%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT231^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:14 AM UTC 2026
% Result : Theorem 8.36s 2.47s
% Output : Refutation 8.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT231^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:12:18 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.49 ---- Original DTF file ---
% 0.34/0.49 thf(spec,logic,$$dhol).
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 % File : DAT231^1 : TPTP v9.2.1. Released v7.0.0.
% 0.34/0.49 % Domain : Data Structures
% 0.34/0.49 % Problem : Red-black trees 312
% 0.34/0.49 % Version : [Bla16] axioms : Especial.
% 0.34/0.49 % English :
% 0.34/0.49
% 0.34/0.49 % Refs : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.34/0.49 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.34/0.49 % Source : [Bla16]
% 0.34/0.49 % Names : rbt_impl__312.p [Bla16]
% 0.34/0.49
% 0.34/0.49 % Status : Theorem
% 0.34/0.49 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.34/0.49 % Syntax : Number of formulae : 368 ( 76 unt; 79 typ; 0 def)
% 0.34/0.49 % Number of atoms : 940 ( 215 equ; 0 cnn)
% 0.34/0.49 % Maximal formula atoms : 9 ( 3 avg)
% 0.34/0.49 % Number of connectives : 4378 ( 85 ~; 19 |; 66 &;3734 @)
% 0.34/0.49 % ( 0 <=>; 474 =>; 0 <=; 0 <~>)
% 0.34/0.49 % Maximal formula depth : 31 ( 9 avg)
% 0.34/0.49 % Number of types : 5 ( 4 usr)
% 0.34/0.49 % Number of type conns : 305 ( 305 >; 0 *; 0 +; 0 <<)
% 0.34/0.49 % Number of symbols : 78 ( 75 usr; 5 con; 0-8 aty)
% 0.34/0.49 % Number of variables : 1254 ( 31 ^;1091 !; 41 ?;1254 :)
% 0.34/0.49 % ( 91 !>; 0 ?*; 0 @-; 0 @+)
% 0.34/0.49 % SPC : TH1_THM_EQU_NAR
% 0.34/0.49
% 0.34/0.49 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.34/0.49 % 2016-07-13 14:40:07.754
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 %----Could-be-implicit typings (7)
% 0.34/0.49 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.34/0.49 rBT_Im1923302023_color: $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.34/0.49 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Set_Oset,type,
% 0.34/0.49 set: $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Nat_Onat,type,
% 0.34/0.49 nat: $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_itself,type,
% 0.34/0.49 itself: $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_tf_b,type,
% 0.34/0.49 b: $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_tf_a,type,
% 0.34/0.49 a: $tType ).
% 0.34/0.49
% 0.34/0.49 %----Explicit typings (72)
% 0.34/0.49 thf(sy_cl_HOL_Otype,type,
% 0.34/0.49 type:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Oord,type,
% 0.34/0.49 ord:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Oorder,type,
% 0.34/0.49 order:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Ono__bot,type,
% 0.34/0.49 no_bot:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Ono__top,type,
% 0.34/0.49 no_top:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Olinorder,type,
% 0.34/0.49 linorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Opreorder,type,
% 0.34/0.49 preorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.34/0.49 zero_neq_one:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Owellorder,type,
% 0.34/0.49 wellorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.34/0.49 zero_less_one:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Odense__order,type,
% 0.34/0.49 dense_order:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.34/0.49 linordered_idom:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Fields_Olinordered__field,type,
% 0.34/0.49 linordered_field:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.34/0.49 dense_linorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.34/0.49 linordered_semidom:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.34/0.49 ordered_ab_group_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.34/0.49 linord219039673up_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.34/0.49 ordere216010020id_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.34/0.49 ordere142940540dd_abs:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.34/0.49 linord1659791738miring:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.34/0.49 canoni770627133id_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.34/0.49 strict797366125id_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.34/0.49 ordere236663937imp_le:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.34/0.49 ordere223160158up_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.34/0.49 strict2144017051up_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.34/0.49 ordere516151231imp_le:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.34/0.49 condit1656338222tinuum:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.34/0.49 condit1037483654norder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_BNF__Def_Oeq__onp,type,
% 0.34/0.49 bNF_eq_onp:
% 0.34/0.49 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.34/0.49 abs_abs:
% 0.34/0.49 !>[A: $tType] : ( A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.34/0.49 one_one:
% 0.34/0.49 !>[A: $tType] : A ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.34/0.49 plus_plus:
% 0.34/0.49 !>[A: $tType] : ( A > A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Osgn__class_Osgn,type,
% 0.34/0.49 sgn_sgn:
% 0.34/0.49 !>[A: $tType] : ( A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.34/0.49 uminus_uminus:
% 0.34/0.49 !>[A: $tType] : ( A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.34/0.49 zero_zero:
% 0.34/0.49 !>[A: $tType] : A ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_If,type,
% 0.34/0.49 if:
% 0.34/0.49 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Nat_OSuc,type,
% 0.34/0.49 suc: nat > nat ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Nat_Osemiring__1__class_Oof__nat,type,
% 0.34/0.50 semiring_1_of_nat:
% 0.34/0.50 !>[A: $tType] : ( nat > A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.34/0.50 size_size:
% 0.34/0.50 !>[A: $tType] : ( A > nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.34/0.50 ord_less:
% 0.34/0.50 !>[A: $tType] : ( A > A > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.34/0.50 ord_less_eq:
% 0.34/0.50 !>[A: $tType] : ( A > A > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Orderings_Oorder__class_Ostrict__mono,type,
% 0.34/0.50 order_strict_mono:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Power_Opower__class_Opower,type,
% 0.34/0.50 power_power:
% 0.34/0.50 !>[A: $tType] : ( A > nat > A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Pure_Otype,type,
% 0.34/0.50 type2:
% 0.34/0.50 !>[A: $tType] : ( itself @ A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obheight,type,
% 0.34/0.50 rBT_Im315265182height:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 0.34/0.50 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 0.34/0.50 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color,type,
% 0.34/0.50 rBT_Im1975547051_color:
% 0.34/0.50 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color,type,
% 0.34/0.50 rBT_Im1059957627_color:
% 0.34/0.50 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color,type,
% 0.34/0.50 rBT_Im800559290_color: rBT_Im1923302023_color > nat ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of,type,
% 0.34/0.50 rBT_Im1805589839lor_of:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > rBT_Im1923302023_color ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1,type,
% 0.34/0.50 rBT_Im1040612427e_inv1:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1l,type,
% 0.34/0.50 rBT_Im1071879905_inv1l:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 0.34/0.50 rBT_Im1259024060reater:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 0.34/0.50 rBT_Im2075124343t_less:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 0.34/0.50 rBT_Im759614907sorted:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater,type,
% 0.34/0.50 rBT_Im1332541288reater:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less,type,
% 0.34/0.50 rBT_Im903026891t_less:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted,type,
% 0.34/0.50 rBT_Im1183586831sorted:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.34/0.50 rBT_Im480247531Branch:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.34/0.50 rBT_Im418718756_Empty:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt,type,
% 0.34/0.50 rBT_Im858806507se_rbt:
% 0.34/0.50 !>[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 ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Opred__rbt,type,
% 0.34/0.50 rBT_Im1931894874ed_rbt:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt,type,
% 0.34/0.50 rBT_Im1947144893ec_rbt:
% 0.34/0.50 !>[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 ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orel__rbt,type,
% 0.34/0.50 rBT_Im1000242676el_rbt:
% 0.34/0.50 !>[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 ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt,type,
% 0.34/0.50 rBT_Im1178217900t1_rbt:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ A ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt,type,
% 0.34/0.50 rBT_Im1550225131t2_rbt:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt,type,
% 0.34/0.50 rBT_Im1485196410ze_rbt:
% 0.34/0.50 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool,type,
% 0.34/0.50 zero_neq_one_of_bool:
% 0.34/0.50 !>[A: $tType] : ( $o > A ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_Set_OCollect,type,
% 0.34/0.50 collect:
% 0.34/0.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_c_member,type,
% 0.34/0.50 member:
% 0.34/0.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(sy_v_t,type,
% 0.34/0.50 t: rBT_Im246033960le_rbt @ a @ b ).
