%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT229^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 08:45:13 AM UTC 2026
% Result : Theorem 2.50s 1.75s
% Output : Refutation 2.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT229^1 : TPTP v9.2.1. Released v7.0.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 06:12:09 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : DAT229^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.43 % Domain : Data Structures
% 0.17/0.43 % Problem : Red-black trees 26
% 0.17/0.43 % Version : [Bla16] axioms : Especial.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.17/0.43 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.17/0.43 % Source : [Bla16]
% 0.17/0.43 % Names : rbt_impl__26.p [Bla16]
% 0.17/0.43
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.33 v8.1.0, 0.50 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.43 % Syntax : Number of formulae : 343 ( 156 unt; 59 typ; 0 def)
% 0.17/0.43 % Number of atoms : 674 ( 329 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 10 ( 2 avg)
% 0.17/0.43 % Number of connectives : 4376 ( 63 ~; 9 |; 49 &;3989 @)
% 0.17/0.43 % ( 0 <=>; 266 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 31 ( 8 avg)
% 0.17/0.43 % Number of types : 5 ( 4 usr)
% 0.17/0.43 % Number of type conns : 489 ( 489 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 58 ( 55 usr; 6 con; 0-10 aty)
% 0.17/0.43 % Number of variables : 1390 ( 51 ^;1249 !; 15 ?;1390 :)
% 0.17/0.43 % ( 75 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.43 % SPC : TH1_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.43 % 2016-07-13 14:38:44.202
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 %----Could-be-implicit typings (7)
% 0.17/0.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.17/0.43 rBT_Im1923302023_color: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.17/0.43 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Set_Oset,type,
% 0.17/0.43 set: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_Nat_Onat,type,
% 0.17/0.43 nat: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_t_itself,type,
% 0.17/0.43 itself: $tType > $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_tf_b,type,
% 0.17/0.43 b: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(ty_tf_a,type,
% 0.17/0.43 a: $tType ).
% 0.17/0.43
% 0.17/0.43 %----Explicit typings (52)
% 0.17/0.43 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.17/0.43 bounded_lattice:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_HOL_Otype,type,
% 0.17/0.43 type:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Obot,type,
% 0.17/0.43 bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Opreorder,type,
% 0.17/0.43 preorder:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.17/0.43 order_bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.17/0.43 bounded_lattice_bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.17/0.43 bounde1808546759up_bot:
% 0.17/0.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_BNF__Composition_Oid__bnf,type,
% 0.17/0.43 bNF_id_bnf:
% 0.17/0.43 !>[A: $tType] : ( A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_BNF__Def_Oeq__onp,type,
% 0.17/0.43 bNF_eq_onp:
% 0.17/0.43 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_BNF__Def_Ovimage2p,type,
% 0.17/0.43 bNF_vimage2p:
% 0.17/0.43 !>[A: $tType,D: $tType,B: $tType,E: $tType,C: $tType] : ( ( A > D ) > ( B > E ) > ( D > E > C ) > A > B > C ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Finite__Set_Ofinite,type,
% 0.17/0.43 finite_finite:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Fun_Obij__betw,type,
% 0.17/0.43 bij_betw:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Fun_Ocomp,type,
% 0.17/0.43 comp:
% 0.17/0.43 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Fun_Omap__fun,type,
% 0.17/0.43 map_fun:
% 0.17/0.43 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Fun_Ooverride__on,type,
% 0.17/0.43 override_on:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( set @ A ) > A > B ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ocomm__monoid,type,
% 0.17/0.43 comm_monoid:
% 0.17/0.43 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Omonoid,type,
% 0.17/0.43 monoid:
% 0.17/0.43 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.17/0.43 zero_zero:
% 0.17/0.43 !>[A: $tType] : A ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_If,type,
% 0.17/0.43 if:
% 0.17/0.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.17/0.43 inf_inf:
% 0.17/0.43 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 0.17/0.43 semilattice_neutr:
% 0.17/0.43 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.17/0.43 sup_sup:
% 0.17/0.43 !>[A: $tType] : ( A > A > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.17/0.43 size_size:
% 0.17/0.43 !>[A: $tType] : ( A > nat ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.17/0.43 bot_bot:
% 0.17/0.43 !>[A: $tType] : A ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.17/0.43 ord_less_eq:
% 0.17/0.43 !>[A: $tType] : ( A > A > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Pure_Otype,type,
% 0.17/0.43 type2:
% 0.17/0.43 !>[A: $tType] : ( itself @ A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 0.17/0.43 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 0.17/0.43 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color,type,
% 0.17/0.43 rBT_Im1975547051_color:
% 0.17/0.43 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color,type,
% 0.17/0.43 rBT_Im1059957627_color:
% 0.17/0.43 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color,type,
% 0.17/0.43 rBT_Im800559290_color: rBT_Im1923302023_color > nat ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.17/0.43 rBT_Im480247531Branch:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.17/0.43 rBT_Im418718756_Empty:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt,type,
% 0.17/0.43 rBT_Im858806507se_rbt:
% 0.17/0.43 !>[C: $tType,A: $tType,B: $tType] : ( C > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C ) > ( rBT_Im246033960le_rbt @ A @ B ) > C ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Omap__rbt,type,
% 0.17/0.43 rBT_Im206295089ap_rbt:
% 0.17/0.43 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ Aa @ Ba ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Opred__rbt,type,
% 0.17/0.43 rBT_Im1931894874ed_rbt:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt,type,
% 0.17/0.43 rBT_Im1947144893ec_rbt:
% 0.17/0.43 !>[E: $tType,A: $tType,B: $tType] : ( E > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E ) > ( rBT_Im246033960le_rbt @ A @ B ) > E ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orel__rbt,type,
% 0.17/0.43 rBT_Im1000242676el_rbt:
% 0.17/0.43 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ C @ D ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt,type,
% 0.17/0.43 rBT_Im1178217900t1_rbt:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt,type,
% 0.17/0.43 rBT_Im1550225131t2_rbt:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ B ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt,type,
% 0.17/0.43 rBT_Im1485196410ze_rbt:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OBall,type,
% 0.17/0.43 ball:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_OCollect,type,
% 0.17/0.43 collect:
% 0.17/0.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Oinsert,type,
% 0.17/0.43 insert:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Ois__empty,type,
% 0.17/0.43 is_empty:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Ois__singleton,type,
% 0.17/0.43 is_singleton:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Opairwise,type,
% 0.17/0.43 pairwise:
% 0.17/0.43 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Othe__elem,type,
% 0.17/0.43 the_elem:
% 0.17/0.43 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_Set_Ovimage,type,
% 0.17/0.43 vimage:
% 0.17/0.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_c_member,type,
% 0.17/0.43 member:
% 0.17/0.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_t,type,
% 0.17/0.43 t: rBT_Im246033960le_rbt @ a @ b ).
% 0.17/0.43
% 0.17/0.43 thf(sy_v_thesis,type,
% 0.17/0.43 thesis: $o ).
% 0.17/0.43
% 0.17/0.43 %----Relevant facts (256)
% 0.17/0.43 thf(fact_0_Empty,axiom,
% 0.17/0.43 ( ( t
% 0.17/0.43 = ( rBT_Im418718756_Empty @ a @ b ) )
% 0.17/0.43 => thesis ) ).
% 0.17/0.43
% 0.17/0.43 % Empty
% 0.17/0.43 thf(fact_1_rbt_Oinject,axiom,
% 0.17/0.43 ! [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] :
% 0.17/0.43 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 0.17/0.43 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.17/0.43 = ( ( X21 = Y21 )
% 0.17/0.43 & ( X22 = Y22 )
% 0.17/0.43 & ( X23 = Y23 )
% 0.17/0.43 & ( X24 = Y24 )
% 0.17/0.43 & ( X25 = Y25 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.inject
% 0.17/0.43 thf(fact_2_Black,axiom,
% 0.17/0.43 ! [L: rBT_Im246033960le_rbt @ a @ b,K: a,V: b,R: rBT_Im246033960le_rbt @ a @ b] :
% 0.17/0.43 ( ( t
% 0.17/0.43 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ L @ K @ V @ R ) )
% 0.17/0.43 => thesis ) ).
% 0.17/0.43
% 0.17/0.43 % Black
% 0.17/0.43 thf(fact_3_Red,axiom,
% 0.17/0.43 ! [L: rBT_Im246033960le_rbt @ a @ b,K: a,V: b,R: rBT_Im246033960le_rbt @ a @ b] :
% 0.17/0.43 ( ( t
% 0.17/0.43 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ L @ K @ V @ R ) )
% 0.17/0.43 => thesis ) ).
% 0.17/0.43
% 0.17/0.43 % Red
% 0.17/0.43 thf(fact_4_rbt_Odistinct_I1_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.17/0.43 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.distinct(1)
% 0.17/0.43 thf(fact_5_color_Odistinct_I1_J,axiom,
% 0.17/0.43 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 0.17/0.43
% 0.17/0.43 % color.distinct(1)
% 0.17/0.43 thf(fact_6_rbt_Oinduct,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 => ( ! [X1: rBT_Im1923302023_color,X2: rBT_Im246033960le_rbt @ A @ B,X3: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( P @ X2 )
% 0.17/0.43 => ( ( P @ X5 )
% 0.17/0.43 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) )
% 0.17/0.43 => ( P @ Rbt ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.induct
% 0.17/0.43 thf(fact_7_rbt_Oexhaust,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( Y
% 0.17/0.43 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( Y
% 0.17/0.43 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.exhaust
% 0.17/0.43 thf(fact_8_color_Oinduct,axiom,
% 0.17/0.43 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 0.17/0.43 ( ( P @ rBT_Impl_Mirabelle_R )
% 0.17/0.43 => ( ( P @ rBT_Impl_Mirabelle_B )
% 0.17/0.43 => ( P @ Color ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.induct
% 0.17/0.43 thf(fact_9_color_Oexhaust,axiom,
% 0.17/0.43 ! [Y: rBT_Im1923302023_color] :
% 0.17/0.43 ( ( Y != rBT_Impl_Mirabelle_R )
% 0.17/0.43 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.exhaust
% 0.17/0.43 thf(fact_10_color_Osimps_I6_J,axiom,
% 0.17/0.43 ! [A: $tType,F1: A,F2: A] :
% 0.17/0.43 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.17/0.43 = F2 ) ).
% 0.17/0.43
% 0.17/0.43 % color.simps(6)
% 0.17/0.43 thf(fact_11_color_Osimps_I5_J,axiom,
% 0.17/0.43 ! [A: $tType,F1: A,F2: A] :
% 0.17/0.43 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.17/0.43 = F1 ) ).
% 0.17/0.43
% 0.17/0.43 % color.simps(5)
% 0.17/0.43 thf(fact_12_color_Osimps_I4_J,axiom,
% 0.17/0.43 ! [A: $tType,F1: A,F2: A] :
% 0.17/0.43 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.17/0.43 = F2 ) ).
% 0.17/0.43
% 0.17/0.43 % color.simps(4)
% 0.17/0.43 thf(fact_13_color_Osimps_I3_J,axiom,
% 0.17/0.43 ! [A: $tType,F1: A,F2: A] :
% 0.17/0.43 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.17/0.43 = F1 ) ).
% 0.17/0.43
% 0.17/0.43 % color.simps(3)
% 0.17/0.43 thf(fact_14_rbt_Osimps_I4_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C: $tType,F1: C,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C] :
% 0.17/0.43 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = F1 ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(4)
% 0.17/0.43 thf(fact_15_rbt_Osimps_I5_J,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,A: $tType,F1: C,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.17/0.43 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(5)
% 0.17/0.43 thf(fact_16_rbt_Osimps_I6_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,E: $tType,F1: E,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E] :
% 0.17/0.43 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = F1 ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(6)
% 0.17/0.43 thf(fact_17_rbt_Osimps_I7_J,axiom,
% 0.17/0.43 ! [E: $tType,B: $tType,A: $tType,F1: E,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.17/0.43 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X22 ) @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X25 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(7)
% 0.17/0.43 thf(fact_18_rbt_Opred__inject_I2_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: rBT_Im1923302023_color,Aa2: rBT_Im246033960le_rbt @ A @ B,Ab: A,Ac: B,Ad: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ ( rBT_Im480247531Branch @ A @ B @ A2 @ Aa2 @ Ab @ Ac @ Ad ) )
% 0.17/0.43 = ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ Aa2 )
% 0.17/0.43 & ( P1 @ Ab )
% 0.17/0.43 & ( P2 @ Ac )
% 0.17/0.43 & ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ Ad ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_inject(2)
% 0.17/0.43 thf(fact_19_rbt_Orel__distinct_I2_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_distinct(2)
% 0.17/0.43 thf(fact_20_rbt_Orel__distinct_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 0.17/0.43 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_distinct(1)
% 0.17/0.43 thf(fact_21_rbt_Opred__inject_I1_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o] : ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_inject(1)
% 0.17/0.43 thf(fact_22_rbt_Orel__eq,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B
% 0.17/0.43 @ ^ [Y2: A,Z: A] : ( Y2 = Z )
% 0.17/0.43 @ ^ [Y2: B,Z: B] : ( Y2 = Z ) )
% 0.17/0.43 = ( ^ [Y2: rBT_Im246033960le_rbt @ A @ B,Z: rBT_Im246033960le_rbt @ A @ B] : ( Y2 = Z ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_eq
% 0.17/0.43 thf(fact_23_rbt_Orel__refl,axiom,
% 0.17/0.43 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: rBT_Im246033960le_rbt @ C @ D] :
% 0.17/0.43 ( ! [X6: C] : ( R1a @ X6 @ X6 )
% 0.17/0.43 => ( ! [X6: D] : ( R2a @ X6 @ X6 )
% 0.17/0.43 => ( rBT_Im1000242676el_rbt @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_refl
% 0.17/0.43 thf(fact_24_color_Ocase__distrib,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,H: A > B,F1: A,F2: A,Color: rBT_Im1923302023_color] :
% 0.17/0.43 ( ( H @ ( rBT_Im1975547051_color @ A @ F1 @ F2 @ Color ) )
% 0.17/0.43 = ( rBT_Im1975547051_color @ B @ ( H @ F1 ) @ ( H @ F2 ) @ Color ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.case_distrib
% 0.17/0.43 thf(fact_25_rbt_Orel__intros_I2_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,X21: rBT_Im1923302023_color,Y21: rBT_Im1923302023_color,R1: A > C > $o,R2: B > D > $o,X22: rBT_Im246033960le_rbt @ A @ B,Y22: rBT_Im246033960le_rbt @ C @ D,X23: A,Y23: C,X24: B,Y24: D,X25: rBT_Im246033960le_rbt @ A @ B,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 0.17/0.43 ( ( X21 = Y21 )
% 0.17/0.43 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 0.17/0.43 => ( ( R1 @ X23 @ Y23 )
% 0.17/0.43 => ( ( R2 @ X24 @ Y24 )
% 0.17/0.43 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X25 @ Y25 )
% 0.17/0.43 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_intros(2)
% 0.17/0.43 thf(fact_26_rbt_Orel__inject_I2_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,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 @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 0.17/0.43 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.17/0.43 = ( ( X21 = Y21 )
% 0.17/0.43 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 0.17/0.43 & ( R1 @ X23 @ Y23 )
% 0.17/0.43 & ( R2 @ X24 @ Y24 )
% 0.17/0.43 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X25 @ Y25 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_inject(2)
% 0.17/0.43 thf(fact_27_rbt_Octr__transfer_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o] : ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.ctr_transfer(1)
% 0.17/0.43 thf(fact_28_rbt_Opred__rel,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.17/0.43 = ( ^ [P12: A > $o,P22: B > $o,X7: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P12 ) @ ( bNF_eq_onp @ B @ P22 ) @ X7 @ X7 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_rel
% 0.17/0.43 thf(fact_29_rbt_Oset__intros_I1_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X: A,A22: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A3: A,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ A22 ) )
% 0.17/0.43 => ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(1)
% 0.17/0.43 thf(fact_30_rbt_Oset__intros_I2_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,A3: A,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] : ( member @ A @ A3 @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(2)
% 0.17/0.43 thf(fact_31_rbt_Oset__intros_I3_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,Xb: A,A5: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A3: A,A4: B] :
% 0.17/0.43 ( ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ A5 ) )
% 0.17/0.43 => ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(3)
% 0.17/0.43 thf(fact_32_rbt_Oset__intros_I4_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,Xe: B,A2a: rBT_Im246033960le_rbt @ A @ B,A1a: rBT_Im1923302023_color,A3a: A,A4a: B,A5a: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2a ) )
% 0.17/0.43 => ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(4)
% 0.17/0.43 thf(fact_33_rbt_Oset__intros_I5_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,A4a: B,A1a: rBT_Im1923302023_color,A2a: rBT_Im246033960le_rbt @ A @ B,A3a: A,A5a: rBT_Im246033960le_rbt @ A @ B] : ( member @ B @ A4a @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(5)
% 0.17/0.43 thf(fact_34_rbt_Oset__intros_I6_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,Xg: B,A5a: rBT_Im246033960le_rbt @ A @ B,A1a: rBT_Im1923302023_color,A2a: rBT_Im246033960le_rbt @ A @ B,A3a: A,A4a: B] :
% 0.17/0.43 ( ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ A5a ) )
% 0.17/0.43 => ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_intros(6)
% 0.17/0.43 thf(fact_35_rbt_Oset__cases_I1_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,E2: A,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ A2 ) )
% 0.17/0.43 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ? [Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( A2
% 0.17/0.43 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 0.17/0.43 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z2 ) ) )
% 0.17/0.43 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( A2
% 0.17/0.43 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ E2 @ Z4 @ Z5 ) )
% 0.17/0.43 => ~ ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 0.17/0.43 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_cases(1)
% 0.17/0.43 thf(fact_36_rbt_Oset__cases_I2_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,E2: B,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2 ) )
% 0.17/0.43 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ? [Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( A2
% 0.17/0.43 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 0.17/0.43 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z2 ) ) )
% 0.17/0.43 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( A2
% 0.17/0.43 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ E2 @ Z5 ) )
% 0.17/0.43 => ~ ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( A2
% 0.17/0.43 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 0.17/0.43 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.set_cases(2)
% 0.17/0.43 thf(fact_37_rbt_Osimps_I8_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,F1: A > C,F2: B > D] :
% 0.17/0.43 ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(8)
% 0.17/0.43 thf(fact_38_rbt_Oinj__map__strong,axiom,
% 0.17/0.43 ! [C: $tType,D: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Xa: rBT_Im246033960le_rbt @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 0.17/0.43 ( ! [Z1: A,Z1a: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( member @ A @ Z1a @ ( rBT_Im1178217900t1_rbt @ A @ B @ Xa ) )
% 0.17/0.43 => ( ( ( F1 @ Z1 )
% 0.17/0.43 = ( F1a @ Z1a ) )
% 0.17/0.43 => ( Z1 = Z1a ) ) ) )
% 0.17/0.43 => ( ! [Z2: B,Z2a: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( member @ B @ Z2a @ ( rBT_Im1550225131t2_rbt @ A @ B @ Xa ) )
% 0.17/0.43 => ( ( ( F2 @ Z2 )
% 0.17/0.43 = ( F2a @ Z2a ) )
% 0.17/0.43 => ( Z2 = Z2a ) ) ) )
% 0.17/0.43 => ( ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.17/0.43 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 0.17/0.43 => ( X = Xa ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.inj_map_strong
% 0.17/0.43 thf(fact_39_rbt_Omap__cong0,axiom,
% 0.17/0.43 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.17/0.43 ( ! [Z1: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( F1 @ Z1 )
% 0.17/0.43 = ( G1 @ Z1 ) ) )
% 0.17/0.43 => ( ! [Z2: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( F2 @ Z2 )
% 0.17/0.43 = ( G2 @ Z2 ) ) )
% 0.17/0.43 => ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.17/0.43 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G1 @ G2 @ X ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.map_cong0
% 0.17/0.43 thf(fact_40_rbt_Omap__cong,axiom,
% 0.17/0.43 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 0.17/0.43 ( ( X = Ya )
% 0.17/0.43 => ( ! [Z1: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( F1 @ Z1 )
% 0.17/0.43 = ( G1 @ Z1 ) ) )
% 0.17/0.43 => ( ! [Z2: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( F2 @ Z2 )
% 0.17/0.43 = ( G2 @ Z2 ) ) )
% 0.17/0.43 => ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 0.17/0.43 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.map_cong
% 0.17/0.43 thf(fact_41_rbt_Orel__refl__strong,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.17/0.43 ( ! [Z1: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( R1a @ Z1 @ Z1 ) )
% 0.17/0.43 => ( ! [Z2: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( R2a @ Z2 @ Z2 ) )
% 0.17/0.43 => ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_refl_strong
% 0.17/0.43 thf(fact_42_rbt_Orel__mono__strong,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.17/0.43 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 0.17/0.43 => ( ! [Z1: A,Y1: C] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Y ) )
% 0.17/0.43 => ( ( R1 @ Z1 @ Y1 )
% 0.17/0.43 => ( R1a @ Z1 @ Y1 ) ) ) )
% 0.17/0.43 => ( ! [Z2: B,Y26: D] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Y ) )
% 0.17/0.43 => ( ( R2 @ Z2 @ Y26 )
% 0.17/0.43 => ( R2a @ Z2 @ Y26 ) ) ) )
% 0.17/0.43 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_mono_strong
% 0.17/0.43 thf(fact_43_rbt_Orel__cong,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,D: $tType,C: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,Xa: rBT_Im246033960le_rbt @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 0.17/0.43 ( ( X = Ya )
% 0.17/0.43 => ( ( Y = Xa )
% 0.17/0.43 => ( ! [Z1: A,Y1: C] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Xa ) )
% 0.17/0.43 => ( ( R1 @ Z1 @ Y1 )
% 0.17/0.43 = ( R1a @ Z1 @ Y1 ) ) ) )
% 0.17/0.43 => ( ! [Z2: B,Y26: D] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Xa ) )
% 0.17/0.43 => ( ( R2 @ Z2 @ Y26 )
% 0.17/0.43 = ( R2a @ Z2 @ Y26 ) ) ) )
% 0.17/0.43 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 0.17/0.43 = ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_cong
% 0.17/0.43 thf(fact_44_rbt_Opred__mono__strong,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X: rBT_Im246033960le_rbt @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.17/0.43 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ X )
% 0.17/0.43 => ( ! [Z1: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( P1 @ Z1 )
% 0.17/0.43 => ( P1a @ Z1 ) ) )
% 0.17/0.43 => ( ! [Z2: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.17/0.43 => ( ( P2 @ Z2 )
% 0.17/0.43 => ( P2a @ Z2 ) ) )
% 0.17/0.43 => ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_mono_strong
% 0.17/0.43 thf(fact_45_mem__Collect__eq,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,P: A > $o] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.17/0.43 = ( P @ A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % mem_Collect_eq
% 0.17/0.43 thf(fact_46_Collect__mem__eq,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( collect @ A
% 0.17/0.43 @ ^ [X7: A] : ( member @ A @ X7 @ A6 ) )
% 0.17/0.43 = A6 ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_mem_eq
% 0.17/0.43 thf(fact_47_Collect__cong,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( P @ X6 )
% 0.17/0.43 = ( Q @ X6 ) )
% 0.17/0.43 => ( ( collect @ A @ P )
% 0.17/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_cong
% 0.17/0.43 thf(fact_48_ext,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( F @ X6 )
% 0.17/0.43 = ( G @ X6 ) )
% 0.17/0.43 => ( F = G ) ) ).
% 0.17/0.43
% 0.17/0.43 % ext
% 0.17/0.43 thf(fact_49_rbt_Opred__cong,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 0.17/0.43 ( ( X = Ya )
% 0.17/0.43 => ( ! [Z1: A] :
% 0.17/0.43 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( P1 @ Z1 )
% 0.17/0.43 = ( P1a @ Z1 ) ) )
% 0.17/0.43 => ( ! [Z2: B] :
% 0.17/0.43 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.17/0.43 => ( ( P2 @ Z2 )
% 0.17/0.43 = ( P2a @ Z2 ) ) )
% 0.17/0.43 => ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ X )
% 0.17/0.43 = ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_cong
% 0.17/0.43 thf(fact_50_rbt_Orel__eq__onp,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o] :
% 0.17/0.43 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P1 ) @ ( bNF_eq_onp @ B @ P2 ) )
% 0.17/0.43 = ( bNF_eq_onp @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.rel_eq_onp
% 0.17/0.43 thf(fact_51_rbt_Osimps_I9_J,axiom,
% 0.17/0.43 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.17/0.43 = ( rBT_Im480247531Branch @ C @ D @ X21 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X22 ) @ ( F1 @ X23 ) @ ( F2 @ X24 ) @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X25 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(9)
% 0.17/0.43 thf(fact_52_eq__onp__live__step,axiom,
% 0.17/0.43 ! [A: $tType,X: $o,Y: $o,P: A > $o,A2: A] :
% 0.17/0.43 ( ( X = Y )
% 0.17/0.43 => ( ( ( bNF_eq_onp @ A @ P @ A2 @ A2 )
% 0.17/0.43 & X )
% 0.17/0.43 = ( ( P @ A2 )
% 0.17/0.43 & Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_onp_live_step
% 0.17/0.43 thf(fact_53_eq__onp__same__args,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,X: A] :
% 0.17/0.43 ( ( bNF_eq_onp @ A @ P @ X @ X )
% 0.17/0.43 = ( P @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_onp_same_args
% 0.17/0.43 thf(fact_54_eq__onp__to__eq,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,X: A,Y: A] :
% 0.17/0.43 ( ( bNF_eq_onp @ A @ P @ X @ Y )
% 0.17/0.43 => ( X = Y ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_onp_to_eq
% 0.17/0.43 thf(fact_55_eq__onp__mono0,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( member @ A @ X6 @ A6 )
% 0.17/0.43 => ( ( P @ X6 )
% 0.17/0.43 => ( Q @ X6 ) ) )
% 0.17/0.43 => ! [X8: A] :
% 0.17/0.43 ( ( member @ A @ X8 @ A6 )
% 0.17/0.43 => ! [Xa2: A] :
% 0.17/0.43 ( ( member @ A @ Xa2 @ A6 )
% 0.17/0.43 => ( ( bNF_eq_onp @ A @ P @ X8 @ Xa2 )
% 0.17/0.43 => ( bNF_eq_onp @ A @ Q @ X8 @ Xa2 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_onp_mono0
% 0.17/0.43 thf(fact_56_eq__onp__eqD,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,Q: A > A > $o,X: A] :
% 0.17/0.43 ( ( ( bNF_eq_onp @ A @ P )
% 0.17/0.43 = Q )
% 0.17/0.43 => ( ( P @ X )
% 0.17/0.43 = ( Q @ X @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % eq_onp_eqD
% 0.17/0.43 thf(fact_57_rbt_Opred__set,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.17/0.43 = ( ^ [P12: A > $o,P22: B > $o,X7: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ! [Y3: A] :
% 0.17/0.43 ( ( member @ A @ Y3 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X7 ) )
% 0.17/0.43 => ( P12 @ Y3 ) )
% 0.17/0.43 & ! [Y3: B] :
% 0.17/0.43 ( ( member @ B @ Y3 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X7 ) )
% 0.17/0.43 => ( P22 @ Y3 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_set
% 0.17/0.43 thf(fact_58_rbt_Osimps_I16_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = ( bot_bot @ ( set @ B ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(16)
% 0.17/0.43 thf(fact_59_rbt_Osimps_I14_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(14)
% 0.17/0.43 thf(fact_60_rbt_Opred__map,axiom,
% 0.17/0.43 ! [D: $tType,C: $tType,B: $tType,A: $tType,Q1: C > $o,Q2: D > $o,F1: A > C,F2: B > D,X: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im1931894874ed_rbt @ C @ D @ Q1 @ Q2 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X ) )
% 0.17/0.43 = ( rBT_Im1931894874ed_rbt @ A @ B @ ( comp @ C @ $o @ A @ Q1 @ F1 ) @ ( comp @ D @ $o @ B @ Q2 @ F2 ) @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.pred_map
% 0.17/0.43 thf(fact_61_comp__apply__eq,axiom,
% 0.17/0.43 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X: C,H: D > A,K: C > D] :
% 0.17/0.43 ( ( ( F @ ( G @ X ) )
% 0.17/0.43 = ( H @ ( K @ X ) ) )
% 0.17/0.43 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 0.17/0.43 = ( comp @ D @ A @ C @ H @ K @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_apply_eq
% 0.17/0.43 thf(fact_62_rewriteL__comp__comp,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.17/0.43 = L )
% 0.17/0.43 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 0.17/0.43 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rewriteL_comp_comp
% 0.17/0.43 thf(fact_63_rewriteR__comp__comp,axiom,
% 0.17/0.43 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.17/0.43 = R )
% 0.17/0.43 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 0.17/0.43 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rewriteR_comp_comp
% 0.17/0.43 thf(fact_64_rewriteL__comp__comp2,axiom,
% 0.17/0.43 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.17/0.43 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.17/0.43 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 0.17/0.43 = R )
% 0.17/0.43 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 0.17/0.43 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rewriteL_comp_comp2
% 0.17/0.43 thf(fact_65_rewriteR__comp__comp2,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R12: D > B,R22: A > D,F: B > E,L: D > E] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.17/0.43 = ( comp @ D @ B @ A @ R12 @ R22 ) )
% 0.17/0.43 => ( ( ( comp @ B @ E @ D @ F @ R12 )
% 0.17/0.43 = L )
% 0.17/0.43 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 0.17/0.43 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rewriteR_comp_comp2
% 0.17/0.43 thf(fact_66_rbt_Omap__comp,axiom,
% 0.17/0.43 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,G1: C > E,G2: D > F3,F1: A > C,F2: B > D,V: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im206295089ap_rbt @ C @ E @ D @ F3 @ G1 @ G2 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ V ) )
% 0.17/0.43 = ( rBT_Im206295089ap_rbt @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G2 @ F2 ) @ V ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.map_comp
% 0.17/0.43 thf(fact_67_ball__empty,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,X8: A] :
% 0.17/0.43 ( ( member @ A @ X8 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 => ( P @ X8 ) ) ).
% 0.17/0.43
% 0.17/0.43 % ball_empty
% 0.17/0.43 thf(fact_68_comp__apply,axiom,
% 0.17/0.43 ! [C: $tType,A: $tType,B: $tType] :
% 0.17/0.43 ( ( comp @ B @ A @ C )
% 0.17/0.43 = ( ^ [F4: B > A,G3: C > B,X7: C] : ( F4 @ ( G3 @ X7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_apply
% 0.17/0.43 thf(fact_69_empty__iff,axiom,
% 0.17/0.43 ! [A: $tType,C2: A] :
% 0.17/0.43 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_iff
% 0.17/0.43 thf(fact_70_all__not__in__conv,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( ! [X7: A] :
% 0.17/0.43 ~ ( member @ A @ X7 @ A6 ) )
% 0.17/0.43 = ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % all_not_in_conv
% 0.17/0.43 thf(fact_71_Collect__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( collect @ A @ P )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( ! [X7: A] :
% 0.17/0.43 ~ ( P @ X7 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_empty_eq
% 0.17/0.43 thf(fact_72_empty__Collect__eq,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.43 = ( collect @ A @ P ) )
% 0.17/0.43 = ( ! [X7: A] :
% 0.17/0.43 ~ ( P @ X7 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % empty_Collect_eq
% 0.17/0.43 thf(fact_73_bot__apply,axiom,
% 0.17/0.43 ! [C: $tType,D: $tType] :
% 0.17/0.43 ( ( bot @ C @ ( type2 @ C ) )
% 0.17/0.43 => ( ( bot_bot @ ( D > C ) )
% 0.17/0.43 = ( ^ [X7: D] : ( bot_bot @ C ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_apply
% 0.17/0.43 thf(fact_74_bot__set__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bot_bot @ ( set @ A ) )
% 0.17/0.43 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_set_def
% 0.17/0.43 thf(fact_75_bot__fun__def,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( bot @ B @ ( type2 @ B ) )
% 0.17/0.43 => ( ( bot_bot @ ( A > B ) )
% 0.17/0.43 = ( ^ [X7: A] : ( bot_bot @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_fun_def
% 0.17/0.43 thf(fact_76_ex__in__conv,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( ? [X7: A] : ( member @ A @ X7 @ A6 ) )
% 0.17/0.43 = ( A6
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ex_in_conv
% 0.17/0.43 thf(fact_77_equals0I,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ! [Y4: A] :
% 0.17/0.43 ~ ( member @ A @ Y4 @ A6 )
% 0.17/0.43 => ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % equals0I
% 0.17/0.43 thf(fact_78_equals0D,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,A2: A] :
% 0.17/0.43 ( ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 => ~ ( member @ A @ A2 @ A6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % equals0D
% 0.17/0.43 thf(fact_79_emptyE,axiom,
% 0.17/0.43 ! [A: $tType,A2: A] :
% 0.17/0.43 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % emptyE
% 0.17/0.43 thf(fact_80_comp__eq__dest__lhs,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.17/0.43 = C2 )
% 0.17/0.43 => ( ( A2 @ ( B2 @ V ) )
% 0.17/0.43 = ( C2 @ V ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_eq_dest_lhs
% 0.17/0.43 thf(fact_81_comp__eq__elim,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.17/0.43 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.17/0.43 => ! [V2: A] :
% 0.17/0.43 ( ( A2 @ ( B2 @ V2 ) )
% 0.17/0.43 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_eq_elim
% 0.17/0.43 thf(fact_82_comp__eq__dest,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 0.17/0.43 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 0.17/0.43 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.17/0.43 => ( ( A2 @ ( B2 @ V ) )
% 0.17/0.43 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_eq_dest
% 0.17/0.43 thf(fact_83_comp__assoc,axiom,
% 0.17/0.43 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 0.17/0.43 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 0.17/0.43 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_assoc
% 0.17/0.43 thf(fact_84_comp__def,axiom,
% 0.17/0.43 ! [A: $tType,C: $tType,B: $tType] :
% 0.17/0.43 ( ( comp @ B @ C @ A )
% 0.17/0.43 = ( ^ [F4: B > C,G3: A > B,X7: A] : ( F4 @ ( G3 @ X7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_def
% 0.17/0.43 thf(fact_85_Ball__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( ball @ A )
% 0.17/0.43 = ( ^ [A7: set @ A,P3: A > $o] :
% 0.17/0.43 ! [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ A7 )
% 0.17/0.43 => ( P3 @ X7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Ball_def
% 0.17/0.43 thf(fact_86_override__on__emptyset,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.17/0.43 ( ( override_on @ A @ B @ F @ G @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = F ) ).
