: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_200, type, sK110: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_201, type, sK111: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_202, type, sK112: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_203, type, sK113: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_204, type, sK114: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_205, type, sK115: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_206, type, sK116: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_207, type, sK117: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_208, type, sK118: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_209, type, sK119: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_210, type, sK120: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_211, type, sK121: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_212, type, sK122: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_213, type, sK123: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_214, type, sK124: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_215, type, sK125: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_216, type, sK126: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_217, type, sK127: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_218, type, sK128: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_219, type, sK129: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_220, type, sK130: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_221, type, sK131: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_222, type, sK132: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_223, type, sK133: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_224, type, sK134: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_225, type, sK135: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_226, type, sK136: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_227, type, sK137: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 185.79/27.61 thf(func_def_228, type, sK138: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 185.79/27.61 thf(func_def_229, type, sK139: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 185.79/27.61 thf(func_def_230, type, sK140: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 185.79/27.61 thf(func_def_231, type, sK141: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_232, type, sK142: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 185.79/27.61 thf(func_def_233, type, sK143: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_234, type, sK144: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_235, type, sK145: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_236, type, sK146: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_237, type, sK147: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_238, type, sK148: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_239, type, sK149: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_240, type, sK150: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_241, type, sK151: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_242, type, sK152: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_243, type, sK153: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_244, type, sK154: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_245, type, sK155: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_246, type, sK156: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_247, type, sK157: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_248, type, sK158: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_249, type, sK159: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_250, type, sK160: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_251, type, sK161: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_252, type, sK162: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_253, type, sK163: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_254, type, sK164: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_255, type, sK165: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_256, type, sK166: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_257, type, sK167: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_258, type, sK168: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_259, type, sK169: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_260, type, sK170: !>[X0: $tType, X1: $tType]:((X1 > list @ X0) > (X1 > list @ X0) > list @ X1 > X1)).
% 185.79/27.61 thf(func_def_261, type, sK171: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_262, type, sK172: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_263, type, sK173: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_264, type, sK174: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_265, type, sK175: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_266, type, sK176: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_267, type, sK177: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_268, type, sK178: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_269, type, sK179: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_270, type, sK180: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_271, type, sK181: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 185.79/27.61 thf(func_def_272, type, sK182: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_273, type, sK183: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 185.79/27.61 thf(func_def_274, type, sK184: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 185.79/27.61 thf(func_def_275, type, sK185: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_276, type, sK186: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_277, type, sK187: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_278, type, sK188: !>[X0: $tType]:(list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_279, type, sK189: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_280, type, sK190: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_281, type, sK191: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_282, type, sK192: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_283, type, sK193: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_284, type, sK194: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_285, type, sK195: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_286, type, sK196: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_287, type, sK197: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_288, type, sK198: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im1923302023_color)).
% 185.79/27.61 thf(func_def_289, type, sK199: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_290, type, sK200: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 185.79/27.61 thf(func_def_291, type, sK201: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 185.79/27.61 thf(func_def_292, type, sK202: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_293, type, sK203: !>[X0: $tType]:(rBT_Im246033960le_rbt @ a @ X0 > a > a)).
% 185.79/27.61 thf(func_def_294, type, sK204: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_295, type, sK205: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_296, type, sK206: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im1923302023_color)).
% 185.79/27.61 thf(func_def_297, type, sK207: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_298, type, sK208: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X1)).
% 185.79/27.61 thf(func_def_299, type, sK209: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_300, type, sK210: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 185.79/27.61 thf(func_def_301, type, sK211: a).
% 185.79/27.61 thf(func_def_302, type, sK212: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_303, type, sK213: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_304, type, sK214: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_305, type, sK215: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_306, type, sK216: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_307, type, sK217: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_308, type, sK218: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_309, type, sK219: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_310, type, sK220: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_311, type, sK221: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_312, type, sK222: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_313, type, sK223: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_314, type, sK224: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_315, type, sK225: a).
% 185.79/27.61 thf(func_def_316, type, sK226: !>[X0: $tType]:(X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_317, type, sK227: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_318, type, sK228: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_319, type, sK229: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_320, type, sK230: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_321, type, sK231: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_322, type, sK232: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_323, type, sK233: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_324, type, sK234: list @ a > a).
% 185.79/27.61 thf(func_def_325, type, sK235: list @ a > list @ a).