% 0.34/0.50
% 0.34/0.50 %----Relevant facts (256)
% 0.34/0.50 thf(fact_0_inv1l_Osimps_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im1071879905_inv1l @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.34/0.50 = ( ( rBT_Im1040612427e_inv1 @ A @ B @ L )
% 0.34/0.50 & ( rBT_Im1040612427e_inv1 @ A @ B @ R ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % inv1l.simps(2)
% 0.34/0.50 thf(fact_1_inv1l_Osimps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] : ( rBT_Im1071879905_inv1l @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % inv1l.simps(1)
% 0.34/0.50 thf(fact_2_inv1_Osimps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] : ( rBT_Im1040612427e_inv1 @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % inv1.simps(1)
% 0.34/0.50 thf(fact_3_inv1_Osimps_I2_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,Rt: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im1040612427e_inv1 @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.34/0.50 = ( ( rBT_Im1040612427e_inv1 @ A @ B @ Lt )
% 0.34/0.50 & ( rBT_Im1040612427e_inv1 @ A @ B @ Rt )
% 0.34/0.50 & ( ( C2 = rBT_Impl_Mirabelle_B )
% 0.34/0.50 | ( ( ( rBT_Im1805589839lor_of @ A @ B @ Lt )
% 0.34/0.50 = rBT_Impl_Mirabelle_B )
% 0.34/0.50 & ( ( rBT_Im1805589839lor_of @ A @ B @ Rt )
% 0.34/0.50 = rBT_Impl_Mirabelle_B ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % inv1.simps(2)
% 0.34/0.50 thf(fact_4_color_Ocase__distrib,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,H: A > B,F1: A,F2: A,Color: rBT_Im1923302023_color] :
% 0.34/0.50 ( ( H @ ( rBT_Im1975547051_color @ A @ F1 @ F2 @ Color ) )
% 0.34/0.50 = ( rBT_Im1975547051_color @ B @ ( H @ F1 ) @ ( H @ F2 ) @ Color ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.case_distrib
% 0.34/0.50 thf(fact_5_rbt_Oinject,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 0.34/0.50 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.34/0.50 = ( ( X21 = Y21 )
% 0.34/0.50 & ( X22 = Y22 )
% 0.34/0.50 & ( X23 = Y23 )
% 0.34/0.50 & ( X24 = Y24 )
% 0.34/0.50 & ( X25 = Y25 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.inject
% 0.34/0.50 thf(fact_6_color_Osimps_I4_J,axiom,
% 0.34/0.50 ! [A: $tType,F1: A,F2: A] :
% 0.34/0.50 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.34/0.50 = F2 ) ).
% 0.34/0.50
% 0.34/0.50 % color.simps(4)
% 0.34/0.50 thf(fact_7_rbt_Odistinct_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.distinct(1)
% 0.34/0.50 thf(fact_8_color__of_Osimps_I2_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,C2: rBT_Im1923302023_color,Uu: rBT_Im246033960le_rbt @ A @ B,Uv: A,Uw: B,Ux: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im1805589839lor_of @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Uu @ Uv @ Uw @ Ux ) )
% 0.34/0.50 = C2 ) ).
% 0.34/0.50
% 0.34/0.50 % color_of.simps(2)
% 0.34/0.50 thf(fact_9_color__of_Osimps_I1_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( rBT_Im1805589839lor_of @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = rBT_Impl_Mirabelle_B ) ).
% 0.34/0.50
% 0.34/0.50 % color_of.simps(1)
% 0.34/0.50 thf(fact_10_rbt_Oinduct,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 => ( ! [X1: rBT_Im1923302023_color,X2: rBT_Im246033960le_rbt @ A @ B,X3: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( P @ X2 )
% 0.34/0.50 => ( ( P @ X5 )
% 0.34/0.50 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) )
% 0.34/0.50 => ( P @ Rbt ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.induct
% 0.34/0.50 thf(fact_11_rbt_Oexhaust,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( Y
% 0.34/0.50 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( Y
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.exhaust
% 0.34/0.50 thf(fact_12_rbt__cases,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( T
% 0.34/0.50 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( T
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K2 @ V2 @ R2 ) )
% 0.34/0.50 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( T
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K2 @ V2 @ R2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_cases
% 0.34/0.50 thf(fact_13_color_Osimps_I6_J,axiom,
% 0.34/0.50 ! [A: $tType,F1: A,F2: A] :
% 0.34/0.50 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.34/0.50 = F2 ) ).
% 0.34/0.50
% 0.34/0.50 % color.simps(6)
% 0.34/0.50 thf(fact_14_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_sorted.simps(1)
% 0.34/0.50 thf(fact_15_color_Osimps_I3_J,axiom,
% 0.34/0.50 ! [A: $tType,F1: A,F2: A] :
% 0.34/0.50 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.34/0.50 = F1 ) ).
% 0.34/0.50
% 0.34/0.50 % color.simps(3)
% 0.34/0.50 thf(fact_16_rbt__less__simps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [K: A] : ( rBT_Im903026891t_less @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_less_simps(1)
% 0.34/0.50 thf(fact_17_rbt__greater__simps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [K: A] : ( rBT_Im1332541288reater @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_greater_simps(1)
% 0.34/0.50 thf(fact_18_color_Odistinct_I1_J,axiom,
% 0.34/0.50 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 0.34/0.50
% 0.34/0.50 % color.distinct(1)
% 0.34/0.50 thf(fact_19_color_Oinduct,axiom,
% 0.34/0.50 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 0.34/0.50 ( ( P @ rBT_Impl_Mirabelle_R )
% 0.34/0.50 => ( ( P @ rBT_Impl_Mirabelle_B )
% 0.34/0.50 => ( P @ Color ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.induct
% 0.34/0.50 thf(fact_20_color_Oexhaust,axiom,
% 0.34/0.50 ! [Y: rBT_Im1923302023_color] :
% 0.34/0.50 ( ( Y != rBT_Impl_Mirabelle_R )
% 0.34/0.50 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.exhaust
% 0.34/0.50 thf(fact_21_rbt_Osimps_I4_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = F1 ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.simps(4)
% 0.34/0.50 thf(fact_22_rbt_Osimps_I5_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.34/0.50 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.simps(5)
% 0.34/0.50 thf(fact_23_color_Osimps_I5_J,axiom,
% 0.34/0.50 ! [A: $tType,F1: A,F2: A] :
% 0.34/0.50 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.34/0.50 = F1 ) ).