% 0.17/0.43
% 0.17/0.43 % override_on_emptyset
% 0.17/0.43 thf(fact_87_Set_Ois__empty__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_empty @ A )
% 0.17/0.43 = ( ^ [A7: set @ A] :
% 0.17/0.43 ( A7
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Set.is_empty_def
% 0.17/0.43 thf(fact_88_ball__reg,axiom,
% 0.17/0.43 ! [A: $tType,R3: set @ A,P: A > $o,Q: A > $o] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( member @ A @ X6 @ R3 )
% 0.17/0.43 => ( ( P @ X6 )
% 0.17/0.43 => ( Q @ X6 ) ) )
% 0.17/0.43 => ( ! [X6: A] :
% 0.17/0.43 ( ( member @ A @ X6 @ R3 )
% 0.17/0.43 => ( P @ X6 ) )
% 0.17/0.43 => ! [X8: A] :
% 0.17/0.43 ( ( member @ A @ X8 @ R3 )
% 0.17/0.43 => ( Q @ X8 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ball_reg
% 0.17/0.43 thf(fact_89_type__copy__map__cong0,axiom,
% 0.17/0.43 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X: C,N: D > A,H: C > D,F: A > E] :
% 0.17/0.43 ( ( ( M @ ( G @ X ) )
% 0.17/0.43 = ( N @ ( H @ X ) ) )
% 0.17/0.43 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X )
% 0.17/0.43 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % type_copy_map_cong0
% 0.17/0.43 thf(fact_90_fun_Omap__comp,axiom,
% 0.17/0.43 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.17/0.43 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.17/0.43 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.17/0.43
% 0.17/0.43 % fun.map_comp
% 0.17/0.43 thf(fact_91_comp__cong,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X: C,F5: D > A,G4: E > D,X9: E] :
% 0.17/0.43 ( ( ( F @ ( G @ X ) )
% 0.17/0.43 = ( F5 @ ( G4 @ X9 ) ) )
% 0.17/0.43 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 0.17/0.43 = ( comp @ D @ A @ E @ F5 @ G4 @ X9 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % comp_cong
% 0.17/0.43 thf(fact_92_override__on__apply__in,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,A2: A,A6: set @ A,F: A > B,G: A > B] :
% 0.17/0.43 ( ( member @ A @ A2 @ A6 )
% 0.17/0.43 => ( ( override_on @ A @ B @ F @ G @ A6 @ A2 )
% 0.17/0.43 = ( G @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % override_on_apply_in
% 0.17/0.43 thf(fact_93_override__on__apply__notin,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,A2: A,A6: set @ A,F: A > B,G: A > B] :
% 0.17/0.43 ( ~ ( member @ A @ A2 @ A6 )
% 0.17/0.43 => ( ( override_on @ A @ B @ F @ G @ A6 @ A2 )
% 0.17/0.43 = ( F @ A2 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % override_on_apply_notin
% 0.17/0.43 thf(fact_94_override__on__def,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType] :
% 0.17/0.43 ( ( override_on @ A @ B )
% 0.17/0.43 = ( ^ [F4: A > B,G3: A > B,A7: set @ A,A8: A] : ( if @ B @ ( member @ A @ A8 @ A7 ) @ ( G3 @ A8 ) @ ( F4 @ A8 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % override_on_def
% 0.17/0.43 thf(fact_95_Collect__empty__eq__bot,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( ( collect @ A @ P )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( P
% 0.17/0.43 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Collect_empty_eq_bot
% 0.17/0.43 thf(fact_96_bot__empty__eq,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bot_bot @ ( A > $o ) )
% 0.17/0.43 = ( ^ [X7: A] : ( member @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_empty_eq
% 0.17/0.43 thf(fact_97_rbt_Osize__gen__o__map,axiom,
% 0.17/0.43 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: C > nat,Fa: D > nat,G: A > C,Ga: B > D] :
% 0.17/0.43 ( ( comp @ ( rBT_Im246033960le_rbt @ C @ D ) @ nat @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1485196410ze_rbt @ C @ D @ F @ Fa ) @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G @ Ga ) )
% 0.17/0.43 = ( rBT_Im1485196410ze_rbt @ A @ B @ ( comp @ C @ nat @ A @ F @ G ) @ ( comp @ D @ nat @ B @ Fa @ Ga ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.size_gen_o_map
% 0.17/0.43 thf(fact_98_is__singletonI_H,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( A6
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 => ( ! [X6: A,Y4: A] :
% 0.17/0.43 ( ( member @ A @ X6 @ A6 )
% 0.17/0.43 => ( ( member @ A @ Y4 @ A6 )
% 0.17/0.43 => ( X6 = Y4 ) ) )
% 0.17/0.43 => ( is_singleton @ A @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonI'
% 0.17/0.43 thf(fact_99_vimage2p__comp,axiom,
% 0.17/0.43 ! [E: $tType,D: $tType,F3: $tType,A: $tType,C: $tType,B: $tType,G5: $tType,F1: F3 > A,F2: D > F3,G1: G5 > B,G2: E > G5] :
% 0.17/0.43 ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ ( comp @ F3 @ A @ D @ F1 @ F2 ) @ ( comp @ G5 @ B @ E @ G1 @ G2 ) )
% 0.17/0.43 = ( comp @ ( F3 > G5 > C ) @ ( D > E > C ) @ ( A > B > C ) @ ( bNF_vimage2p @ D @ F3 @ E @ G5 @ C @ F2 @ G2 ) @ ( bNF_vimage2p @ F3 @ A @ G5 @ B @ C @ F1 @ G1 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage2p_comp
% 0.17/0.43 thf(fact_100_vimage2p__cong,axiom,
% 0.17/0.43 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,R3: A > B > C,S: A > B > C,F: D > A,G: E > B] :
% 0.17/0.43 ( ( R3 = S )
% 0.17/0.43 => ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ F @ G @ R3 )
% 0.17/0.43 = ( bNF_vimage2p @ D @ A @ E @ B @ C @ F @ G @ S ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage2p_cong
% 0.17/0.43 thf(fact_101_rbt_Osize__gen_I1_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,Xa: A > nat,X: B > nat] :
% 0.17/0.43 ( ( rBT_Im1485196410ze_rbt @ A @ B @ Xa @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.size_gen(1)
% 0.17/0.43 thf(fact_102_is__singletonI,axiom,
% 0.17/0.43 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonI
% 0.17/0.43 thf(fact_103_map__fun_Ocomp,axiom,
% 0.17/0.43 ! [E: $tType,C: $tType,A: $tType,F3: $tType,D: $tType,B: $tType,F: E > C,G: D > F3,H: C > A,I: B > D] :
% 0.17/0.43 ( ( comp @ ( C > D ) @ ( E > F3 ) @ ( A > B ) @ ( map_fun @ E @ C @ D @ F3 @ F @ G ) @ ( map_fun @ C @ A @ B @ D @ H @ I ) )
% 0.17/0.43 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_fun.comp
% 0.17/0.43 thf(fact_104_is__singletonE,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( is_singleton @ A @ A6 )
% 0.17/0.43 => ~ ! [X6: A] :
% 0.17/0.43 ( A6
% 0.17/0.43 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singletonE
% 0.17/0.43 thf(fact_105_is__singleton__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_singleton @ A )
% 0.17/0.43 = ( ^ [A7: set @ A] :
% 0.17/0.43 ? [X7: A] :
% 0.17/0.43 ( A7
% 0.17/0.43 = ( insert @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singleton_def
% 0.17/0.43 thf(fact_106_insert__absorb2,axiom,
% 0.17/0.43 ! [A: $tType,X: A,A6: set @ A] :
% 0.17/0.43 ( ( insert @ A @ X @ ( insert @ A @ X @ A6 ) )
% 0.17/0.43 = ( insert @ A @ X @ A6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_absorb2
% 0.17/0.43 thf(fact_107_insert__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B2: A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A6 ) )
% 0.17/0.43 = ( ( A2 = B2 )
% 0.17/0.43 | ( member @ A @ A2 @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_iff
% 0.17/0.43 thf(fact_108_insertCI,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.17/0.43 ( ( ~ ( member @ A @ A2 @ B3 )
% 0.17/0.43 => ( A2 = B2 ) )
% 0.17/0.43 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertCI
% 0.17/0.43 thf(fact_109_map__fun__apply,axiom,
% 0.17/0.43 ! [D: $tType,A: $tType,C: $tType,B: $tType] :
% 0.17/0.43 ( ( map_fun @ B @ C @ D @ A )
% 0.17/0.43 = ( ^ [F4: B > C,G3: D > A,H2: C > D,X7: B] : ( G3 @ ( H2 @ ( F4 @ X7 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_fun_apply
% 0.17/0.43 thf(fact_110_singletonI,axiom,
% 0.17/0.43 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singletonI
% 0.17/0.43 thf(fact_111_singletonD,axiom,
% 0.17/0.43 ! [A: $tType,B2: A,A2: A] :
% 0.17/0.43 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( B2 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singletonD
% 0.17/0.43 thf(fact_112_singleton__iff,axiom,
% 0.17/0.43 ! [A: $tType,B2: A,A2: A] :
% 0.17/0.43 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( B2 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_iff
% 0.17/0.43 thf(fact_113_doubleton__eq__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B2: A,C2: A,D2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 = ( ( ( A2 = C2 )
% 0.17/0.43 & ( B2 = D2 ) )
% 0.17/0.43 | ( ( A2 = D2 )
% 0.17/0.43 & ( B2 = C2 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % doubleton_eq_iff
% 0.17/0.43 thf(fact_114_insert__not__empty,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,A6: set @ A] :
% 0.17/0.43 ( ( insert @ A @ A2 @ A6 )
% 0.17/0.43 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_not_empty
% 0.17/0.43 thf(fact_115_singleton__inject,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( A2 = B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_inject
% 0.17/0.43 thf(fact_116_mk__disjoint__insert,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ A2 @ A6 )
% 0.17/0.43 => ? [B4: set @ A] :
% 0.17/0.43 ( ( A6
% 0.17/0.43 = ( insert @ A @ A2 @ B4 ) )
% 0.17/0.43 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % mk_disjoint_insert
% 0.17/0.43 thf(fact_117_insert__commute,axiom,
% 0.17/0.43 ! [A: $tType,X: A,Y: A,A6: set @ A] :
% 0.17/0.43 ( ( insert @ A @ X @ ( insert @ A @ Y @ A6 ) )
% 0.17/0.43 = ( insert @ A @ Y @ ( insert @ A @ X @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_commute
% 0.17/0.43 thf(fact_118_insert__eq__iff,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,A6: set @ A,B2: A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ A2 @ A6 )
% 0.17/0.43 => ( ~ ( member @ A @ B2 @ B3 )
% 0.17/0.43 => ( ( ( insert @ A @ A2 @ A6 )
% 0.17/0.43 = ( insert @ A @ B2 @ B3 ) )
% 0.17/0.43 = ( ( ( A2 = B2 )
% 0.17/0.43 => ( A6 = B3 ) )
% 0.17/0.43 & ( ( A2 != B2 )
% 0.17/0.43 => ? [C3: set @ A] :
% 0.17/0.43 ( ( A6
% 0.17/0.43 = ( insert @ A @ B2 @ C3 ) )
% 0.17/0.43 & ~ ( member @ A @ B2 @ C3 )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ A2 @ C3 ) )
% 0.17/0.43 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_eq_iff
% 0.17/0.43 thf(fact_119_insert__absorb,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ A2 @ A6 )
% 0.17/0.43 => ( ( insert @ A @ A2 @ A6 )
% 0.17/0.43 = A6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_absorb
% 0.17/0.43 thf(fact_120_insert__ident,axiom,
% 0.17/0.43 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ~ ( member @ A @ X @ A6 )
% 0.17/0.43 => ( ~ ( member @ A @ X @ B3 )
% 0.17/0.43 => ( ( ( insert @ A @ X @ A6 )
% 0.17/0.43 = ( insert @ A @ X @ B3 ) )
% 0.17/0.43 = ( A6 = B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_ident
% 0.17/0.43 thf(fact_121_Set_Oset__insert,axiom,
% 0.17/0.43 ! [A: $tType,X: A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ X @ A6 )
% 0.17/0.43 => ~ ! [B4: set @ A] :
% 0.17/0.43 ( ( A6
% 0.17/0.43 = ( insert @ A @ X @ B4 ) )
% 0.17/0.43 => ( member @ A @ X @ B4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Set.set_insert
% 0.17/0.43 thf(fact_122_insertI2,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 0.17/0.43 ( ( member @ A @ A2 @ B3 )
% 0.17/0.43 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertI2
% 0.17/0.43 thf(fact_123_insertI1,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B3: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertI1
% 0.17/0.43 thf(fact_124_insertE,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B2: A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A6 ) )
% 0.17/0.43 => ( ( A2 != B2 )
% 0.17/0.43 => ( member @ A @ A2 @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insertE
% 0.17/0.43 thf(fact_125_map__fun_Ocompositionality,axiom,
% 0.17/0.43 ! [D: $tType,F3: $tType,C: $tType,E: $tType,B: $tType,A: $tType,F: E > C,G: D > F3,H: C > A,I: B > D,Fun: A > B] :
% 0.17/0.43 ( ( map_fun @ E @ C @ D @ F3 @ F @ G @ ( map_fun @ C @ A @ B @ D @ H @ I @ Fun ) )
% 0.17/0.43 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Fun ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_fun.compositionality
% 0.17/0.43 thf(fact_126_map__fun__def,axiom,
% 0.17/0.43 ! [B: $tType,D: $tType,A: $tType,C: $tType] :
% 0.17/0.43 ( ( map_fun @ C @ A @ B @ D )
% 0.17/0.43 = ( ^ [F4: C > A,G3: B > D,H2: A > B] : ( comp @ A @ D @ C @ ( comp @ B @ D @ A @ G3 @ H2 ) @ F4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % map_fun_def
% 0.17/0.43 thf(fact_127_color_Osize__gen_I1_J,axiom,
% 0.17/0.43 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_R )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.size_gen(1)
% 0.17/0.43 thf(fact_128_color_Osize__gen_I2_J,axiom,
% 0.17/0.43 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_B )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.size_gen(2)
% 0.17/0.43 thf(fact_129_is__singleton__the__elem,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( is_singleton @ A )
% 0.17/0.43 = ( ^ [A7: set @ A] :
% 0.17/0.43 ( A7
% 0.17/0.43 = ( insert @ A @ ( the_elem @ A @ A7 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % is_singleton_the_elem
% 0.17/0.43 thf(fact_130_the__elem__eq,axiom,
% 0.17/0.43 ! [A: $tType,X: A] :
% 0.17/0.43 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = X ) ).
% 0.17/0.43
% 0.17/0.43 % the_elem_eq
% 0.17/0.43 thf(fact_131_color_Osize_I3_J,axiom,
% 0.17/0.43 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_R )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.size(3)
% 0.17/0.43 thf(fact_132_color_Osize_I4_J,axiom,
% 0.17/0.43 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_B )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % color.size(4)
% 0.17/0.43 thf(fact_133_rbt_Osize_I3_J,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType] :
% 0.17/0.43 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.size(3)
% 0.17/0.43 thf(fact_134_rbt_Osimps_I15_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.17/0.43 = ( insert @ A @ X23 @ ( sup_sup @ ( set @ A ) @ ( rBT_Im1178217900t1_rbt @ A @ B @ X22 ) @ ( rBT_Im1178217900t1_rbt @ A @ B @ X25 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(15)
% 0.17/0.43 thf(fact_135_rbt_Osimps_I17_J,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.17/0.43 ( ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.17/0.43 = ( insert @ B @ X24 @ ( sup_sup @ ( set @ B ) @ ( rBT_Im1550225131t2_rbt @ A @ B @ X22 ) @ ( rBT_Im1550225131t2_rbt @ A @ B @ X25 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % rbt.simps(17)
% 0.17/0.43 thf(fact_136_pairwise__singleton,axiom,
% 0.17/0.43 ! [A: $tType,P: A > A > $o,A6: A] : ( pairwise @ A @ P @ ( insert @ A @ A6 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_singleton
% 0.17/0.43 thf(fact_137_Un__iff,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 = ( ( member @ A @ C2 @ A6 )
% 0.17/0.43 | ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_iff
% 0.17/0.43 thf(fact_138_UnCI,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,B3: set @ A,A6: set @ A] :
% 0.17/0.43 ( ( ~ ( member @ A @ C2 @ B3 )
% 0.17/0.43 => ( member @ A @ C2 @ A6 ) )
% 0.17/0.43 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UnCI
% 0.17/0.43 thf(fact_139_Un__empty,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ( sup_sup @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_empty
% 0.17/0.43 thf(fact_140_Un__insert__left,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,B3: set @ A,C4: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 0.17/0.43 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_insert_left
% 0.17/0.43 thf(fact_141_Un__insert__right,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,A2: A,B3: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.43 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_insert_right
% 0.17/0.43 thf(fact_142_Un__empty__left,axiom,
% 0.17/0.43 ! [A: $tType,B3: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 0.17/0.43 = B3 ) ).
% 0.17/0.43
% 0.17/0.43 % Un_empty_left
% 0.17/0.43 thf(fact_143_Un__empty__right,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = A6 ) ).
% 0.17/0.43
% 0.17/0.43 % Un_empty_right
% 0.17/0.43 thf(fact_144_Un__left__commute,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A6 @ C4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_left_commute
% 0.17/0.43 thf(fact_145_Un__left__absorb,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_left_absorb
% 0.17/0.43 thf(fact_146_pairwise__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( pairwise @ A )
% 0.17/0.43 = ( ^ [R4: A > A > $o,S2: set @ A] :
% 0.17/0.43 ! [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ S2 )
% 0.17/0.43 => ! [Y3: A] :
% 0.17/0.43 ( ( member @ A @ Y3 @ S2 )
% 0.17/0.43 => ( ( X7 != Y3 )
% 0.17/0.43 => ( R4 @ X7 @ Y3 ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_def
% 0.17/0.43 thf(fact_147_Un__commute,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) )
% 0.17/0.43 = ( ^ [A7: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_commute
% 0.17/0.43 thf(fact_148_Un__absorb,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ A6 @ A6 )
% 0.17/0.43 = A6 ) ).
% 0.17/0.43
% 0.17/0.43 % Un_absorb
% 0.17/0.43 thf(fact_149_Un__assoc,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.43 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_assoc
% 0.17/0.43 thf(fact_150_ball__Un,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A,P: A > $o] :
% 0.17/0.43 ( ( ! [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 => ( P @ X7 ) ) )
% 0.17/0.43 = ( ! [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ A6 )
% 0.17/0.43 => ( P @ X7 ) )
% 0.17/0.43 & ! [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ B3 )
% 0.17/0.43 => ( P @ X7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ball_Un
% 0.17/0.43 thf(fact_151_bex__Un,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A,P: A > $o] :
% 0.17/0.43 ( ( ? [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 & ( P @ X7 ) ) )
% 0.17/0.43 = ( ? [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ A6 )
% 0.17/0.43 & ( P @ X7 ) )
% 0.17/0.43 | ? [X7: A] :
% 0.17/0.43 ( ( member @ A @ X7 @ B3 )
% 0.17/0.43 & ( P @ X7 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bex_Un
% 0.17/0.43 thf(fact_152_UnI2,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,B3: set @ A,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ B3 )
% 0.17/0.43 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UnI2
% 0.17/0.43 thf(fact_153_UnI1,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ A6 )
% 0.17/0.43 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UnI1
% 0.17/0.43 thf(fact_154_UnE,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 => ( ~ ( member @ A @ C2 @ A6 )
% 0.17/0.43 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % UnE
% 0.17/0.43 thf(fact_155_singleton__Un__iff,axiom,
% 0.17/0.43 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 = ( ( ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 | ( ( A6
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 | ( ( A6
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_Un_iff
% 0.17/0.43 thf(fact_156_Un__singleton__iff,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 0.17/0.43 ( ( ( sup_sup @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( ( ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.17/0.43 | ( ( A6
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 | ( ( A6
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 & ( B3
% 0.17/0.43 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Un_singleton_iff
% 0.17/0.43 thf(fact_157_insert__is__Un,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( insert @ A )
% 0.17/0.43 = ( ^ [A8: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A8 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % insert_is_Un
% 0.17/0.43 thf(fact_158_pairwise__empty,axiom,
% 0.17/0.43 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_empty
% 0.17/0.43 thf(fact_159_pairwise__insert,axiom,
% 0.17/0.43 ! [A: $tType,R: A > A > $o,X: A,S3: set @ A] :
% 0.17/0.43 ( ( pairwise @ A @ R @ ( insert @ A @ X @ S3 ) )
% 0.17/0.43 = ( ! [Y3: A] :
% 0.17/0.43 ( ( ( member @ A @ Y3 @ S3 )
% 0.17/0.43 & ( Y3 != X ) )
% 0.17/0.43 => ( ( R @ X @ Y3 )
% 0.17/0.43 & ( R @ Y3 @ X ) ) )
% 0.17/0.43 & ( pairwise @ A @ R @ S3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % pairwise_insert
% 0.17/0.43 thf(fact_160_sup__bot_Oright__neutral,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A2: A] :
% 0.17/0.43 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot.right_neutral
% 0.17/0.43 thf(fact_161_sup__bot_Oleft__neutral,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [A2: A] :
% 0.17/0.43 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.17/0.43 = A2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot.left_neutral
% 0.17/0.43 thf(fact_162_sup__eq__bot__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A,Y: A] :
% 0.17/0.43 ( ( ( sup_sup @ A @ X @ Y )
% 0.17/0.43 = ( bot_bot @ A ) )
% 0.17/0.43 = ( ( X
% 0.17/0.43 = ( bot_bot @ A ) )
% 0.17/0.43 & ( Y
% 0.17/0.43 = ( bot_bot @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_eq_bot_iff
% 0.17/0.43 thf(fact_163_bot__eq__sup__iff,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A,Y: A] :
% 0.17/0.43 ( ( ( bot_bot @ A )
% 0.17/0.43 = ( sup_sup @ A @ X @ Y ) )
% 0.17/0.43 = ( ( X
% 0.17/0.43 = ( bot_bot @ A ) )
% 0.17/0.43 & ( Y
% 0.17/0.43 = ( bot_bot @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_eq_sup_iff
% 0.17/0.43 thf(fact_164_sup__bot__left,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A] :
% 0.17/0.43 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.17/0.43 = X ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot_left
% 0.17/0.43 thf(fact_165_sup__bot__right,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A] :
% 0.17/0.43 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.17/0.43 = X ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot_right
% 0.17/0.43 thf(fact_166_ID_Opred__set,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( A > $o ) )
% 0.17/0.43 = ( ^ [P3: A > $o,X7: A] :
% 0.17/0.43 ! [Y3: A] :
% 0.17/0.43 ( ( member @ A @ Y3 @ ( insert @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( P3 @ Y3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.pred_set
% 0.17/0.43 thf(fact_167_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot.semilattice_neutr_axioms
% 0.17/0.43 thf(fact_168_bot__nat__def,axiom,
% 0.17/0.43 ( ( bot_bot @ nat )
% 0.17/0.43 = ( zero_zero @ nat ) ) ).
% 0.17/0.43
% 0.17/0.43 % bot_nat_def
% 0.17/0.43 thf(fact_169_id__bnf__apply,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bNF_id_bnf @ A )
% 0.17/0.43 = ( ^ [X7: A] : X7 ) ) ).
% 0.17/0.43
% 0.17/0.43 % id_bnf_apply
% 0.17/0.43 thf(fact_170_BNF__Composition_Oid__bnf__def,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bNF_id_bnf @ A )
% 0.17/0.43 = ( ^ [X7: A] : X7 ) ) ).
% 0.17/0.43
% 0.17/0.43 % BNF_Composition.id_bnf_def
% 0.17/0.43 thf(fact_171_ID_Opred__map,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X: A] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( B > $o ) @ Q @ ( bNF_id_bnf @ ( A > B ) @ F @ X ) )
% 0.17/0.43 = ( bNF_id_bnf @ ( A > $o ) @ ( comp @ B @ $o @ A @ Q @ F ) @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.pred_map
% 0.17/0.43 thf(fact_172_ID_Opred__mono__strong,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o,X: A,Pa: A > $o] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( A > $o ) @ P @ X )
% 0.17/0.43 => ( ! [Z6: A] :
% 0.17/0.43 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( ( P @ Z6 )
% 0.17/0.43 => ( Pa @ Z6 ) ) )
% 0.17/0.43 => ( bNF_id_bnf @ ( A > $o ) @ Pa @ X ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.pred_mono_strong
% 0.17/0.43 thf(fact_173_ID_Opred__cong,axiom,
% 0.17/0.43 ! [A: $tType,X: A,Ya: A,P: A > $o,Pa: A > $o] :
% 0.17/0.43 ( ( X = Ya )
% 0.17/0.43 => ( ! [Z6: A] :
% 0.17/0.43 ( ( member @ A @ Z6 @ ( insert @ A @ Ya @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( ( P @ Z6 )
% 0.17/0.43 = ( Pa @ Z6 ) ) )
% 0.17/0.43 => ( ( bNF_id_bnf @ ( A > $o ) @ P @ X )
% 0.17/0.43 = ( bNF_id_bnf @ ( A > $o ) @ Pa @ Ya ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.pred_cong
% 0.17/0.43 thf(fact_174_sup__bot_Omonoid__axioms,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( monoid @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot.monoid_axioms
% 0.17/0.43 thf(fact_175_ID_Orel__eq__onp,axiom,
% 0.17/0.43 ! [A: $tType,P: A > $o] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P ) )
% 0.17/0.43 = ( bNF_eq_onp @ A @ ( bNF_id_bnf @ ( A > $o ) @ P ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.rel_eq_onp
% 0.17/0.43 thf(fact_176_ID_Opred__rel,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( A > $o ) )
% 0.17/0.43 = ( ^ [P3: A > $o,X7: A] : ( bNF_id_bnf @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P3 ) @ X7 @ X7 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.pred_rel
% 0.17/0.43 thf(fact_177_ID_Orel__refl,axiom,
% 0.17/0.43 ! [A: $tType,Ra: A > A > $o,X: A] :
% 0.17/0.43 ( ! [X6: A] : ( Ra @ X6 @ X6 )
% 0.17/0.43 => ( bNF_id_bnf @ ( A > A > $o ) @ Ra @ X @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.rel_refl
% 0.17/0.43 thf(fact_178_ID_Orel__cong,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,X: A,Ya: A,Y: B,Xa: B,R3: A > B > $o,Ra: A > B > $o] :
% 0.17/0.43 ( ( X = Ya )
% 0.17/0.43 => ( ( Y = Xa )
% 0.17/0.43 => ( ! [Z6: A,Yb: B] :
% 0.17/0.43 ( ( member @ A @ Z6 @ ( insert @ A @ Ya @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( ( member @ B @ Yb @ ( insert @ B @ Xa @ ( bot_bot @ ( set @ B ) ) ) )
% 0.17/0.43 => ( ( R3 @ Z6 @ Yb )
% 0.17/0.43 = ( Ra @ Z6 @ Yb ) ) ) )
% 0.17/0.43 => ( ( bNF_id_bnf @ ( A > B > $o ) @ R3 @ X @ Y )
% 0.17/0.43 = ( bNF_id_bnf @ ( A > B > $o ) @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.rel_cong
% 0.17/0.43 thf(fact_179_ID_Orel__mono__strong,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,R3: A > B > $o,X: A,Y: B,Ra: A > B > $o] :
% 0.17/0.43 ( ( bNF_id_bnf @ ( A > B > $o ) @ R3 @ X @ Y )
% 0.17/0.43 => ( ! [Z6: A,Yb: B] :
% 0.17/0.43 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( ( member @ B @ Yb @ ( insert @ B @ Y @ ( bot_bot @ ( set @ B ) ) ) )
% 0.17/0.43 => ( ( R3 @ Z6 @ Yb )
% 0.17/0.43 => ( Ra @ Z6 @ Yb ) ) ) )
% 0.17/0.43 => ( bNF_id_bnf @ ( A > B > $o ) @ Ra @ X @ Y ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.rel_mono_strong
% 0.17/0.43 thf(fact_180_ID_Orel__refl__strong,axiom,
% 0.17/0.43 ! [A: $tType,X: A,Ra: A > A > $o] :
% 0.17/0.43 ( ! [Z6: A] :
% 0.17/0.43 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 => ( Ra @ Z6 @ Z6 ) )
% 0.17/0.43 => ( bNF_id_bnf @ ( A > A > $o ) @ Ra @ X @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % ID.rel_refl_strong
% 0.17/0.43 thf(fact_181_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ( comm_monoid @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % sup_bot.comm_monoid_axioms
% 0.17/0.43 thf(fact_182_vimage__insert,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,F: A > B,A2: B,B3: set @ B] :
% 0.17/0.43 ( ( vimage @ A @ B @ F @ ( insert @ B @ A2 @ B3 ) )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ ( insert @ B @ A2 @ ( bot_bot @ ( set @ B ) ) ) ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_insert
% 0.17/0.43 thf(fact_183_notIn__Un__bij__betw3,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,B2: A,A6: set @ A,F: A > B,A9: set @ B] :
% 0.17/0.43 ( ~ ( member @ A @ B2 @ A6 )
% 0.17/0.43 => ( ~ ( member @ B @ ( F @ B2 ) @ A9 )
% 0.17/0.43 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 0.17/0.43 = ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( sup_sup @ ( set @ B ) @ A9 @ ( insert @ B @ ( F @ B2 ) @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % notIn_Un_bij_betw3
% 0.17/0.43 thf(fact_184_vimage__eq,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.17/0.43 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_eq
% 0.17/0.43 thf(fact_185_vimageI,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 0.17/0.43 ( ( ( F @ A2 )
% 0.17/0.43 = B2 )
% 0.17/0.43 => ( ( member @ A @ B2 @ B3 )
% 0.17/0.43 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimageI
% 0.17/0.43 thf(fact_186_vimage__empty,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B] :
% 0.17/0.43 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_empty
% 0.17/0.43 thf(fact_187_vimage__Un,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,F: A > B,A6: set @ B,B3: set @ B] :
% 0.17/0.43 ( ( vimage @ A @ B @ F @ ( sup_sup @ ( set @ B ) @ A6 @ B3 ) )
% 0.17/0.43 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ A6 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_Un
% 0.17/0.43 thf(fact_188_vimage__Collect,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( P @ ( F @ X6 ) )
% 0.17/0.43 = ( Q @ X6 ) )
% 0.17/0.43 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 0.17/0.43 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_Collect
% 0.17/0.43 thf(fact_189_bij__betw__cong,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A6: set @ A,F: A > B,G: A > B,A9: set @ B] :
% 0.17/0.43 ( ! [A10: A] :
% 0.17/0.43 ( ( member @ A @ A10 @ A6 )
% 0.17/0.43 => ( ( F @ A10 )
% 0.17/0.43 = ( G @ A10 ) ) )
% 0.17/0.43 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 0.17/0.43 = ( bij_betw @ A @ B @ G @ A6 @ A9 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_cong
% 0.17/0.43 thf(fact_190_bij__betw__inv,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B3: set @ B] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 0.17/0.43 => ? [G6: B > A] : ( bij_betw @ B @ A @ G6 @ B3 @ A6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_inv
% 0.17/0.43 thf(fact_191_vimageI2,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: B > A,A2: B,A6: set @ A] :
% 0.17/0.43 ( ( member @ A @ ( F @ A2 ) @ A6 )
% 0.17/0.43 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A6 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimageI2
% 0.17/0.43 thf(fact_192_vimageE,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 0.17/0.43 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimageE
% 0.17/0.43 thf(fact_193_vimageD,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,A6: set @ B] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A6 ) )
% 0.17/0.43 => ( member @ B @ ( F @ A2 ) @ A6 ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimageD
% 0.17/0.43 thf(fact_194_set_Ocomp,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 0.17/0.43 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 0.17/0.43 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % set.comp
% 0.17/0.43 thf(fact_195_vimage__comp,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X: set @ C] :
% 0.17/0.43 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X ) )
% 0.17/0.43 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_comp
% 0.17/0.43 thf(fact_196_set_Ocompositionality,axiom,
% 0.17/0.43 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 0.17/0.43 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 0.17/0.43 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 0.17/0.43
% 0.17/0.43 % set.compositionality
% 0.17/0.43 thf(fact_197_bij__betw__trans,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C: $tType,F: A > B,A6: set @ A,B3: set @ B,G: B > C,C4: set @ C] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 0.17/0.43 => ( ( bij_betw @ B @ C @ G @ B3 @ C4 )
% 0.17/0.43 => ( bij_betw @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A6 @ C4 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_trans
% 0.17/0.43 thf(fact_198_bij__betw__comp__iff,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,C: $tType,F: A > B,A6: set @ A,A9: set @ B,F5: B > C,A11: set @ C] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 0.17/0.43 => ( ( bij_betw @ B @ C @ F5 @ A9 @ A11 )
% 0.17/0.43 = ( bij_betw @ A @ C @ ( comp @ B @ C @ A @ F5 @ F ) @ A6 @ A11 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_comp_iff
% 0.17/0.43 thf(fact_199_vimage__singleton__eq,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,A2: A,F: A > B,B2: B] :
% 0.17/0.43 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 0.17/0.43 = ( ( F @ A2 )
% 0.17/0.43 = B2 ) ) ).