% 185.79/27.61 thf(func_def_326, type, sK236: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_327, type, sK237: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_328, type, sK238: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_329, type, sK239: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_330, type, sK240: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 185.79/27.61 thf(func_def_331, type, sK241: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 185.79/27.61 thf(func_def_332, type, sK242: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_333, type, sK243: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_334, type, sK244: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 185.79/27.61 thf(func_def_335, type, sK245: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_336, type, sK246: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > X0)).
% 185.79/27.61 thf(func_def_337, type, sK247: !>[X0: $tType]:(product_prod @ list @ X0 @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_338, type, sK248: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_339, type, sK249: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_340, type, sK250: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_341, type, sK251: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_342, type, sK252: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_343, type, sK253: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_344, type, sK254: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_345, type, sK255: !>[X0: $tType]:((a > X0) > a)).
% 185.79/27.61 thf(func_def_346, type, sK256: !>[X0: $tType]:((a > X0) > a)).
% 185.79/27.61 thf(func_def_347, type, sK257: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_348, type, sK258: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_349, type, sK259: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_350, type, sK260: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_351, type, sK261: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_352, type, sK262: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_353, type, sK263: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_354, type, sK264: (list @ a > list @ a > $o) > a).
% 185.79/27.61 thf(func_def_355, type, sK265: (list @ a > list @ a > $o) > list @ a).
% 185.79/27.61 thf(func_def_356, type, sK266: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_357, type, sK267: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_358, type, sK268: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_359, type, sK269: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_360, type, sK270: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_361, type, sK271: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_362, type, sK272: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_363, type, sK273: list @ a > a > a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_364, type, sK274: list @ a > list @ a).
% 185.79/27.61 thf(func_def_365, type, sK275: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_366, type, sK276: list @ a > list @ a > a).
% 185.79/27.61 thf(func_def_367, type, sK277: list @ a > list @ a > list @ a).
% 185.79/27.61 thf(func_def_368, type, sK278: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_369, type, sK279: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_370, type, sK280: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_371, type, sK281: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_372, type, sK282: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_373, type, sK283: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_374, type, sK284: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 185.79/27.61 thf(func_def_375, type, sK285: !>[X0: $tType]:(list @ X0 > X0)).
% 185.79/27.61 thf(func_def_376, type, sK286: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 185.79/27.61 thf(func_def_377, type, sK287: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 185.79/27.61 thf(func_def_378, type, sK288: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_379, type, sK289: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 185.79/27.61 thf(func_def_380, type, sK290: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_381, type, sK291: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_382, type, sK292: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_383, type, sK293: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_384, type, sK294: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_385, type, sK295: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_386, type, sK296: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_387, type, sK297: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 185.79/27.61 thf(func_def_388, type, sK298: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_389, type, sK299: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 185.79/27.61 thf(func_def_390, type, sK300: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 185.79/27.61 thf(func_def_391, type, sK301: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 185.79/27.61 thf(func_def_392, type, sK302: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1)).
% 185.79/27.61 thf(func_def_393, type, sK303: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0)).
% 185.79/27.61 thf(func_def_394, type, sK304: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0)).
% 185.79/27.61 thf(func_def_395, type, sK305: !>[X0: $tType, X1: $tType]:(product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1)).
% 185.79/27.61 thf(func_def_397, type, ph307: !>[X0: $tType]:(X0)).
% 185.79/27.61 thf(f18285,plain,(
% 185.79/27.61 $false),
% 185.79/27.61 inference(avatar_sat_refutation,[status(thm)],[f2098,f3455,f18284])).
% 185.79/27.61 thf(f18284,plain,(
% 185.79/27.61 spl306_2),
% 185.79/27.61 inference(avatar_contradiction_clause,[status(thm)],[f18283])).
% 185.79/27.61 thf(f18283,plain,(
% 185.79/27.61 $false | spl306_2),
% 185.79/27.61 inference(trivial_inequality_removal,[status(thm)],[f18275])).
% 185.79/27.61 thf(f18275,plain,(
% 185.79/27.61 ($true != $true) | spl306_2),
% 185.79/27.61 inference(superposition,[status(thm)],[f7942,f1733])).
% 185.79/27.61 thf(f1733,plain,(
% 185.79/27.61 ((rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c) @ z @ t @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf))) = $true)),
% 185.79/27.61 inference(cnf_transformation,[status(thm)],[f667])).