% 0.34/0.50
% 0.34/0.50 % color.simps(5)
% 0.34/0.50 thf(fact_24_rbt__sorted_Osimps_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.34/0.50 = ( ( rBT_Im903026891t_less @ A @ B @ K @ L )
% 0.34/0.50 & ( rBT_Im1332541288reater @ A @ B @ K @ R )
% 0.34/0.50 & ( rBT_Im1183586831sorted @ A @ B @ L )
% 0.34/0.50 & ( rBT_Im1183586831sorted @ A @ B @ R ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_sorted.simps(2)
% 0.34/0.50 thf(fact_25_rbt__greater__simps_I2_J,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.34/0.50 ( ( rBT_Im1332541288reater @ A @ C @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.34/0.50 = ( ( ord_less @ A @ K @ Kt )
% 0.34/0.50 & ( rBT_Im1332541288reater @ A @ C @ K @ Lt )
% 0.34/0.50 & ( rBT_Im1332541288reater @ A @ C @ K @ Rt ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_greater_simps(2)
% 0.34/0.50 thf(fact_26_rbt__less__simps_I2_J,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.34/0.50 ( ( rBT_Im903026891t_less @ A @ C @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.34/0.50 = ( ( ord_less @ A @ Kt @ K )
% 0.34/0.50 & ( rBT_Im903026891t_less @ A @ C @ K @ Lt )
% 0.34/0.50 & ( rBT_Im903026891t_less @ A @ C @ K @ Rt ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_less_simps(2)
% 0.34/0.50 thf(fact_27_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Less: A > A > $o,C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.34/0.50 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 0.34/0.50 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 0.34/0.50 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 0.34/0.50 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_sorted.simps(2)
% 0.34/0.50 thf(fact_28_ord_Orbt__greater__simps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_greater_simps(1)
% 0.34/0.50 thf(fact_29_ord_Orbt__less__simps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_less_simps(1)
% 0.34/0.50 thf(fact_30_ord_Orbt__greater__simps_I2_J,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType,Less: A > A > $o,K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.34/0.50 ( ( rBT_Im1259024060reater @ A @ C @ Less @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.34/0.50 = ( ( Less @ K @ Kt )
% 0.34/0.50 & ( rBT_Im1259024060reater @ A @ C @ Less @ K @ Lt )
% 0.34/0.50 & ( rBT_Im1259024060reater @ A @ C @ Less @ K @ Rt ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_greater_simps(2)
% 0.34/0.50 thf(fact_31_ord_Orbt__less__simps_I2_J,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType,Less: A > A > $o,K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.34/0.50 ( ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.34/0.50 = ( ( Less @ Kt @ K )
% 0.34/0.50 & ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ Lt )
% 0.34/0.50 & ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ Rt ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord.rbt_less_simps(2)
% 0.34/0.50 thf(fact_32_rbt_Osimps_I6_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = F1 ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.simps(6)
% 0.34/0.50 thf(fact_33_rbt_Osimps_I7_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.34/0.50 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X22 ) @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X25 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.simps(7)
% 0.34/0.50 thf(fact_34_rbt__less__trans,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,T: rBT_Im246033960le_rbt @ A @ C,Y: A] :
% 0.34/0.50 ( ( rBT_Im903026891t_less @ A @ C @ X @ T )
% 0.34/0.50 => ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( rBT_Im903026891t_less @ A @ C @ Y @ T ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_less_trans
% 0.34/0.50 thf(fact_35_rbt__greater__trans,axiom,
% 0.34/0.50 ! [C: $tType,A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,T: rBT_Im246033960le_rbt @ A @ C] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( rBT_Im1332541288reater @ A @ C @ Y @ T )
% 0.34/0.50 => ( rBT_Im1332541288reater @ A @ C @ X @ T ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_greater_trans
% 0.34/0.50 thf(fact_36_rbt__sorted_Osimps_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt_sorted.simps(1)
% 0.34/0.50 thf(fact_37_minf_I11_J,axiom,
% 0.34/0.50 ! [C: $tType,D: $tType] :
% 0.34/0.50 ( ( ord @ C @ ( type2 @ C ) )
% 0.34/0.50 => ! [F: D] :
% 0.34/0.50 ? [Z: C] :
% 0.34/0.50 ! [X6: C] :
% 0.34/0.50 ( ( ord_less @ C @ X6 @ Z )
% 0.34/0.50 => ( F = F ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(11)
% 0.34/0.50 thf(fact_38_minf_I7_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ~ ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(7)
% 0.34/0.50 thf(fact_39_minf_I5_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(5)
% 0.34/0.50 thf(fact_40_minf_I4_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( X6 != T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(4)
% 0.34/0.50 thf(fact_41_minf_I3_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( X6 != T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(3)
% 0.34/0.50 thf(fact_42_minf_I2_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.34/0.50 ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Z2 )
% 0.34/0.50 => ( ( P @ X7 )
% 0.34/0.50 = ( P2 @ X7 ) ) )
% 0.34/0.50 => ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Z2 )
% 0.34/0.50 => ( ( Q @ X7 )
% 0.34/0.50 = ( Q2 @ X7 ) ) )
% 0.34/0.50 => ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( ( ( P @ X6 )
% 0.34/0.50 | ( Q @ X6 ) )
% 0.34/0.50 = ( ( P2 @ X6 )
% 0.34/0.50 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(2)
% 0.34/0.50 thf(fact_43_minf_I1_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.34/0.50 ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Z2 )
% 0.34/0.50 => ( ( P @ X7 )
% 0.34/0.50 = ( P2 @ X7 ) ) )
% 0.34/0.50 => ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Z2 )
% 0.34/0.50 => ( ( Q @ X7 )
% 0.34/0.50 = ( Q2 @ X7 ) ) )
% 0.34/0.50 => ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( ( ( P @ X6 )
% 0.34/0.50 & ( Q @ X6 ) )
% 0.34/0.50 = ( ( P2 @ X6 )
% 0.34/0.50 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(1)
% 0.34/0.50 thf(fact_44_pinf_I11_J,axiom,
% 0.34/0.50 ! [C: $tType,D: $tType] :
% 0.34/0.50 ( ( ord @ C @ ( type2 @ C ) )
% 0.34/0.50 => ! [F: D] :
% 0.34/0.50 ? [Z: C] :
% 0.34/0.50 ! [X6: C] :
% 0.34/0.50 ( ( ord_less @ C @ Z @ X6 )
% 0.34/0.50 => ( F = F ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(11)
% 0.34/0.50 thf(fact_45_mem__Collect__eq,axiom,
% 0.34/0.50 ! [A: $tType,A2: A,P: A > $o] :
% 0.34/0.50 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.34/0.50 = ( P @ A2 ) ) ).
% 0.34/0.50
% 0.34/0.50 % mem_Collect_eq
% 0.34/0.50 thf(fact_46_Collect__mem__eq,axiom,
% 0.34/0.50 ! [A: $tType,A3: set @ A] :
% 0.34/0.50 ( ( collect @ A
% 0.34/0.50 @ ^ [X8: A] : ( member @ A @ X8 @ A3 ) )
% 0.34/0.50 = A3 ) ).
% 0.34/0.50
% 0.34/0.50 % Collect_mem_eq
% 0.34/0.50 thf(fact_47_Collect__cong,axiom,
% 0.34/0.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ( P @ X7 )
% 0.34/0.50 = ( Q @ X7 ) )
% 0.34/0.50 => ( ( collect @ A @ P )
% 0.34/0.50 = ( collect @ A @ Q ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % Collect_cong
% 0.34/0.50 thf(fact_48_ext,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ( F3 @ X7 )
% 0.34/0.50 = ( G @ X7 ) )
% 0.34/0.50 => ( F3 = G ) ) ).