% 0.17/0.43
% 0.17/0.43 % vimage_singleton_eq
% 0.17/0.43 thf(fact_200_bij__betw__empty2,axiom,
% 0.17/0.43 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ A6 @ ( bot_bot @ ( set @ B ) ) )
% 0.17/0.43 => ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_empty2
% 0.17/0.43 thf(fact_201_bij__betw__empty1,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,F: A > B,A6: set @ B] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ ( bot_bot @ ( set @ A ) ) @ A6 )
% 0.17/0.43 => ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_empty1
% 0.17/0.43 thf(fact_202_notIn__Un__bij__betw,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,B2: A,A6: set @ A,F: A > B,A9: set @ B] :
% 0.17/0.43 ( ~ ( member @ A @ B2 @ A6 )
% 0.17/0.43 => ( ~ ( member @ B @ ( F @ B2 ) @ A9 )
% 0.17/0.43 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 0.17/0.43 => ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( sup_sup @ ( set @ B ) @ A9 @ ( insert @ B @ ( F @ B2 ) @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % notIn_Un_bij_betw
% 0.17/0.43 thf(fact_203_bij__betw__combine,axiom,
% 0.17/0.43 ! [A: $tType,B: $tType,F: A > B,A6: set @ A,B3: set @ B,C4: set @ A,D3: set @ B] :
% 0.17/0.43 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 0.17/0.43 => ( ( bij_betw @ A @ B @ F @ C4 @ D3 )
% 0.17/0.43 => ( ( ( inf_inf @ ( set @ B ) @ B3 @ D3 )
% 0.17/0.43 = ( bot_bot @ ( set @ B ) ) )
% 0.17/0.43 => ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ C4 ) @ ( sup_sup @ ( set @ B ) @ B3 @ D3 ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % bij_betw_combine
% 0.17/0.43 thf(fact_204_infinite__imp__bij__betw2,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,A2: A] :
% 0.17/0.43 ( ~ ( finite_finite @ A @ A6 )
% 0.17/0.43 => ? [H3: A > A] : ( bij_betw @ A @ A @ H3 @ A6 @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % infinite_imp_bij_betw2
% 0.17/0.43 thf(fact_205_singleton__insert__inj__eq_H,axiom,
% 0.17/0.43 ! [A: $tType,A2: A,A6: set @ A,B2: A] :
% 0.17/0.43 ( ( ( insert @ A @ A2 @ A6 )
% 0.17/0.43 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.17/0.43 = ( ( A2 = B2 )
% 0.17/0.43 & ( ord_less_eq @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % singleton_insert_inj_eq'
% 0.17/0.43 thf(fact_206_order__refl,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( preorder @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.17/0.43
% 0.17/0.43 % order_refl
% 0.17/0.43 thf(fact_207_subsetI,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ! [X6: A] :
% 0.17/0.43 ( ( member @ A @ X6 @ A6 )
% 0.17/0.43 => ( member @ A @ X6 @ B3 ) )
% 0.17/0.43 => ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ).
% 0.17/0.43
% 0.17/0.43 % subsetI
% 0.17/0.43 thf(fact_208_subset__antisym,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.43 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A6 )
% 0.17/0.43 => ( A6 = B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_antisym
% 0.17/0.43 thf(fact_209_IntI,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ A6 )
% 0.17/0.43 => ( ( member @ A @ C2 @ B3 )
% 0.17/0.43 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % IntI
% 0.17/0.43 thf(fact_210_Int__iff,axiom,
% 0.17/0.43 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.43 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.43 = ( ( member @ A @ C2 @ A6 )
% 0.17/0.43 & ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % Int_iff
% 0.17/0.43 thf(fact_211_inf__bot__left,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A] :
% 0.17/0.43 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 0.17/0.43 = ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inf_bot_left
% 0.17/0.43 thf(fact_212_inf__bot__right,axiom,
% 0.17/0.43 ! [A: $tType] :
% 0.17/0.43 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.17/0.43 => ! [X: A] :
% 0.17/0.43 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 0.17/0.43 = ( bot_bot @ A ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % inf_bot_right
% 0.17/0.43 thf(fact_213_subset__empty,axiom,
% 0.17/0.43 ! [A: $tType,A6: set @ A] :
% 0.17/0.43 ( ( ord_less_eq @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.43 = ( A6
% 0.17/0.43 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 % subset_empty
% 0.17/0.44 thf(fact_214_empty__subsetI,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A6 ) ).
% 0.17/0.44
% 0.17/0.44 % empty_subsetI
% 0.17/0.44 thf(fact_215_insert__subset,axiom,
% 0.17/0.44 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A6 ) @ B3 )
% 0.17/0.44 = ( ( member @ A @ X @ B3 )
% 0.17/0.44 & ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % insert_subset
% 0.17/0.44 thf(fact_216_Int__subset__iff,axiom,
% 0.17/0.44 ! [A: $tType,C4: set @ A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.44 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A6 )
% 0.17/0.44 & ( ord_less_eq @ ( set @ A ) @ C4 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_subset_iff
% 0.17/0.44 thf(fact_217_Int__insert__right__if1,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( member @ A @ A2 @ A6 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.44 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_right_if1
% 0.17/0.44 thf(fact_218_Int__insert__right__if0,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ~ ( member @ A @ A2 @ A6 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_right_if0
% 0.17/0.44 thf(fact_219_insert__inter__insert,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.44 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % insert_inter_insert
% 0.17/0.44 thf(fact_220_Int__insert__left__if1,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( member @ A @ A2 @ C4 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 0.17/0.44 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_left_if1
% 0.17/0.44 thf(fact_221_Int__insert__left__if0,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 0.17/0.44 ( ~ ( member @ A @ A2 @ C4 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_left_if0
% 0.17/0.44 thf(fact_222_Un__subset__iff,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 0.17/0.44 = ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 0.17/0.44 & ( ord_less_eq @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Un_subset_iff
% 0.17/0.44 thf(fact_223_vimage__Int,axiom,
% 0.17/0.44 ! [A: $tType,B: $tType,F: A > B,A6: set @ B,B3: set @ B] :
% 0.17/0.44 ( ( vimage @ A @ B @ F @ ( inf_inf @ ( set @ B ) @ A6 @ B3 ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A6 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % vimage_Int
% 0.17/0.44 thf(fact_224_singleton__insert__inj__eq,axiom,
% 0.17/0.44 ! [A: $tType,B2: A,A2: A,A6: set @ A] :
% 0.17/0.44 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.44 = ( insert @ A @ A2 @ A6 ) )
% 0.17/0.44 = ( ( A2 = B2 )
% 0.17/0.44 & ( ord_less_eq @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % singleton_insert_inj_eq
% 0.17/0.44 thf(fact_225_disjoint__insert_I2_J,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B2: A,B3: set @ A] :
% 0.17/0.44 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ B3 ) ) )
% 0.17/0.44 = ( ~ ( member @ A @ B2 @ A6 )
% 0.17/0.44 & ( ( bot_bot @ ( set @ A ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % disjoint_insert(2)
% 0.17/0.44 thf(fact_226_disjoint__insert_I1_J,axiom,
% 0.17/0.44 ! [A: $tType,B3: set @ A,A2: A,A6: set @ A] :
% 0.17/0.44 ( ( ( inf_inf @ ( set @ A ) @ B3 @ ( insert @ A @ A2 @ A6 ) )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.44 = ( ~ ( member @ A @ A2 @ B3 )
% 0.17/0.44 & ( ( inf_inf @ ( set @ A ) @ B3 @ A6 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % disjoint_insert(1)
% 0.17/0.44 thf(fact_227_insert__disjoint_I2_J,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ( bot_bot @ ( set @ A ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ B3 ) )
% 0.17/0.44 = ( ~ ( member @ A @ A2 @ B3 )
% 0.17/0.44 & ( ( bot_bot @ ( set @ A ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % insert_disjoint(2)
% 0.17/0.44 thf(fact_228_insert__disjoint_I1_J,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ B3 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.44 = ( ~ ( member @ A @ A2 @ B3 )
% 0.17/0.44 & ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % insert_disjoint(1)
% 0.17/0.44 thf(fact_229_vimage__inter__cong,axiom,
% 0.17/0.44 ! [B: $tType,A: $tType,S: set @ A,F: A > B,G: A > B,Y: set @ B] :
% 0.17/0.44 ( ! [W: A] :
% 0.17/0.44 ( ( member @ A @ W @ S )
% 0.17/0.44 => ( ( F @ W )
% 0.17/0.44 = ( G @ W ) ) )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ Y ) @ S )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ G @ Y ) @ S ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % vimage_inter_cong
% 0.17/0.44 thf(fact_230_vimage__mono,axiom,
% 0.17/0.44 ! [B: $tType,A: $tType,A6: set @ A,B3: set @ A,F: B > A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ( ord_less_eq @ ( set @ B ) @ ( vimage @ B @ A @ F @ A6 ) @ ( vimage @ B @ A @ F @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % vimage_mono
% 0.17/0.44 thf(fact_231_Int__emptyI,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ! [X6: A] :
% 0.17/0.44 ( ( member @ A @ X6 @ A6 )
% 0.17/0.44 => ~ ( member @ A @ X6 @ B3 ) )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_emptyI
% 0.17/0.44 thf(fact_232_Int__empty__left,axiom,
% 0.17/0.44 ! [A: $tType,B3: set @ A] :
% 0.17/0.44 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_empty_left
% 0.17/0.44 thf(fact_233_Int__empty__right,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A] :
% 0.17/0.44 ( ( inf_inf @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_empty_right
% 0.17/0.44 thf(fact_234_disjoint__iff__not__equal,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.17/0.44 = ( ! [X7: A] :
% 0.17/0.44 ( ( member @ A @ X7 @ A6 )
% 0.17/0.44 => ! [Y3: A] :
% 0.17/0.44 ( ( member @ A @ Y3 @ B3 )
% 0.17/0.44 => ( X7 != Y3 ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % disjoint_iff_not_equal
% 0.17/0.44 thf(fact_235_bot_Oextremum,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.44 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum
% 0.17/0.44 thf(fact_236_bot_Oextremum__unique,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.44 => ! [A2: A] :
% 0.17/0.44 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.17/0.44 = ( A2
% 0.17/0.44 = ( bot_bot @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum_unique
% 0.17/0.44 thf(fact_237_bot_Oextremum__uniqueI,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.17/0.44 => ! [A2: A] :
% 0.17/0.44 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.17/0.44 => ( A2
% 0.17/0.44 = ( bot_bot @ A ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % bot.extremum_uniqueI
% 0.17/0.44 thf(fact_238_Int__insert__right,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ( member @ A @ A2 @ A6 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.44 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) )
% 0.17/0.44 & ( ~ ( member @ A @ A2 @ A6 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_right
% 0.17/0.44 thf(fact_239_Int__insert__left,axiom,
% 0.17/0.44 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( ( member @ A @ A2 @ C4 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 0.17/0.44 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) )
% 0.17/0.44 & ( ~ ( member @ A @ A2 @ C4 )
% 0.17/0.44 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_insert_left
% 0.17/0.44 thf(fact_240_IntE,axiom,
% 0.17/0.44 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.44 => ~ ( ( member @ A @ C2 @ A6 )
% 0.17/0.44 => ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntE
% 0.17/0.44 thf(fact_241_IntD1,axiom,
% 0.17/0.44 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.44 => ( member @ A @ C2 @ A6 ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntD1
% 0.17/0.44 thf(fact_242_IntD2,axiom,
% 0.17/0.44 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 0.17/0.44 => ( member @ A @ C2 @ B3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % IntD2
% 0.17/0.44 thf(fact_243_set__mp,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ( ( member @ A @ X @ A6 )
% 0.17/0.44 => ( member @ A @ X @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % set_mp
% 0.17/0.44 thf(fact_244_in__mono,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ( ( member @ A @ X @ A6 )
% 0.17/0.44 => ( member @ A @ X @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % in_mono
% 0.17/0.44 thf(fact_245_subsetD,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,C2: A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ( ( member @ A @ C2 @ A6 )
% 0.17/0.44 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subsetD
% 0.17/0.44 thf(fact_246_Int__mono,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,C4: set @ A,B3: set @ A,D3: set @ A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 0.17/0.44 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D3 )
% 0.17/0.44 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ ( inf_inf @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_mono
% 0.17/0.44 thf(fact_247_subsetCE,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,C2: A] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ( ( member @ A @ C2 @ A6 )
% 0.17/0.44 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subsetCE
% 0.17/0.44 thf(fact_248_Int__assoc,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 0.17/0.44 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 0.17/0.44 = ( inf_inf @ ( set @ A ) @ A6 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % Int_assoc
% 0.17/0.44 thf(fact_249_equalityE,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( A6 = B3 )
% 0.17/0.44 => ~ ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 0.17/0.44 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A6 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % equalityE
% 0.17/0.44 thf(fact_250_subset__eq,axiom,
% 0.17/0.44 ! [A: $tType] :
% 0.17/0.44 ( ( ord_less_eq @ ( set @ A ) )
% 0.17/0.44 = ( ^ [A7: set @ A,B5: set @ A] :
% 0.17/0.44 ! [X7: A] :
% 0.17/0.44 ( ( member @ A @ X7 @ A7 )
% 0.17/0.44 => ( member @ A @ X7 @ B5 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 % subset_eq
% 0.17/0.44 thf(fact_251_Int__absorb,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A] :
% 0.17/0.44 ( ( inf_inf @ ( set @ A ) @ A6 @ A6 )
% 0.17/0.44 = A6 ) ).
% 0.17/0.44
% 0.17/0.44 % Int_absorb
% 0.17/0.44 thf(fact_252_Int__lower1,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ A6 ) ).
% 0.17/0.44
% 0.17/0.44 % Int_lower1
% 0.17/0.44 thf(fact_253_Int__lower2,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ B3 ) ).
% 0.17/0.44
% 0.17/0.44 % Int_lower2
% 0.17/0.44 thf(fact_254_equalityD1,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( A6 = B3 )
% 0.17/0.44 => ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ).
% 0.17/0.44
% 0.17/0.44 % equalityD1
% 0.17/0.44 thf(fact_255_equalityD2,axiom,
% 0.17/0.44 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 0.17/0.44 ( ( A6 = B3 )
% 0.17/0.44 => ( ord_less_eq @ ( set @ A ) @ B3 @ A6 ) ) ).
% 0.17/0.44
% 0.17/0.44 % equalityD2
% 0.17/0.44
% 0.17/0.44 %----Type constructors (21)
% 0.17/0.44 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.17/0.44 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.17/0.44 ! [A12: $tType] : ( bounded_lattice @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( bounded_lattice @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( bounde1808546759up_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( bounded_lattice_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( order_bot @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( order_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( preorder @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( preorder @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_fun___Orderings_Obot,axiom,
% 0.17/0.44 ! [A12: $tType,A13: $tType] :
% 0.17/0.44 ( ( bot @ A13 @ ( type2 @ A13 ) )
% 0.17/0.44 => ( bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3,axiom,
% 0.17/0.44 order_bot @ nat @ ( type2 @ nat ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 0.17/0.44 preorder @ nat @ ( type2 @ nat ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 0.17/0.44 bot @ nat @ ( type2 @ nat ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_6,axiom,
% 0.17/0.44 ! [A12: $tType] : ( bounde1808546759up_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_7,axiom,
% 0.17/0.44 ! [A12: $tType] : ( bounded_lattice_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Orderings_Oorder__bot_8,axiom,
% 0.17/0.44 ! [A12: $tType] : ( order_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 0.17/0.44 ! [A12: $tType] : ( preorder @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 0.17/0.44 ! [A12: $tType] : ( bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_11,axiom,
% 0.17/0.44 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 0.17/0.44 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 0.17/0.44 order_bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 0.17/0.44 preorder @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 thf(tcon_HOL_Obool___Orderings_Obot_15,axiom,
% 0.17/0.44 bot @ $o @ ( type2 @ $o ) ).
% 0.17/0.44
% 0.17/0.44 %----Helper facts (3)
% 0.17/0.44 thf(help_If_3_1_T,axiom,
% 0.17/0.44 ! [P: $o] :
% 0.17/0.44 ( ( P = $true )
% 0.17/0.44 | ( P = $false ) ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_2_1_T,axiom,
% 0.17/0.44 ! [A: $tType,X: A,Y: A] :
% 0.17/0.44 ( ( if @ A @ $false @ X @ Y )
% 0.17/0.44 = Y ) ).
% 0.17/0.44
% 0.17/0.44 thf(help_If_1_1_T,axiom,
% 0.17/0.44 ! [A: $tType,X: A,Y: A] :
% 0.17/0.44 ( ( if @ A @ $true @ X @ Y )
% 0.17/0.44 = X ) ).
% 0.17/0.44
% 0.17/0.44 %----Conjectures (4)
% 0.17/0.44 thf(conj_0,hypothesis,
% 0.17/0.44 $true ).
% 0.17/0.44
% 0.17/0.44 thf(conj_1,hypothesis,
% 0.17/0.44 ! [L3: rBT_Im246033960le_rbt @ a @ b,K2: a,V2: b,R5: rBT_Im246033960le_rbt @ a @ b] :
% 0.17/0.44 ( ( t
% 0.17/0.44 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ L3 @ K2 @ V2 @ R5 ) )
% 0.17/0.44 => thesis ) ).
% 0.17/0.44
% 0.17/0.44 thf(conj_2,hypothesis,
% 0.17/0.44 ! [L3: rBT_Im246033960le_rbt @ a @ b,K2: a,V2: b,R5: rBT_Im246033960le_rbt @ a @ b] :
% 0.17/0.44 ( ( t
% 0.17/0.44 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ L3 @ K2 @ V2 @ R5 ) )
% 0.17/0.44 => thesis ) ).
% 0.17/0.44
% 0.17/0.44 thf(conj_3,conjecture,
% 0.17/0.44 thesis ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 2.34/1.44 ---- Embedded in THF ---
% 2.34/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.34/1.45 %%% Generated on Tue Feb 24 06:12:10 EST 2026
% 2.34/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.34/1.45 %%% Logic specification used:
% 2.34/1.45 %%% thf(spec, logic, $$dhol).
% 2.34/1.45
% 2.34/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2DTF7073.p
% 2.34/1.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor, type, rBT_Im1923302023_color: $tType).
% 2.34/1.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt, type, rBT_Im246033960le_rbt: ($tType > ($tType > $tType))).
% 2.34/1.45 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.34/1.45 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.34/1.45 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.34/1.45 thf(ty_tf_b, type, b: $tType).
% 2.34/1.45 thf(ty_tf_a, type, a: $tType).
% 2.34/1.45 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.34/1.45 thf(sy_c_BNF__Composition_Oid__bnf, type, bNF_id_bnf: (!> [A:$tType]: ((A > A)))).
% 2.34/1.45 thf(sy_c_BNF__Def_Oeq__onp, type, bNF_eq_onp: (!> [A:$tType]: (((A > $o) > (A > (A > $o)))))).
% 2.34/1.45 thf(sy_c_BNF__Def_Ovimage2p, type, bNF_vimage2p: (!> [A:$tType,D:$tType,B:$tType,E:$tType,C:$tType]: (((A > D) > ((B > E) > ((D > (E > C)) > (A > (B > C)))))))).
% 2.34/1.45 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.34/1.45 thf(sy_c_Fun_Obij__betw, type, bij_betw: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > ((set @ B) > $o)))))).
% 2.34/1.45 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 2.34/1.45 thf(sy_c_Fun_Omap__fun, type, map_fun: (!> [C:$tType,A:$tType,B:$tType,D:$tType]: (((C > A) > ((B > D) > ((A > B) > (C > D))))))).
% 2.34/1.45 thf(sy_c_Fun_Ooverride__on, type, override_on: (!> [A:$tType,B:$tType]: (((A > B) > ((A > B) > ((set @ A) > (A > B))))))).
% 2.34/1.45 thf(sy_c_Groups_Ocomm__monoid, type, comm_monoid: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 2.34/1.45 thf(sy_c_Groups_Omonoid, type, monoid: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 2.34/1.45 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.34/1.45 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.34/1.45 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 2.34/1.45 thf(sy_c_Lattices_Osemilattice__neutr, type, semilattice_neutr: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 2.34/1.45 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.34/1.45 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.34/1.45 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.34/1.45 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.34/1.45 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color, type, rBT_Im1975547051_color: (!> [A:$tType]: ((A > (A > (rBT_Im1923302023_color > A)))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color, type, rBT_Im1059957627_color: (!> [A:$tType]: ((A > (A > (rBT_Im1923302023_color > A)))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color, type, rBT_Im800559290_color: (rBT_Im1923302023_color > nat)).
% 2.34/1.45 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))))))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty, type, rBT_Im418718756_Empty: (!> [A:$tType,B:$tType]: (((rBT_Im246033960le_rbt @ A) @ B)))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt, type, rBT_Im858806507se_rbt: (!> [C:$tType,A:$tType,B:$tType]: ((C > ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > C))))) > (((rBT_Im246033960le_rbt @ A) @ B) > C)))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Omap__rbt, type, rBT_Im206295089ap_rbt: (!> [A:$tType,Aa:$tType,B:$tType,Ba:$tType]: (((A > Aa) > ((B > Ba) > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ Aa) @ Ba))))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Opred__rbt, type, rBT_Im1931894874ed_rbt: (!> [A:$tType,B:$tType]: (((A > $o) > ((B > $o) > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt, type, rBT_Im1947144893ec_rbt: (!> [E:$tType,A:$tType,B:$tType]: ((E > ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > (E > (E > E))))))) > (((rBT_Im246033960le_rbt @ A) @ B) > E)))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orel__rbt, type, rBT_Im1000242676el_rbt: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > (((rBT_Im246033960le_rbt @ C) @ D) > $o))))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt, type, rBT_Im1178217900t1_rbt: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (set @ A))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt, type, rBT_Im1550225131t2_rbt: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (set @ B))))).
% 2.34/1.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt, type, rBT_Im1485196410ze_rbt: (!> [A:$tType,B:$tType]: (((A > nat) > ((B > nat) > (((rBT_Im246033960le_rbt @ A) @ B) > nat)))))).
% 2.34/1.45 thf(sy_c_Set_OBall, type, ball: (!> [A:$tType]: (((set @ A) > ((A > $o) > $o))))).
% 2.34/1.45 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.34/1.45 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.34/1.45 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.34/1.45 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.34/1.45 thf(sy_c_Set_Opairwise, type, pairwise: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 2.34/1.45 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.34/1.45 thf(sy_c_Set_Ovimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 2.34/1.45 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.34/1.45 thf(sy_v_t, type, t: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.34/1.45 thf(sy_v_thesis, type, thesis: $o).
% 2.34/1.45 thf(fact_0_Empty, axiom, ((t = ((rBT_Im418718756_Empty @ a) @ b)) => thesis)).
% 2.34/1.45 thf(fact_1_rbt_Oinject, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25) = (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & ((X22 = Y22) & ((X23 = Y23) & ((X24 = Y24) & (X25 = Y25))))))))).
% 2.34/1.45 thf(fact_2_Black, axiom, (! [L:((rBT_Im246033960le_rbt @ a) @ b),K:a,V:b,R:((rBT_Im246033960le_rbt @ a) @ b)]: (((t = (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ L) @ K) @ V) @ R)) => thesis)))).
% 2.34/1.45 thf(fact_3_Red, axiom, (! [L:((rBT_Im246033960le_rbt @ a) @ b),K:a,V:b,R:((rBT_Im246033960le_rbt @ a) @ b)]: (((t = (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ L) @ K) @ V) @ R)) => thesis)))).
% 2.34/1.45 thf(fact_4_rbt_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((rBT_Im418718756_Empty @ A) @ B) != (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25))))).
% 2.34/1.45 thf(fact_5_color_Odistinct_I1_J, axiom, (rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B)).
% 2.34/1.45 thf(fact_6_rbt_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > $o),Rbt:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) => ((! [X1:rBT_Im1923302023_color,X2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,X4:B,X5:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ X2) => ((P @ X5) => (P @ (((((((rBT_Im480247531Branch @ A) @ B) @ X1) @ X2) @ X3) @ X4) @ X5)))))) => (P @ Rbt)))))).
% 2.34/1.45 thf(fact_7_rbt_Oexhaust, axiom, (! [B:$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)))))))))).
% 2.34/1.45 thf(fact_8_color_Oinduct, axiom, (! [P:(rBT_Im1923302023_color > $o),Color:rBT_Im1923302023_color]: (((P @ rBT_Impl_Mirabelle_R) => ((P @ rBT_Impl_Mirabelle_B) => (P @ Color)))))).
% 2.34/1.45 thf(fact_9_color_Oexhaust, axiom, (! [Y:rBT_Im1923302023_color]: (((Y != rBT_Impl_Mirabelle_R) => (Y = rBT_Impl_Mirabelle_B))))).
% 2.34/1.45 thf(fact_10_color_Osimps_I6_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1059957627_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_B) = F2)))).
% 2.34/1.45 thf(fact_11_color_Osimps_I5_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1059957627_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_R) = F1)))).
% 2.34/1.45 thf(fact_12_color_Osimps_I4_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_B) = F2)))).
% 2.34/1.45 thf(fact_13_color_Osimps_I3_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_R) = F1)))).
% 2.34/1.45 thf(fact_14_rbt_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,F1:C,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > C)))))]: ((((((((rBT_Im858806507se_rbt @ C) @ A) @ B) @ F1) @ F2) @ ((rBT_Im418718756_Empty @ A) @ B)) = F1)))).
% 2.34/1.45 thf(fact_15_rbt_Osimps_I5_J, axiom, (! [C:$tType,B:$tType,A:$tType,F1:C,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > C))))),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im858806507se_rbt @ C) @ A) @ B) @ F1) @ F2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((((F2 @ X21) @ X22) @ X23) @ X24) @ X25))))).
% 2.34/1.45 thf(fact_16_rbt_Osimps_I6_J, axiom, (! [A:$tType,B:$tType,E:$tType,F1:E,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > (E > (E > E)))))))]: ((((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ ((rBT_Im418718756_Empty @ A) @ B)) = F1)))).
% 2.34/1.45 thf(fact_17_rbt_Osimps_I7_J, axiom, (! [E:$tType,B:$tType,A:$tType,F1:E,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > (E > (E > E))))))),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((((((F2 @ X21) @ X22) @ X23) @ X24) @ X25) @ ((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ X22)) @ ((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ X25)))))).
% 2.34/1.45 thf(fact_18_rbt_Opred__inject_I2_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),A2:rBT_Im1923302023_color,Aa2:((rBT_Im246033960le_rbt @ A) @ B),Ab:A,Ac:B,Ad:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A2) @ Aa2) @ Ab) @ Ac) @ Ad)) = ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ Aa2) & ((P1 @ Ab) & ((P2 @ Ac) & (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ Ad)))))))).
% 2.34/1.45 thf(fact_19_rbt_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((~ (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) @ ((rBT_Im418718756_Empty @ C) @ D))))))).
% 2.34/1.45 thf(fact_20_rbt_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ C) @ D),Y23:C,Y24:D,Y25:((rBT_Im246033960le_rbt @ C) @ D)]: ((~ (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((rBT_Im418718756_Empty @ A) @ B)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25))))))).
% 2.34/1.45 thf(fact_21_rbt_Opred__inject_I1_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o)]: ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.34/1.45 thf(fact_22_rbt_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ (^ [Y2:A,Z:A]: ((Y2 = Z)))) @ (^ [Y2:B,Z:B]: ((Y2 = Z)))) = (^ [Y2:((rBT_Im246033960le_rbt @ A) @ B),Z:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y2 = Z))))))).
% 2.34/1.45 thf(fact_23_rbt_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X:((rBT_Im246033960le_rbt @ C) @ D)]: (((! [X6:C]: (((R1a @ X6) @ X6))) => ((! [X6:D]: (((R2a @ X6) @ X6))) => ((((((((rBT_Im1000242676el_rbt @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X) @ X)))))).
% 2.34/1.45 thf(fact_24_color_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F1:A,F2:A,Color:rBT_Im1923302023_color]: (((H @ ((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ Color)) = ((((rBT_Im1975547051_color @ B) @ (H @ F1)) @ (H @ F2)) @ Color))))).
% 2.34/1.45 thf(fact_25_rbt_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X21:rBT_Im1923302023_color,Y21:rBT_Im1923302023_color,R1:(A > (C > $o)),R2:(B > (D > $o)),X22:((rBT_Im246033960le_rbt @ A) @ B),Y22:((rBT_Im246033960le_rbt @ C) @ D),X23:A,Y23:C,X24:B,Y24:D,X25:((rBT_Im246033960le_rbt @ A) @ B),Y25:((rBT_Im246033960le_rbt @ C) @ D)]: (((X21 = Y21) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22) => (((R1 @ X23) @ Y23) => (((R2 @ X24) @ Y24) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X25) @ Y25) => ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)))))))))).
% 2.34/1.45 thf(fact_26_rbt_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ C) @ D),Y23:C,Y24:D,Y25:((rBT_Im246033960le_rbt @ C) @ D)]: ((((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X22) @ Y22) & (((R1 @ X23) @ Y23) & (((R2 @ X24) @ Y24) & ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X25) @ Y25))))))))).
% 2.34/1.45 thf(fact_27_rbt_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o))]: (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ ((rBT_Im418718756_Empty @ A) @ B)) @ ((rBT_Im418718756_Empty @ C) @ D))))).
% 2.34/1.45 thf(fact_28_rbt_Opred__rel, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1931894874ed_rbt @ A) @ B) = (^ [P12:(A > $o),P22:(B > $o),X7:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ ((bNF_eq_onp @ A) @ P12)) @ ((bNF_eq_onp @ B) @ P22)) @ X7) @ X7))))))).
% 2.34/1.45 thf(fact_29_rbt_Oset__intros_I1_J, axiom, (! [B:$tType,A:$tType,X:A,A22:((rBT_Im246033960le_rbt @ A) @ B),A1:rBT_Im1923302023_color,A3:A,A4:B,A5:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ A) @ X) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A22)) => (((member @ A) @ X) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A3) @ A4) @ A5))))))).
% 2.34/1.45 thf(fact_30_rbt_Oset__intros_I2_J, axiom, (! [B:$tType,A:$tType,A3:A,A1:rBT_Im1923302023_color,A22:((rBT_Im246033960le_rbt @ A) @ B),A4:B,A5:((rBT_Im246033960le_rbt @ A) @ B)]: ((((member @ A) @ A3) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A3) @ A4) @ A5)))))).
% 2.34/1.45 thf(fact_31_rbt_Oset__intros_I3_J, axiom, (! [B:$tType,A:$tType,Xb:A,A5:((rBT_Im246033960le_rbt @ A) @ B),A1:rBT_Im1923302023_color,A22:((rBT_Im246033960le_rbt @ A) @ B),A3:A,A4:B]: (((((member @ A) @ Xb) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A5)) => (((member @ A) @ Xb) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A3) @ A4) @ A5))))))).
% 2.34/1.45 thf(fact_32_rbt_Oset__intros_I4_J, axiom, (! [B:$tType,A:$tType,Xe:B,A2a:((rBT_Im246033960le_rbt @ A) @ B),A1a:rBT_Im1923302023_color,A3a:A,A4a:B,A5a:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ B) @ Xe) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A2a)) => (((member @ B) @ Xe) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a))))))).
% 2.34/1.45 thf(fact_33_rbt_Oset__intros_I5_J, axiom, (! [B:$tType,A:$tType,A4a:B,A1a:rBT_Im1923302023_color,A2a:((rBT_Im246033960le_rbt @ A) @ B),A3a:A,A5a:((rBT_Im246033960le_rbt @ A) @ B)]: ((((member @ B) @ A4a) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a)))))).
% 2.34/1.45 thf(fact_34_rbt_Oset__intros_I6_J, axiom, (! [B:$tType,A:$tType,Xg:B,A5a:((rBT_Im246033960le_rbt @ A) @ B),A1a:rBT_Im1923302023_color,A2a:((rBT_Im246033960le_rbt @ A) @ B),A3a:A,A4a:B]: (((((member @ B) @ Xg) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A5a)) => (((member @ B) @ Xg) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a))))))).
% 2.34/1.45 thf(fact_35_rbt_Oset__cases_I1_J, axiom, (! [B:$tType,A:$tType,E2:A,A2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A2)) => ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B)]: (((? [Z3:A,Z4:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ Z3) @ Z4) @ Z5)))) => (~ ((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Z2))))))) => ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B),Z4:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 != (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ E2) @ Z4) @ Z5)))) => (~ ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B),Z3:A,Z4:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: (((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ Z3) @ Z4) @ Z5)) => (~ ((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Z5))))))))))))))).
% 2.34/1.45 thf(fact_36_rbt_Oset__cases_I2_J, axiom, (! [B:$tType,A:$tType,E2:B,A2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A2)) => ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B)]: (((? [Z3:A,Z4:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ Z3) @ Z4) @ Z5)))) => (~ ((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Z2))))))) => ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B),Z3:A,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 != (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ Z3) @ E2) @ Z5)))) => (~ ((! [Z1:rBT_Im1923302023_color,Z2:((rBT_Im246033960le_rbt @ A) @ B),Z3:A,Z4:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: (((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z2) @ Z3) @ Z4) @ Z5)) => (~ ((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Z5))))))))))))))).
% 2.34/1.45 thf(fact_37_rbt_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,F1:(A > C),F2:(B > D)]: (((((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ C) @ D))))).
% 2.34/1.45 thf(fact_38_rbt_Oinj__map__strong, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),Xa:((rBT_Im246033960le_rbt @ A) @ B),F1:(A > C),F1a:(A > C),F2:(B > D),F2a:(B > D)]: (((! [Z1:A,Z1a:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((((member @ A) @ Z1a) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Xa)) => (((F1 @ Z1) = (F1a @ Z1a)) => (Z1 = Z1a)))))) => ((! [Z2:B,Z2a:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((((member @ B) @ Z2a) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Xa)) => (((F2 @ Z2) = (F2a @ Z2a)) => (Z2 = Z2a)))))) => (((((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1a) @ F2a) @ Xa)) => (X = Xa))))))).
% 2.34/1.45 thf(fact_39_rbt_Omap__cong0, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((F1 @ Z1) = (G1 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ G1) @ G2) @ X))))))).
% 2.34/1.45 thf(fact_40_rbt_Omap__cong, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),Ya:((rBT_Im246033960le_rbt @ A) @ B),F1:(A > C),G1:(A > C),F2:(B > D),G2:(B > D)]: (((X = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Ya)) => ((F1 @ Z1) = (G1 @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Ya)) => ((F2 @ Z2) = (G2 @ Z2))))) => ((((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X) = (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ G1) @ G2) @ Ya)))))))).
% 2.34/1.45 thf(fact_41_rbt_Orel__refl__strong, axiom, (! [B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),R1a:(A > (A > $o)),R2a:(B > (B > $o))]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((R1a @ Z1) @ Z1)))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((R2a @ Z2) @ Z2)))) => ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ R1a) @ R2a) @ X) @ X)))))).