% 185.79/27.61 thf(f667,plain,(
% 185.79/27.61 ((rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c) @ z @ t @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf))) = $true)),
% 185.79/27.61 inference(fool_elimination,[status(thm)],[f666])).
% 185.79/27.61 thf(f666,plain,(
% 185.79/27.61 (rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c) @ z @ t @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)))),
% 185.79/27.61 inference(rectify,[status(thm)],[f42])).
% 185.79/27.61 thf(f42,axiom,(
% 185.79/27.61 (rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ b2 @ y @ s @ c) @ z @ t @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)))),
% 185.79/27.61 file('/export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2THF_30182.p',fact_41__C5__4_Oprems_C_I2_J)).
% 185.79/27.61 thf(f7942,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : X0,X1 : rBT_Im1923302023_color,X6 : X0,X7 : rBT_Im246033960le_rbt @ a @ X0,X4 : rBT_Im246033960le_rbt @ a @ X0,X5 : rBT_Im1923302023_color] : (((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X5 @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ y @ X3 @ X4) @ z @ X6 @ X7)) != $true)) ) | spl306_2),
% 185.79/27.61 inference(trivial_inequality_removal,[status(thm)],[f7920])).
% 185.79/27.61 thf(f7920,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : X0,X1 : rBT_Im1923302023_color,X6 : X0,X7 : rBT_Im246033960le_rbt @ a @ X0,X4 : rBT_Im246033960le_rbt @ a @ X0,X5 : rBT_Im1923302023_color] : (($true != $true) | ((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X5 @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ y @ X3 @ X4) @ z @ X6 @ X7)) != $true)) ) | spl306_2),
% 185.79/27.61 inference(superposition,[status(thm)],[f3543,f1617])).
% 185.79/27.61 thf(f1617,plain,(
% 185.79/27.61 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X1 > $o,X3 : rBT_Im1923302023_color,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1] : (($true != (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7))) | ($true = (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4))) )),
% 185.79/27.61 inference(cnf_transformation,[status(thm)],[f1167])).
% 185.79/27.61 thf(f1167,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > $o,X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7))) | ($true != (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4)) | ($true != (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4)) | ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) != $true) | ($true != (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7))) & ((($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4)) & ($true = (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4)) & ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) = $true) & ($true = (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7))) | ($true != (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7)))))),
% 185.79/27.61 inference(flattening,[status(thm)],[f1166])).
% 185.79/27.61 thf(f1166,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > $o,X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7))) | (($true != (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4)) | ($true != (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4)) | ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) != $true) | ($true != (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7)))) & ((($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4)) & ($true = (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4)) & ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) = $true) & ($true = (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7))) | ($true != (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7)))))),
% 185.79/27.61 inference(nnf_transformation,[status(thm)],[f333])).
% 185.79/27.61 thf(f333,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > $o,X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : (($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7))) <=> (($true = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4)) & ($true = (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4)) & ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) = $true) & ($true = (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7))))),
% 185.79/27.61 inference(fool_elimination,[status(thm)],[f332])).
% 185.79/27.61 thf(f332,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : $tType,X2 : X1 > X1 > $o,X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im759614907sorted @ X1 @ X0 @ X2 @ (rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7)) = (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X4) & (rBT_Im1259024060reater @ X1 @ X0 @ X2 @ X5 @ X7) & (rBT_Im759614907sorted @ X1 @ X0 @ X2 @ X7) & (rBT_Im2075124343t_less @ X1 @ X0 @ X2 @ X5 @ X4))),
% 185.79/27.61 inference(rectify,[status(thm)],[f43])).
% 185.79/27.61 thf(f43,axiom,(
% 185.79/27.61 ! [X1 : $tType,X0 : $tType,X29 : X0 > X0 > $o,X6 : rBT_Im1923302023_color,X21 : rBT_Im246033960le_rbt @ X0 @ X1,X22 : X0,X23 : X1,X24 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im759614907sorted @ X0 @ X1 @ X29 @ (rBT_Im480247531Branch @ X0 @ X1 @ X6 @ X21 @ X22 @ X23 @ X24)) = (rBT_Im759614907sorted @ X0 @ X1 @ X29 @ X21) & (rBT_Im1259024060reater @ X0 @ X1 @ X29 @ X22 @ X24) & (rBT_Im759614907sorted @ X0 @ X1 @ X29 @ X24) & (rBT_Im2075124343t_less @ X0 @ X1 @ X29 @ X22 @ X21))),
% 185.79/27.61 file('/export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2THF_30182.p',fact_42_ord_Orbt__sorted_Osimps_I2_J)).