% 0.34/0.50
% 0.34/0.50 % ext
% 0.34/0.50 thf(fact_49_pinf_I7_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(7)
% 0.34/0.50 thf(fact_50_pinf_I1_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.34/0.50 ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z2 @ X7 )
% 0.34/0.50 => ( ( P @ X7 )
% 0.34/0.50 = ( P2 @ X7 ) ) )
% 0.34/0.50 => ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z2 @ X7 )
% 0.34/0.50 => ( ( Q @ X7 )
% 0.34/0.50 = ( Q2 @ X7 ) ) )
% 0.34/0.50 => ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( ( ( P @ X6 )
% 0.34/0.50 & ( Q @ X6 ) )
% 0.34/0.50 = ( ( P2 @ X6 )
% 0.34/0.50 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(1)
% 0.34/0.50 thf(fact_51_pinf_I2_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.34/0.50 ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z2 @ X7 )
% 0.34/0.50 => ( ( P @ X7 )
% 0.34/0.50 = ( P2 @ X7 ) ) )
% 0.34/0.50 => ( ? [Z2: A] :
% 0.34/0.50 ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z2 @ X7 )
% 0.34/0.50 => ( ( Q @ X7 )
% 0.34/0.50 = ( Q2 @ X7 ) ) )
% 0.34/0.50 => ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( ( ( P @ X6 )
% 0.34/0.50 | ( Q @ X6 ) )
% 0.34/0.50 = ( ( P2 @ X6 )
% 0.34/0.50 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(2)
% 0.34/0.50 thf(fact_52_pinf_I3_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( X6 != T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(3)
% 0.34/0.50 thf(fact_53_pinf_I4_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( X6 != T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(4)
% 0.34/0.50 thf(fact_54_pinf_I5_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ~ ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(5)
% 0.34/0.50 thf(fact_55_ex__gt__or__lt,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ? [B2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B2 )
% 0.34/0.50 | ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ex_gt_or_lt
% 0.34/0.50 thf(fact_56_linorder__neqE__linordered__idom,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( X != Y )
% 0.34/0.50 => ( ~ ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % linorder_neqE_linordered_idom
% 0.34/0.50 thf(fact_57_dual__order_Ostrict__implies__not__eq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ B3 @ A2 )
% 0.34/0.50 => ( A2 != B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_implies_not_eq
% 0.34/0.50 thf(fact_58_linordered__field__no__ub,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X6: A] :
% 0.34/0.50 ? [X1: A] : ( ord_less @ A @ X6 @ X1 ) ) ).
% 0.34/0.50
% 0.34/0.50 % linordered_field_no_ub
% 0.34/0.50 thf(fact_59_linordered__field__no__lb,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X6: A] :
% 0.34/0.50 ? [Y2: A] : ( ord_less @ A @ Y2 @ X6 ) ) ).
% 0.34/0.50
% 0.34/0.50 % linordered_field_no_lb
% 0.34/0.50 thf(fact_60_order_Ostrict__implies__not__eq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( A2 != B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_implies_not_eq
% 0.34/0.50 thf(fact_61_dependent__wellorder__choice,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: ( A > B ) > A > B > $o] :
% 0.34/0.50 ( ! [R2: B,F4: A > B,G2: A > B,X7: A] :
% 0.34/0.50 ( ! [Y3: A] :
% 0.34/0.50 ( ( ord_less @ A @ Y3 @ X7 )
% 0.34/0.50 => ( ( F4 @ Y3 )
% 0.34/0.50 = ( G2 @ Y3 ) ) )
% 0.34/0.50 => ( ( P @ F4 @ X7 @ R2 )
% 0.34/0.50 = ( P @ G2 @ X7 @ R2 ) ) )
% 0.34/0.50 => ( ! [X7: A,F4: A > B] :
% 0.34/0.50 ( ! [Y3: A] :
% 0.34/0.50 ( ( ord_less @ A @ Y3 @ X7 )
% 0.34/0.50 => ( P @ F4 @ Y3 @ ( F4 @ Y3 ) ) )
% 0.34/0.50 => ? [X12: B] : ( P @ F4 @ X7 @ X12 ) )
% 0.34/0.50 => ? [F4: A > B] :
% 0.34/0.50 ! [X6: A] : ( P @ F4 @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dependent_wellorder_choice
% 0.34/0.50 thf(fact_62_not__less__iff__gr__or__eq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.34/0.50 = ( ( ord_less @ A @ Y @ X )
% 0.34/0.50 | ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_less_iff_gr_or_eq
% 0.34/0.50 thf(fact_63_ord__eq__less__subst,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.50 & ( ord @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.34/0.50 ( ( A2
% 0.34/0.50 = ( F3 @ B3 ) )
% 0.34/0.50 => ( ( ord_less @ B @ B3 @ C2 )
% 0.34/0.50 => ( ! [X7: B,Y2: B] :
% 0.34/0.50 ( ( ord_less @ B @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord_eq_less_subst
% 0.34/0.50 thf(fact_64_ord__less__eq__subst,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.50 & ( ord @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,B3: A,F3: A > B,C2: B] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ( F3 @ B3 )
% 0.34/0.50 = C2 )
% 0.34/0.50 => ( ! [X7: A,Y2: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ B @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord_less_eq_subst
% 0.34/0.50 thf(fact_65_order__less__subst1,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( ( order @ B @ ( type2 @ B ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( F3 @ B3 ) )
% 0.34/0.50 => ( ( ord_less @ B @ B3 @ C2 )
% 0.34/0.50 => ( ! [X7: B,Y2: B] :
% 0.34/0.50 ( ( ord_less @ B @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_less_subst1
% 0.34/0.50 thf(fact_66_order__less__subst2,axiom,
% 0.34/0.50 ! [A: $tType,C: $tType] :
% 0.34/0.50 ( ( ( order @ C @ ( type2 @ C ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less @ C @ ( F3 @ B3 ) @ C2 )
% 0.34/0.50 => ( ! [X7: A,Y2: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_less_subst2
% 0.34/0.50 thf(fact_67_lt__ex,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A] :
% 0.34/0.50 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.34/0.50
% 0.34/0.50 % lt_ex
% 0.34/0.50 thf(fact_68_gt__ex,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( no_top @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A] :
% 0.34/0.50 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.34/0.50
% 0.34/0.50 % gt_ex
% 0.34/0.50 thf(fact_69_neqE,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( X != Y )
% 0.34/0.50 => ( ~ ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neqE
% 0.34/0.50 thf(fact_70_neq__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( X != Y )
% 0.34/0.50 = ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neq_iff
% 0.34/0.50 thf(fact_71_order_Oasym,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.asym
% 0.34/0.50 thf(fact_72_dense,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ? [Z: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Z )
% 0.34/0.50 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dense
% 0.34/0.50 thf(fact_73_less__imp__neq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( X != Y ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_neq
% 0.34/0.50 thf(fact_74_less__asym,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_asym
% 0.34/0.50 thf(fact_75_less__asym_H,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_asym'
% 0.34/0.50 thf(fact_76_less__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,Z3: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less @ A @ Y @ Z3 )
% 0.34/0.50 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_trans
% 0.34/0.50 thf(fact_77_less__linear,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 | ( X = Y )
% 0.34/0.50 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_linear
% 0.34/0.50 thf(fact_78_less__irrefl,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A] :
% 0.34/0.50 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_irrefl
% 0.34/0.50 thf(fact_79_ord__eq__less__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( A2 = B3 )
% 0.34/0.50 => ( ( ord_less @ A @ B3 @ C2 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord_eq_less_trans
% 0.34/0.50 thf(fact_80_ord__less__eq__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( B3 = C2 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % ord_less_eq_trans
% 0.34/0.50 thf(fact_81_dual__order_Oasym,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ B3 @ A2 )
% 0.34/0.50 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.asym
% 0.34/0.50 thf(fact_82_less__imp__not__eq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( X != Y ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_not_eq