% 2.34/1.45 thf(fact_42_rbt_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R2:(B > (D > $o)),X:((rBT_Im246033960le_rbt @ A) @ B),Y:((rBT_Im246033960le_rbt @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: ((((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X) @ Y) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((((member @ C) @ Y1) @ (((rBT_Im1178217900t1_rbt @ C) @ D) @ Y)) => (((R1 @ Z1) @ Y1) => ((R1a @ Z1) @ Y1)))))) => ((! [Z2:B,Y26:D]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((((member @ D) @ Y26) @ (((rBT_Im1550225131t2_rbt @ C) @ D) @ Y)) => (((R2 @ Z2) @ Y26) => ((R2a @ Z2) @ Y26)))))) => ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ X) @ Y))))))).
% 2.34/1.45 thf(fact_43_rbt_Orel__cong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),Ya:((rBT_Im246033960le_rbt @ A) @ B),Y:((rBT_Im246033960le_rbt @ C) @ D),Xa:((rBT_Im246033960le_rbt @ C) @ D),R1:(A > (C > $o)),R1a:(A > (C > $o)),R2:(B > (D > $o)),R2a:(B > (D > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Ya)) => ((((member @ C) @ Y1) @ (((rBT_Im1178217900t1_rbt @ C) @ D) @ Xa)) => (((R1 @ Z1) @ Y1) = ((R1a @ Z1) @ Y1)))))) => ((! [Z2:B,Y26:D]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Ya)) => ((((member @ D) @ Y26) @ (((rBT_Im1550225131t2_rbt @ C) @ D) @ Xa)) => (((R2 @ Z2) @ Y26) = ((R2a @ Z2) @ Y26)))))) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R2) @ X) @ Y) = ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ Ya) @ Xa))))))))).
% 2.34/1.45 thf(fact_44_rbt_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P2:(B > $o),X:((rBT_Im246033960le_rbt @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: (((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ X) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((P1 @ Z1) => (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((P2 @ Z2) => (P2a @ Z2))))) => (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1a) @ P2a) @ X))))))).
% 2.34/1.45 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.34/1.45 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A6:(set @ A)]: ((((collect @ A) @ (^ [X7:A]: ((((member @ A) @ X7) @ A6)))) = A6)))).
% 2.34/1.45 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((P @ X6) = (Q @ X6)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.34/1.45 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X6:A]: (((F @ X6) = (G @ X6)))) => (F = G))))).
% 2.34/1.45 thf(fact_49_rbt_Opred__cong, axiom, (! [B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),Ya:((rBT_Im246033960le_rbt @ A) @ B),P1:(A > $o),P1a:(A > $o),P2:(B > $o),P2a:(B > $o)]: (((X = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Ya)) => ((P1 @ Z1) = (P1a @ Z1))))) => ((! [Z2:B]: (((((member @ B) @ Z2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Ya)) => ((P2 @ Z2) = (P2a @ Z2))))) => ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2) @ X) = (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1a) @ P2a) @ Ya)))))))).
% 2.34/1.45 thf(fact_50_rbt_Orel__eq__onp, axiom, (! [A:$tType,B:$tType,P1:(A > $o),P2:(B > $o)]: ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ ((bNF_eq_onp @ A) @ P1)) @ ((bNF_eq_onp @ B) @ P2)) = ((bNF_eq_onp @ ((rBT_Im246033960le_rbt @ A) @ B)) @ ((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P2)))))).
% 2.34/1.45 thf(fact_51_rbt_Osimps_I9_J, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,F1:(A > C),F2:(B > D),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((((((rBT_Im480247531Branch @ C) @ D) @ X21) @ (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X22)) @ (F1 @ X23)) @ (F2 @ X24)) @ (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X25)))))).
% 2.34/1.45 thf(fact_52_eq__onp__live__step, axiom, (! [A:$tType,X:$o,Y:$o,P:(A > $o),A2:A]: (((X = Y) => ((((((bNF_eq_onp @ A) @ P) @ A2) @ A2) & X) = ((P @ A2) & Y)))))).
% 2.34/1.45 thf(fact_53_eq__onp__same__args, axiom, (! [A:$tType,P:(A > $o),X:A]: ((((((bNF_eq_onp @ A) @ P) @ X) @ X) = (P @ X))))).
% 2.34/1.45 thf(fact_54_eq__onp__to__eq, axiom, (! [A:$tType,P:(A > $o),X:A,Y:A]: ((((((bNF_eq_onp @ A) @ P) @ X) @ Y) => (X = Y))))).
% 2.34/1.45 thf(fact_55_eq__onp__mono0, axiom, (! [A:$tType,A6:(set @ A),P:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((((member @ A) @ X6) @ A6) => ((P @ X6) => (Q @ X6))))) => (! [X8:A]: (((((member @ A) @ X8) @ A6) => (! [Xa2:A]: (((((member @ A) @ Xa2) @ A6) => (((((bNF_eq_onp @ A) @ P) @ X8) @ Xa2) => ((((bNF_eq_onp @ A) @ Q) @ X8) @ Xa2)))))))))))).
% 2.34/1.45 thf(fact_56_eq__onp__eqD, axiom, (! [A:$tType,P:(A > $o),Q:(A > (A > $o)),X:A]: (((((bNF_eq_onp @ A) @ P) = Q) => ((P @ X) = ((Q @ X) @ X)))))).
% 2.34/1.45 thf(fact_57_rbt_Opred__set, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1931894874ed_rbt @ A) @ B) = (^ [P12:(A > $o),P22:(B > $o),X7:((rBT_Im246033960le_rbt @ A) @ B)]: (((! [Y3:A]: (((((member @ A) @ Y3) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X7)) => (P12 @ Y3)))) & (! [Y3:B]: (((((member @ B) @ Y3) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X7)) => (P22 @ Y3))))))))))).
% 2.34/1.45 thf(fact_58_rbt_Osimps_I16_J, axiom, (! [A:$tType,B:$tType]: (((((rBT_Im1550225131t2_rbt @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (bot_bot @ (set @ B)))))).
% 2.34/1.45 thf(fact_59_rbt_Osimps_I14_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im1178217900t1_rbt @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_60_rbt_Opred__map, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,Q1:(C > $o),Q2:(D > $o),F1:(A > C),F2:(B > D),X:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1931894874ed_rbt @ C) @ D) @ Q1) @ Q2) @ (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ X)) = (((((rBT_Im1931894874ed_rbt @ A) @ B) @ (((((comp @ C) @ $o) @ A) @ Q1) @ F1)) @ (((((comp @ D) @ $o) @ B) @ Q2) @ F2)) @ X))))).
% 2.34/1.45 thf(fact_61_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),X:C,H:(D > A),K:(C > D)]: ((((F @ (G @ X)) = (H @ (K @ X))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X) = ((((((comp @ D) @ A) @ C) @ H) @ K) @ X)))))).
% 2.34/1.45 thf(fact_62_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 2.34/1.45 thf(fact_63_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H:(A > C),R:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = R) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H) = (((((comp @ B) @ D) @ A) @ F) @ R)))))).
% 2.34/1.45 thf(fact_64_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H:(E > A),R:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H) = R) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G) @ H)) = (((((comp @ D) @ B) @ E) @ L1) @ R))))))).
% 2.34/1.45 thf(fact_65_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G:(C > B),H:(A > C),R12:(D > B),R22:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = (((((comp @ D) @ B) @ A) @ R12) @ R22)) => (((((((comp @ B) @ E) @ D) @ F) @ R12) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ E) @ A) @ L) @ R22))))))).
% 2.34/1.45 thf(fact_66_rbt_Omap__comp, axiom, (! [D:$tType,F3:$tType,E:$tType,C:$tType,B:$tType,A:$tType,G1:(C > E),G2:(D > F3),F1:(A > C),F2:(B > D),V:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((((rBT_Im206295089ap_rbt @ C) @ E) @ D) @ F3) @ G1) @ G2) @ (((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ F1) @ F2) @ V)) = (((((((rBT_Im206295089ap_rbt @ A) @ E) @ B) @ F3) @ (((((comp @ C) @ E) @ A) @ G1) @ F1)) @ (((((comp @ D) @ F3) @ B) @ G2) @ F2)) @ V))))).
% 2.34/1.45 thf(fact_67_ball__empty, axiom, (! [A:$tType,P:(A > $o),X8:A]: (((((member @ A) @ X8) @ (bot_bot @ (set @ A))) => (P @ X8))))).
% 2.34/1.45 thf(fact_68_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F4:(B > A),G3:(C > B),X7:C]: ((F4 @ (G3 @ X7)))))))).
% 2.34/1.45 thf(fact_69_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.34/1.45 thf(fact_70_all__not__in__conv, axiom, (! [A:$tType,A6:(set @ A)]: (((! [X7:A]: ((~ ((((member @ A) @ X7) @ A6))))) = (A6 = (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_71_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X7:A]: ((~ ((P @ X7))))))))).
% 2.34/1.45 thf(fact_72_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X7:A]: ((~ ((P @ X7))))))))).
% 2.34/1.45 thf(fact_73_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X7:D]: ((bot_bot @ C)))))))).
% 2.34/1.45 thf(fact_74_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.34/1.45 thf(fact_75_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X7:A]: ((bot_bot @ B)))))))).
% 2.34/1.45 thf(fact_76_ex__in__conv, axiom, (! [A:$tType,A6:(set @ A)]: (((? [X7:A]: ((((member @ A) @ X7) @ A6))) = (A6 != (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_77_equals0I, axiom, (! [A:$tType,A6:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A6))))) => (A6 = (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_78_equals0D, axiom, (! [A:$tType,A6:(set @ A),A2:A]: (((A6 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A6))))))).
% 2.34/1.45 thf(fact_79_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 2.34/1.45 thf(fact_80_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = C2) => ((A2 @ (B2 @ V)) = (C2 @ V)))))).
% 2.34/1.45 thf(fact_81_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A2 @ (B2 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 2.34/1.45 thf(fact_82_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A2:(C > B),B2:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A2) @ B2) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A2 @ (B2 @ V)) = (C2 @ (D2 @ V))))))).
% 2.34/1.45 thf(fact_83_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G)) @ H) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G) @ H)))))).
% 2.34/1.45 thf(fact_84_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F4:(B > C),G3:(A > B),X7:A]: ((F4 @ (G3 @ X7)))))))).
% 2.34/1.45 thf(fact_85_Ball__def, axiom, (! [A:$tType]: (((ball @ A) = (^ [A7:(set @ A),P3:(A > $o)]: ((! [X7:A]: (((((member @ A) @ X7) @ A7) => (P3 @ X7)))))))))).
% 2.34/1.45 thf(fact_86_override__on__emptyset, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((((((override_on @ A) @ B) @ F) @ G) @ (bot_bot @ (set @ A))) = F)))).
% 2.34/1.45 thf(fact_87_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A7:(set @ A)]: ((A7 = (bot_bot @ (set @ A))))))))).
% 2.34/1.45 thf(fact_88_ball__reg, axiom, (! [A:$tType,R3:(set @ A),P:(A > $o),Q:(A > $o)]: (((! [X6:A]: (((((member @ A) @ X6) @ R3) => ((P @ X6) => (Q @ X6))))) => ((! [X6:A]: (((((member @ A) @ X6) @ R3) => (P @ X6)))) => (! [X8:A]: (((((member @ A) @ X8) @ R3) => (Q @ X8))))))))).
% 2.34/1.45 thf(fact_89_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E:$tType,A:$tType,C:$tType,M:(B > A),G:(C > B),X:C,N:(D > A),H:(C > D),F:(A > E)]: ((((M @ (G @ X)) = (N @ (H @ X))) => (((((((comp @ B) @ E) @ C) @ (((((comp @ A) @ E) @ B) @ F) @ M)) @ G) @ X) = ((((((comp @ D) @ E) @ C) @ (((((comp @ A) @ E) @ D) @ F) @ N)) @ H) @ X)))))).
% 2.34/1.45 thf(fact_90_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G:(B > C),F:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G) @ (((((comp @ A) @ B) @ D) @ F) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 2.34/1.45 thf(fact_91_comp__cong, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,E:$tType,F:(B > A),G:(C > B),X:C,F5:(D > A),G4:(E > D),X9:E]: ((((F @ (G @ X)) = (F5 @ (G4 @ X9))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X) = ((((((comp @ D) @ A) @ E) @ F5) @ G4) @ X9)))))).
% 2.34/1.45 thf(fact_92_override__on__apply__in, axiom, (! [B:$tType,A:$tType,A2:A,A6:(set @ A),F:(A > B),G:(A > B)]: (((((member @ A) @ A2) @ A6) => (((((((override_on @ A) @ B) @ F) @ G) @ A6) @ A2) = (G @ A2)))))).
% 2.34/1.45 thf(fact_93_override__on__apply__notin, axiom, (! [B:$tType,A:$tType,A2:A,A6:(set @ A),F:(A > B),G:(A > B)]: (((~ ((((member @ A) @ A2) @ A6))) => (((((((override_on @ A) @ B) @ F) @ G) @ A6) @ A2) = (F @ A2)))))).
% 2.34/1.45 thf(fact_94_override__on__def, axiom, (! [B:$tType,A:$tType]: ((((override_on @ A) @ B) = (^ [F4:(A > B),G3:(A > B),A7:(set @ A),A8:A]: (((((if @ B) @ (((member @ A) @ A8) @ A7)) @ (G3 @ A8)) @ (F4 @ A8)))))))).
% 2.34/1.45 thf(fact_95_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.34/1.45 thf(fact_96_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X7:A]: ((((member @ A) @ X7) @ (bot_bot @ (set @ A))))))))).
% 2.34/1.45 thf(fact_97_rbt_Osize__gen__o__map, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F:(C > nat),Fa:(D > nat),G:(A > C),Ga:(B > D)]: (((((((comp @ ((rBT_Im246033960le_rbt @ C) @ D)) @ nat) @ ((rBT_Im246033960le_rbt @ A) @ B)) @ ((((rBT_Im1485196410ze_rbt @ C) @ D) @ F) @ Fa)) @ ((((((rBT_Im206295089ap_rbt @ A) @ C) @ B) @ D) @ G) @ Ga)) = ((((rBT_Im1485196410ze_rbt @ A) @ B) @ (((((comp @ C) @ nat) @ A) @ F) @ G)) @ (((((comp @ D) @ nat) @ B) @ Fa) @ Ga)))))).
% 2.34/1.45 thf(fact_98_is__singletonI_H, axiom, (! [A:$tType,A6:(set @ A)]: (((A6 != (bot_bot @ (set @ A))) => ((! [X6:A,Y4:A]: (((((member @ A) @ X6) @ A6) => ((((member @ A) @ Y4) @ A6) => (X6 = Y4))))) => ((is_singleton @ A) @ A6)))))).
% 2.34/1.45 thf(fact_99_vimage2p__comp, axiom, (! [E:$tType,D:$tType,F3:$tType,A:$tType,C:$tType,B:$tType,G5:$tType,F1:(F3 > A),F2:(D > F3),G1:(G5 > B),G2:(E > G5)]: (((((((((bNF_vimage2p @ D) @ A) @ E) @ B) @ C) @ (((((comp @ F3) @ A) @ D) @ F1) @ F2)) @ (((((comp @ G5) @ B) @ E) @ G1) @ G2)) = (((((comp @ (F3 > (G5 > C))) @ (D > (E > C))) @ (A > (B > C))) @ (((((((bNF_vimage2p @ D) @ F3) @ E) @ G5) @ C) @ F2) @ G2)) @ (((((((bNF_vimage2p @ F3) @ A) @ G5) @ B) @ C) @ F1) @ G1)))))).
% 2.34/1.45 thf(fact_100_vimage2p__cong, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,R3:(A > (B > C)),S:(A > (B > C)),F:(D > A),G:(E > B)]: (((R3 = S) => (((((((((bNF_vimage2p @ D) @ A) @ E) @ B) @ C) @ F) @ G) @ R3) = ((((((((bNF_vimage2p @ D) @ A) @ E) @ B) @ C) @ F) @ G) @ S)))))).
% 2.34/1.45 thf(fact_101_rbt_Osize__gen_I1_J, axiom, (! [A:$tType,B:$tType,Xa:(A > nat),X:(B > nat)]: (((((((rBT_Im1485196410ze_rbt @ A) @ B) @ Xa) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = (zero_zero @ nat))))).
% 2.34/1.45 thf(fact_102_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_103_map__fun_Ocomp, axiom, (! [E:$tType,C:$tType,A:$tType,F3:$tType,D:$tType,B:$tType,F:(E > C),G:(D > F3),H:(C > A),I:(B > D)]: (((((((comp @ (C > D)) @ (E > F3)) @ (A > B)) @ ((((((map_fun @ E) @ C) @ D) @ F3) @ F) @ G)) @ ((((((map_fun @ C) @ A) @ B) @ D) @ H) @ I)) = ((((((map_fun @ E) @ A) @ B) @ F3) @ (((((comp @ C) @ A) @ E) @ H) @ F)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)))))).
% 2.34/1.45 thf(fact_104_is__singletonE, axiom, (! [A:$tType,A6:(set @ A)]: ((((is_singleton @ A) @ A6) => (~ ((! [X6:A]: ((A6 != (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))))).
% 2.34/1.45 thf(fact_105_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A7:(set @ A)]: ((? [X7:A]: ((A7 = (((insert @ A) @ X7) @ (bot_bot @ (set @ A)))))))))))).
% 2.34/1.45 thf(fact_106_insert__absorb2, axiom, (! [A:$tType,X:A,A6:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A6)) = (((insert @ A) @ X) @ A6))))).
% 2.34/1.45 thf(fact_107_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A6)) = ((A2 = B2) | (((member @ A) @ A2) @ A6)))))).
% 2.34/1.45 thf(fact_108_insertCI, axiom, (! [A:$tType,A2:A,B3:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B3))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 2.34/1.45 thf(fact_109_map__fun__apply, axiom, (! [D:$tType,A:$tType,C:$tType,B:$tType]: ((((((map_fun @ B) @ C) @ D) @ A) = (^ [F4:(B > C),G3:(D > A),H2:(C > D),X7:B]: ((G3 @ (H2 @ (F4 @ X7))))))))).
% 2.34/1.45 thf(fact_110_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_111_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 2.34/1.45 thf(fact_112_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 2.34/1.45 thf(fact_113_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C2:A,D2:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C2) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A2 = C2) & (B2 = D2)) | ((A2 = D2) & (B2 = C2))))))).
% 2.34/1.45 thf(fact_114_insert__not__empty, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((insert @ A) @ A2) @ A6) != (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_115_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 2.34/1.45 thf(fact_116_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ A6) => (? [B4:(set @ A)]: (((A6 = (((insert @ A) @ A2) @ B4)) & (~ ((((member @ A) @ A2) @ B4)))))))))).
% 2.34/1.45 thf(fact_117_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A6:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A6)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A6)))))).
% 2.34/1.45 thf(fact_118_insert__eq__iff, axiom, (! [A:$tType,A2:A,A6:(set @ A),B2:A,B3:(set @ A)]: (((~ ((((member @ A) @ A2) @ A6))) => ((~ ((((member @ A) @ B2) @ B3))) => (((((insert @ A) @ A2) @ A6) = (((insert @ A) @ B2) @ B3)) = (((A2 = B2) => (A6 = B3)) & ((A2 != B2) => (? [C3:(set @ A)]: (((A6 = (((insert @ A) @ B2) @ C3)) & ((~ ((((member @ A) @ B2) @ C3))) & ((B3 = (((insert @ A) @ A2) @ C3)) & (~ ((((member @ A) @ A2) @ C3)))))))))))))))).
% 2.34/1.45 thf(fact_119_insert__absorb, axiom, (! [A:$tType,A2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ A6) => ((((insert @ A) @ A2) @ A6) = A6))))).
% 2.34/1.45 thf(fact_120_insert__ident, axiom, (! [A:$tType,X:A,A6:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ X) @ A6))) => ((~ ((((member @ A) @ X) @ B3))) => (((((insert @ A) @ X) @ A6) = (((insert @ A) @ X) @ B3)) = (A6 = B3))))))).
% 2.34/1.45 thf(fact_121_Set_Oset__insert, axiom, (! [A:$tType,X:A,A6:(set @ A)]: (((((member @ A) @ X) @ A6) => (~ ((! [B4:(set @ A)]: (((A6 = (((insert @ A) @ X) @ B4)) => (((member @ A) @ X) @ B4)))))))))).
% 2.34/1.45 thf(fact_122_insertI2, axiom, (! [A:$tType,A2:A,B3:(set @ A),B2:A]: (((((member @ A) @ A2) @ B3) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B3)))))).
% 2.34/1.45 thf(fact_123_insertI1, axiom, (! [A:$tType,A2:A,B3:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B3))))).
% 2.34/1.45 thf(fact_124_insertE, axiom, (! [A:$tType,A2:A,B2:A,A6:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A6)) => ((A2 != B2) => (((member @ A) @ A2) @ A6)))))).
% 2.34/1.45 thf(fact_125_map__fun_Ocompositionality, axiom, (! [D:$tType,F3:$tType,C:$tType,E:$tType,B:$tType,A:$tType,F:(E > C),G:(D > F3),H:(C > A),I:(B > D),Fun:(A > B)]: (((((((((map_fun @ E) @ C) @ D) @ F3) @ F) @ G) @ (((((((map_fun @ C) @ A) @ B) @ D) @ H) @ I) @ Fun)) = (((((((map_fun @ E) @ A) @ B) @ F3) @ (((((comp @ C) @ A) @ E) @ H) @ F)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)) @ Fun))))).
% 2.34/1.45 thf(fact_126_map__fun__def, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType]: ((((((map_fun @ C) @ A) @ B) @ D) = (^ [F4:(C > A),G3:(B > D),H2:(A > B)]: ((((((comp @ A) @ D) @ C) @ (((((comp @ B) @ D) @ A) @ G3) @ H2)) @ F4))))))).
% 2.34/1.45 thf(fact_127_color_Osize__gen_I1_J, axiom, ((rBT_Im800559290_color @ rBT_Impl_Mirabelle_R) = (zero_zero @ nat))).
% 2.34/1.45 thf(fact_128_color_Osize__gen_I2_J, axiom, ((rBT_Im800559290_color @ rBT_Impl_Mirabelle_B) = (zero_zero @ nat))).
% 2.34/1.45 thf(fact_129_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A7:(set @ A)]: ((A7 = (((insert @ A) @ ((the_elem @ A) @ A7)) @ (bot_bot @ (set @ A)))))))))).
% 2.34/1.45 thf(fact_130_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 2.34/1.45 thf(fact_131_color_Osize_I3_J, axiom, (((size_size @ rBT_Im1923302023_color) @ rBT_Impl_Mirabelle_R) = (zero_zero @ nat))).
% 2.34/1.45 thf(fact_132_color_Osize_I4_J, axiom, (((size_size @ rBT_Im1923302023_color) @ rBT_Impl_Mirabelle_B) = (zero_zero @ nat))).
% 2.34/1.45 thf(fact_133_rbt_Osize_I3_J, axiom, (! [A:$tType,B:$tType]: ((((size_size @ ((rBT_Im246033960le_rbt @ A) @ B)) @ ((rBT_Im418718756_Empty @ A) @ B)) = (zero_zero @ nat))))).
% 2.34/1.45 thf(fact_134_rbt_Osimps_I15_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((insert @ A) @ X23) @ (((sup_sup @ (set @ A)) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X22)) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X25))))))).
% 2.34/1.45 thf(fact_135_rbt_Osimps_I17_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((insert @ B) @ X24) @ (((sup_sup @ (set @ B)) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X22)) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X25))))))).
% 2.34/1.45 thf(fact_136_pairwise__singleton, axiom, (! [A:$tType,P:(A > (A > $o)),A6:A]: ((((pairwise @ A) @ P) @ (((insert @ A) @ A6) @ (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_137_Un__iff, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) = ((((member @ A) @ C2) @ A6) | (((member @ A) @ C2) @ B3)))))).
% 2.34/1.45 thf(fact_138_UnCI, axiom, (! [A:$tType,C2:A,B3:(set @ A),A6:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B3))) => (((member @ A) @ C2) @ A6)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_139_Un__empty, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A6) @ B3) = (bot_bot @ (set @ A))) = ((A6 = (bot_bot @ (set @ A))) & (B3 = (bot_bot @ (set @ A)))))))).
% 2.34/1.45 thf(fact_140_Un__insert__left, axiom, (! [A:$tType,A2:A,B3:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ B3)) @ C4) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B3) @ C4)))))).
% 2.34/1.45 thf(fact_141_Un__insert__right, axiom, (! [A:$tType,A6:(set @ A),A2:A,B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ B3)) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_142_Un__empty__left, axiom, (! [A:$tType,B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B3) = B3)))).
% 2.34/1.45 thf(fact_143_Un__empty__right, axiom, (! [A:$tType,A6:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ (bot_bot @ (set @ A))) = A6)))).
% 2.34/1.45 thf(fact_144_Un__left__commute, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ (((sup_sup @ (set @ A)) @ B3) @ C4)) = (((sup_sup @ (set @ A)) @ B3) @ (((sup_sup @ (set @ A)) @ A6) @ C4)))))).
% 2.34/1.45 thf(fact_145_Un__left__absorb, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) = (((sup_sup @ (set @ A)) @ A6) @ B3))))).
% 2.34/1.45 thf(fact_146_pairwise__def, axiom, (! [A:$tType]: (((pairwise @ A) = (^ [R4:(A > (A > $o)),S2:(set @ A)]: ((! [X7:A]: (((((member @ A) @ X7) @ S2) => (! [Y3:A]: (((((member @ A) @ Y3) @ S2) => ((X7 != Y3) => ((R4 @ X7) @ Y3)))))))))))))).
% 2.34/1.45 thf(fact_147_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A7:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A7))))))).
% 2.34/1.45 thf(fact_148_Un__absorb, axiom, (! [A:$tType,A6:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ A6) = A6)))).
% 2.34/1.45 thf(fact_149_Un__assoc, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) @ C4) = (((sup_sup @ (set @ A)) @ A6) @ (((sup_sup @ (set @ A)) @ B3) @ C4)))))).
% 2.34/1.45 thf(fact_150_ball__Un, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),P:(A > $o)]: (((! [X7:A]: (((((member @ A) @ X7) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) => (P @ X7)))) = ((! [X7:A]: (((((member @ A) @ X7) @ A6) => (P @ X7)))) & (! [X7:A]: (((((member @ A) @ X7) @ B3) => (P @ X7))))))))).
% 2.34/1.45 thf(fact_151_bex__Un, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) & (P @ X7)))) = ((? [X7:A]: (((((member @ A) @ X7) @ A6) & (P @ X7)))) | (? [X7:A]: (((((member @ A) @ X7) @ B3) & (P @ X7))))))))).
% 2.34/1.45 thf(fact_152_UnI2, axiom, (! [A:$tType,C2:A,B3:(set @ A),A6:(set @ A)]: (((((member @ A) @ C2) @ B3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_153_UnI1, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A6) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_154_UnE, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) => ((~ ((((member @ A) @ C2) @ A6))) => (((member @ A) @ C2) @ B3)))))).
% 2.34/1.45 thf(fact_155_singleton__Un__iff, axiom, (! [A:$tType,X:A,A6:(set @ A),B3:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A6) @ B3)) = (((A6 = (bot_bot @ (set @ A))) & (B3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A6 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B3 = (bot_bot @ (set @ A)))) | ((A6 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.34/1.45 thf(fact_156_Un__singleton__iff, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A6) @ B3) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A6 = (bot_bot @ (set @ A))) & (B3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A6 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B3 = (bot_bot @ (set @ A)))) | ((A6 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.34/1.45 thf(fact_157_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A8:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A8) @ (bot_bot @ (set @ A)))))))))).
% 2.34/1.45 thf(fact_158_pairwise__empty, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((pairwise @ A) @ P) @ (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_159_pairwise__insert, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,S3:(set @ A)]: (((((pairwise @ A) @ R) @ (((insert @ A) @ X) @ S3)) = ((! [Y3:A]: ((((((member @ A) @ Y3) @ S3) & (Y3 != X)) => (((R @ X) @ Y3) & ((R @ Y3) @ X))))) & (((pairwise @ A) @ R) @ S3)))))).
% 2.34/1.45 thf(fact_160_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 2.34/1.45 thf(fact_161_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 2.34/1.45 thf(fact_162_sup__eq__bot__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.34/1.45 thf(fact_163_bot__eq__sup__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.34/1.45 thf(fact_164_sup__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.34/1.45 thf(fact_165_sup__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.34/1.45 thf(fact_166_ID_Opred__set, axiom, (! [A:$tType]: (((bNF_id_bnf @ (A > $o)) = (^ [P3:(A > $o),X7:A]: ((! [Y3:A]: (((((member @ A) @ Y3) @ (((insert @ A) @ X7) @ (bot_bot @ (set @ A)))) => (P3 @ Y3)))))))))).
% 2.34/1.45 thf(fact_167_sup__bot_Osemilattice__neutr__axioms, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (((semilattice_neutr @ A) @ (sup_sup @ A)) @ (bot_bot @ A)))))).
% 2.34/1.45 thf(fact_168_bot__nat__def, axiom, ((bot_bot @ nat) = (zero_zero @ nat))).
% 2.34/1.45 thf(fact_169_id__bnf__apply, axiom, (! [A:$tType]: (((bNF_id_bnf @ A) = (^ [X7:A]: (X7)))))).
% 2.34/1.45 thf(fact_170_BNF__Composition_Oid__bnf__def, axiom, (! [A:$tType]: (((bNF_id_bnf @ A) = (^ [X7:A]: (X7)))))).
% 2.34/1.45 thf(fact_171_ID_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F:(A > B),X:A]: (((((bNF_id_bnf @ (B > $o)) @ Q) @ (((bNF_id_bnf @ (A > B)) @ F) @ X)) = (((bNF_id_bnf @ (A > $o)) @ (((((comp @ B) @ $o) @ A) @ Q) @ F)) @ X))))).
% 2.34/1.45 thf(fact_172_ID_Opred__mono__strong, axiom, (! [A:$tType,P:(A > $o),X:A,Pa:(A > $o)]: (((((bNF_id_bnf @ (A > $o)) @ P) @ X) => ((! [Z6:A]: (((((member @ A) @ Z6) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((P @ Z6) => (Pa @ Z6))))) => (((bNF_id_bnf @ (A > $o)) @ Pa) @ X)))))).
% 2.34/1.45 thf(fact_173_ID_Opred__cong, axiom, (! [A:$tType,X:A,Ya:A,P:(A > $o),Pa:(A > $o)]: (((X = Ya) => ((! [Z6:A]: (((((member @ A) @ Z6) @ (((insert @ A) @ Ya) @ (bot_bot @ (set @ A)))) => ((P @ Z6) = (Pa @ Z6))))) => ((((bNF_id_bnf @ (A > $o)) @ P) @ X) = (((bNF_id_bnf @ (A > $o)) @ Pa) @ Ya))))))).
% 2.34/1.45 thf(fact_174_sup__bot_Omonoid__axioms, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (((monoid @ A) @ (sup_sup @ A)) @ (bot_bot @ A)))))).
% 2.34/1.45 thf(fact_175_ID_Orel__eq__onp, axiom, (! [A:$tType,P:(A > $o)]: ((((bNF_id_bnf @ (A > (A > $o))) @ ((bNF_eq_onp @ A) @ P)) = ((bNF_eq_onp @ A) @ ((bNF_id_bnf @ (A > $o)) @ P)))))).
% 2.34/1.45 thf(fact_176_ID_Opred__rel, axiom, (! [A:$tType]: (((bNF_id_bnf @ (A > $o)) = (^ [P3:(A > $o),X7:A]: (((((bNF_id_bnf @ (A > (A > $o))) @ ((bNF_eq_onp @ A) @ P3)) @ X7) @ X7))))))).
% 2.34/1.45 thf(fact_177_ID_Orel__refl, axiom, (! [A:$tType,Ra:(A > (A > $o)),X:A]: (((! [X6:A]: (((Ra @ X6) @ X6))) => ((((bNF_id_bnf @ (A > (A > $o))) @ Ra) @ X) @ X))))).
% 2.34/1.45 thf(fact_178_ID_Orel__cong, axiom, (! [A:$tType,B:$tType,X:A,Ya:A,Y:B,Xa:B,R3:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z6:A,Yb:B]: (((((member @ A) @ Z6) @ (((insert @ A) @ Ya) @ (bot_bot @ (set @ A)))) => ((((member @ B) @ Yb) @ (((insert @ B) @ Xa) @ (bot_bot @ (set @ B)))) => (((R3 @ Z6) @ Yb) = ((Ra @ Z6) @ Yb)))))) => (((((bNF_id_bnf @ (A > (B > $o))) @ R3) @ X) @ Y) = ((((bNF_id_bnf @ (A > (B > $o))) @ Ra) @ Ya) @ Xa)))))))).
% 2.34/1.45 thf(fact_179_ID_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X:A,Y:B,Ra:(A > (B > $o))]: ((((((bNF_id_bnf @ (A > (B > $o))) @ R3) @ X) @ Y) => ((! [Z6:A,Yb:B]: (((((member @ A) @ Z6) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((((member @ B) @ Yb) @ (((insert @ B) @ Y) @ (bot_bot @ (set @ B)))) => (((R3 @ Z6) @ Yb) => ((Ra @ Z6) @ Yb)))))) => ((((bNF_id_bnf @ (A > (B > $o))) @ Ra) @ X) @ Y)))))).
% 2.34/1.45 thf(fact_180_ID_Orel__refl__strong, axiom, (! [A:$tType,X:A,Ra:(A > (A > $o))]: (((! [Z6:A]: (((((member @ A) @ Z6) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((Ra @ Z6) @ Z6)))) => ((((bNF_id_bnf @ (A > (A > $o))) @ Ra) @ X) @ X))))).
% 2.34/1.45 thf(fact_181_sup__bot_Ocomm__monoid__axioms, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (((comm_monoid @ A) @ (sup_sup @ A)) @ (bot_bot @ A)))))).