% 185.79/27.61 thf(f3543,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : X0,X1 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ a @ X0] : (((rBT_Im2075124343t_less @ a @ X0 @ less @ z @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ y @ X3 @ X4)) != $true)) ) | spl306_2),
% 185.79/27.61 inference(trivial_inequality_removal,[status(thm)],[f3485])).
% 185.79/27.61 thf(f3485,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : X0,X1 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ a @ X0] : (($true != $true) | ((rBT_Im2075124343t_less @ a @ X0 @ less @ z @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ y @ X3 @ X4)) != $true)) ) | spl306_2),
% 185.79/27.61 inference(superposition,[status(thm)],[f2097,f1845])).
% 185.79/27.61 thf(f1845,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ a @ X0,X1 : a,X6 : rBT_Im246033960le_rbt @ a @ X0,X4 : a,X5 : X0] : (($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | ($true = (less @ X4 @ X1))) )),
% 185.79/27.61 inference(cnf_transformation,[status(thm)],[f1311])).
% 185.79/27.61 thf(f1311,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : a,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ a @ X0,X4 : a,X5 : X0,X6 : rBT_Im246033960le_rbt @ a @ X0] : ((($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | ($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6)) | ($true != (less @ X4 @ X1)) | ($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3))) & ((($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6)) & ($true = (less @ X4 @ X1)) & ($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3))) | ($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)))))),
% 185.79/27.61 inference(flattening,[status(thm)],[f1310])).
% 185.79/27.61 thf(f1310,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : a,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ a @ X0,X4 : a,X5 : X0,X6 : rBT_Im246033960le_rbt @ a @ X0] : ((($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | (($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6)) | ($true != (less @ X4 @ X1)) | ($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3)))) & ((($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6)) & ($true = (less @ X4 @ X1)) & ($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3))) | ($true != (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)))))),
% 185.79/27.61 inference(nnf_transformation,[status(thm)],[f469])).
% 185.79/27.61 thf(f469,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : a,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ a @ X0,X4 : a,X5 : X0,X6 : rBT_Im246033960le_rbt @ a @ X0] : (($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) <=> (($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6)) & ($true = (less @ X4 @ X1)) & ($true = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3))))),
% 185.79/27.61 inference(fool_elimination,[status(thm)],[f468])).
% 185.79/27.61 thf(f468,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : a,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ a @ X0,X4 : a,X5 : X0,X6 : rBT_Im246033960le_rbt @ a @ X0] : ((rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X3) & (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ X6) & (less @ X4 @ X1) = (rBT_Im2075124343t_less @ a @ X0 @ less @ X1 @ (rBT_Im480247531Branch @ a @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)))),
% 185.79/27.61 inference(rectify,[status(thm)],[f37])).
% 185.79/27.61 thf(f37,axiom,(
% 185.79/27.61 ! [X9 : $tType,X22 : a,X6 : rBT_Im1923302023_color,X25 : rBT_Im246033960le_rbt @ a @ X9,X26 : a,X23 : X9,X27 : rBT_Im246033960le_rbt @ a @ X9] : ((rBT_Im2075124343t_less @ a @ X9 @ less @ X22 @ X25) & (rBT_Im2075124343t_less @ a @ X9 @ less @ X22 @ X27) & (less @ X26 @ X22) = (rBT_Im2075124343t_less @ a @ X9 @ less @ X22 @ (rBT_Im480247531Branch @ a @ X9 @ X6 @ X25 @ X26 @ X23 @ X27)))),
% 185.79/27.61 file('/export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2THF_30182.p',fact_36_local_Orbt__less__simps_I2_J)).
% 185.79/27.61 thf(f2097,plain,(
% 185.79/27.61 ((less @ y @ z) != $true) | spl306_2),
% 185.79/27.61 inference(avatar_component_clause,[status(thm)],[f2095])).
% 185.79/27.61 thf(f2095,definition,(
% 185.79/27.61 spl306_2 <=> ((less @ y @ z) = $true)),
% 185.79/27.61 introduced(definition,[new_symbols(naming,[spl306_2])],[avatar_definition])).