% 0.34/0.50 thf(fact_83_less__not__sym,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_not_sym
% 0.34/0.50 thf(fact_84_less__induct,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,A2: A] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ! [Y3: A] :
% 0.34/0.50 ( ( ord_less @ A @ Y3 @ X7 )
% 0.34/0.50 => ( P @ Y3 ) )
% 0.34/0.50 => ( P @ X7 ) )
% 0.34/0.50 => ( P @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_induct
% 0.34/0.50 thf(fact_85_antisym__conv3,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Y: A,X: A] :
% 0.34/0.50 ( ~ ( ord_less @ A @ Y @ X )
% 0.34/0.50 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.34/0.50 = ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % antisym_conv3
% 0.34/0.50 thf(fact_86_less__imp__not__eq2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( Y != X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_not_eq2
% 0.34/0.50 thf(fact_87_less__imp__triv,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,P: $o] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less @ A @ Y @ X )
% 0.34/0.50 => P ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_triv
% 0.34/0.50 thf(fact_88_linorder__cases,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ~ ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( X != Y )
% 0.34/0.50 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % linorder_cases
% 0.34/0.50 thf(fact_89_dual__order_Oirrefl,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.irrefl
% 0.34/0.50 thf(fact_90_order_Ostrict__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less @ A @ B3 @ C2 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_trans
% 0.34/0.50 thf(fact_91_less__imp__not__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_not_less
% 0.34/0.50 thf(fact_92_dual__order_Ostrict__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ B3 @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ C2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_trans
% 0.34/0.50 thf(fact_93_rbt_Opred__inject_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,A2: rBT_Im1923302023_color,Aa: rBT_Im246033960le_rbt @ A @ B,Ab: A,Ac: B,Ad: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ ( rBT_Im480247531Branch @ A @ B @ A2 @ Aa @ Ab @ Ac @ Ad ) )
% 0.34/0.50 = ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ Aa )
% 0.34/0.50 & ( P1 @ Ab )
% 0.34/0.50 & ( P22 @ Ac )
% 0.34/0.50 & ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ Ad ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_inject(2)
% 0.34/0.50 thf(fact_94_rbt_Orel__distinct_I2_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_distinct(2)
% 0.34/0.50 thf(fact_95_rbt_Orel__distinct_I1_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 0.34/0.50 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_distinct(1)
% 0.34/0.50 thf(fact_96_strict__monoD,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ! [F3: A > B,X: A,Y: A] :
% 0.34/0.50 ( ( order_strict_mono @ A @ B @ F3 )
% 0.34/0.50 => ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ord_less @ B @ ( F3 @ X ) @ ( F3 @ Y ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_monoD
% 0.34/0.50 thf(fact_97_strict__monoI,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ! [F3: A > B] :
% 0.34/0.50 ( ! [X7: A,Y2: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ B @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( order_strict_mono @ A @ B @ F3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_monoI
% 0.34/0.50 thf(fact_98_strict__mono__def,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ( ( order_strict_mono @ A @ B )
% 0.34/0.50 = ( ^ [F5: A > B] :
% 0.34/0.50 ! [X8: A,Y4: A] :
% 0.34/0.50 ( ( ord_less @ A @ X8 @ Y4 )
% 0.34/0.50 => ( ord_less @ B @ ( F5 @ X8 ) @ ( F5 @ Y4 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_mono_def
% 0.34/0.50 thf(fact_99_strict__mono__less,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ! [F3: A > B,X: A,Y: A] :
% 0.34/0.50 ( ( order_strict_mono @ A @ B @ F3 )
% 0.34/0.50 => ( ( ord_less @ B @ ( F3 @ X ) @ ( F3 @ Y ) )
% 0.34/0.50 = ( ord_less @ A @ X @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_mono_less
% 0.34/0.50 thf(fact_100_strict__mono__eq,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ! [F3: A > B,X: A,Y: A] :
% 0.34/0.50 ( ( order_strict_mono @ A @ B @ F3 )
% 0.34/0.50 => ( ( ( F3 @ X )
% 0.34/0.50 = ( F3 @ Y ) )
% 0.34/0.50 = ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_mono_eq
% 0.34/0.50 thf(fact_101_rbt_Orel__refl,axiom,
% 0.34/0.50 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: rBT_Im246033960le_rbt @ C @ D] :
% 0.34/0.50 ( ! [X7: C] : ( R1a @ X7 @ X7 )
% 0.34/0.50 => ( ! [X7: D] : ( R2a @ X7 @ X7 )
% 0.34/0.50 => ( rBT_Im1000242676el_rbt @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_refl
% 0.34/0.50 thf(fact_102_rbt_Orel__eq,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B
% 0.34/0.50 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.34/0.50 @ ^ [Y5: B,Z4: B] : ( Y5 = Z4 ) )
% 0.34/0.50 = ( ^ [Y5: rBT_Im246033960le_rbt @ A @ B,Z4: rBT_Im246033960le_rbt @ A @ B] : ( Y5 = Z4 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_eq
% 0.34/0.50 thf(fact_103_rbt_Orel__intros_I2_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,X21: rBT_Im1923302023_color,Y21: rBT_Im1923302023_color,R1: A > C > $o,R22: 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] :
% 0.34/0.50 ( ( X21 = Y21 )
% 0.34/0.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X22 @ Y22 )
% 0.34/0.50 => ( ( R1 @ X23 @ Y23 )
% 0.34/0.50 => ( ( R22 @ X24 @ Y24 )
% 0.34/0.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X25 @ Y25 )
% 0.34/0.50 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_intros(2)
% 0.34/0.50 thf(fact_104_rbt_Orel__inject_I2_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: 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] :
% 0.34/0.50 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.34/0.50 = ( ( X21 = Y21 )
% 0.34/0.50 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X22 @ Y22 )
% 0.34/0.50 & ( R1 @ X23 @ Y23 )
% 0.34/0.50 & ( R22 @ X24 @ Y24 )
% 0.34/0.50 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X25 @ Y25 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_inject(2)
% 0.34/0.50 thf(fact_105_rbt_Octr__transfer_I1_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] : ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.ctr_transfer(1)
% 0.34/0.50 thf(fact_106_rbt_Opred__inject_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o] : ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_inject(1)
% 0.34/0.50 thf(fact_107_rbt_Opred__rel,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.34/0.50 = ( ^ [P12: A > $o,P23: B > $o,X8: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P12 ) @ ( bNF_eq_onp @ B @ P23 ) @ X8 @ X8 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_rel
% 0.34/0.50 thf(fact_108_bheight_Osimps_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,Rt: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( ( C2 = rBT_Impl_Mirabelle_B )
% 0.34/0.50 => ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.34/0.50 = ( suc @ ( rBT_Im315265182height @ A @ B @ Lt ) ) ) )
% 0.34/0.50 & ( ( C2 != rBT_Impl_Mirabelle_B )
% 0.34/0.50 => ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.34/0.50 = ( rBT_Im315265182height @ A @ B @ Lt ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % bheight.simps(2)
% 0.34/0.50 thf(fact_109_rbt_Oset__intros_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,X: A,A22: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A32: A,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ A22 ) )
% 0.34/0.50 => ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(1)
% 0.34/0.50 thf(fact_110_rbt_Oset__intros_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,A32: A,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] : ( member @ A @ A32 @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(2)
% 0.34/0.50 thf(fact_111_rbt_Oset__intros_I3_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,Xb: A,A5: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A32: A,A4: B] :