% 2.34/1.45 thf(fact_182_vimage__insert, axiom, (! [A:$tType,B:$tType,F:(A > B),A2:B,B3:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((insert @ B) @ A2) @ B3)) = (((sup_sup @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ (((insert @ B) @ A2) @ (bot_bot @ (set @ B))))) @ ((((vimage @ A) @ B) @ F) @ B3)))))).
% 2.34/1.45 thf(fact_183_notIn__Un__bij__betw3, axiom, (! [A:$tType,B:$tType,B2:A,A6:(set @ A),F:(A > B),A9:(set @ B)]: (((~ ((((member @ A) @ B2) @ A6))) => ((~ ((((member @ B) @ (F @ B2)) @ A9))) => ((((((bij_betw @ A) @ B) @ F) @ A6) @ A9) = (((((bij_betw @ A) @ B) @ F) @ (((sup_sup @ (set @ A)) @ A6) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))) @ (((sup_sup @ (set @ B)) @ A9) @ (((insert @ B) @ (F @ B2)) @ (bot_bot @ (set @ B))))))))))).
% 2.34/1.45 thf(fact_184_vimage__eq, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) = (((member @ B) @ (F @ A2)) @ B3))))).
% 2.34/1.45 thf(fact_185_vimageI, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,B2:A,B3:(set @ A)]: ((((F @ A2) = B2) => ((((member @ A) @ B2) @ B3) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ B3))))))).
% 2.34/1.45 thf(fact_186_vimage__empty, axiom, (! [B:$tType,A:$tType,F:(A > B)]: ((((((vimage @ A) @ B) @ F) @ (bot_bot @ (set @ B))) = (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_187_vimage__Un, axiom, (! [A:$tType,B:$tType,F:(A > B),A6:(set @ B),B3:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((sup_sup @ (set @ B)) @ A6) @ B3)) = (((sup_sup @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A6)) @ ((((vimage @ A) @ B) @ F) @ B3)))))).
% 2.34/1.45 thf(fact_188_vimage__Collect, axiom, (! [B:$tType,A:$tType,P:(B > $o),F:(A > B),Q:(A > $o)]: (((! [X6:A]: (((P @ (F @ X6)) = (Q @ X6)))) => (((((vimage @ A) @ B) @ F) @ ((collect @ B) @ P)) = ((collect @ A) @ Q)))))).
% 2.34/1.45 thf(fact_189_bij__betw__cong, axiom, (! [A:$tType,B:$tType,A6:(set @ A),F:(A > B),G:(A > B),A9:(set @ B)]: (((! [A10:A]: (((((member @ A) @ A10) @ A6) => ((F @ A10) = (G @ A10))))) => ((((((bij_betw @ A) @ B) @ F) @ A6) @ A9) = (((((bij_betw @ A) @ B) @ G) @ A6) @ A9)))))).
% 2.34/1.45 thf(fact_190_bij__betw__inv, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A),B3:(set @ B)]: (((((((bij_betw @ A) @ B) @ F) @ A6) @ B3) => (? [G6:(B > A)]: ((((((bij_betw @ B) @ A) @ G6) @ B3) @ A6))))))).
% 2.34/1.45 thf(fact_191_vimageI2, axiom, (! [B:$tType,A:$tType,F:(B > A),A2:B,A6:(set @ A)]: (((((member @ A) @ (F @ A2)) @ A6) => (((member @ B) @ A2) @ ((((vimage @ B) @ A) @ F) @ A6)))))).
% 2.34/1.45 thf(fact_192_vimageE, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B3:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B3)) => (((member @ B) @ (F @ A2)) @ B3))))).
% 2.34/1.45 thf(fact_193_vimageD, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),A6:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ A6)) => (((member @ B) @ (F @ A2)) @ A6))))).
% 2.34/1.45 thf(fact_194_set_Ocomp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),G:(B > A)]: (((((((comp @ (set @ B)) @ (set @ C)) @ (set @ A)) @ (((vimage @ C) @ B) @ F)) @ (((vimage @ B) @ A) @ G)) = (((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)))))).
% 2.34/1.45 thf(fact_195_vimage__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(B > C),X:(set @ C)]: ((((((vimage @ A) @ B) @ F) @ ((((vimage @ B) @ C) @ G) @ X)) = ((((vimage @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ X))))).
% 2.34/1.45 thf(fact_196_set_Ocompositionality, axiom, (! [C:$tType,B:$tType,A:$tType,F:(C > B),G:(B > A),Set:(set @ A)]: ((((((vimage @ C) @ B) @ F) @ ((((vimage @ B) @ A) @ G) @ Set)) = ((((vimage @ C) @ A) @ (((((comp @ B) @ A) @ C) @ G) @ F)) @ Set))))).
% 2.34/1.45 thf(fact_197_bij__betw__trans, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),A6:(set @ A),B3:(set @ B),G:(B > C),C4:(set @ C)]: (((((((bij_betw @ A) @ B) @ F) @ A6) @ B3) => ((((((bij_betw @ B) @ C) @ G) @ B3) @ C4) => (((((bij_betw @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ A6) @ C4)))))).
% 2.34/1.45 thf(fact_198_bij__betw__comp__iff, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),A6:(set @ A),A9:(set @ B),F5:(B > C),A11:(set @ C)]: (((((((bij_betw @ A) @ B) @ F) @ A6) @ A9) => ((((((bij_betw @ B) @ C) @ F5) @ A9) @ A11) = (((((bij_betw @ A) @ C) @ (((((comp @ B) @ C) @ A) @ F5) @ F)) @ A6) @ A11)))))).
% 2.34/1.45 thf(fact_199_vimage__singleton__eq, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B2:B]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ (((insert @ B) @ B2) @ (bot_bot @ (set @ B))))) = ((F @ A2) = B2))))).
% 2.34/1.45 thf(fact_200_bij__betw__empty2, axiom, (! [B:$tType,A:$tType,F:(A > B),A6:(set @ A)]: (((((((bij_betw @ A) @ B) @ F) @ A6) @ (bot_bot @ (set @ B))) => (A6 = (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_201_bij__betw__empty1, axiom, (! [A:$tType,B:$tType,F:(A > B),A6:(set @ B)]: (((((((bij_betw @ A) @ B) @ F) @ (bot_bot @ (set @ A))) @ A6) => (A6 = (bot_bot @ (set @ B))))))).
% 2.34/1.45 thf(fact_202_notIn__Un__bij__betw, axiom, (! [A:$tType,B:$tType,B2:A,A6:(set @ A),F:(A > B),A9:(set @ B)]: (((~ ((((member @ A) @ B2) @ A6))) => ((~ ((((member @ B) @ (F @ B2)) @ A9))) => ((((((bij_betw @ A) @ B) @ F) @ A6) @ A9) => (((((bij_betw @ A) @ B) @ F) @ (((sup_sup @ (set @ A)) @ A6) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))) @ (((sup_sup @ (set @ B)) @ A9) @ (((insert @ B) @ (F @ B2)) @ (bot_bot @ (set @ B))))))))))).
% 2.34/1.45 thf(fact_203_bij__betw__combine, axiom, (! [A:$tType,B:$tType,F:(A > B),A6:(set @ A),B3:(set @ B),C4:(set @ A),D3:(set @ B)]: (((((((bij_betw @ A) @ B) @ F) @ A6) @ B3) => ((((((bij_betw @ A) @ B) @ F) @ C4) @ D3) => (((((inf_inf @ (set @ B)) @ B3) @ D3) = (bot_bot @ (set @ B))) => (((((bij_betw @ A) @ B) @ F) @ (((sup_sup @ (set @ A)) @ A6) @ C4)) @ (((sup_sup @ (set @ B)) @ B3) @ D3)))))))).
% 2.34/1.45 thf(fact_204_infinite__imp__bij__betw2, axiom, (! [A:$tType,A6:(set @ A),A2:A]: (((~ (((finite_finite @ A) @ A6))) => (? [H3:(A > A)]: ((((((bij_betw @ A) @ A) @ H3) @ A6) @ (((sup_sup @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))))).
% 2.34/1.45 thf(fact_205_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A6:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A6) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A6) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.34/1.45 thf(fact_206_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.34/1.45 thf(fact_207_subsetI, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((! [X6:A]: (((((member @ A) @ X6) @ A6) => (((member @ A) @ X6) @ B3)))) => (((ord_less_eq @ (set @ A)) @ A6) @ B3))))).
% 2.34/1.45 thf(fact_208_subset__antisym, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => ((((ord_less_eq @ (set @ A)) @ B3) @ A6) => (A6 = B3)))))).
% 2.34/1.45 thf(fact_209_IntI, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A6) => ((((member @ A) @ C2) @ B3) => (((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A6) @ B3))))))).
% 2.34/1.45 thf(fact_210_Int__iff, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) = ((((member @ A) @ C2) @ A6) & (((member @ A) @ C2) @ B3)))))).
% 2.34/1.45 thf(fact_211_inf__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ (bot_bot @ A)) @ X) = (bot_bot @ A)))))))).
% 2.34/1.45 thf(fact_212_inf__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ (bot_bot @ A)) = (bot_bot @ A)))))))).
% 2.34/1.45 thf(fact_213_subset__empty, axiom, (! [A:$tType,A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ (bot_bot @ (set @ A))) = (A6 = (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_214_empty__subsetI, axiom, (! [A:$tType,A6:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A6)))).
% 2.34/1.45 thf(fact_215_insert__subset, axiom, (! [A:$tType,X:A,A6:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A6)) @ B3) = ((((member @ A) @ X) @ B3) & (((ord_less_eq @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_216_Int__subset__iff, axiom, (! [A:$tType,C4:(set @ A),A6:(set @ A),B3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) = ((((ord_less_eq @ (set @ A)) @ C4) @ A6) & (((ord_less_eq @ (set @ A)) @ C4) @ B3)))))).
% 2.34/1.45 thf(fact_217_Int__insert__right__if1, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ A2) @ A6) => ((((inf_inf @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ B3)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A6) @ B3))))))).
% 2.34/1.45 thf(fact_218_Int__insert__right__if0, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ A2) @ A6))) => ((((inf_inf @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ B3)) = (((inf_inf @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_219_insert__inter__insert, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A6)) @ (((insert @ A) @ A2) @ B3)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)))))).
% 2.34/1.45 thf(fact_220_Int__insert__left__if1, axiom, (! [A:$tType,A2:A,C4:(set @ A),B3:(set @ A)]: (((((member @ A) @ A2) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B3)) @ C4) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ B3) @ C4))))))).
% 2.34/1.45 thf(fact_221_Int__insert__left__if0, axiom, (! [A:$tType,A2:A,C4:(set @ A),B3:(set @ A)]: (((~ ((((member @ A) @ A2) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B3)) @ C4) = (((inf_inf @ (set @ A)) @ B3) @ C4)))))).
% 2.34/1.45 thf(fact_222_Un__subset__iff, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A6) @ B3)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A6) @ C4) & (((ord_less_eq @ (set @ A)) @ B3) @ C4)))))).
% 2.34/1.45 thf(fact_223_vimage__Int, axiom, (! [A:$tType,B:$tType,F:(A > B),A6:(set @ B),B3:(set @ B)]: ((((((vimage @ A) @ B) @ F) @ (((inf_inf @ (set @ B)) @ A6) @ B3)) = (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ A6)) @ ((((vimage @ A) @ B) @ F) @ B3)))))).
% 2.34/1.45 thf(fact_224_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A6:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A6)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A6) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.34/1.45 thf(fact_225_disjoint__insert_I2_J, axiom, (! [A:$tType,A6:(set @ A),B2:A,B3:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A6) @ (((insert @ A) @ B2) @ B3))) = ((~ ((((member @ A) @ B2) @ A6))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A6) @ B3))))))).
% 2.34/1.45 thf(fact_226_disjoint__insert_I1_J, axiom, (! [A:$tType,B3:(set @ A),A2:A,A6:(set @ A)]: ((((((inf_inf @ (set @ A)) @ B3) @ (((insert @ A) @ A2) @ A6)) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A2) @ B3))) & ((((inf_inf @ (set @ A)) @ B3) @ A6) = (bot_bot @ (set @ A)))))))).
% 2.34/1.45 thf(fact_227_insert__disjoint_I2_J, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: ((((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A6)) @ B3)) = ((~ ((((member @ A) @ A2) @ B3))) & ((bot_bot @ (set @ A)) = (((inf_inf @ (set @ A)) @ A6) @ B3))))))).
% 2.34/1.45 thf(fact_228_insert__disjoint_I1_J, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: ((((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ A6)) @ B3) = (bot_bot @ (set @ A))) = ((~ ((((member @ A) @ A2) @ B3))) & ((((inf_inf @ (set @ A)) @ A6) @ B3) = (bot_bot @ (set @ A)))))))).
% 2.34/1.45 thf(fact_229_vimage__inter__cong, axiom, (! [B:$tType,A:$tType,S:(set @ A),F:(A > B),G:(A > B),Y:(set @ B)]: (((! [W:A]: (((((member @ A) @ W) @ S) => ((F @ W) = (G @ W))))) => ((((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ F) @ Y)) @ S) = (((inf_inf @ (set @ A)) @ ((((vimage @ A) @ B) @ G) @ Y)) @ S)))))).
% 2.34/1.45 thf(fact_230_vimage__mono, axiom, (! [B:$tType,A:$tType,A6:(set @ A),B3:(set @ A),F:(B > A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => (((ord_less_eq @ (set @ B)) @ ((((vimage @ B) @ A) @ F) @ A6)) @ ((((vimage @ B) @ A) @ F) @ B3)))))).
% 2.34/1.45 thf(fact_231_Int__emptyI, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((! [X6:A]: (((((member @ A) @ X6) @ A6) => (~ ((((member @ A) @ X6) @ B3)))))) => ((((inf_inf @ (set @ A)) @ A6) @ B3) = (bot_bot @ (set @ A))))))).
% 2.34/1.45 thf(fact_232_Int__empty__left, axiom, (! [A:$tType,B3:(set @ A)]: (((((inf_inf @ (set @ A)) @ (bot_bot @ (set @ A))) @ B3) = (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_233_Int__empty__right, axiom, (! [A:$tType,A6:(set @ A)]: (((((inf_inf @ (set @ A)) @ A6) @ (bot_bot @ (set @ A))) = (bot_bot @ (set @ A)))))).
% 2.34/1.45 thf(fact_234_disjoint__iff__not__equal, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: ((((((inf_inf @ (set @ A)) @ A6) @ B3) = (bot_bot @ (set @ A))) = (! [X7:A]: (((((member @ A) @ X7) @ A6) => (! [Y3:A]: (((((member @ A) @ Y3) @ B3) => (X7 != Y3))))))))))).
% 2.34/1.45 thf(fact_235_bot_Oextremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 2.34/1.45 thf(fact_236_bot_Oextremum__unique, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 2.34/1.45 thf(fact_237_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 2.34/1.45 thf(fact_238_Int__insert__right, axiom, (! [A:$tType,A2:A,A6:(set @ A),B3:(set @ A)]: ((((((member @ A) @ A2) @ A6) => ((((inf_inf @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ B3)) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)))) & ((~ ((((member @ A) @ A2) @ A6))) => ((((inf_inf @ (set @ A)) @ A6) @ (((insert @ A) @ A2) @ B3)) = (((inf_inf @ (set @ A)) @ A6) @ B3))))))).
% 2.34/1.45 thf(fact_239_Int__insert__left, axiom, (! [A:$tType,A2:A,C4:(set @ A),B3:(set @ A)]: ((((((member @ A) @ A2) @ C4) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B3)) @ C4) = (((insert @ A) @ A2) @ (((inf_inf @ (set @ A)) @ B3) @ C4)))) & ((~ ((((member @ A) @ A2) @ C4))) => ((((inf_inf @ (set @ A)) @ (((insert @ A) @ A2) @ B3)) @ C4) = (((inf_inf @ (set @ A)) @ B3) @ C4))))))).
% 2.34/1.45 thf(fact_240_IntE, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) => (~ (((((member @ A) @ C2) @ A6) => (~ ((((member @ A) @ C2) @ B3)))))))))).
% 2.34/1.45 thf(fact_241_IntD1, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) => (((member @ A) @ C2) @ A6))))).
% 2.34/1.45 thf(fact_242_IntD2, axiom, (! [A:$tType,C2:A,A6:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) => (((member @ A) @ C2) @ B3))))).
% 2.34/1.45 thf(fact_243_set__mp, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => ((((member @ A) @ X) @ A6) => (((member @ A) @ X) @ B3)))))).
% 2.34/1.45 thf(fact_244_in__mono, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => ((((member @ A) @ X) @ A6) => (((member @ A) @ X) @ B3)))))).
% 2.34/1.45 thf(fact_245_subsetD, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => ((((member @ A) @ C2) @ A6) => (((member @ A) @ C2) @ B3)))))).
% 2.34/1.45 thf(fact_246_Int__mono, axiom, (! [A:$tType,A6:(set @ A),C4:(set @ A),B3:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ C4) => ((((ord_less_eq @ (set @ A)) @ B3) @ D3) => (((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) @ (((inf_inf @ (set @ A)) @ C4) @ D3))))))).
% 2.34/1.45 thf(fact_247_subsetCE, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => ((((member @ A) @ C2) @ A6) => (((member @ A) @ C2) @ B3)))))).
% 2.34/1.45 thf(fact_248_Int__assoc, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A),C4:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) @ C4) = (((inf_inf @ (set @ A)) @ A6) @ (((inf_inf @ (set @ A)) @ B3) @ C4)))))).
% 2.34/1.45 thf(fact_249_equalityE, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((A6 = B3) => (~ (((((ord_less_eq @ (set @ A)) @ A6) @ B3) => (~ ((((ord_less_eq @ (set @ A)) @ B3) @ A6)))))))))).
% 2.34/1.45 thf(fact_250_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B5:(set @ A)]: ((! [X7:A]: (((((member @ A) @ X7) @ A7) => (((member @ A) @ X7) @ B5)))))))))).
% 2.34/1.45 thf(fact_251_Int__absorb, axiom, (! [A:$tType,A6:(set @ A)]: (((((inf_inf @ (set @ A)) @ A6) @ A6) = A6)))).
% 2.34/1.45 thf(fact_252_Int__lower1, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) @ A6)))).
% 2.34/1.45 thf(fact_253_Int__lower2, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A6) @ B3)) @ B3)))).
% 2.34/1.45 thf(fact_254_equalityD1, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((A6 = B3) => (((ord_less_eq @ (set @ A)) @ A6) @ B3))))).
% 2.34/1.45 thf(fact_255_equalityD2, axiom, (! [A:$tType,A6:(set @ A),B3:(set @ A)]: (((A6 = B3) => (((ord_less_eq @ (set @ A)) @ B3) @ A6))))).
% 2.34/1.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A12:$tType]: (((bounded_lattice @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A12:$tType,A13:$tType]: ((((bounded_lattice @ A13) @ (type2 @ A13)) => ((bounded_lattice @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A12:$tType,A13:$tType]: ((((bounded_lattice @ A13) @ (type2 @ A13)) => ((bounde1808546759up_bot @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A12:$tType,A13:$tType]: ((((bounded_lattice @ A13) @ (type2 @ A13)) => ((bounded_lattice_bot @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A12:$tType,A13:$tType]: ((((order_bot @ A13) @ (type2 @ A13)) => ((order_bot @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A12:$tType,A13:$tType]: ((((preorder @ A13) @ (type2 @ A13)) => ((preorder @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_fun___Orderings_Obot, axiom, (! [A12:$tType,A13:$tType]: ((((bot @ A13) @ (type2 @ A13)) => ((bot @ (A12 > A13)) @ (type2 @ (A12 > A13))))))).
% 2.34/1.45 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3, axiom, ((order_bot @ nat) @ (type2 @ nat))).
% 2.34/1.45 thf(tcon_Nat_Onat___Orderings_Opreorder_4, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.34/1.45 thf(tcon_Nat_Onat___Orderings_Obot_5, axiom, ((bot @ nat) @ (type2 @ nat))).
% 2.34/1.45 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_6, axiom, (! [A12:$tType]: (((bounde1808546759up_bot @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_7, axiom, (! [A12:$tType]: (((bounded_lattice_bot @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_Set_Oset___Orderings_Oorder__bot_8, axiom, (! [A12:$tType]: (((order_bot @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_Set_Oset___Orderings_Opreorder_9, axiom, (! [A12:$tType]: (((preorder @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_Set_Oset___Orderings_Obot_10, axiom, (! [A12:$tType]: (((bot @ (set @ A12)) @ (type2 @ (set @ A12)))))).
% 2.34/1.45 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_11, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(tcon_HOL_Obool___Orderings_Opreorder_14, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(tcon_HOL_Obool___Orderings_Obot_15, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.34/1.45 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.34/1.45 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.34/1.45 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.34/1.45 thf(conj_0, hypothesis, $true).
% 2.34/1.45 thf(conj_1, hypothesis, (! [L3:((rBT_Im246033960le_rbt @ a) @ b),K2:a,V2:b,R5:((rBT_Im246033960le_rbt @ a) @ b)]: (((t = (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_R) @ L3) @ K2) @ V2) @ R5)) => thesis)))).
% 2.34/1.45 thf(conj_2, hypothesis, (! [L3:((rBT_Im246033960le_rbt @ a) @ b),K2:a,V2:b,R5:((rBT_Im246033960le_rbt @ a) @ b)]: (((t = (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ L3) @ K2) @ V2) @ R5)) => thesis)))).
% 2.34/1.45 thf(conj_3, conjecture, thesis).
% 2.34/1.45 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2DTF7073.p
% 2.34/1.45 ------------------------
% 2.46/1.50 ---- Cleaned THF ---
% 2.46/1.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 2.46/1.50 rBT_Im1923302023_color: $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 2.46/1.50 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_t_Set_Oset,type,
% 2.46/1.50 set: $tType > $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_t_Nat_Onat,type,
% 2.46/1.50 nat: $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_t_itself,type,
% 2.46/1.50 itself: $tType > $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_tf_b,type,
% 2.46/1.50 b: $tType ).
% 2.46/1.50
% 2.46/1.50 thf(ty_tf_a,type,
% 2.46/1.50 a: $tType ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.46/1.50 bounded_lattice:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_HOL_Otype,type,
% 2.46/1.50 type:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Orderings_Obot,type,
% 2.46/1.50 bot:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Orderings_Opreorder,type,
% 2.46/1.50 preorder:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.46/1.50 order_bot:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.46/1.50 bounded_lattice_bot:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.46/1.50 bounde1808546759up_bot:
% 2.46/1.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_BNF__Composition_Oid__bnf,type,
% 2.46/1.50 bNF_id_bnf:
% 2.46/1.50 !>[A: $tType] : ( A > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_BNF__Def_Oeq__onp,type,
% 2.46/1.50 bNF_eq_onp:
% 2.46/1.50 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_BNF__Def_Ovimage2p,type,
% 2.46/1.50 bNF_vimage2p:
% 2.46/1.50 !>[A: $tType,D: $tType,B: $tType,E: $tType,C: $tType] : ( ( A > D ) > ( B > E ) > ( D > E > C ) > A > B > C ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Finite__Set_Ofinite,type,
% 2.46/1.50 finite_finite:
% 2.46/1.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Fun_Obij__betw,type,
% 2.46/1.50 bij_betw:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Fun_Ocomp,type,
% 2.46/1.50 comp:
% 2.46/1.50 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Fun_Omap__fun,type,
% 2.46/1.50 map_fun:
% 2.46/1.50 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Fun_Ooverride__on,type,
% 2.46/1.50 override_on:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( A > B ) > ( A > B ) > ( set @ A ) > A > B ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Groups_Ocomm__monoid,type,
% 2.46/1.50 comm_monoid:
% 2.46/1.50 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Groups_Omonoid,type,
% 2.46/1.50 monoid:
% 2.46/1.50 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.46/1.50 zero_zero:
% 2.46/1.50 !>[A: $tType] : A ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_If,type,
% 2.46/1.50 if:
% 2.46/1.50 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 2.46/1.50 inf_inf:
% 2.46/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 2.46/1.50 semilattice_neutr:
% 2.46/1.50 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.46/1.50 sup_sup:
% 2.46/1.50 !>[A: $tType] : ( A > A > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.46/1.50 size_size:
% 2.46/1.50 !>[A: $tType] : ( A > nat ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.46/1.50 bot_bot:
% 2.46/1.50 !>[A: $tType] : A ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.46/1.50 ord_less_eq:
% 2.46/1.50 !>[A: $tType] : ( A > A > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Pure_Otype,type,
% 2.46/1.50 type2:
% 2.46/1.50 !>[A: $tType] : ( itself @ A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 2.46/1.50 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 2.46/1.50 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color,type,
% 2.46/1.50 rBT_Im1975547051_color:
% 2.46/1.50 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color,type,
% 2.46/1.50 rBT_Im1059957627_color:
% 2.46/1.50 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color,type,
% 2.46/1.50 rBT_Im800559290_color: rBT_Im1923302023_color > nat ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 2.46/1.50 rBT_Im480247531Branch:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 2.46/1.50 rBT_Im418718756_Empty:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt,type,
% 2.46/1.50 rBT_Im858806507se_rbt:
% 2.46/1.50 !>[C: $tType,A: $tType,B: $tType] : ( C > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C ) > ( rBT_Im246033960le_rbt @ A @ B ) > C ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Omap__rbt,type,
% 2.46/1.50 rBT_Im206295089ap_rbt:
% 2.46/1.50 !>[A: $tType,Aa: $tType,B: $tType,Ba: $tType] : ( ( A > Aa ) > ( B > Ba ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ Aa @ Ba ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Opred__rbt,type,
% 2.46/1.50 rBT_Im1931894874ed_rbt:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt,type,
% 2.46/1.50 rBT_Im1947144893ec_rbt:
% 2.46/1.50 !>[E: $tType,A: $tType,B: $tType] : ( E > ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E ) > ( rBT_Im246033960le_rbt @ A @ B ) > E ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orel__rbt,type,
% 2.46/1.50 rBT_Im1000242676el_rbt:
% 2.46/1.50 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ C @ D ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt,type,
% 2.46/1.50 rBT_Im1178217900t1_rbt:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ A ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt,type,
% 2.46/1.50 rBT_Im1550225131t2_rbt:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ B ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt,type,
% 2.46/1.50 rBT_Im1485196410ze_rbt:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_OBall,type,
% 2.46/1.50 ball:
% 2.46/1.50 !>[A: $tType] : ( ( set @ A ) > ( A > $o ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_OCollect,type,
% 2.46/1.50 collect:
% 2.46/1.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Oinsert,type,
% 2.46/1.50 insert:
% 2.46/1.50 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Ois__empty,type,
% 2.46/1.50 is_empty:
% 2.46/1.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Ois__singleton,type,
% 2.46/1.50 is_singleton:
% 2.46/1.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Opairwise,type,
% 2.46/1.50 pairwise:
% 2.46/1.50 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Othe__elem,type,
% 2.46/1.50 the_elem:
% 2.46/1.50 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_Set_Ovimage,type,
% 2.46/1.50 vimage:
% 2.46/1.50 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_c_member,type,
% 2.46/1.50 member:
% 2.46/1.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(sy_v_t,type,
% 2.46/1.50 t: rBT_Im246033960le_rbt @ a @ b ).
% 2.46/1.50
% 2.46/1.50 thf(sy_v_thesis,type,
% 2.46/1.50 thesis: $o ).