% 185.79/27.61 thf(f3455,plain,(
% 185.79/27.61 spl306_1),
% 185.79/27.61 inference(avatar_contradiction_clause,[status(thm)],[f3454])).
% 185.79/27.61 thf(f3454,plain,(
% 185.79/27.61 $false | spl306_1),
% 185.79/27.61 inference(trivial_inequality_removal,[status(thm)],[f3430])).
% 185.79/27.61 thf(f3430,plain,(
% 185.79/27.61 ($true != $true) | spl306_1),
% 185.79/27.61 inference(superposition,[status(thm)],[f2125,f1733])).
% 185.79/27.61 thf(f2125,plain,(
% 185.79/27.61 ( ! [X2 : b,X0 : rBT_Im1923302023_color,X1 : rBT_Im246033960le_rbt @ a @ b] : (($true != (rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ X0 @ X1 @ z @ X2 @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf))))) ) | spl306_1),
% 185.79/27.61 inference(trivial_inequality_removal,[status(thm)],[f2103])).
% 185.79/27.61 thf(f2103,plain,(
% 185.79/27.61 ( ! [X2 : b,X0 : rBT_Im1923302023_color,X1 : rBT_Im246033960le_rbt @ a @ b] : (($true != $true) | ($true != (rBT_Im759614907sorted @ a @ b @ less @ (rBT_Im480247531Branch @ a @ b @ X0 @ X1 @ z @ X2 @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf))))) ) | spl306_1),
% 185.79/27.61 inference(superposition,[status(thm)],[f2093,f1488])).
% 185.79/27.61 thf(f1488,plain,(
% 185.79/27.61 ( ! [X0 : $tType,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : a,X1 : rBT_Im1923302023_color,X4 : X0,X5 : rBT_Im246033960le_rbt @ a @ X0] : (((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) != $true) | ($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5))) )),
% 185.79/27.61 inference(cnf_transformation,[status(thm)],[f1060])).
% 185.79/27.61 thf(f1060,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : rBT_Im1923302023_color,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : a,X4 : X0,X5 : rBT_Im246033960le_rbt @ a @ X0] : (((($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5)) & ((rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) = $true) & ($true = (rBT_Im759614907sorted @ a @ X0 @ less @ X5)) & ((rBT_Im759614907sorted @ a @ X0 @ less @ X2) = $true)) | ((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) != $true)) & (((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) = $true) | ($true != (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5)) | ((rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) != $true) | ($true != (rBT_Im759614907sorted @ a @ X0 @ less @ X5)) | ((rBT_Im759614907sorted @ a @ X0 @ less @ X2) != $true)))),
% 185.79/27.61 inference(flattening,[status(thm)],[f1059])).
% 185.79/27.61 thf(f1059,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : rBT_Im1923302023_color,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : a,X4 : X0,X5 : rBT_Im246033960le_rbt @ a @ X0] : (((($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5)) & ((rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) = $true) & ($true = (rBT_Im759614907sorted @ a @ X0 @ less @ X5)) & ((rBT_Im759614907sorted @ a @ X0 @ less @ X2) = $true)) | ((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) != $true)) & (((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) = $true) | (($true != (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5)) | ((rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) != $true) | ($true != (rBT_Im759614907sorted @ a @ X0 @ less @ X5)) | ((rBT_Im759614907sorted @ a @ X0 @ less @ X2) != $true))))),
% 185.79/27.61 inference(nnf_transformation,[status(thm)],[f445])).
% 185.79/27.61 thf(f445,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : rBT_Im1923302023_color,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : a,X4 : X0,X5 : rBT_Im246033960le_rbt @ a @ X0] : ((($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5)) & ((rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) = $true) & ($true = (rBT_Im759614907sorted @ a @ X0 @ less @ X5)) & ((rBT_Im759614907sorted @ a @ X0 @ less @ X2) = $true)) <=> ((rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)) = $true))),
% 185.79/27.61 inference(fool_elimination,[status(thm)],[f444])).