% 0.34/0.50 ( ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ A5 ) )
% 0.34/0.50 => ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(3)
% 0.34/0.50 thf(fact_112_rbt_Orel__eq__onp,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,P1: A > $o,P22: B > $o] :
% 0.34/0.50 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P1 ) @ ( bNF_eq_onp @ B @ P22 ) )
% 0.34/0.50 = ( bNF_eq_onp @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_eq_onp
% 0.34/0.50 thf(fact_113_rbt_Oset__cases_I1_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,E2: A,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ A2 ) )
% 0.34/0.50 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ? [Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( A2
% 0.34/0.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.34/0.50 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z22 ) ) )
% 0.34/0.50 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( A2
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ E2 @ Z42 @ Z5 ) )
% 0.34/0.50 => ~ ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( A2
% 0.34/0.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.34/0.50 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_cases(1)
% 0.34/0.50 thf(fact_114_lift__Suc__mono__less__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [F3: nat > A,N: nat,M: nat] :
% 0.34/0.50 ( ! [N2: nat] : ( ord_less @ A @ ( F3 @ N2 ) @ ( F3 @ ( suc @ N2 ) ) )
% 0.34/0.50 => ( ( ord_less @ A @ ( F3 @ N ) @ ( F3 @ M ) )
% 0.34/0.50 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % lift_Suc_mono_less_iff
% 0.34/0.50 thf(fact_115_lift__Suc__mono__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [F3: nat > A,N: nat,N3: nat] :
% 0.34/0.50 ( ! [N2: nat] : ( ord_less @ A @ ( F3 @ N2 ) @ ( F3 @ ( suc @ N2 ) ) )
% 0.34/0.50 => ( ( ord_less @ nat @ N @ N3 )
% 0.34/0.50 => ( ord_less @ A @ ( F3 @ N ) @ ( F3 @ N3 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % lift_Suc_mono_less
% 0.34/0.50 thf(fact_116_bheight_Osimps_I1_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % bheight.simps(1)
% 0.34/0.50 thf(fact_117_rbt_Opred__mono__strong,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,X: rBT_Im246033960le_rbt @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.34/0.50 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ X )
% 0.34/0.50 => ( ! [Z1: A] :
% 0.34/0.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( ( P1 @ Z1 )
% 0.34/0.50 => ( P1a @ Z1 ) ) )
% 0.34/0.50 => ( ! [Z22: B] :
% 0.34/0.50 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( ( P22 @ Z22 )
% 0.34/0.50 => ( P2a @ Z22 ) ) )
% 0.34/0.50 => ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_mono_strong
% 0.34/0.50 thf(fact_118_rbt_Opred__cong,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 0.34/0.50 ( ( X = Ya )
% 0.34/0.50 => ( ! [Z1: A] :
% 0.34/0.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.34/0.50 => ( ( P1 @ Z1 )
% 0.34/0.50 = ( P1a @ Z1 ) ) )
% 0.34/0.50 => ( ! [Z22: B] :
% 0.34/0.50 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.34/0.50 => ( ( P22 @ Z22 )
% 0.34/0.50 = ( P2a @ Z22 ) ) )
% 0.34/0.50 => ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ X )
% 0.34/0.50 = ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_cong
% 0.34/0.50 thf(fact_119_rbt_Oset__intros_I4_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2a ) )
% 0.34/0.50 => ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(4)
% 0.34/0.50 thf(fact_120_rbt_Oset__intros_I5_J,axiom,
% 0.34/0.50 ! [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 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(5)
% 0.34/0.50 thf(fact_121_rbt_Oset__intros_I6_J,axiom,
% 0.34/0.50 ! [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] :
% 0.34/0.50 ( ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ A5a ) )
% 0.34/0.50 => ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_intros(6)
% 0.34/0.50 thf(fact_122_rbt_Oset__cases_I2_J,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,E2: B,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2 ) )
% 0.34/0.50 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ? [Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( A2
% 0.34/0.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.34/0.50 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z22 ) ) )
% 0.34/0.50 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( A2
% 0.34/0.50 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ E2 @ Z5 ) )
% 0.34/0.50 => ~ ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( A2
% 0.34/0.50 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.34/0.50 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.set_cases(2)
% 0.34/0.50 thf(fact_123_rbt_Orel__cong,axiom,
% 0.34/0.50 ! [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,R22: B > D > $o,R2a: B > D > $o] :
% 0.34/0.50 ( ( X = Ya )
% 0.34/0.50 => ( ( Y = Xa )
% 0.34/0.50 => ( ! [Z1: A,Y1: C] :
% 0.34/0.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.34/0.50 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Xa ) )
% 0.34/0.50 => ( ( R1 @ Z1 @ Y1 )
% 0.34/0.50 = ( R1a @ Z1 @ Y1 ) ) ) )
% 0.34/0.50 => ( ! [Z22: B,Y26: D] :
% 0.34/0.50 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.34/0.50 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Xa ) )
% 0.34/0.50 => ( ( R22 @ Z22 @ Y26 )
% 0.34/0.50 = ( R2a @ Z22 @ Y26 ) ) ) )
% 0.34/0.50 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X @ Y )
% 0.34/0.50 = ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_cong
% 0.34/0.50 thf(fact_124_rbt_Orel__mono__strong,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,X: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.34/0.50 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X @ Y )
% 0.34/0.50 => ( ! [Z1: A,Y1: C] :
% 0.34/0.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Y ) )
% 0.34/0.50 => ( ( R1 @ Z1 @ Y1 )
% 0.34/0.50 => ( R1a @ Z1 @ Y1 ) ) ) )
% 0.34/0.50 => ( ! [Z22: B,Y26: D] :
% 0.34/0.50 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Y ) )
% 0.34/0.50 => ( ( R22 @ Z22 @ Y26 )
% 0.34/0.50 => ( R2a @ Z22 @ Y26 ) ) ) )
% 0.34/0.50 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_mono_strong
% 0.34/0.50 thf(fact_125_rbt_Orel__refl__strong,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.34/0.50 ( ! [Z1: A] :
% 0.34/0.50 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( R1a @ Z1 @ Z1 ) )
% 0.34/0.50 => ( ! [Z22: B] :
% 0.34/0.50 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.34/0.50 => ( R2a @ Z22 @ Z22 ) )
% 0.34/0.50 => ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_refl_strong
% 0.34/0.50 thf(fact_126_not__gr__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: A] :
% 0.34/0.50 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.34/0.50 = ( N
% 0.34/0.50 = ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_gr_zero
% 0.34/0.50 thf(fact_127_color_Osize__gen_I1_J,axiom,
% 0.34/0.50 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_R )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.size_gen(1)
% 0.34/0.50 thf(fact_128_color_Osize__gen_I2_J,axiom,
% 0.34/0.50 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_B )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.size_gen(2)
% 0.34/0.50 thf(fact_129_less__numeral__extra_I3_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_numeral_extra(3)
% 0.34/0.50 thf(fact_130_zero__less__iff__neq__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.34/0.50 = ( N
% 0.34/0.50 != ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_iff_neq_zero
% 0.34/0.50 thf(fact_131_gr__implies__not__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [M: A,N: A] :
% 0.34/0.50 ( ( ord_less @ A @ M @ N )
% 0.34/0.50 => ( N
% 0.34/0.50 != ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % gr_implies_not_zero
% 0.34/0.50 thf(fact_132_not__less__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: A] :
% 0.34/0.50 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_less_zero
% 0.34/0.50 thf(fact_133_gr__zeroI,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: A] :
% 0.34/0.50 ( ( N
% 0.34/0.50 != ( zero_zero @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % gr_zeroI