% 2.46/1.50
% 2.46/1.50 thf(fact_0_Empty,axiom,
% 2.46/1.50 ( ( t
% 2.46/1.50 = ( rBT_Im418718756_Empty @ a @ b ) )
% 2.46/1.50 => thesis ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_1_rbt_Oinject,axiom,
% 2.46/1.50 ! [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] :
% 2.46/1.50 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 2.46/1.50 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 2.46/1.50 = ( ( X21 = Y21 )
% 2.46/1.50 & ( X22 = Y22 )
% 2.46/1.50 & ( X23 = Y23 )
% 2.46/1.50 & ( X24 = Y24 )
% 2.46/1.50 & ( X25 = Y25 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_2_Black,axiom,
% 2.46/1.50 ! [L: rBT_Im246033960le_rbt @ a @ b,K: a,V: b,R: rBT_Im246033960le_rbt @ a @ b] :
% 2.46/1.50 ( ( t
% 2.46/1.50 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ L @ K @ V @ R ) )
% 2.46/1.50 => thesis ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_3_Red,axiom,
% 2.46/1.50 ! [L: rBT_Im246033960le_rbt @ a @ b,K: a,V: b,R: rBT_Im246033960le_rbt @ a @ b] :
% 2.46/1.50 ( ( t
% 2.46/1.50 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ L @ K @ V @ R ) )
% 2.46/1.50 => thesis ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_4_rbt_Odistinct_I1_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im418718756_Empty @ A @ B )
% 2.46/1.50 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_5_color_Odistinct_I1_J,axiom,
% 2.46/1.50 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 2.46/1.50
% 2.46/1.50 thf(fact_6_rbt_Oinduct,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 => ( ! [X1: rBT_Im1923302023_color,X2: rBT_Im246033960le_rbt @ A @ B,X3: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( P @ X2 )
% 2.46/1.50 => ( ( P @ X5 )
% 2.46/1.50 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) )
% 2.46/1.50 => ( P @ Rbt ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_7_rbt_Oexhaust,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( Y
% 2.46/1.50 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( Y
% 2.46/1.50 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_8_color_Oinduct,axiom,
% 2.46/1.50 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 2.46/1.50 ( ( P @ rBT_Impl_Mirabelle_R )
% 2.46/1.50 => ( ( P @ rBT_Impl_Mirabelle_B )
% 2.46/1.50 => ( P @ Color ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_9_color_Oexhaust,axiom,
% 2.46/1.50 ! [Y: rBT_Im1923302023_color] :
% 2.46/1.50 ( ( Y != rBT_Impl_Mirabelle_R )
% 2.46/1.50 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_10_color_Osimps_I6_J,axiom,
% 2.46/1.50 ! [A: $tType,F1: A,F2: A] :
% 2.46/1.50 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 2.46/1.50 = F2 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_11_color_Osimps_I5_J,axiom,
% 2.46/1.50 ! [A: $tType,F1: A,F2: A] :
% 2.46/1.50 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 2.46/1.50 = F1 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_12_color_Osimps_I4_J,axiom,
% 2.46/1.50 ! [A: $tType,F1: A,F2: A] :
% 2.46/1.50 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 2.46/1.50 = F2 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_13_color_Osimps_I3_J,axiom,
% 2.46/1.50 ! [A: $tType,F1: A,F2: A] :
% 2.46/1.50 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 2.46/1.50 = F1 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_14_rbt_Osimps_I4_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,C: $tType,F1: C,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C] :
% 2.46/1.50 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = F1 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_15_rbt_Osimps_I5_J,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,A: $tType,F1: C,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > C,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 2.46/1.50 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_16_rbt_Osimps_I6_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,E: $tType,F1: E,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E] :
% 2.46/1.50 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = F1 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_17_rbt_Osimps_I7_J,axiom,
% 2.46/1.50 ! [E: $tType,B: $tType,A: $tType,F1: E,F2: rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > E > E > E,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 2.46/1.50 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X22 ) @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X25 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_18_rbt_Opred__inject_I2_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,A2: rBT_Im1923302023_color,Aa2: rBT_Im246033960le_rbt @ A @ B,Ab: A,Ac: B,Ad: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ ( rBT_Im480247531Branch @ A @ B @ A2 @ Aa2 @ Ab @ Ac @ Ad ) )
% 2.46/1.50 = ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ Aa2 )
% 2.46/1.50 & ( P1 @ Ab )
% 2.46/1.50 & ( P2 @ Ac )
% 2.46/1.50 & ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ Ad ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_19_rbt_Orel__distinct_I2_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_20_rbt_Orel__distinct_I1_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 2.46/1.50 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_21_rbt_Opred__inject_I1_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o] : ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_22_rbt_Orel__eq,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B
% 2.46/1.50 @ ^ [Y2: A,Z: A] : ( Y2 = Z )
% 2.46/1.50 @ ^ [Y2: B,Z: B] : ( Y2 = Z ) )
% 2.46/1.50 = ( ^ [Y2: rBT_Im246033960le_rbt @ A @ B,Z: rBT_Im246033960le_rbt @ A @ B] : ( Y2 = Z ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_23_rbt_Orel__refl,axiom,
% 2.46/1.50 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: rBT_Im246033960le_rbt @ C @ D] :
% 2.46/1.50 ( ! [X6: C] : ( R1a @ X6 @ X6 )
% 2.46/1.50 => ( ! [X6: D] : ( R2a @ X6 @ X6 )
% 2.46/1.50 => ( rBT_Im1000242676el_rbt @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_24_color_Ocase__distrib,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,H: A > B,F1: A,F2: A,Color: rBT_Im1923302023_color] :
% 2.46/1.50 ( ( H @ ( rBT_Im1975547051_color @ A @ F1 @ F2 @ Color ) )
% 2.46/1.50 = ( rBT_Im1975547051_color @ B @ ( H @ F1 ) @ ( H @ F2 ) @ Color ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_25_rbt_Orel__intros_I2_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,X21: rBT_Im1923302023_color,Y21: rBT_Im1923302023_color,R1: A > C > $o,R2: B > D > $o,X22: rBT_Im246033960le_rbt @ A @ B,Y22: rBT_Im246033960le_rbt @ C @ D,X23: A,Y23: C,X24: B,Y24: D,X25: rBT_Im246033960le_rbt @ A @ B,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 2.46/1.50 ( ( X21 = Y21 )
% 2.46/1.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 2.46/1.50 => ( ( R1 @ X23 @ Y23 )
% 2.46/1.50 => ( ( R2 @ X24 @ Y24 )
% 2.46/1.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X25 @ Y25 )
% 2.46/1.50 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_26_rbt_Orel__inject_I2_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,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 @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 2.46/1.50 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 2.46/1.50 = ( ( X21 = Y21 )
% 2.46/1.50 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X22 @ Y22 )
% 2.46/1.50 & ( R1 @ X23 @ Y23 )
% 2.46/1.50 & ( R2 @ X24 @ Y24 )
% 2.46/1.50 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X25 @ Y25 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_27_rbt_Octr__transfer_I1_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o] : ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_28_rbt_Opred__rel,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 2.46/1.50 = ( ^ [P12: A > $o,P22: B > $o,X7: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P12 ) @ ( bNF_eq_onp @ B @ P22 ) @ X7 @ X7 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_29_rbt_Oset__intros_I1_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X: A,A22: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A3: A,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ A22 ) )
% 2.46/1.50 => ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_30_rbt_Oset__intros_I2_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,A3: A,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] : ( member @ A @ A3 @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_31_rbt_Oset__intros_I3_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,Xb: A,A5: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A3: A,A4: B] :
% 2.46/1.50 ( ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ A5 ) )
% 2.46/1.50 => ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A3 @ A4 @ A5 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_32_rbt_Oset__intros_I4_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,Xe: B,A2a: rBT_Im246033960le_rbt @ A @ B,A1a: rBT_Im1923302023_color,A3a: A,A4a: B,A5a: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2a ) )
% 2.46/1.50 => ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_33_rbt_Oset__intros_I5_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,A4a: B,A1a: rBT_Im1923302023_color,A2a: rBT_Im246033960le_rbt @ A @ B,A3a: A,A5a: rBT_Im246033960le_rbt @ A @ B] : ( member @ B @ A4a @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_34_rbt_Oset__intros_I6_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,Xg: B,A5a: rBT_Im246033960le_rbt @ A @ B,A1a: rBT_Im1923302023_color,A2a: rBT_Im246033960le_rbt @ A @ B,A3a: A,A4a: B] :
% 2.46/1.50 ( ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ A5a ) )
% 2.46/1.50 => ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_35_rbt_Oset__cases_I1_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,E2: A,A2: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ A2 ) )
% 2.46/1.50 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ? [Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( A2
% 2.46/1.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 2.46/1.50 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z2 ) ) )
% 2.46/1.50 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( A2
% 2.46/1.50 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ E2 @ Z4 @ Z5 ) )
% 2.46/1.50 => ~ ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( A2
% 2.46/1.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 2.46/1.50 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_36_rbt_Oset__cases_I2_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,E2: B,A2: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2 ) )
% 2.46/1.50 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ? [Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( A2
% 2.46/1.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 2.46/1.50 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z2 ) ) )
% 2.46/1.50 => ( ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( A2
% 2.46/1.50 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ E2 @ Z5 ) )
% 2.46/1.50 => ~ ! [Z1: rBT_Im1923302023_color,Z2: rBT_Im246033960le_rbt @ A @ B,Z3: A,Z4: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( A2
% 2.46/1.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z2 @ Z3 @ Z4 @ Z5 ) )
% 2.46/1.50 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_37_rbt_Osimps_I8_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,F1: A > C,F2: B > D] :
% 2.46/1.50 ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_38_rbt_Oinj__map__strong,axiom,
% 2.46/1.50 ! [C: $tType,D: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Xa: rBT_Im246033960le_rbt @ A @ B,F1: A > C,F1a: A > C,F2: B > D,F2a: B > D] :
% 2.46/1.50 ( ! [Z1: A,Z1a: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( member @ A @ Z1a @ ( rBT_Im1178217900t1_rbt @ A @ B @ Xa ) )
% 2.46/1.50 => ( ( ( F1 @ Z1 )
% 2.46/1.50 = ( F1a @ Z1a ) )
% 2.46/1.50 => ( Z1 = Z1a ) ) ) )
% 2.46/1.50 => ( ! [Z2: B,Z2a: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( member @ B @ Z2a @ ( rBT_Im1550225131t2_rbt @ A @ B @ Xa ) )
% 2.46/1.50 => ( ( ( F2 @ Z2 )
% 2.46/1.50 = ( F2a @ Z2a ) )
% 2.46/1.50 => ( Z2 = Z2a ) ) ) )
% 2.46/1.50 => ( ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.46/1.50 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1a @ F2a @ Xa ) )
% 2.46/1.50 => ( X = Xa ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_39_rbt_Omap__cong0,axiom,
% 2.46/1.50 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 2.46/1.50 ( ! [Z1: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( F1 @ Z1 )
% 2.46/1.50 = ( G1 @ Z1 ) ) )
% 2.46/1.50 => ( ! [Z2: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( F2 @ Z2 )
% 2.46/1.50 = ( G2 @ Z2 ) ) )
% 2.46/1.50 => ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.46/1.50 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G1 @ G2 @ X ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_40_rbt_Omap__cong,axiom,
% 2.46/1.50 ! [D: $tType,C: $tType,B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,F1: A > C,G1: A > C,F2: B > D,G2: B > D] :
% 2.46/1.50 ( ( X = Ya )
% 2.46/1.50 => ( ! [Z1: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( F1 @ Z1 )
% 2.46/1.50 = ( G1 @ Z1 ) ) )
% 2.46/1.50 => ( ! [Z2: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( F2 @ Z2 )
% 2.46/1.50 = ( G2 @ Z2 ) ) )
% 2.46/1.50 => ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X )
% 2.46/1.50 = ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G1 @ G2 @ Ya ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_41_rbt_Orel__refl__strong,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 2.46/1.50 ( ! [Z1: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( R1a @ Z1 @ Z1 ) )
% 2.46/1.50 => ( ! [Z2: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( R2a @ Z2 @ Z2 ) )
% 2.46/1.50 => ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_42_rbt_Orel__mono__strong,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R2: B > D > $o,X: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 2.46/1.50 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 2.46/1.50 => ( ! [Z1: A,Y1: C] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Y ) )
% 2.46/1.50 => ( ( R1 @ Z1 @ Y1 )
% 2.46/1.50 => ( R1a @ Z1 @ Y1 ) ) ) )
% 2.46/1.50 => ( ! [Z2: B,Y26: D] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Y ) )
% 2.46/1.50 => ( ( R2 @ Z2 @ Y26 )
% 2.46/1.50 => ( R2a @ Z2 @ Y26 ) ) ) )
% 2.46/1.50 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_43_rbt_Orel__cong,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,Xa: rBT_Im246033960le_rbt @ C @ D,R1: A > C > $o,R1a: A > C > $o,R2: B > D > $o,R2a: B > D > $o] :
% 2.46/1.50 ( ( X = Ya )
% 2.46/1.50 => ( ( Y = Xa )
% 2.46/1.50 => ( ! [Z1: A,Y1: C] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Xa ) )
% 2.46/1.50 => ( ( R1 @ Z1 @ Y1 )
% 2.46/1.50 = ( R1a @ Z1 @ Y1 ) ) ) )
% 2.46/1.50 => ( ! [Z2: B,Y26: D] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Xa ) )
% 2.46/1.50 => ( ( R2 @ Z2 @ Y26 )
% 2.46/1.50 = ( R2a @ Z2 @ Y26 ) ) ) )
% 2.46/1.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R2 @ X @ Y )
% 2.46/1.50 = ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_44_rbt_Opred__mono__strong,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,P1: A > $o,P2: B > $o,X: rBT_Im246033960le_rbt @ A @ B,P1a: A > $o,P2a: B > $o] :
% 2.46/1.50 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ X )
% 2.46/1.50 => ( ! [Z1: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( P1 @ Z1 )
% 2.46/1.50 => ( P1a @ Z1 ) ) )
% 2.46/1.50 => ( ! [Z2: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 2.46/1.50 => ( ( P2 @ Z2 )
% 2.46/1.50 => ( P2a @ Z2 ) ) )
% 2.46/1.50 => ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_45_mem__Collect__eq,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,P: A > $o] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.46/1.50 = ( P @ A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_46_Collect__mem__eq,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( collect @ A
% 2.46/1.50 @ ^ [X7: A] : ( member @ A @ X7 @ A6 ) )
% 2.46/1.50 = A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_47_Collect__cong,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( P @ X6 )
% 2.46/1.50 = ( Q @ X6 ) )
% 2.46/1.50 => ( ( collect @ A @ P )
% 2.46/1.50 = ( collect @ A @ Q ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_48_ext,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( F @ X6 )
% 2.46/1.50 = ( G @ X6 ) )
% 2.46/1.50 => ( F = G ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_49_rbt_Opred__cong,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,P1: A > $o,P1a: A > $o,P2: B > $o,P2a: B > $o] :
% 2.46/1.50 ( ( X = Ya )
% 2.46/1.50 => ( ! [Z1: A] :
% 2.46/1.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( P1 @ Z1 )
% 2.46/1.50 = ( P1a @ Z1 ) ) )
% 2.46/1.50 => ( ! [Z2: B] :
% 2.46/1.50 ( ( member @ B @ Z2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 2.46/1.50 => ( ( P2 @ Z2 )
% 2.46/1.50 = ( P2a @ Z2 ) ) )
% 2.46/1.50 => ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 @ X )
% 2.46/1.50 = ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_50_rbt_Orel__eq__onp,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,P1: A > $o,P2: B > $o] :
% 2.46/1.50 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P1 ) @ ( bNF_eq_onp @ B @ P2 ) )
% 2.46/1.50 = ( bNF_eq_onp @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_51_rbt_Osimps_I9_J,axiom,
% 2.46/1.50 ! [D: $tType,C: $tType,B: $tType,A: $tType,F1: A > C,F2: B > D,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 2.46/1.50 = ( rBT_Im480247531Branch @ C @ D @ X21 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X22 ) @ ( F1 @ X23 ) @ ( F2 @ X24 ) @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X25 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_52_eq__onp__live__step,axiom,
% 2.46/1.50 ! [A: $tType,X: $o,Y: $o,P: A > $o,A2: A] :
% 2.46/1.50 ( ( X = Y )
% 2.46/1.50 => ( ( ( bNF_eq_onp @ A @ P @ A2 @ A2 )
% 2.46/1.50 & X )
% 2.46/1.50 = ( ( P @ A2 )
% 2.46/1.50 & Y ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_53_eq__onp__same__args,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,X: A] :
% 2.46/1.50 ( ( bNF_eq_onp @ A @ P @ X @ X )
% 2.46/1.50 = ( P @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_54_eq__onp__to__eq,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,X: A,Y: A] :
% 2.46/1.50 ( ( bNF_eq_onp @ A @ P @ X @ Y )
% 2.46/1.50 => ( X = Y ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_55_eq__onp__mono0,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,P: A > $o,Q: A > $o] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ A6 )
% 2.46/1.50 => ( ( P @ X6 )
% 2.46/1.50 => ( Q @ X6 ) ) )
% 2.46/1.50 => ! [X8: A] :
% 2.46/1.50 ( ( member @ A @ X8 @ A6 )
% 2.46/1.50 => ! [Xa2: A] :
% 2.46/1.50 ( ( member @ A @ Xa2 @ A6 )
% 2.46/1.50 => ( ( bNF_eq_onp @ A @ P @ X8 @ Xa2 )
% 2.46/1.50 => ( bNF_eq_onp @ A @ Q @ X8 @ Xa2 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_56_eq__onp__eqD,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,Q: A > A > $o,X: A] :
% 2.46/1.50 ( ( ( bNF_eq_onp @ A @ P )
% 2.46/1.50 = Q )
% 2.46/1.50 => ( ( P @ X )
% 2.46/1.50 = ( Q @ X @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_57_rbt_Opred__set,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 2.46/1.50 = ( ^ [P12: A > $o,P22: B > $o,X7: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ! [Y3: A] :
% 2.46/1.50 ( ( member @ A @ Y3 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X7 ) )
% 2.46/1.50 => ( P12 @ Y3 ) )
% 2.46/1.50 & ! [Y3: B] :
% 2.46/1.50 ( ( member @ B @ Y3 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X7 ) )
% 2.46/1.50 => ( P22 @ Y3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_58_rbt_Osimps_I16_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType] :
% 2.46/1.50 ( ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = ( bot_bot @ ( set @ B ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_59_rbt_Osimps_I14_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_60_rbt_Opred__map,axiom,
% 2.46/1.50 ! [D: $tType,C: $tType,B: $tType,A: $tType,Q1: C > $o,Q2: D > $o,F1: A > C,F2: B > D,X: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im1931894874ed_rbt @ C @ D @ Q1 @ Q2 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ X ) )
% 2.46/1.50 = ( rBT_Im1931894874ed_rbt @ A @ B @ ( comp @ C @ $o @ A @ Q1 @ F1 ) @ ( comp @ D @ $o @ B @ Q2 @ F2 ) @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_61_comp__apply__eq,axiom,
% 2.46/1.50 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X: C,H: D > A,K: C > D] :
% 2.46/1.50 ( ( ( F @ ( G @ X ) )
% 2.46/1.50 = ( H @ ( K @ X ) ) )
% 2.46/1.50 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 2.46/1.50 = ( comp @ D @ A @ C @ H @ K @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_62_rewriteL__comp__comp,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H: D > A] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.46/1.50 = L )
% 2.46/1.50 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H ) )
% 2.46/1.50 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_63_rewriteR__comp__comp,axiom,
% 2.46/1.50 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R: A > B,F: B > D] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.46/1.50 = R )
% 2.46/1.50 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H )
% 2.46/1.50 = ( comp @ B @ D @ A @ F @ R ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_64_rewriteL__comp__comp2,axiom,
% 2.46/1.50 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H: E > A,R: E > D] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ F @ G )
% 2.46/1.50 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 2.46/1.50 => ( ( ( comp @ A @ D @ E @ L2 @ H )
% 2.46/1.50 = R )
% 2.46/1.50 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H ) )
% 2.46/1.50 = ( comp @ D @ B @ E @ L1 @ R ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_65_rewriteR__comp__comp2,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R12: D > B,R22: A > D,F: B > E,L: D > E] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ G @ H )
% 2.46/1.50 = ( comp @ D @ B @ A @ R12 @ R22 ) )
% 2.46/1.50 => ( ( ( comp @ B @ E @ D @ F @ R12 )
% 2.46/1.50 = L )
% 2.46/1.50 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H )
% 2.46/1.50 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_66_rbt_Omap__comp,axiom,
% 2.46/1.50 ! [D: $tType,F3: $tType,E: $tType,C: $tType,B: $tType,A: $tType,G1: C > E,G2: D > F3,F1: A > C,F2: B > D,V: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im206295089ap_rbt @ C @ E @ D @ F3 @ G1 @ G2 @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ F1 @ F2 @ V ) )
% 2.46/1.50 = ( rBT_Im206295089ap_rbt @ A @ E @ B @ F3 @ ( comp @ C @ E @ A @ G1 @ F1 ) @ ( comp @ D @ F3 @ B @ G2 @ F2 ) @ V ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_67_ball__empty,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,X8: A] :
% 2.46/1.50 ( ( member @ A @ X8 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 => ( P @ X8 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_68_comp__apply,axiom,
% 2.46/1.50 ! [C: $tType,A: $tType,B: $tType] :
% 2.46/1.50 ( ( comp @ B @ A @ C )
% 2.46/1.50 = ( ^ [F4: B > A,G3: C > B,X7: C] : ( F4 @ ( G3 @ X7 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_69_empty__iff,axiom,
% 2.46/1.50 ! [A: $tType,C2: A] :
% 2.46/1.50 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_70_all__not__in__conv,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( ! [X7: A] :
% 2.46/1.50 ~ ( member @ A @ X7 @ A6 ) )
% 2.46/1.50 = ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_71_Collect__empty__eq,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o] :
% 2.46/1.50 ( ( ( collect @ A @ P )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( ! [X7: A] :
% 2.46/1.50 ~ ( P @ X7 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_72_empty__Collect__eq,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o] :
% 2.46/1.50 ( ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( collect @ A @ P ) )
% 2.46/1.50 = ( ! [X7: A] :
% 2.46/1.50 ~ ( P @ X7 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_73_bot__apply,axiom,
% 2.46/1.50 ! [C: $tType,D: $tType] :
% 2.46/1.50 ( ( bot @ C @ ( type2 @ C ) )
% 2.46/1.50 => ( ( bot_bot @ ( D > C ) )
% 2.46/1.50 = ( ^ [X7: D] : ( bot_bot @ C ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_74_bot__set__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_75_bot__fun__def,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( bot @ B @ ( type2 @ B ) )
% 2.46/1.50 => ( ( bot_bot @ ( A > B ) )
% 2.46/1.50 = ( ^ [X7: A] : ( bot_bot @ B ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_76_ex__in__conv,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( ? [X7: A] : ( member @ A @ X7 @ A6 ) )
% 2.46/1.50 = ( A6
% 2.46/1.50 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_77_equals0I,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ! [Y4: A] :
% 2.46/1.50 ~ ( member @ A @ Y4 @ A6 )
% 2.46/1.50 => ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_78_equals0D,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,A2: A] :
% 2.46/1.50 ( ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 => ~ ( member @ A @ A2 @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_79_emptyE,axiom,
% 2.46/1.50 ! [A: $tType,A2: A] :
% 2.46/1.50 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_80_comp__eq__dest__lhs,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,A: $tType,A2: C > B,B2: A > C,C2: A > B,V: A] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.46/1.50 = C2 )
% 2.46/1.50 => ( ( A2 @ ( B2 @ V ) )
% 2.46/1.50 = ( C2 @ V ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_81_comp__eq__elim,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.46/1.50 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.46/1.50 => ! [V2: A] :
% 2.46/1.50 ( ( A2 @ ( B2 @ V2 ) )
% 2.46/1.50 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_82_comp__eq__dest,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,D: $tType,A: $tType,A2: C > B,B2: A > C,C2: D > B,D2: A > D,V: A] :
% 2.46/1.50 ( ( ( comp @ C @ B @ A @ A2 @ B2 )
% 2.46/1.50 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 2.46/1.50 => ( ( A2 @ ( B2 @ V ) )
% 2.46/1.50 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_83_comp__assoc,axiom,
% 2.46/1.50 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H: A > C] :
% 2.46/1.50 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H )
% 2.46/1.50 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_84_comp__def,axiom,
% 2.46/1.50 ! [A: $tType,C: $tType,B: $tType] :
% 2.46/1.50 ( ( comp @ B @ C @ A )
% 2.46/1.50 = ( ^ [F4: B > C,G3: A > B,X7: A] : ( F4 @ ( G3 @ X7 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_85_Ball__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( ball @ A )
% 2.46/1.50 = ( ^ [A7: set @ A,P3: A > $o] :
% 2.46/1.50 ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ A7 )
% 2.46/1.50 => ( P3 @ X7 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_86_override__on__emptyset,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.46/1.50 ( ( override_on @ A @ B @ F @ G @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = F ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_87_Set_Ois__empty__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( is_empty @ A )
% 2.46/1.50 = ( ^ [A7: set @ A] :
% 2.46/1.50 ( A7
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_88_ball__reg,axiom,
% 2.46/1.50 ! [A: $tType,R3: set @ A,P: A > $o,Q: A > $o] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ R3 )
% 2.46/1.50 => ( ( P @ X6 )
% 2.46/1.50 => ( Q @ X6 ) ) )
% 2.46/1.50 => ( ! [X6: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ R3 )
% 2.46/1.50 => ( P @ X6 ) )
% 2.46/1.50 => ! [X8: A] :
% 2.46/1.50 ( ( member @ A @ X8 @ R3 )
% 2.46/1.50 => ( Q @ X8 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_89_type__copy__map__cong0,axiom,
% 2.46/1.50 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X: C,N: D > A,H: C > D,F: A > E] :
% 2.46/1.50 ( ( ( M @ ( G @ X ) )
% 2.46/1.50 = ( N @ ( H @ X ) ) )
% 2.46/1.50 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X )
% 2.46/1.50 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_90_fun_Omap__comp,axiom,
% 2.46/1.50 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 2.46/1.50 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 2.46/1.50 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_91_comp__cong,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X: C,F5: D > A,G4: E > D,X9: E] :
% 2.46/1.50 ( ( ( F @ ( G @ X ) )
% 2.46/1.50 = ( F5 @ ( G4 @ X9 ) ) )
% 2.46/1.50 => ( ( comp @ B @ A @ C @ F @ G @ X )
% 2.46/1.50 = ( comp @ D @ A @ E @ F5 @ G4 @ X9 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_92_override__on__apply__in,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,A2: A,A6: set @ A,F: A > B,G: A > B] :
% 2.46/1.50 ( ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( override_on @ A @ B @ F @ G @ A6 @ A2 )
% 2.46/1.50 = ( G @ A2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_93_override__on__apply__notin,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,A2: A,A6: set @ A,F: A > B,G: A > B] :
% 2.46/1.50 ( ~ ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( override_on @ A @ B @ F @ G @ A6 @ A2 )
% 2.46/1.50 = ( F @ A2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_94_override__on__def,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType] :
% 2.46/1.50 ( ( override_on @ A @ B )
% 2.46/1.50 = ( ^ [F4: A > B,G3: A > B,A7: set @ A,A8: A] : ( if @ B @ ( member @ A @ A8 @ A7 ) @ ( G3 @ A8 ) @ ( F4 @ A8 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_95_Collect__empty__eq__bot,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o] :
% 2.46/1.50 ( ( ( collect @ A @ P )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( P
% 2.46/1.50 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_96_bot__empty__eq,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bot_bot @ ( A > $o ) )
% 2.46/1.50 = ( ^ [X7: A] : ( member @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_97_rbt_Osize__gen__o__map,axiom,
% 2.46/1.50 ! [A: $tType,C: $tType,D: $tType,B: $tType,F: C > nat,Fa: D > nat,G: A > C,Ga: B > D] :
% 2.46/1.50 ( ( comp @ ( rBT_Im246033960le_rbt @ C @ D ) @ nat @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1485196410ze_rbt @ C @ D @ F @ Fa ) @ ( rBT_Im206295089ap_rbt @ A @ C @ B @ D @ G @ Ga ) )
% 2.46/1.50 = ( rBT_Im1485196410ze_rbt @ A @ B @ ( comp @ C @ nat @ A @ F @ G ) @ ( comp @ D @ nat @ B @ Fa @ Ga ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_98_is__singletonI_H,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( A6
% 2.46/1.50 != ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 => ( ! [X6: A,Y4: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ A6 )
% 2.46/1.50 => ( ( member @ A @ Y4 @ A6 )
% 2.46/1.50 => ( X6 = Y4 ) ) )
% 2.46/1.50 => ( is_singleton @ A @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_99_vimage2p__comp,axiom,
% 2.46/1.50 ! [E: $tType,D: $tType,F3: $tType,A: $tType,C: $tType,B: $tType,G5: $tType,F1: F3 > A,F2: D > F3,G1: G5 > B,G2: E > G5] :
% 2.46/1.50 ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ ( comp @ F3 @ A @ D @ F1 @ F2 ) @ ( comp @ G5 @ B @ E @ G1 @ G2 ) )
% 2.46/1.50 = ( comp @ ( F3 > G5 > C ) @ ( D > E > C ) @ ( A > B > C ) @ ( bNF_vimage2p @ D @ F3 @ E @ G5 @ C @ F2 @ G2 ) @ ( bNF_vimage2p @ F3 @ A @ G5 @ B @ C @ F1 @ G1 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_100_vimage2p__cong,axiom,
% 2.46/1.50 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,R3: A > B > C,S: A > B > C,F: D > A,G: E > B] :
% 2.46/1.50 ( ( R3 = S )
% 2.46/1.50 => ( ( bNF_vimage2p @ D @ A @ E @ B @ C @ F @ G @ R3 )
% 2.46/1.50 = ( bNF_vimage2p @ D @ A @ E @ B @ C @ F @ G @ S ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_101_rbt_Osize__gen_I1_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,Xa: A > nat,X: B > nat] :
% 2.46/1.50 ( ( rBT_Im1485196410ze_rbt @ A @ B @ Xa @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_102_is__singletonI,axiom,
% 2.46/1.50 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_103_map__fun_Ocomp,axiom,
% 2.46/1.50 ! [E: $tType,C: $tType,A: $tType,F3: $tType,D: $tType,B: $tType,F: E > C,G: D > F3,H: C > A,I: B > D] :
% 2.46/1.50 ( ( comp @ ( C > D ) @ ( E > F3 ) @ ( A > B ) @ ( map_fun @ E @ C @ D @ F3 @ F @ G ) @ ( map_fun @ C @ A @ B @ D @ H @ I ) )
% 2.46/1.50 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_104_is__singletonE,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( is_singleton @ A @ A6 )
% 2.46/1.50 => ~ ! [X6: A] :
% 2.46/1.50 ( A6
% 2.46/1.50 != ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_105_is__singleton__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( is_singleton @ A )
% 2.46/1.50 = ( ^ [A7: set @ A] :
% 2.46/1.50 ? [X7: A] :
% 2.46/1.50 ( A7
% 2.46/1.50 = ( insert @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_106_insert__absorb2,axiom,
% 2.46/1.50 ! [A: $tType,X: A,A6: set @ A] :
% 2.46/1.50 ( ( insert @ A @ X @ ( insert @ A @ X @ A6 ) )
% 2.46/1.50 = ( insert @ A @ X @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_107_insert__iff,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B2: A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A6 ) )
% 2.46/1.50 = ( ( A2 = B2 )
% 2.46/1.50 | ( member @ A @ A2 @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_108_insertCI,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 2.46/1.50 ( ( ~ ( member @ A @ A2 @ B3 )
% 2.46/1.50 => ( A2 = B2 ) )
% 2.46/1.50 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_109_map__fun__apply,axiom,
% 2.46/1.50 ! [D: $tType,A: $tType,C: $tType,B: $tType] :
% 2.46/1.50 ( ( map_fun @ B @ C @ D @ A )
% 2.46/1.50 = ( ^ [F4: B > C,G3: D > A,H2: C > D,X7: B] : ( G3 @ ( H2 @ ( F4 @ X7 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_110_singletonI,axiom,
% 2.46/1.50 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_111_singletonD,axiom,
% 2.46/1.50 ! [A: $tType,B2: A,A2: A] :
% 2.46/1.50 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( B2 = A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_112_singleton__iff,axiom,
% 2.46/1.50 ! [A: $tType,B2: A,A2: A] :
% 2.46/1.50 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 = ( B2 = A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_113_doubleton__eq__iff,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B2: A,C2: A,D2: A] :
% 2.46/1.50 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 = ( insert @ A @ C2 @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.46/1.50 = ( ( ( A2 = C2 )
% 2.46/1.50 & ( B2 = D2 ) )
% 2.46/1.50 | ( ( A2 = D2 )
% 2.46/1.50 & ( B2 = C2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_114_insert__not__empty,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A] :
% 2.46/1.50 ( ( insert @ A @ A2 @ A6 )
% 2.46/1.50 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_115_singleton__inject,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B2: A] :
% 2.46/1.50 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( A2 = B2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_116_mk__disjoint__insert,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ? [B4: set @ A] :
% 2.46/1.50 ( ( A6
% 2.46/1.50 = ( insert @ A @ A2 @ B4 ) )
% 2.46/1.50 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_117_insert__commute,axiom,
% 2.46/1.50 ! [A: $tType,X: A,Y: A,A6: set @ A] :
% 2.46/1.50 ( ( insert @ A @ X @ ( insert @ A @ Y @ A6 ) )
% 2.46/1.50 = ( insert @ A @ Y @ ( insert @ A @ X @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_118_insert__eq__iff,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B2: A,B3: set @ A] :
% 2.46/1.50 ( ~ ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ~ ( member @ A @ B2 @ B3 )
% 2.46/1.50 => ( ( ( insert @ A @ A2 @ A6 )
% 2.46/1.50 = ( insert @ A @ B2 @ B3 ) )
% 2.46/1.50 = ( ( ( A2 = B2 )
% 2.46/1.50 => ( A6 = B3 ) )
% 2.46/1.50 & ( ( A2 != B2 )
% 2.46/1.50 => ? [C3: set @ A] :
% 2.46/1.50 ( ( A6
% 2.46/1.50 = ( insert @ A @ B2 @ C3 ) )
% 2.46/1.50 & ~ ( member @ A @ B2 @ C3 )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( insert @ A @ A2 @ C3 ) )
% 2.46/1.50 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_119_insert__absorb,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( insert @ A @ A2 @ A6 )
% 2.46/1.50 = A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_120_insert__ident,axiom,
% 2.46/1.50 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ~ ( member @ A @ X @ A6 )
% 2.46/1.50 => ( ~ ( member @ A @ X @ B3 )
% 2.46/1.50 => ( ( ( insert @ A @ X @ A6 )
% 2.46/1.50 = ( insert @ A @ X @ B3 ) )
% 2.46/1.50 = ( A6 = B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_121_Set_Oset__insert,axiom,
% 2.46/1.50 ! [A: $tType,X: A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ X @ A6 )
% 2.46/1.50 => ~ ! [B4: set @ A] :
% 2.46/1.50 ( ( A6
% 2.46/1.50 = ( insert @ A @ X @ B4 ) )
% 2.46/1.50 => ( member @ A @ X @ B4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_122_insertI2,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B3: set @ A,B2: A] :
% 2.46/1.50 ( ( member @ A @ A2 @ B3 )
% 2.46/1.50 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_123_insertI1,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B3: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_124_insertE,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B2: A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A6 ) )
% 2.46/1.50 => ( ( A2 != B2 )
% 2.46/1.50 => ( member @ A @ A2 @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_125_map__fun_Ocompositionality,axiom,
% 2.46/1.50 ! [D: $tType,F3: $tType,C: $tType,E: $tType,B: $tType,A: $tType,F: E > C,G: D > F3,H: C > A,I: B > D,Fun: A > B] :
% 2.46/1.50 ( ( map_fun @ E @ C @ D @ F3 @ F @ G @ ( map_fun @ C @ A @ B @ D @ H @ I @ Fun ) )
% 2.46/1.50 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Fun ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_126_map__fun__def,axiom,
% 2.46/1.50 ! [B: $tType,D: $tType,A: $tType,C: $tType] :
% 2.46/1.50 ( ( map_fun @ C @ A @ B @ D )
% 2.46/1.50 = ( ^ [F4: C > A,G3: B > D,H2: A > B] : ( comp @ A @ D @ C @ ( comp @ B @ D @ A @ G3 @ H2 ) @ F4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_127_color_Osize__gen_I1_J,axiom,
% 2.46/1.50 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_R )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_128_color_Osize__gen_I2_J,axiom,
% 2.46/1.50 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_B )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_129_is__singleton__the__elem,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( is_singleton @ A )
% 2.46/1.50 = ( ^ [A7: set @ A] :
% 2.46/1.50 ( A7
% 2.46/1.50 = ( insert @ A @ ( the_elem @ A @ A7 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_130_the__elem__eq,axiom,
% 2.46/1.50 ! [A: $tType,X: A] :
% 2.46/1.50 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 = X ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_131_color_Osize_I3_J,axiom,
% 2.46/1.50 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_R )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_132_color_Osize_I4_J,axiom,
% 2.46/1.50 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_B )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_133_rbt_Osize_I3_J,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType] :
% 2.46/1.50 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_134_rbt_Osimps_I15_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 2.46/1.50 = ( insert @ A @ X23 @ ( sup_sup @ ( set @ A ) @ ( rBT_Im1178217900t1_rbt @ A @ B @ X22 ) @ ( rBT_Im1178217900t1_rbt @ A @ B @ X25 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_135_rbt_Osimps_I17_J,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.46/1.50 ( ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 2.46/1.50 = ( insert @ B @ X24 @ ( sup_sup @ ( set @ B ) @ ( rBT_Im1550225131t2_rbt @ A @ B @ X22 ) @ ( rBT_Im1550225131t2_rbt @ A @ B @ X25 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_136_pairwise__singleton,axiom,