% 185.79/27.61 thf(f444,plain,(
% 185.79/27.61 ! [X0 : $tType,X1 : rBT_Im1923302023_color,X2 : rBT_Im246033960le_rbt @ a @ X0,X3 : a,X4 : X0,X5 : rBT_Im246033960le_rbt @ a @ X0] : ((rBT_Im759614907sorted @ a @ X0 @ less @ X5) & (rBT_Im1259024060reater @ a @ X0 @ less @ X3 @ X5) & (rBT_Im2075124343t_less @ a @ X0 @ less @ X3 @ X2) & (rBT_Im759614907sorted @ a @ X0 @ less @ X2) = (rBT_Im759614907sorted @ a @ X0 @ less @ (rBT_Im480247531Branch @ a @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)))),
% 185.79/27.61 inference(rectify,[status(thm)],[f33])).
% 185.79/27.61 thf(f33,axiom,(
% 185.79/27.61 ! [X1 : $tType,X6 : rBT_Im1923302023_color,X21 : rBT_Im246033960le_rbt @ a @ X1,X22 : a,X23 : X1,X24 : rBT_Im246033960le_rbt @ a @ X1] : ((rBT_Im759614907sorted @ a @ X1 @ less @ X24) & (rBT_Im1259024060reater @ a @ X1 @ less @ X22 @ X24) & (rBT_Im2075124343t_less @ a @ X1 @ less @ X22 @ X21) & (rBT_Im759614907sorted @ a @ X1 @ less @ X21) = (rBT_Im759614907sorted @ a @ X1 @ less @ (rBT_Im480247531Branch @ a @ X1 @ X6 @ X21 @ X22 @ X23 @ X24)))),
% 185.79/27.61 file('/export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2THF_30182.p',fact_32_local_Orbt__sorted_Osimps_I2_J)).
% 185.79/27.61 thf(f2093,plain,(
% 185.79/27.61 ((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) != $true) | spl306_1),
% 185.79/27.61 inference(avatar_component_clause,[status(thm)],[f2091])).
% 185.79/27.61 thf(f2091,definition,(
% 185.79/27.61 spl306_1 <=> ((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) = $true)),
% 185.79/27.61 introduced(definition,[new_symbols(naming,[spl306_1])],[avatar_definition])).
% 185.79/27.61 thf(f2098,plain,(
% 185.79/27.61 ~spl306_1 | ~spl306_2),
% 185.79/27.61 inference(avatar_split_clause,[status(thm)],[f1462,f2095,f2091])).
% 185.79/27.61 thf(f1462,plain,(
% 185.79/27.61 ((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) != $true) | ((less @ y @ z) != $true)),
% 185.79/27.61 inference(cnf_transformation,[status(thm)],[f795])).
% 185.79/27.61 thf(f795,plain,(
% 185.79/27.61 ((less @ y @ z) != $true) | ((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) != $true)),
% 185.79/27.61 inference(ennf_transformation,[status(thm)],[f563])).
% 185.79/27.61 thf(f563,plain,(
% 185.79/27.61 ~(((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) = $true) & ((less @ y @ z) = $true))),
% 185.79/27.61 inference(fool_elimination,[status(thm)],[f562])).
% 185.79/27.61 thf(f562,plain,(
% 185.79/27.61 ~((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) & (less @ y @ z))),
% 185.79/27.61 inference(rectify,[status(thm)],[f260])).
% 185.79/27.61 thf(f260,negated_conjecture,(
% 185.79/27.61 ~((rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) & (less @ y @ z))),
% 185.79/27.61 inference(negated_conjecture,[status(cth)],[f259])).
% 185.79/27.61 thf(f259,conjecture,(
% 185.79/27.61 (rBT_Im1259024060reater @ a @ b @ less @ z @ (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ vd @ ve @ vii @ vf)) & (less @ y @ z)),
% 185.79/27.61 file('/export/starexec/sandbox/tmp/tmp.yT5e3JCqBc/DTF2THF_30182.p',conj_0)).
% 185.79/27.61 % SZS output end Proof for DTF2THF_30182
% 185.79/27.61 % (31420)------------------------------
% 185.79/27.61 % (31420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 185.79/27.61 % (31420)Termination reason: Refutation
% 185.79/27.61
% 185.79/27.61 % (31420)Memory used [KB]: 15991
% 185.79/27.61 % (31420)Time elapsed: 3.041 s
% 185.79/27.61 % (31420)Instructions burned: 9790 (million)
% 185.79/27.61 % (31420)------------------------------
% 185.79/27.61 % (31420)------------------------------
% 185.79/27.61 % (30329)Success in time 26.121 s
%------------------------------------------------------------------------------