% 0.34/0.50 thf(fact_134_color_Osize_I3_J,axiom,
% 0.34/0.50 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_R )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.size(3)
% 0.34/0.50 thf(fact_135_color_Osize_I4_J,axiom,
% 0.34/0.50 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_B )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % color.size(4)
% 0.34/0.50 thf(fact_136_rbt_Osize__gen_I1_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,Xa: A > nat,X: B > nat] :
% 0.34/0.50 ( ( rBT_Im1485196410ze_rbt @ A @ B @ Xa @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.size_gen(1)
% 0.34/0.50 thf(fact_137_rbt_Osize_I3_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.34/0.50 = ( zero_zero @ nat ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.size(3)
% 0.34/0.50 thf(fact_138_rbt_Osize_I4_J,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.34/0.50 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ X22 ) @ ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ X25 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.size(4)
% 0.34/0.50 thf(fact_139_of__nat__0__less__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.34/0.50 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_nat_0_less_iff
% 0.34/0.50 thf(fact_140_sgn__greater,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( sgn_sgn @ A @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_greater
% 0.34/0.50 thf(fact_141_sgn__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( sgn_sgn @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_less
% 0.34/0.50 thf(fact_142_sgn__sgn,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( sgn_sgn @ A @ ( sgn_sgn @ A @ A2 ) )
% 0.34/0.50 = ( sgn_sgn @ A @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_sgn
% 0.34/0.50 thf(fact_143_add__less__cancel__right,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,C2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_cancel_right
% 0.34/0.50 thf(fact_144_add__less__cancel__left,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [C2: A,A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_cancel_left
% 0.34/0.50 thf(fact_145_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_double_add_iff_zero_less_single_add
% 0.34/0.50 thf(fact_146_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % double_add_less_zero_iff_single_add_less_zero
% 0.34/0.50 thf(fact_147_less__add__same__cancel2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B3 @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_add_same_cancel2
% 0.34/0.50 thf(fact_148_less__add__same__cancel1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B3 ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_add_same_cancel1
% 0.34/0.50 thf(fact_149_add__less__same__cancel2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B3 ) @ B3 )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_same_cancel2
% 0.34/0.50 thf(fact_150_add__less__same__cancel1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ B3 @ A2 ) @ B3 )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_same_cancel1
% 0.34/0.50 thf(fact_151_of__nat__less__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.34/0.50 = ( ord_less @ nat @ M @ N ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_nat_less_iff
% 0.34/0.50 thf(fact_152_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C2 )
% 0.34/0.50 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % linordered_field_class.sign_simps(26)
% 0.34/0.50 thf(fact_153_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( plus_plus @ A )
% 0.34/0.50 = ( ^ [A6: A,B4: A] : ( plus_plus @ A @ B4 @ A6 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % linordered_field_class.sign_simps(27)
% 0.34/0.50 thf(fact_154_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A,C2: A] :
% 0.34/0.50 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.34/0.50 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % linordered_field_class.sign_simps(28)
% 0.34/0.50 thf(fact_155_add__less__imp__less__right,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,C2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_imp_less_right
% 0.34/0.50 thf(fact_156_add__less__imp__less__left,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [C2: A,A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_less_imp_less_left
% 0.34/0.50 thf(fact_157_add__strict__right__mono,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_strict_right_mono
% 0.34/0.50 thf(fact_158_add__strict__left__mono,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_strict_left_mono
% 0.34/0.50 thf(fact_159_add__strict__mono,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A,D2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less @ A @ C2 @ D2 )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ D2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_strict_mono
% 0.34/0.50 thf(fact_160_add__mono__thms__linordered__field_I1_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [I: A,J: A,K: A,L: A] :
% 0.34/0.50 ( ( ( ord_less @ A @ I @ J )
% 0.34/0.50 & ( K = L ) )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_mono_thms_linordered_field(1)
% 0.34/0.50 thf(fact_161_add__mono__thms__linordered__field_I2_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [I: A,J: A,K: A,L: A] :
% 0.34/0.50 ( ( ( I = J )
% 0.34/0.50 & ( ord_less @ A @ K @ L ) )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_mono_thms_linordered_field(2)
% 0.34/0.50 thf(fact_162_add__mono__thms__linordered__field_I5_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [I: A,J: A,K: A,L: A] :
% 0.34/0.50 ( ( ( ord_less @ A @ I @ J )
% 0.34/0.50 & ( ord_less @ A @ K @ L ) )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_mono_thms_linordered_field(5)
% 0.34/0.50 thf(fact_163_sgn__0__0,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ( sgn_sgn @ A @ A2 )
% 0.34/0.50 = ( zero_zero @ A ) )
% 0.34/0.50 = ( A2
% 0.34/0.50 = ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_0_0
% 0.34/0.50 thf(fact_164_of__nat__less__0__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [M: nat] :
% 0.34/0.50 ~ ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_nat_less_0_iff
% 0.34/0.50 thf(fact_165_of__nat__less__imp__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.34/0.50 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_nat_less_imp_less
% 0.34/0.50 thf(fact_166_less__imp__of__nat__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ nat @ M @ N )
% 0.34/0.50 => ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_of_nat_less
% 0.34/0.50 thf(fact_167_add__neg__neg,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.34/0.50 => ( ( ord_less @ A @ B3 @ ( zero_zero @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_neg_neg
% 0.34/0.50 thf(fact_168_add__pos__pos,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B3 )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % add_pos_pos
% 0.34/0.50 thf(fact_169_pos__add__strict,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( strict797366125id_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ B3 @ C2 )
% 0.34/0.50 => ( ord_less @ A @ B3 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pos_add_strict
% 0.34/0.50 thf(fact_170_sgn__pos,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( sgn_sgn @ A @ A2 )
% 0.34/0.50 = ( one_one @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_pos
% 0.34/0.50 thf(fact_171_of__nat__zero__less__power__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ ( semiring_1_of_nat @ A @ X ) @ N ) )
% 0.34/0.50 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ X )
% 0.34/0.50 | ( N
% 0.34/0.50 = ( zero_zero @ nat ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_nat_zero_less_power_iff
% 0.34/0.50 thf(fact_172_of__bool__eq_I1_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( zero_neq_one_of_bool @ A @ $false )
% 0.34/0.50 = ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_bool_eq(1)
% 0.34/0.50 thf(fact_173_rbt_Opred__set,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.34/0.50 = ( ^ [P12: A > $o,P23: B > $o,X8: rBT_Im246033960le_rbt @ A @ B] :