% 2.46/1.50 ! [A: $tType,P: A > A > $o,A6: A] : ( pairwise @ A @ P @ ( insert @ A @ A6 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_137_Un__iff,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 = ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 | ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_138_UnCI,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,B3: set @ A,A6: set @ A] :
% 2.46/1.50 ( ( ~ ( member @ A @ C2 @ B3 )
% 2.46/1.50 => ( member @ A @ C2 @ A6 ) )
% 2.46/1.50 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_139_Un__empty,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( sup_sup @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_140_Un__insert__left,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,B3: set @ A,C4: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 2.46/1.50 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_141_Un__insert__right,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,A2: A,B3: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_142_Un__empty__left,axiom,
% 2.46/1.50 ! [A: $tType,B3: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 2.46/1.50 = B3 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_143_Un__empty__right,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_144_Un__left__commute,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A6 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_145_Un__left__absorb,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_146_pairwise__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( pairwise @ A )
% 2.46/1.50 = ( ^ [R4: A > A > $o,S2: set @ A] :
% 2.46/1.50 ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ S2 )
% 2.46/1.50 => ! [Y3: A] :
% 2.46/1.50 ( ( member @ A @ Y3 @ S2 )
% 2.46/1.50 => ( ( X7 != Y3 )
% 2.46/1.50 => ( R4 @ X7 @ Y3 ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_147_Un__commute,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) )
% 2.46/1.50 = ( ^ [A7: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A7 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_148_Un__absorb,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ A6 @ A6 )
% 2.46/1.50 = A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_149_Un__assoc,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 2.46/1.50 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ A6 @ ( sup_sup @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_150_ball__Un,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,P: A > $o] :
% 2.46/1.50 ( ( ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 => ( P @ X7 ) ) )
% 2.46/1.50 = ( ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ A6 )
% 2.46/1.50 => ( P @ X7 ) )
% 2.46/1.50 & ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ B3 )
% 2.46/1.50 => ( P @ X7 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_151_bex__Un,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,P: A > $o] :
% 2.46/1.50 ( ( ? [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 & ( P @ X7 ) ) )
% 2.46/1.50 = ( ? [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ A6 )
% 2.46/1.50 & ( P @ X7 ) )
% 2.46/1.50 | ? [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ B3 )
% 2.46/1.50 & ( P @ X7 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_152_UnI2,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,B3: set @ A,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ B3 )
% 2.46/1.50 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_153_UnI1,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_154_UnE,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 => ( ~ ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_155_singleton__Un__iff,axiom,
% 2.46/1.50 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 = ( ( ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.46/1.50 | ( ( A6
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 | ( ( A6
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_156_Un__singleton__iff,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 2.46/1.50 ( ( ( sup_sup @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 = ( ( ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.46/1.50 | ( ( A6
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 | ( ( A6
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 & ( B3
% 2.46/1.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_157_insert__is__Un,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( insert @ A )
% 2.46/1.50 = ( ^ [A8: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A8 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_158_pairwise__empty,axiom,
% 2.46/1.50 ! [A: $tType,P: A > A > $o] : ( pairwise @ A @ P @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_159_pairwise__insert,axiom,
% 2.46/1.50 ! [A: $tType,R: A > A > $o,X: A,S3: set @ A] :
% 2.46/1.50 ( ( pairwise @ A @ R @ ( insert @ A @ X @ S3 ) )
% 2.46/1.50 = ( ! [Y3: A] :
% 2.46/1.50 ( ( ( member @ A @ Y3 @ S3 )
% 2.46/1.50 & ( Y3 != X ) )
% 2.46/1.50 => ( ( R @ X @ Y3 )
% 2.46/1.50 & ( R @ Y3 @ X ) ) )
% 2.46/1.50 & ( pairwise @ A @ R @ S3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_160_sup__bot_Oright__neutral,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 2.46/1.50 = A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_161_sup__bot_Oleft__neutral,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 2.46/1.50 = A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_162_sup__eq__bot__iff,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A,Y: A] :
% 2.46/1.50 ( ( ( sup_sup @ A @ X @ Y )
% 2.46/1.50 = ( bot_bot @ A ) )
% 2.46/1.50 = ( ( X
% 2.46/1.50 = ( bot_bot @ A ) )
% 2.46/1.50 & ( Y
% 2.46/1.50 = ( bot_bot @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_163_bot__eq__sup__iff,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A,Y: A] :
% 2.46/1.50 ( ( ( bot_bot @ A )
% 2.46/1.50 = ( sup_sup @ A @ X @ Y ) )
% 2.46/1.50 = ( ( X
% 2.46/1.50 = ( bot_bot @ A ) )
% 2.46/1.50 & ( Y
% 2.46/1.50 = ( bot_bot @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_164_sup__bot__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A] :
% 2.46/1.50 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 2.46/1.50 = X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_165_sup__bot__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A] :
% 2.46/1.50 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 2.46/1.50 = X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_166_ID_Opred__set,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( A > $o ) )
% 2.46/1.50 = ( ^ [P3: A > $o,X7: A] :
% 2.46/1.50 ! [Y3: A] :
% 2.46/1.50 ( ( member @ A @ Y3 @ ( insert @ A @ X7 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( P3 @ Y3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_167_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_168_bot__nat__def,axiom,
% 2.46/1.50 ( ( bot_bot @ nat )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_169_id__bnf__apply,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bNF_id_bnf @ A )
% 2.46/1.50 = ( ^ [X7: A] : X7 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_170_BNF__Composition_Oid__bnf__def,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bNF_id_bnf @ A )
% 2.46/1.50 = ( ^ [X7: A] : X7 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_171_ID_Opred__map,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X: A] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( B > $o ) @ Q @ ( bNF_id_bnf @ ( A > B ) @ F @ X ) )
% 2.46/1.50 = ( bNF_id_bnf @ ( A > $o ) @ ( comp @ B @ $o @ A @ Q @ F ) @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_172_ID_Opred__mono__strong,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o,X: A,Pa: A > $o] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( A > $o ) @ P @ X )
% 2.46/1.50 => ( ! [Z6: A] :
% 2.46/1.50 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( ( P @ Z6 )
% 2.46/1.50 => ( Pa @ Z6 ) ) )
% 2.46/1.50 => ( bNF_id_bnf @ ( A > $o ) @ Pa @ X ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_173_ID_Opred__cong,axiom,
% 2.46/1.50 ! [A: $tType,X: A,Ya: A,P: A > $o,Pa: A > $o] :
% 2.46/1.50 ( ( X = Ya )
% 2.46/1.50 => ( ! [Z6: A] :
% 2.46/1.50 ( ( member @ A @ Z6 @ ( insert @ A @ Ya @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( ( P @ Z6 )
% 2.46/1.50 = ( Pa @ Z6 ) ) )
% 2.46/1.50 => ( ( bNF_id_bnf @ ( A > $o ) @ P @ X )
% 2.46/1.50 = ( bNF_id_bnf @ ( A > $o ) @ Pa @ Ya ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_174_sup__bot_Omonoid__axioms,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ( monoid @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_175_ID_Orel__eq__onp,axiom,
% 2.46/1.50 ! [A: $tType,P: A > $o] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P ) )
% 2.46/1.50 = ( bNF_eq_onp @ A @ ( bNF_id_bnf @ ( A > $o ) @ P ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_176_ID_Opred__rel,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( A > $o ) )
% 2.46/1.50 = ( ^ [P3: A > $o,X7: A] : ( bNF_id_bnf @ ( A > A > $o ) @ ( bNF_eq_onp @ A @ P3 ) @ X7 @ X7 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_177_ID_Orel__refl,axiom,
% 2.46/1.50 ! [A: $tType,Ra: A > A > $o,X: A] :
% 2.46/1.50 ( ! [X6: A] : ( Ra @ X6 @ X6 )
% 2.46/1.50 => ( bNF_id_bnf @ ( A > A > $o ) @ Ra @ X @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_178_ID_Orel__cong,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,X: A,Ya: A,Y: B,Xa: B,R3: A > B > $o,Ra: A > B > $o] :
% 2.46/1.50 ( ( X = Ya )
% 2.46/1.50 => ( ( Y = Xa )
% 2.46/1.50 => ( ! [Z6: A,Yb: B] :
% 2.46/1.50 ( ( member @ A @ Z6 @ ( insert @ A @ Ya @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( ( member @ B @ Yb @ ( insert @ B @ Xa @ ( bot_bot @ ( set @ B ) ) ) )
% 2.46/1.50 => ( ( R3 @ Z6 @ Yb )
% 2.46/1.50 = ( Ra @ Z6 @ Yb ) ) ) )
% 2.46/1.50 => ( ( bNF_id_bnf @ ( A > B > $o ) @ R3 @ X @ Y )
% 2.46/1.50 = ( bNF_id_bnf @ ( A > B > $o ) @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_179_ID_Orel__mono__strong,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,R3: A > B > $o,X: A,Y: B,Ra: A > B > $o] :
% 2.46/1.50 ( ( bNF_id_bnf @ ( A > B > $o ) @ R3 @ X @ Y )
% 2.46/1.50 => ( ! [Z6: A,Yb: B] :
% 2.46/1.50 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( ( member @ B @ Yb @ ( insert @ B @ Y @ ( bot_bot @ ( set @ B ) ) ) )
% 2.46/1.50 => ( ( R3 @ Z6 @ Yb )
% 2.46/1.50 => ( Ra @ Z6 @ Yb ) ) ) )
% 2.46/1.50 => ( bNF_id_bnf @ ( A > B > $o ) @ Ra @ X @ Y ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_180_ID_Orel__refl__strong,axiom,
% 2.46/1.50 ! [A: $tType,X: A,Ra: A > A > $o] :
% 2.46/1.50 ( ! [Z6: A] :
% 2.46/1.50 ( ( member @ A @ Z6 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 => ( Ra @ Z6 @ Z6 ) )
% 2.46/1.50 => ( bNF_id_bnf @ ( A > A > $o ) @ Ra @ X @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_181_sup__bot_Ocomm__monoid__axioms,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ( comm_monoid @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_182_vimage__insert,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,F: A > B,A2: B,B3: set @ B] :
% 2.46/1.50 ( ( vimage @ A @ B @ F @ ( insert @ B @ A2 @ B3 ) )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ ( insert @ B @ A2 @ ( bot_bot @ ( set @ B ) ) ) ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_183_notIn__Un__bij__betw3,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,B2: A,A6: set @ A,F: A > B,A9: set @ B] :
% 2.46/1.50 ( ~ ( member @ A @ B2 @ A6 )
% 2.46/1.50 => ( ~ ( member @ B @ ( F @ B2 ) @ A9 )
% 2.46/1.50 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 2.46/1.50 = ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( sup_sup @ ( set @ B ) @ A9 @ ( insert @ B @ ( F @ B2 ) @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_184_vimage__eq,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 2.46/1.50 = ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_185_vimageI,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: B > A,A2: B,B2: A,B3: set @ A] :
% 2.46/1.50 ( ( ( F @ A2 )
% 2.46/1.50 = B2 )
% 2.46/1.50 => ( ( member @ A @ B2 @ B3 )
% 2.46/1.50 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_186_vimage__empty,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: A > B] :
% 2.46/1.50 ( ( vimage @ A @ B @ F @ ( bot_bot @ ( set @ B ) ) )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_187_vimage__Un,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,F: A > B,A6: set @ B,B3: set @ B] :
% 2.46/1.50 ( ( vimage @ A @ B @ F @ ( sup_sup @ ( set @ B ) @ A6 @ B3 ) )
% 2.46/1.50 = ( sup_sup @ ( set @ A ) @ ( vimage @ A @ B @ F @ A6 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_188_vimage__Collect,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,P: B > $o,F: A > B,Q: A > $o] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( P @ ( F @ X6 ) )
% 2.46/1.50 = ( Q @ X6 ) )
% 2.46/1.50 => ( ( vimage @ A @ B @ F @ ( collect @ B @ P ) )
% 2.46/1.50 = ( collect @ A @ Q ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_189_bij__betw__cong,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,A6: set @ A,F: A > B,G: A > B,A9: set @ B] :
% 2.46/1.50 ( ! [A10: A] :
% 2.46/1.50 ( ( member @ A @ A10 @ A6 )
% 2.46/1.50 => ( ( F @ A10 )
% 2.46/1.50 = ( G @ A10 ) ) )
% 2.46/1.50 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 2.46/1.50 = ( bij_betw @ A @ B @ G @ A6 @ A9 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_190_bij__betw__inv,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: A > B,A6: set @ A,B3: set @ B] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 2.46/1.50 => ? [G6: B > A] : ( bij_betw @ B @ A @ G6 @ B3 @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_191_vimageI2,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: B > A,A2: B,A6: set @ A] :
% 2.46/1.50 ( ( member @ A @ ( F @ A2 ) @ A6 )
% 2.46/1.50 => ( member @ B @ A2 @ ( vimage @ B @ A @ F @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_192_vimageE,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,A2: A,F: A > B,B3: set @ B] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B3 ) )
% 2.46/1.50 => ( member @ B @ ( F @ A2 ) @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_193_vimageD,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,A2: A,F: A > B,A6: set @ B] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ A6 ) )
% 2.46/1.50 => ( member @ B @ ( F @ A2 ) @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_194_set_Ocomp,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: B > A] :
% 2.46/1.50 ( ( comp @ ( set @ B ) @ ( set @ C ) @ ( set @ A ) @ ( vimage @ C @ B @ F ) @ ( vimage @ B @ A @ G ) )
% 2.46/1.50 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_195_vimage__comp,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: B > C,X: set @ C] :
% 2.46/1.50 ( ( vimage @ A @ B @ F @ ( vimage @ B @ C @ G @ X ) )
% 2.46/1.50 = ( vimage @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_196_set_Ocompositionality,axiom,
% 2.46/1.50 ! [C: $tType,B: $tType,A: $tType,F: C > B,G: B > A,Set: set @ A] :
% 2.46/1.50 ( ( vimage @ C @ B @ F @ ( vimage @ B @ A @ G @ Set ) )
% 2.46/1.50 = ( vimage @ C @ A @ ( comp @ B @ A @ C @ G @ F ) @ Set ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_197_bij__betw__trans,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,C: $tType,F: A > B,A6: set @ A,B3: set @ B,G: B > C,C4: set @ C] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 2.46/1.50 => ( ( bij_betw @ B @ C @ G @ B3 @ C4 )
% 2.46/1.50 => ( bij_betw @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ A6 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_198_bij__betw__comp__iff,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,C: $tType,F: A > B,A6: set @ A,A9: set @ B,F5: B > C,A11: set @ C] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 2.46/1.50 => ( ( bij_betw @ B @ C @ F5 @ A9 @ A11 )
% 2.46/1.50 = ( bij_betw @ A @ C @ ( comp @ B @ C @ A @ F5 @ F ) @ A6 @ A11 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_199_vimage__singleton__eq,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,A2: A,F: A > B,B2: B] :
% 2.46/1.50 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ ( insert @ B @ B2 @ ( bot_bot @ ( set @ B ) ) ) ) )
% 2.46/1.50 = ( ( F @ A2 )
% 2.46/1.50 = B2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_200_bij__betw__empty2,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,F: A > B,A6: set @ A] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ A6 @ ( bot_bot @ ( set @ B ) ) )
% 2.46/1.50 => ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_201_bij__betw__empty1,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,F: A > B,A6: set @ B] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ ( bot_bot @ ( set @ A ) ) @ A6 )
% 2.46/1.50 => ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ B ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_202_notIn__Un__bij__betw,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,B2: A,A6: set @ A,F: A > B,A9: set @ B] :
% 2.46/1.50 ( ~ ( member @ A @ B2 @ A6 )
% 2.46/1.50 => ( ~ ( member @ B @ ( F @ B2 ) @ A9 )
% 2.46/1.50 => ( ( bij_betw @ A @ B @ F @ A6 @ A9 )
% 2.46/1.50 => ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) @ ( sup_sup @ ( set @ B ) @ A9 @ ( insert @ B @ ( F @ B2 ) @ ( bot_bot @ ( set @ B ) ) ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_203_bij__betw__combine,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,F: A > B,A6: set @ A,B3: set @ B,C4: set @ A,D3: set @ B] :
% 2.46/1.50 ( ( bij_betw @ A @ B @ F @ A6 @ B3 )
% 2.46/1.50 => ( ( bij_betw @ A @ B @ F @ C4 @ D3 )
% 2.46/1.50 => ( ( ( inf_inf @ ( set @ B ) @ B3 @ D3 )
% 2.46/1.50 = ( bot_bot @ ( set @ B ) ) )
% 2.46/1.50 => ( bij_betw @ A @ B @ F @ ( sup_sup @ ( set @ A ) @ A6 @ C4 ) @ ( sup_sup @ ( set @ B ) @ B3 @ D3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_204_infinite__imp__bij__betw2,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,A2: A] :
% 2.46/1.50 ( ~ ( finite_finite @ A @ A6 )
% 2.46/1.50 => ? [H3: A > A] : ( bij_betw @ A @ A @ H3 @ A6 @ ( sup_sup @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_205_singleton__insert__inj__eq_H,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B2: A] :
% 2.46/1.50 ( ( ( insert @ A @ A2 @ A6 )
% 2.46/1.50 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.46/1.50 = ( ( A2 = B2 )
% 2.46/1.50 & ( ord_less_eq @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_206_order__refl,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( preorder @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_207_subsetI,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ A6 )
% 2.46/1.50 => ( member @ A @ X6 @ B3 ) )
% 2.46/1.50 => ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_208_subset__antisym,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ A6 )
% 2.46/1.50 => ( A6 = B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_209_IntI,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ( ( member @ A @ C2 @ B3 )
% 2.46/1.50 => ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_210_Int__iff,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 = ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 & ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_211_inf__bot__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A] :
% 2.46/1.50 ( ( inf_inf @ A @ ( bot_bot @ A ) @ X )
% 2.46/1.50 = ( bot_bot @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_212_inf__bot__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [X: A] :
% 2.46/1.50 ( ( inf_inf @ A @ X @ ( bot_bot @ A ) )
% 2.46/1.50 = ( bot_bot @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_213_subset__empty,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( A6
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_214_empty__subsetI,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_215_insert__subset,axiom,
% 2.46/1.50 ! [A: $tType,X: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A6 ) @ B3 )
% 2.46/1.50 = ( ( member @ A @ X @ B3 )
% 2.46/1.50 & ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_216_Int__subset__iff,axiom,
% 2.46/1.50 ! [A: $tType,C4: set @ A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 = ( ( ord_less_eq @ ( set @ A ) @ C4 @ A6 )
% 2.46/1.50 & ( ord_less_eq @ ( set @ A ) @ C4 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_217_Int__insert__right__if1,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_218_Int__insert__right__if0,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ~ ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_219_insert__inter__insert,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_220_Int__insert__left__if1,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ A2 @ C4 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 2.46/1.50 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_221_Int__insert__left__if0,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 2.46/1.50 ( ~ ( member @ A @ A2 @ C4 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_222_Un__subset__iff,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 2.46/1.50 = ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 2.46/1.50 & ( ord_less_eq @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_223_vimage__Int,axiom,
% 2.46/1.50 ! [A: $tType,B: $tType,F: A > B,A6: set @ B,B3: set @ B] :
% 2.46/1.50 ( ( vimage @ A @ B @ F @ ( inf_inf @ ( set @ B ) @ A6 @ B3 ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ A6 ) @ ( vimage @ A @ B @ F @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_224_singleton__insert__inj__eq,axiom,
% 2.46/1.50 ! [A: $tType,B2: A,A2: A,A6: set @ A] :
% 2.46/1.50 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( insert @ A @ A2 @ A6 ) )
% 2.46/1.50 = ( ( A2 = B2 )
% 2.46/1.50 & ( ord_less_eq @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_225_disjoint__insert_I2_J,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B2: A,B3: set @ A] :
% 2.46/1.50 ( ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ B2 @ B3 ) ) )
% 2.46/1.50 = ( ~ ( member @ A @ B2 @ A6 )
% 2.46/1.50 & ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_226_disjoint__insert_I1_J,axiom,
% 2.46/1.50 ! [A: $tType,B3: set @ A,A2: A,A6: set @ A] :
% 2.46/1.50 ( ( ( inf_inf @ ( set @ A ) @ B3 @ ( insert @ A @ A2 @ A6 ) )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( ~ ( member @ A @ A2 @ B3 )
% 2.46/1.50 & ( ( inf_inf @ ( set @ A ) @ B3 @ A6 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_227_insert__disjoint_I2_J,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ B3 ) )
% 2.46/1.50 = ( ~ ( member @ A @ A2 @ B3 )
% 2.46/1.50 & ( ( bot_bot @ ( set @ A ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_228_insert__disjoint_I1_J,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ A6 ) @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( ~ ( member @ A @ A2 @ B3 )
% 2.46/1.50 & ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_229_vimage__inter__cong,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,S: set @ A,F: A > B,G: A > B,Y: set @ B] :
% 2.46/1.50 ( ! [W: A] :
% 2.46/1.50 ( ( member @ A @ W @ S )
% 2.46/1.50 => ( ( F @ W )
% 2.46/1.50 = ( G @ W ) ) )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ F @ Y ) @ S )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ ( vimage @ A @ B @ G @ Y ) @ S ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_230_vimage__mono,axiom,
% 2.46/1.50 ! [B: $tType,A: $tType,A6: set @ A,B3: set @ A,F: B > A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ord_less_eq @ ( set @ B ) @ ( vimage @ B @ A @ F @ A6 ) @ ( vimage @ B @ A @ F @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_231_Int__emptyI,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ! [X6: A] :
% 2.46/1.50 ( ( member @ A @ X6 @ A6 )
% 2.46/1.50 => ~ ( member @ A @ X6 @ B3 ) )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_232_Int__empty__left,axiom,
% 2.46/1.50 ! [A: $tType,B3: set @ A] :
% 2.46/1.50 ( ( inf_inf @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_233_Int__empty__right,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( inf_inf @ ( set @ A ) @ A6 @ ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_234_disjoint__iff__not__equal,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( inf_inf @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 = ( bot_bot @ ( set @ A ) ) )
% 2.46/1.50 = ( ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ A6 )
% 2.46/1.50 => ! [Y3: A] :
% 2.46/1.50 ( ( member @ A @ Y3 @ B3 )
% 2.46/1.50 => ( X7 != Y3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_235_bot_Oextremum,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_236_bot_Oextremum__unique,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.46/1.50 = ( A2
% 2.46/1.50 = ( bot_bot @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_237_bot_Oextremum__uniqueI,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 2.46/1.50 => ( A2
% 2.46/1.50 = ( bot_bot @ A ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_238_Int__insert__right,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) )
% 2.46/1.50 & ( ~ ( member @ A @ A2 @ A6 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ A6 @ ( insert @ A @ A2 @ B3 ) )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ B3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_239_Int__insert__left,axiom,
% 2.46/1.50 ! [A: $tType,A2: A,C4: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( ( member @ A @ A2 @ C4 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 2.46/1.50 = ( insert @ A @ A2 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) )
% 2.46/1.50 & ( ~ ( member @ A @ A2 @ C4 )
% 2.46/1.50 => ( ( inf_inf @ ( set @ A ) @ ( insert @ A @ A2 @ B3 ) @ C4 )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_240_IntE,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 => ~ ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ~ ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_241_IntD1,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 => ( member @ A @ C2 @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_242_IntD2,axiom,
% 2.46/1.50 ! [A: $tType,C2: A,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( member @ A @ C2 @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) )
% 2.46/1.50 => ( member @ A @ C2 @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_243_set__mp,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ( member @ A @ X @ A6 )
% 2.46/1.50 => ( member @ A @ X @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_244_in__mono,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,X: A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ( member @ A @ X @ A6 )
% 2.46/1.50 => ( member @ A @ X @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_245_subsetD,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C2: A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_246_Int__mono,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,C4: set @ A,B3: set @ A,D3: set @ A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ C4 )
% 2.46/1.50 => ( ( ord_less_eq @ ( set @ A ) @ B3 @ D3 )
% 2.46/1.50 => ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ ( inf_inf @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_247_subsetCE,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C2: A] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ( ( member @ A @ C2 @ A6 )
% 2.46/1.50 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_248_Int__assoc,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A,C4: set @ A] :
% 2.46/1.50 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ C4 )
% 2.46/1.50 = ( inf_inf @ ( set @ A ) @ A6 @ ( inf_inf @ ( set @ A ) @ B3 @ C4 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_249_equalityE,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( A6 = B3 )
% 2.46/1.50 => ~ ( ( ord_less_eq @ ( set @ A ) @ A6 @ B3 )
% 2.46/1.50 => ~ ( ord_less_eq @ ( set @ A ) @ B3 @ A6 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_250_subset__eq,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( ord_less_eq @ ( set @ A ) )
% 2.46/1.50 = ( ^ [A7: set @ A,B5: set @ A] :
% 2.46/1.50 ! [X7: A] :
% 2.46/1.50 ( ( member @ A @ X7 @ A7 )
% 2.46/1.50 => ( member @ A @ X7 @ B5 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_251_Int__absorb,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A] :
% 2.46/1.50 ( ( inf_inf @ ( set @ A ) @ A6 @ A6 )
% 2.46/1.50 = A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_252_Int__lower1,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ A6 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_253_Int__lower2,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A6 @ B3 ) @ B3 ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_254_equalityD1,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( A6 = B3 )
% 2.46/1.50 => ( ord_less_eq @ ( set @ A ) @ A6 @ B3 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_255_equalityD2,axiom,
% 2.46/1.50 ! [A: $tType,A6: set @ A,B3: set @ A] :
% 2.46/1.50 ( ( A6 = B3 )
% 2.46/1.50 => ( ord_less_eq @ ( set @ A ) @ B3 @ A6 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.46/1.50 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.46/1.50 ! [A12: $tType] : ( bounded_lattice @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( bounded_lattice @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( bounde1808546759up_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( bounded_lattice @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( bounded_lattice_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( order_bot @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( order_bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( preorder @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( preorder @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_fun___Orderings_Obot,axiom,
% 2.46/1.50 ! [A12: $tType,A13: $tType] :
% 2.46/1.50 ( ( bot @ A13 @ ( type2 @ A13 ) )
% 2.46/1.50 => ( bot @ ( A12 > A13 ) @ ( type2 @ ( A12 > A13 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3,axiom,
% 2.46/1.50 order_bot @ nat @ ( type2 @ nat ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 2.46/1.50 preorder @ nat @ ( type2 @ nat ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 2.46/1.50 bot @ nat @ ( type2 @ nat ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_6,axiom,
% 2.46/1.50 ! [A12: $tType] : ( bounde1808546759up_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_7,axiom,
% 2.46/1.50 ! [A12: $tType] : ( bounded_lattice_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Orderings_Oorder__bot_8,axiom,
% 2.46/1.50 ! [A12: $tType] : ( order_bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 2.46/1.50 ! [A12: $tType] : ( preorder @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_Set_Oset___Orderings_Obot_10,axiom,
% 2.46/1.50 ! [A12: $tType] : ( bot @ ( set @ A12 ) @ ( type2 @ ( set @ A12 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_11,axiom,
% 2.46/1.50 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_12,axiom,
% 2.46/1.50 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Orderings_Oorder__bot_13,axiom,
% 2.46/1.50 order_bot @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_14,axiom,
% 2.46/1.50 preorder @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(tcon_HOL_Obool___Orderings_Obot_15,axiom,
% 2.46/1.50 bot @ $o @ ( type2 @ $o ) ).
% 2.46/1.50
% 2.46/1.50 thf(help_If_3_1_T,axiom,
% 2.46/1.50 ! [P: $o] :
% 2.46/1.50 ( ( P = $true )
% 2.46/1.50 | ( P = $false ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(help_If_2_1_T,axiom,
% 2.46/1.50 ! [A: $tType,X: A,Y: A] :
% 2.46/1.50 ( ( if @ A @ $false @ X @ Y )
% 2.46/1.50 = Y ) ).
% 2.46/1.50
% 2.46/1.50 thf(help_If_1_1_T,axiom,
% 2.46/1.50 ! [A: $tType,X: A,Y: A] :
% 2.46/1.50 ( ( if @ A @ $true @ X @ Y )
% 2.46/1.50 = X ) ).
% 2.46/1.50
% 2.46/1.50 thf(conj_0,hypothesis,
% 2.46/1.50 $true ).
% 2.46/1.50
% 2.46/1.50 thf(conj_1,hypothesis,
% 2.46/1.50 ! [L3: rBT_Im246033960le_rbt @ a @ b,K2: a,V2: b,R5: rBT_Im246033960le_rbt @ a @ b] :
% 2.46/1.50 ( ( t
% 2.46/1.50 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ L3 @ K2 @ V2 @ R5 ) )
% 2.46/1.50 => thesis ) ).
% 2.46/1.50
% 2.46/1.50 thf(conj_2,hypothesis,
% 2.46/1.50 ! [L3: rBT_Im246033960le_rbt @ a @ b,K2: a,V2: b,R5: rBT_Im246033960le_rbt @ a @ b] :
% 2.46/1.50 ( ( t
% 2.46/1.50 = ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ L3 @ K2 @ V2 @ R5 ) )
% 2.46/1.50 => thesis ) ).
% 2.46/1.50
% 2.46/1.50 thf(conj_3,conjecture,
% 2.46/1.50 thesis ).
% 2.46/1.50 ------------------------
% 2.46/1.52 % (7365)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/18Mi)
% 2.46/1.52 % (7361)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_7073 for (2999ds/27Mi)
% 2.46/1.52 % (7364)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_7073 for (2999ds/275Mi)
% 2.46/1.53 % (7365)Instruction limit reached!
% 2.46/1.53 % (7365)------------------------------
% 2.46/1.53 % (7365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (7365)Termination reason: Unknown
% 2.46/1.53 % (7365)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (7365)Memory used [KB]: 1791
% 2.46/1.53 % (7365)Time elapsed: 0.008 s
% 2.46/1.53 % (7365)Instructions burned: 20 (million)
% 2.46/1.53 % (7365)------------------------------
% 2.46/1.53 % (7365)------------------------------
% 2.46/1.53 % (7359)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/183Mi)
% 2.46/1.53 % (7362)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/2Mi)
% 2.46/1.53 % (7360)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_7073 for (2999ds/4Mi)
% 2.46/1.53 % (7363)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_7073 for (2999ds/2Mi)
% 2.46/1.53 % (7361)Instruction limit reached!
% 2.46/1.53 % (7361)------------------------------
% 2.46/1.53 % (7361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (7361)Termination reason: Unknown
% 2.46/1.53 % (7361)Termination phase: Property scanning
% 2.46/1.53
% 2.46/1.53 % (7361)Memory used [KB]: 1918
% 2.46/1.53 % (7361)Time elapsed: 0.011 s
% 2.46/1.53 % (7361)Instructions burned: 30 (million)
% 2.46/1.53 % (7361)------------------------------
% 2.46/1.53 % (7361)------------------------------
% 2.46/1.53 % (7362)Instruction limit reached!
% 2.46/1.53 % (7362)------------------------------
% 2.46/1.53 % (7362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (7362)Termination reason: Unknown
% 2.46/1.53 % (7362)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (7362)Memory used [KB]: 1407
% 2.46/1.53 % (7362)Time elapsed: 0.004 s
% 2.46/1.53 % (7362)Instructions burned: 3 (million)
% 2.46/1.53 % (7362)------------------------------
% 2.46/1.53 % (7362)------------------------------
% 2.46/1.53 % (7363)Instruction limit reached!
% 2.46/1.53 % (7363)------------------------------
% 2.46/1.53 % (7363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (7363)Termination reason: Unknown
% 2.46/1.53 % (7363)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (7363)Memory used [KB]: 1407
% 2.46/1.53 % (7363)Time elapsed: 0.004 s
% 2.46/1.53 % (7363)Instructions burned: 3 (million)
% 2.46/1.53 % (7363)------------------------------
% 2.46/1.53 % (7363)------------------------------
% 2.46/1.53 % (7360)Instruction limit reached!
% 2.46/1.53 % (7360)------------------------------
% 2.46/1.53 % (7360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.53 % (7360)Termination reason: Unknown
% 2.46/1.53 % (7360)Termination phase: shuffling
% 2.46/1.53
% 2.46/1.53 % (7360)Memory used [KB]: 1407
% 2.46/1.53 % (7360)Time elapsed: 0.004 s
% 2.46/1.53 % (7360)Instructions burned: 4 (million)
% 2.46/1.53 % (7360)------------------------------
% 2.46/1.53 % (7360)------------------------------
% 2.46/1.54 % (7364)Refutation not found, incomplete strategy
% 2.46/1.54 % (7364)------------------------------
% 2.46/1.54 % (7364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.54 % (7364)Termination reason: Refutation not found, incomplete strategy
% 2.46/1.54
% 2.46/1.54
% 2.46/1.54 % (7364)Memory used [KB]: 6524
% 2.46/1.54 % (7364)Time elapsed: 0.016 s
% 2.46/1.54 % (7364)Instructions burned: 45 (million)
% 2.46/1.54 % (7364)------------------------------
% 2.46/1.54 % (7364)------------------------------
% 2.46/1.54 % (7371)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/3Mi)
% 2.46/1.54 % (7371)Instruction limit reached!
% 2.46/1.54 % (7371)------------------------------
% 2.46/1.54 % (7371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.54 % (7371)Termination reason: Unknown
% 2.46/1.54 % (7371)Termination phase: shuffling
% 2.46/1.54
% 2.46/1.54 % (7371)Memory used [KB]: 1407
% 2.46/1.54 % (7371)Time elapsed: 0.002 s
% 2.46/1.54 % (7371)Instructions burned: 3 (million)
% 2.46/1.54 % (7371)------------------------------
% 2.46/1.54 % (7371)------------------------------
% 2.46/1.54 % (7373)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_7073 for (2999ds/37Mi)
% 2.46/1.55 % (7380)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/7Mi)
% 2.46/1.55 % (7381)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/16Mi)
% 2.46/1.55 % (7375)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_7073 for (2999ds/15Mi)
% 2.46/1.55 % (7376)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_7073 for (2999ds/3Mi)
% 2.46/1.55 % (7380)Instruction limit reached!
% 2.46/1.55 % (7380)------------------------------
% 2.46/1.55 % (7380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.55 % (7380)Termination reason: Unknown
% 2.46/1.55 % (7380)Termination phase: shuffling
% 2.46/1.55
% 2.46/1.55 % (7380)Memory used [KB]: 1663
% 2.46/1.55 % (7380)Time elapsed: 0.004 s
% 2.46/1.55 % (7380)Instructions burned: 9 (million)
% 2.46/1.55 % (7380)------------------------------
% 2.46/1.55 % (7380)------------------------------
% 2.46/1.55 % (7377)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_7073 for (2999ds/1041Mi)
% 2.46/1.55 % (7376)Instruction limit reached!
% 2.46/1.55 % (7376)------------------------------
% 2.46/1.55 % (7376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.55 % (7376)Termination reason: Unknown
% 2.46/1.55 % (7376)Termination phase: shuffling
% 2.46/1.55
% 2.46/1.55 % (7376)Memory used [KB]: 1407
% 2.46/1.55 % (7376)Time elapsed: 0.004 s
% 2.46/1.55 % (7376)Instructions burned: 3 (million)
% 2.46/1.55 % (7376)------------------------------
% 2.46/1.55 % (7376)------------------------------
% 2.46/1.55 % (7373)Instruction limit reached!
% 2.46/1.55 % (7373)------------------------------
% 2.46/1.55 % (7373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.55 % (7373)Termination reason: Unknown
% 2.46/1.55 % (7373)Termination phase: shuffling
% 2.46/1.55
% 2.46/1.55 % (7373)Memory used [KB]: 2174
% 2.46/1.55 % (7373)Time elapsed: 0.012 s
% 2.46/1.55 % (7373)Instructions burned: 39 (million)
% 2.46/1.55 % (7373)------------------------------
% 2.46/1.55 % (7373)------------------------------
% 2.46/1.56 % (7381)Instruction limit reached!
% 2.46/1.56 % (7381)------------------------------
% 2.46/1.56 % (7381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (7381)Termination reason: Unknown
% 2.46/1.56 % (7381)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (7381)Memory used [KB]: 1791
% 2.46/1.56 % (7381)Time elapsed: 0.007 s
% 2.46/1.56 % (7381)Instructions burned: 18 (million)
% 2.46/1.56 % (7381)------------------------------
% 2.46/1.56 % (7381)------------------------------
% 2.46/1.56 % (7387)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_7073 for (2999ds/3Mi)
% 2.46/1.56 % (7387)Instruction limit reached!
% 2.46/1.56 % (7387)------------------------------
% 2.46/1.56 % (7387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (7387)Termination reason: Unknown
% 2.46/1.56 % (7387)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (7387)Memory used [KB]: 1407
% 2.46/1.56 % (7387)Time elapsed: 0.002 s
% 2.46/1.56 % (7387)Instructions burned: 3 (million)
% 2.46/1.56 % (7387)------------------------------
% 2.46/1.56 % (7387)------------------------------
% 2.46/1.56 % (7375)Instruction limit reached!
% 2.46/1.56 % (7375)------------------------------
% 2.46/1.56 % (7375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (7375)Termination reason: Unknown
% 2.46/1.56 % (7375)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (7375)Memory used [KB]: 1791
% 2.46/1.56 % (7375)Time elapsed: 0.013 s
% 2.46/1.56 % (7375)Instructions burned: 15 (million)
% 2.46/1.56 % (7375)------------------------------
% 2.46/1.56 % (7375)------------------------------
% 2.46/1.56 % (7390)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/7Mi)
% 2.46/1.56 % (7391)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/3Mi)
% 2.46/1.56 % (7390)Instruction limit reached!
% 2.46/1.56 % (7390)------------------------------
% 2.46/1.56 % (7390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.56 % (7390)Termination reason: Unknown
% 2.46/1.56 % (7390)Termination phase: shuffling
% 2.46/1.56
% 2.46/1.56 % (7390)Memory used [KB]: 1663
% 2.46/1.56 % (7390)Time elapsed: 0.004 s
% 2.46/1.56 % (7390)Instructions burned: 9 (million)
% 2.46/1.56 % (7390)------------------------------
% 2.46/1.56 % (7390)------------------------------
% 2.46/1.57 % (7391)Instruction limit reached!
% 2.46/1.57 % (7391)------------------------------
% 2.46/1.57 % (7391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (7391)Termination reason: Unknown
% 2.46/1.57 % (7391)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (7391)Memory used [KB]: 1407
% 2.46/1.57 % (7391)Time elapsed: 0.002 s
% 2.46/1.57 % (7391)Instructions burned: 3 (million)
% 2.46/1.57 % (7391)------------------------------
% 2.46/1.57 % (7391)------------------------------
% 2.46/1.57 % (7389)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_7073 for (2999ds/3Mi)
% 2.46/1.57 % (7392)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/4Mi)
% 2.46/1.57 % (7393)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/18Mi)
% 2.46/1.57 % (7389)Instruction limit reached!
% 2.46/1.57 % (7389)------------------------------
% 2.46/1.57 % (7389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (7389)Termination reason: Unknown
% 2.46/1.57 % (7389)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (7389)Memory used [KB]: 1407
% 2.46/1.57 % (7389)Time elapsed: 0.004 s
% 2.46/1.57 % (7389)Instructions burned: 3 (million)
% 2.46/1.57 % (7389)------------------------------
% 2.46/1.57 % (7389)------------------------------
% 2.46/1.57 % (7392)Instruction limit reached!
% 2.46/1.57 % (7392)------------------------------
% 2.46/1.57 % (7392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.57 % (7392)Termination reason: Unknown
% 2.46/1.57 % (7392)Termination phase: shuffling
% 2.46/1.57
% 2.46/1.57 % (7392)Memory used [KB]: 1407
% 2.46/1.57 % (7392)Time elapsed: 0.003 s
% 2.46/1.57 % (7392)Instructions burned: 5 (million)
% 2.46/1.57 % (7392)------------------------------
% 2.46/1.57 % (7392)------------------------------
% 2.46/1.57 % (7396)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/710Mi)
% 2.46/1.57 % (7397)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/6Mi)
% 2.46/1.58 % (7393)Instruction limit reached!
% 2.46/1.58 % (7393)------------------------------
% 2.46/1.58 % (7393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.58 % (7393)Termination reason: Unknown
% 2.46/1.58 % (7393)Termination phase: shuffling
% 2.46/1.58
% 2.46/1.58 % (7393)Memory used [KB]: 1791
% 2.46/1.58 % (7393)Time elapsed: 0.007 s
% 2.46/1.58 % (7393)Instructions burned: 18 (million)
% 2.46/1.58 % (7393)------------------------------
% 2.46/1.58 % (7393)------------------------------
% 2.46/1.58 % (7397)Instruction limit reached!
% 2.46/1.58 % (7397)------------------------------
% 2.46/1.58 % (7397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.58 % (7397)Termination reason: Unknown
% 2.46/1.58 % (7397)Termination phase: shuffling
% 2.46/1.58
% 2.46/1.58 % (7397)Memory used [KB]: 1535
% 2.46/1.58 % (7397)Time elapsed: 0.003 s
% 2.46/1.58 % (7397)Instructions burned: 6 (million)
% 2.46/1.58 % (7397)------------------------------
% 2.46/1.58 % (7397)------------------------------
% 2.46/1.58 % (7401)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_7073 for (2999ds/21Mi)
% 2.46/1.59 % (7404)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/5Mi)
% 2.46/1.59 % (7405)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_7073 for (2999ds/6Mi)
% 2.46/1.59 % (7404)Instruction limit reached!
% 2.46/1.59 % (7404)------------------------------
% 2.46/1.59 % (7404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (7404)Termination reason: Unknown
% 2.46/1.59 % (7404)Termination phase: shuffling
% 2.46/1.59
% 2.46/1.59 % (7404)Memory used [KB]: 1535
% 2.46/1.59 % (7404)Time elapsed: 0.003 s
% 2.46/1.59 % (7404)Instructions burned: 7 (million)
% 2.46/1.59 % (7404)------------------------------
% 2.46/1.59 % (7404)------------------------------
% 2.46/1.59 % (7405)Instruction limit reached!
% 2.46/1.59 % (7405)------------------------------
% 2.46/1.59 % (7405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (7405)Termination reason: Unknown
% 2.46/1.59 % (7405)Termination phase: shuffling
% 2.46/1.59
% 2.46/1.59 % (7405)Memory used [KB]: 1535
% 2.46/1.59 % (7405)Time elapsed: 0.003 s
% 2.46/1.59 % (7405)Instructions burned: 7 (million)
% 2.46/1.59 % (7405)------------------------------
% 2.46/1.59 % (7405)------------------------------
% 2.46/1.59 % (7401)Instruction limit reached!
% 2.46/1.59 % (7401)------------------------------
% 2.46/1.59 % (7401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.46/1.59 % (7401)Termination reason: Unknown
% 2.46/1.59 % (7401)Termination phase: shuffling
% 2.46/1.59
% 2.46/1.59 % (7401)Memory used [KB]: 1791
% 2.46/1.59 % (7401)Time elapsed: 0.008 s
% 2.46/1.59 % (7401)Instructions burned: 21 (million)
% 2.46/1.59 % (7401)------------------------------
% 2.46/1.59 % (7401)------------------------------
% 2.46/1.59 % (7400)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_7073 for (2999ds/902Mi)
% 2.50/1.60 % (7415)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_7073 for (2999ds/779Mi)
% 2.50/1.60 % (7417)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_7073 for (2999ds/19Mi)
% 2.50/1.60 % (7417)Instruction limit reached!
% 2.50/1.60 % (7417)------------------------------
% 2.50/1.60 % (7417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.60 % (7417)Termination reason: Unknown
% 2.50/1.60 % (7417)Termination phase: shuffling
% 2.50/1.60
% 2.50/1.60 % (7417)Memory used [KB]: 1791
% 2.50/1.60 % (7417)Time elapsed: 0.007 s
% 2.50/1.60 % (7417)Instructions burned: 19 (million)
% 2.50/1.60 % (7417)------------------------------
% 2.50/1.60 % (7417)------------------------------
% 2.50/1.61 % (7359)Instruction limit reached!
% 2.50/1.61 % (7359)------------------------------
% 2.50/1.61 % (7359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.61 % (7359)Termination reason: Unknown
% 2.50/1.61 % (7359)Termination phase: Saturation
% 2.50/1.61
% 2.50/1.61 % (7359)Memory used [KB]: 7419
% 2.50/1.61 % (7359)Time elapsed: 0.077 s
% 2.50/1.61 % (7359)Instructions burned: 183 (million)
% 2.50/1.61 % (7359)------------------------------
% 2.50/1.61 % (7359)------------------------------
% 2.50/1.61 % (7414)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/377Mi)
% 2.50/1.61 % (7428)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/879Mi)
% 2.50/1.62 % (7430)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7073 for (2999ds/17Mi)
% 2.50/1.62 % (7430)Instruction limit reached!
% 2.50/1.62 % (7430)------------------------------
% 2.50/1.62 % (7430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.62 % (7430)Termination reason: Unknown
% 2.50/1.62 % (7430)Termination phase: shuffling
% 2.50/1.62
% 2.50/1.62 % (7430)Memory used [KB]: 1791
% 2.50/1.62 % (7430)Time elapsed: 0.007 s
% 2.50/1.62 % (7430)Instructions burned: 17 (million)
% 2.50/1.62 % (7430)------------------------------
% 2.50/1.62 % (7430)------------------------------
% 2.50/1.63 % (7442)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7073 for (2998ds/3Mi)
% 2.50/1.63 % (7442)Instruction limit reached!
% 2.50/1.63 % (7442)------------------------------
% 2.50/1.63 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.63 % (7442)Termination reason: Unknown
% 2.50/1.63 % (7442)Termination phase: shuffling
% 2.50/1.63
% 2.50/1.63 % (7442)Memory used [KB]: 1407
% 2.50/1.63 % (7442)Time elapsed: 0.002 s
% 2.50/1.63 % (7442)Instructions burned: 3 (million)
% 2.50/1.63 % (7442)------------------------------
% 2.50/1.63 % (7442)------------------------------
% 2.50/1.64 % (7445)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7073 for (2998ds/30Mi)
% 2.50/1.65 % (7445)Instruction limit reached!
% 2.50/1.65 % (7445)------------------------------
% 2.50/1.65 % (7445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.65 % (7445)Termination reason: Unknown
% 2.50/1.65 % (7445)Termination phase: shuffling
% 2.50/1.65
% 2.50/1.65 % (7445)Memory used [KB]: 2046
% 2.50/1.65 % (7445)Time elapsed: 0.013 s
% 2.50/1.65 % (7445)Instructions burned: 31 (million)
% 2.50/1.65 % (7445)------------------------------
% 2.50/1.65 % (7445)------------------------------
% 2.50/1.66 % (7451)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7073 for (2998ds/127Mi)
% 2.50/1.71 % (7451)Instruction limit reached!
% 2.50/1.71 % (7451)------------------------------
% 2.50/1.71 % (7451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.71 % (7451)Termination reason: Unknown
% 2.50/1.71 % (7451)Termination phase: Saturation
% 2.50/1.71
% 2.50/1.71 % (7451)Memory used [KB]: 7164
% 2.50/1.71 % (7451)Time elapsed: 0.043 s
% 2.50/1.71 % (7451)Instructions burned: 130 (million)
% 2.50/1.71 % (7451)------------------------------
% 2.50/1.71 % (7451)------------------------------
% 2.50/1.72 % (7452)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7073 for (2998ds/100Mi)
% 2.50/1.74 % (7414)Instruction limit reached!
% 2.50/1.74 % (7414)------------------------------
% 2.50/1.74 % (7414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.74 % (7414)Termination reason: Unknown
% 2.50/1.74 % (7414)Termination phase: Saturation
% 2.50/1.74
% 2.50/1.74 % (7414)Memory used [KB]: 8315
% 2.50/1.74 % (7414)Time elapsed: 0.132 s
% 2.50/1.74 % (7414)Instructions burned: 377 (million)
% 2.50/1.74 % (7414)------------------------------
% 2.50/1.74 % (7414)------------------------------
% 2.50/1.75 % (7453)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_7073 for (2997ds/3Mi)
% 2.50/1.75 % (7453)Instruction limit reached!
% 2.50/1.75 % (7453)------------------------------
% 2.50/1.75 % (7453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.75 % (7453)Termination reason: Unknown
% 2.50/1.75 % (7453)Termination phase: shuffling
% 2.50/1.75
% 2.50/1.75 % (7453)Memory used [KB]: 1407
% 2.50/1.75 % (7453)Time elapsed: 0.002 s
% 2.50/1.75 % (7453)Instructions burned: 3 (million)
% 2.50/1.75 % (7453)------------------------------
% 2.50/1.75 % (7453)------------------------------
% 2.50/1.75 % (7452)Instruction limit reached!
% 2.50/1.75 % (7452)------------------------------
% 2.50/1.75 % (7452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.75 % (7452)Termination reason: Unknown
% 2.50/1.75 % (7452)Termination phase: Preprocessing 3
% 2.50/1.75
% 2.50/1.75 % (7452)Memory used [KB]: 2814
% 2.50/1.75 % (7452)Time elapsed: 0.032 s
% 2.50/1.75 % (7452)Instructions burned: 101 (million)
% 2.50/1.75 % (7452)------------------------------
% 2.50/1.75 % (7452)------------------------------
% 2.50/1.75 % (7428)First to succeed.
% 2.50/1.75 % (7428)Refutation found. Thanks to Tanya!
% 2.50/1.75 % SZS status Theorem for DTF2THF_7073
% 2.50/1.75 % SZS output start Proof for DTF2THF_7073
% 2.50/1.75 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.50/1.75 thf(type_def_7, type, set: ($tType) > $tType).
% 2.50/1.75 thf(type_def_8, type, nat: $tType).
% 2.50/1.75 thf(type_def_9, type, rBT_Im1923302023_color: $tType).
% 2.50/1.75 thf(type_def_10, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.50/1.75 thf(type_def_11, type, a: $tType).
% 2.50/1.75 thf(type_def_12, type, b: $tType).
% 2.50/1.75 thf(func_def_0, type, rBT_Im1923302023_color: $tType).
% 2.50/1.75 thf(func_def_1, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.50/1.75 thf(func_def_2, type, set: ($tType) > $tType).
% 2.50/1.75 thf(func_def_3, type, nat: $tType).
% 2.50/1.75 thf(func_def_4, type, itself: ($tType) > $tType).
% 2.50/1.75 thf(func_def_5, type, b: $tType).
% 2.50/1.75 thf(func_def_6, type, a: $tType).
% 2.50/1.75 thf(func_def_7, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_8, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_9, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_10, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_11, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_12, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_13, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.50/1.75 thf(func_def_14, type, bNF_id_bnf: !>[X0: $tType]:(X0 > X0)).
% 2.50/1.75 thf(func_def_15, type, bNF_eq_onp: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 2.50/1.75 thf(func_def_16, type, bNF_vimage2p: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((X0 > X1) > (X2 > X3) > (X1 > X3 > X4) > X0 > X2 > X4)).
% 2.50/1.75 thf(func_def_17, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.75 thf(func_def_18, type, bij_betw: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1 > $o)).
% 2.50/1.75 thf(func_def_19, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 2.50/1.75 thf(func_def_20, type, map_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > (X1 > X2) > X0 > X3)).
% 2.50/1.75 thf(func_def_21, type, override_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > set @ X0 > X0 > X1)).
% 2.50/1.75 thf(func_def_22, type, comm_monoid: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 2.50/1.75 thf(func_def_23, type, monoid: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 2.50/1.75 thf(func_def_24, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.50/1.75 thf(func_def_25, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.50/1.75 thf(func_def_26, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.50/1.75 thf(func_def_27, type, semilattice_neutr: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 2.50/1.75 thf(func_def_28, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.50/1.75 thf(func_def_29, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 2.50/1.75 thf(func_def_30, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.50/1.75 thf(func_def_31, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.50/1.75 thf(func_def_32, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.50/1.75 thf(func_def_33, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 2.50/1.75 thf(func_def_34, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 2.50/1.75 thf(func_def_35, type, rBT_Im1975547051_color: !>[X0: $tType]:(X0 > X0 > rBT_Im1923302023_color > X0)).
% 2.50/1.75 thf(func_def_36, type, rBT_Im1059957627_color: !>[X0: $tType]:(X0 > X0 > rBT_Im1923302023_color > X0)).
% 2.50/1.75 thf(func_def_37, type, rBT_Im800559290_color: rBT_Im1923302023_color > nat).
% 2.50/1.75 thf(func_def_38, 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)).
% 2.50/1.75 thf(func_def_39, type, rBT_Im418718756_Empty: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.50/1.75 thf(func_def_40, type, rBT_Im858806507se_rbt: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > (rBT_Im1923302023_color > rBT_Im246033960le_rbt @ X1 @ X2 > X1 > X2 > rBT_Im246033960le_rbt @ X1 @ X2 > X0) > rBT_Im246033960le_rbt @ X1 @ X2 > X0)).
% 2.50/1.75 thf(func_def_41, type, rBT_Im206295089ap_rbt: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > rBT_Im246033960le_rbt @ X0 @ X2 > rBT_Im246033960le_rbt @ X1 @ X3)).
% 2.50/1.75 thf(func_def_42, type, rBT_Im1931894874ed_rbt: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.50/1.75 thf(func_def_43, type, rBT_Im1947144893ec_rbt: !>[X0: $tType, X1: $tType, X2: $tType]:(X0 > (rBT_Im1923302023_color > rBT_Im246033960le_rbt @ X1 @ X2 > X1 > X2 > rBT_Im246033960le_rbt @ X1 @ X2 > X0 > X0 > X0) > rBT_Im246033960le_rbt @ X1 @ X2 > X0)).
% 2.50/1.75 thf(func_def_44, type, rBT_Im1000242676el_rbt: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > rBT_Im246033960le_rbt @ X0 @ X2 > rBT_Im246033960le_rbt @ X1 @ X3 > $o)).
% 2.50/1.75 thf(func_def_45, type, rBT_Im1178217900t1_rbt: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > set @ X0)).
% 2.50/1.75 thf(func_def_46, type, rBT_Im1550225131t2_rbt: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > set @ X1)).
% 2.50/1.75 thf(func_def_47, type, rBT_Im1485196410ze_rbt: !>[X0: $tType, X1: $tType]:((X0 > nat) > (X1 > nat) > rBT_Im246033960le_rbt @ X0 @ X1 > nat)).
% 2.50/1.75 thf(func_def_48, type, ball: !>[X0: $tType]:(set @ X0 > (X0 > $o) > $o)).
% 2.50/1.75 thf(func_def_49, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.50/1.75 thf(func_def_50, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 2.50/1.75 thf(func_def_51, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.75 thf(func_def_52, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 2.50/1.75 thf(func_def_53, type, pairwise: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.50/1.75 thf(func_def_54, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.50/1.75 thf(func_def_55, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 2.50/1.75 thf(func_def_56, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.50/1.75 thf(func_def_57, type, t: rBT_Im246033960le_rbt @ a @ b).
% 2.50/1.75 thf(func_def_74, type, sK0: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_75, type, sK1: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_76, type, sK2: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 2.50/1.75 thf(func_def_77, type, sK3: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 2.50/1.75 thf(func_def_78, type, sK4: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_79, type, sK5: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_80, type, sK6: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_81, type, sK7: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X1)).
% 2.50/1.75 thf(func_def_82, type, sK8: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X0)).
% 2.50/1.75 thf(func_def_83, type, sK9: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_84, type, sK10: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_85, type, sK11: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_86, type, sK12: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > X1)).
% 2.50/1.75 thf(func_def_87, type, sK13: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > X0)).
% 2.50/1.75 thf(func_def_88, type, sK14: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_89, type, sK15: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_90, type, sK16: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_91, type, sK17: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > X1)).
% 2.50/1.75 thf(func_def_92, type, sK18: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > X0)).
% 2.50/1.75 thf(func_def_93, type, sK19: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_94, type, sK20: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_95, type, sK21: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_96, type, sK22: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > X0)).
% 2.50/1.75 thf(func_def_97, type, sK23: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_98, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.50/1.75 thf(func_def_99, type, sK25: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_100, type, sK26: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_101, type, sK27: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > X1)).
% 2.50/1.75 thf(func_def_102, type, sK28: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_103, type, sK29: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_104, type, sK30: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_105, type, sK31: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > X1)).
% 2.50/1.75 thf(func_def_106, type, sK32: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > X0)).
% 2.50/1.75 thf(func_def_107, type, sK33: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_108, type, sK34: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im1923302023_color)).
% 2.50/1.75 thf(func_def_109, type, sK35: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_110, type, sK36: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > X1)).
% 2.50/1.75 thf(func_def_111, type, sK37: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > X0)).
% 2.50/1.75 thf(func_def_112, type, sK38: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.50/1.75 thf(func_def_114, type, ph40: !>[X0: $tType]:(X0)).
% 2.50/1.75 thf(f1384,plain,(
% 2.50/1.75 $false),
% 2.50/1.75 inference(avatar_sat_refutation,[status(thm)],[f863,f864,f869,f874,f1383])).
% 2.50/1.75 thf(f1383,plain,(
% 2.50/1.75 spl39_2 | ~spl39_3 | ~spl39_4),
% 2.50/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1382])).
% 2.50/1.75 thf(f1382,plain,(
% 2.50/1.75 $false | (spl39_2 | ~spl39_3 | ~spl39_4)),
% 2.50/1.75 inference(subsumption_resolution,[status(thm)],[f1381,f872])).
% 2.50/1.75 thf(f872,plain,(
% 2.50/1.75 ( ! [X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a] : ((t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3))) ) | ~spl39_4),
% 2.50/1.75 inference(avatar_component_clause,[status(thm)],[f871])).
% 2.50/1.75 thf(f871,definition,(
% 2.50/1.75 spl39_4 <=> ! [X2 : b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X3 : rBT_Im246033960le_rbt @ a @ b] : (t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3))),
% 2.50/1.75 introduced(definition,[new_symbols(naming,[spl39_4])],[avatar_definition])).
% 2.50/1.75 thf(f1381,plain,(
% 2.50/1.75 (t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ (sK1 @ b @ a @ t) @ (sK2 @ b @ a @ t) @ (sK3 @ b @ a @ t) @ (sK4 @ b @ a @ t))) | (spl39_2 | ~spl39_3)),
% 2.50/1.75 inference(subsumption_resolution,[status(thm)],[f1378,f862])).
% 2.50/1.75 thf(f862,plain,(
% 2.50/1.75 (t != rBT_Im418718756_Empty @ a @ b) | spl39_2),
% 2.50/1.75 inference(avatar_component_clause,[status(thm)],[f860])).
% 2.50/1.75 thf(f860,definition,(
% 2.50/1.75 spl39_2 <=> (t = rBT_Im418718756_Empty @ a @ b)),
% 2.50/1.75 introduced(definition,[new_symbols(naming,[spl39_2])],[avatar_definition])).
% 2.50/1.75 thf(f1378,plain,(
% 2.50/1.75 (t = rBT_Im418718756_Empty @ a @ b) | (t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ (sK1 @ b @ a @ t) @ (sK2 @ b @ a @ t) @ (sK3 @ b @ a @ t) @ (sK4 @ b @ a @ t))) | (spl39_2 | ~spl39_3)),
% 2.50/1.75 inference(superposition,[status(thm)],[f754,f1317])).
% 2.50/1.75 thf(f1317,plain,(
% 2.50/1.75 (rBT_Impl_Mirabelle_B = (sK0 @ b @ a @ t)) | (spl39_2 | ~spl39_3)),
% 2.50/1.75 inference(subsumption_resolution,[status(thm)],[f1316,f862])).
% 2.50/1.75 thf(f1316,plain,(
% 2.50/1.75 (rBT_Impl_Mirabelle_B = (sK0 @ b @ a @ t)) | (t = rBT_Im418718756_Empty @ a @ b) | ~spl39_3),
% 2.50/1.75 inference(equality_resolution,[status(thm)],[f1150])).
% 2.50/1.75 thf(f1150,plain,(
% 2.50/1.75 ( ! [X0 : rBT_Im246033960le_rbt @ a @ b] : ((t != X0) | (rBT_Im418718756_Empty @ a @ b = X0) | (rBT_Impl_Mirabelle_B = (sK0 @ b @ a @ X0))) ) | ~spl39_3),
% 2.50/1.75 inference(superposition,[status(thm)],[f882,f754])).
% 2.50/1.75 thf(f882,plain,(
% 2.50/1.75 ( ! [X2 : a,X3 : b,X0 : rBT_Im1923302023_color,X1 : rBT_Im246033960le_rbt @ a @ b,X4 : rBT_Im246033960le_rbt @ a @ b] : ((t != (rBT_Im480247531Branch @ a @ b @ X0 @ X1 @ X2 @ X3 @ X4)) | (rBT_Impl_Mirabelle_B = X0)) ) | ~spl39_3),
% 2.50/1.75 inference(superposition,[status(thm)],[f867,f793])).
% 2.50/1.75 thf(f793,plain,(
% 2.50/1.75 ( ! [X0 : rBT_Im1923302023_color] : ((rBT_Impl_Mirabelle_R = X0) | (rBT_Impl_Mirabelle_B = X0)) )),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f719])).
% 2.50/1.75 thf(f719,plain,(
% 2.50/1.75 ! [X0 : rBT_Im1923302023_color] : ((rBT_Impl_Mirabelle_B = X0) | (rBT_Impl_Mirabelle_R = X0))),
% 2.50/1.75 inference(ennf_transformation,[status(thm)],[f708])).
% 2.50/1.75 thf(f708,plain,(
% 2.50/1.75 ! [X0 : rBT_Im1923302023_color] : ((rBT_Impl_Mirabelle_R != X0) => (rBT_Impl_Mirabelle_B = X0))),
% 2.50/1.75 inference(rectify,[status(thm)],[f10])).
% 2.50/1.75 thf(f10,axiom,(
% 2.50/1.75 ! [X28 : rBT_Im1923302023_color] : ((rBT_Impl_Mirabelle_R != X28) => (rBT_Impl_Mirabelle_B = X28))),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',fact_9_color_Oexhaust)).
% 2.50/1.75 thf(f867,plain,(
% 2.50/1.75 ( ! [X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a] : ((t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3))) ) | ~spl39_3),
% 2.50/1.75 inference(avatar_component_clause,[status(thm)],[f866])).
% 2.50/1.75 thf(f866,definition,(
% 2.50/1.75 spl39_3 <=> ! [X2 : b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X3 : rBT_Im246033960le_rbt @ a @ b] : (t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3))),
% 2.50/1.75 introduced(definition,[new_symbols(naming,[spl39_3])],[avatar_definition])).
% 2.50/1.75 thf(f754,plain,(
% 2.50/1.75 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : (((rBT_Im480247531Branch @ X1 @ X0 @ (sK0 @ X0 @ X1 @ X2) @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2) @ (sK3 @ X0 @ X1 @ X2) @ (sK4 @ X0 @ X1 @ X2)) = X2) | (rBT_Im418718756_Empty @ X1 @ X0 = X2)) )),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f733])).
% 2.50/1.75 thf(f733,plain,(
% 2.50/1.75 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im418718756_Empty @ X1 @ X0 = X2) | ((rBT_Im480247531Branch @ X1 @ X0 @ (sK0 @ X0 @ X1 @ X2) @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2) @ (sK3 @ X0 @ X1 @ X2) @ (sK4 @ X0 @ X1 @ X2)) = X2))),
% 2.50/1.75 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f723,f732])).
% 2.50/1.75 thf(f732,plain,(
% 2.50/1.75 ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : (? [X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7) = X2) => ((rBT_Im480247531Branch @ X1 @ X0 @ (sK0 @ X0 @ X1 @ X2) @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2) @ (sK3 @ X0 @ X1 @ X2) @ (sK4 @ X0 @ X1 @ X2)) = X2))),
% 2.50/1.75 introduced(definition,[],[choice_axiom])).
% 2.50/1.75 thf(f723,plain,(
% 2.50/1.75 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im418718756_Empty @ X1 @ X0 = X2) | ? [X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7) = X2))),
% 2.50/1.75 inference(ennf_transformation,[status(thm)],[f705])).
% 2.50/1.75 thf(f705,plain,(
% 2.50/1.75 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im418718756_Empty @ X1 @ X0 != X2) => ~! [X3 : rBT_Im1923302023_color,X4 : rBT_Im246033960le_rbt @ X1 @ X0,X5 : X1,X6 : X0,X7 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im480247531Branch @ X1 @ X0 @ X3 @ X4 @ X5 @ X6 @ X7) != X2))),
% 2.50/1.75 inference(rectify,[status(thm)],[f8])).
% 2.50/1.75 thf(f8,axiom,(
% 2.50/1.75 ! [X2 : $tType,X0 : $tType,X28 : rBT_Im246033960le_rbt @ X0 @ X2] : ((rBT_Im418718756_Empty @ X0 @ X2 != X28) => ~! [X29 : rBT_Im1923302023_color,X30 : rBT_Im246033960le_rbt @ X0 @ X2,X31 : X0,X32 : X2,X33 : rBT_Im246033960le_rbt @ X0 @ X2] : ((rBT_Im480247531Branch @ X0 @ X2 @ X29 @ X30 @ X31 @ X32 @ X33) != X28))),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',fact_7_rbt_Oexhaust)).
% 2.50/1.75 thf(f874,plain,(
% 2.50/1.75 spl39_1 | spl39_4),
% 2.50/1.75 inference(avatar_split_clause,[status(thm)],[f750,f871,f856])).
% 2.50/1.75 thf(f856,definition,(
% 2.50/1.75 spl39_1 <=> (thesis = $true)),
% 2.50/1.75 introduced(definition,[new_symbols(naming,[spl39_1])],[avatar_definition])).
% 2.50/1.75 thf(f750,plain,(
% 2.50/1.75 ( ! [X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a] : ((t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3)) | (thesis = $true)) )),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f710])).
% 2.50/1.75 thf(f710,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((thesis = $true) | (t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3)))),
% 2.50/1.75 inference(ennf_transformation,[status(thm)],[f440])).
% 2.50/1.75 thf(f440,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3)) => (thesis = $true))),
% 2.50/1.75 inference(fool_elimination,[status(thm)],[f439])).
% 2.50/1.75 thf(f439,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X0 @ X1 @ X2 @ X3)) => thesis)),
% 2.50/1.75 inference(rectify,[status(thm)],[f3])).
% 2.50/1.75 thf(f3,axiom,(
% 2.50/1.75 ! [X17 : rBT_Im246033960le_rbt @ a @ b,X18 : a,X19 : b,X20 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ X17 @ X18 @ X19 @ X20)) => thesis)),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',fact_2_Black)).
% 2.50/1.75 thf(f869,plain,(
% 2.50/1.75 spl39_1 | spl39_3),
% 2.50/1.75 inference(avatar_split_clause,[status(thm)],[f758,f866,f856])).
% 2.50/1.75 thf(f758,plain,(
% 2.50/1.75 ( ! [X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b,X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a] : ((thesis = $true) | (t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3))) )),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f729])).
% 2.50/1.75 thf(f729,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((t != (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3)) | (thesis = $true))),
% 2.50/1.75 inference(ennf_transformation,[status(thm)],[f316])).
% 2.50/1.75 thf(f316,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3)) => (thesis = $true))),
% 2.50/1.75 inference(fool_elimination,[status(thm)],[f315])).
% 2.50/1.75 thf(f315,plain,(
% 2.50/1.75 ! [X0 : rBT_Im246033960le_rbt @ a @ b,X1 : a,X2 : b,X3 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X0 @ X1 @ X2 @ X3)) => thesis)),
% 2.50/1.75 inference(rectify,[status(thm)],[f4])).
% 2.50/1.75 thf(f4,axiom,(
% 2.50/1.75 ! [X17 : rBT_Im246033960le_rbt @ a @ b,X18 : a,X19 : b,X20 : rBT_Im246033960le_rbt @ a @ b] : ((t = (rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_R @ X17 @ X18 @ X19 @ X20)) => thesis)),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',fact_3_Red)).
% 2.50/1.75 thf(f864,plain,(
% 2.50/1.75 ~spl39_1),
% 2.50/1.75 inference(avatar_split_clause,[status(thm)],[f794,f856])).
% 2.50/1.75 thf(f794,plain,(
% 2.50/1.75 (thesis != $true)),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f689])).
% 2.50/1.75 thf(f689,plain,(
% 2.50/1.75 (thesis != $true)),
% 2.50/1.75 inference(flattening,[status(thm)],[f512])).
% 2.50/1.75 thf(f512,plain,(
% 2.50/1.75 ~(thesis = $true)),
% 2.50/1.75 inference(fool_elimination,[status(thm)],[f511])).
% 2.50/1.75 thf(f511,plain,(
% 2.50/1.75 ~thesis),
% 2.50/1.75 inference(rectify,[status(thm)],[f285])).
% 2.50/1.75 thf(f285,negated_conjecture,(
% 2.50/1.75 ~thesis),
% 2.50/1.75 inference(negated_conjecture,[status(cth)],[f284])).
% 2.50/1.75 thf(f284,conjecture,(
% 2.50/1.75 thesis),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',conj_3)).
% 2.50/1.75 thf(f863,plain,(
% 2.50/1.75 spl39_1 | ~spl39_2),
% 2.50/1.75 inference(avatar_split_clause,[status(thm)],[f772,f860,f856])).
% 2.50/1.75 thf(f772,plain,(
% 2.50/1.75 (t != rBT_Im418718756_Empty @ a @ b) | (thesis = $true)),
% 2.50/1.75 inference(cnf_transformation,[status(thm)],[f726])).
% 2.50/1.75 thf(f726,plain,(
% 2.50/1.75 (thesis = $true) | (t != rBT_Im418718756_Empty @ a @ b)),
% 2.50/1.75 inference(ennf_transformation,[status(thm)],[f502])).
% 2.50/1.75 thf(f502,plain,(
% 2.50/1.75 (t = rBT_Im418718756_Empty @ a @ b) => (thesis = $true)),
% 2.50/1.75 inference(fool_elimination,[status(thm)],[f501])).
% 2.50/1.75 thf(f501,plain,(
% 2.50/1.75 (t = rBT_Im418718756_Empty @ a @ b) => thesis),
% 2.50/1.75 inference(rectify,[status(thm)],[f1])).
% 2.50/1.75 thf(f1,axiom,(
% 2.50/1.75 (t = rBT_Im418718756_Empty @ a @ b) => thesis),
% 2.50/1.75 file('/export/starexec/sandbox2/tmp/tmp.yaaOyqLDFS/DTF2THF_7073.p',fact_0_Empty)).
% 2.50/1.75 % SZS output end Proof for DTF2THF_7073
% 2.50/1.75 % (7428)------------------------------
% 2.50/1.75 % (7428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.75 % (7428)Termination reason: Refutation
% 2.50/1.75
% 2.50/1.75 % (7428)Memory used [KB]: 7675
% 2.50/1.75 % (7428)Time elapsed: 0.137 s
% 2.50/1.75 % (7428)Instructions burned: 421 (million)
% 2.50/1.75 % (7428)------------------------------
% 2.50/1.75 % (7428)------------------------------
% 2.50/1.75 % (7354)Success in time 0.253 s
%------------------------------------------------------------------------------