% 0.34/0.50 ( ! [Y4: A] :
% 0.34/0.50 ( ( member @ A @ Y4 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X8 ) )
% 0.34/0.50 => ( P12 @ Y4 ) )
% 0.34/0.50 & ! [Y4: B] :
% 0.34/0.50 ( ( member @ B @ Y4 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X8 ) )
% 0.34/0.50 => ( P23 @ Y4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.pred_set
% 0.34/0.50 thf(fact_174_of__bool__eq_I2_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( zero_neq_one_of_bool @ A @ $true )
% 0.34/0.50 = ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_bool_eq(2)
% 0.34/0.50 thf(fact_175_power__inject__exp,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ( ( power_power @ A @ A2 @ M )
% 0.34/0.50 = ( power_power @ A @ A2 @ N ) )
% 0.34/0.50 = ( M = N ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_inject_exp
% 0.34/0.50 thf(fact_176_power__strict__increasing__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,X: nat,Y: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ B3 )
% 0.34/0.50 => ( ( ord_less @ A @ ( power_power @ A @ B3 @ X ) @ ( power_power @ A @ B3 @ Y ) )
% 0.34/0.50 = ( ord_less @ nat @ X @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_strict_increasing_iff
% 0.34/0.50 thf(fact_177_power__Suc__less__one,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ A2 @ ( one_one @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( power_power @ A @ A2 @ ( suc @ N ) ) @ ( one_one @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_Suc_less_one
% 0.34/0.50 thf(fact_178_of__bool__def,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( zero_neq_one_of_bool @ A )
% 0.34/0.50 = ( ^ [P3: $o] : ( if @ A @ P3 @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_bool_def
% 0.34/0.50 thf(fact_179_zero__neq__one,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( zero_zero @ A )
% 0.34/0.50 != ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_neq_one
% 0.34/0.50 thf(fact_180_split__of__bool,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P4: $o] :
% 0.34/0.50 ( ( P @ ( zero_neq_one_of_bool @ A @ P4 ) )
% 0.34/0.50 = ( ( P4
% 0.34/0.50 => ( P @ ( one_one @ A ) ) )
% 0.34/0.50 & ( ~ P4
% 0.34/0.50 => ( P @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % split_of_bool
% 0.34/0.50 thf(fact_181_split__of__bool__asm,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P: A > $o,P4: $o] :
% 0.34/0.50 ( ( P @ ( zero_neq_one_of_bool @ A @ P4 ) )
% 0.34/0.50 = ( ~ ( ( P4
% 0.34/0.50 & ~ ( P @ ( one_one @ A ) ) )
% 0.34/0.50 | ( ~ P4
% 0.34/0.50 & ~ ( P @ ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % split_of_bool_asm
% 0.34/0.50 thf(fact_182_less__numeral__extra_I4_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_numeral_extra(4)
% 0.34/0.50 thf(fact_183_one__less__power,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.34/0.50 => ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ A2 @ N ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % one_less_power
% 0.34/0.50 thf(fact_184_zero__less__power,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ A2 @ N ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_power
% 0.34/0.50 thf(fact_185_power__strict__decreasing,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: nat,N4: nat,A2: A] :
% 0.34/0.50 ( ( ord_less @ nat @ N @ N4 )
% 0.34/0.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ A2 @ ( one_one @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( power_power @ A @ A2 @ N4 ) @ ( power_power @ A @ A2 @ N ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_strict_decreasing
% 0.34/0.50 thf(fact_186_of__bool__eq__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [P4: $o,Q3: $o] :
% 0.34/0.50 ( ( ( zero_neq_one_of_bool @ A @ P4 )
% 0.34/0.50 = ( zero_neq_one_of_bool @ A @ Q3 ) )
% 0.34/0.50 = ( P4 = Q3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % of_bool_eq_iff
% 0.34/0.50 thf(fact_187_power__strict__increasing,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [N: nat,N4: nat,A2: A] :
% 0.34/0.50 ( ( ord_less @ nat @ N @ N4 )
% 0.34/0.50 => ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ord_less @ A @ ( power_power @ A @ A2 @ N ) @ ( power_power @ A @ A2 @ N4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_strict_increasing
% 0.34/0.50 thf(fact_188_power__less__imp__less__exp,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ ( power_power @ A @ A2 @ M ) @ ( power_power @ A @ A2 @ N ) )
% 0.34/0.50 => ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_less_imp_less_exp
% 0.34/0.50 thf(fact_189_power__gt1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ A2 @ ( suc @ N ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_gt1
% 0.34/0.50 thf(fact_190_not__one__less__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.34/0.50 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_one_less_zero
% 0.34/0.50 thf(fact_191_zero__less__one,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( zero_less_one @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_one
% 0.34/0.50 thf(fact_192_less__numeral__extra_I1_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_numeral_extra(1)
% 0.34/0.50 thf(fact_193_less__numeral__extra_I2_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_numeral_extra(2)
% 0.34/0.50 thf(fact_194_less__add__one,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_add_one
% 0.34/0.50 thf(fact_195_zero__less__two,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_two
% 0.34/0.50 thf(fact_196_sgn__1__pos,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ( sgn_sgn @ A @ A2 )
% 0.34/0.50 = ( one_one @ A ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_1_pos
% 0.34/0.50 thf(fact_197_power__strict__mono,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.34/0.50 => ( ord_less @ A @ ( power_power @ A @ A2 @ N ) @ ( power_power @ A @ B3 @ N ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_strict_mono
% 0.34/0.50 thf(fact_198_sgn__neg,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.34/0.50 => ( ( sgn_sgn @ A @ A2 )
% 0.34/0.50 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % sgn_neg
% 0.34/0.50 thf(fact_199_zero__less__power__abs__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ ( abs_abs @ A @ A2 ) @ N ) )
% 0.34/0.50 = ( ( A2
% 0.34/0.50 != ( zero_zero @ A ) )
% 0.34/0.50 | ( N
% 0.34/0.50 = ( zero_zero @ nat ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_power_abs_iff
% 0.34/0.50 thf(fact_200_order__refl,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_refl
% 0.34/0.50 thf(fact_201_neg__less__iff__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neg_less_iff_less
% 0.34/0.50 thf(fact_202_abs__one,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.34/0.50 = ( one_one @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % abs_one
% 0.34/0.50 thf(fact_203_neg__less__0__iff__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neg_less_0_iff_less
% 0.34/0.50 thf(fact_204_neg__0__less__iff__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neg_0_less_iff_less
% 0.34/0.50 thf(fact_205_neg__less__pos,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ A2 )
% 0.34/0.50 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % neg_less_pos
% 0.34/0.50 thf(fact_206_less__neg__neg,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ A2 ) )
% 0.34/0.50 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_neg_neg
% 0.34/0.50 thf(fact_207_zero__less__abs__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( abs_abs @ A @ A2 ) )
% 0.34/0.50 = ( A2
% 0.34/0.50 != ( zero_zero @ A ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % zero_less_abs_iff
% 0.34/0.50 thf(fact_208_power__increasing__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,X: nat,Y: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ B3 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ ( power_power @ A @ B3 @ X ) @ ( power_power @ A @ B3 @ Y ) )
% 0.34/0.50 = ( ord_less_eq @ nat @ X @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_increasing_iff
% 0.34/0.50 thf(fact_209_power__le__imp__le__exp,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,M: nat,N: nat] :
% 0.34/0.50 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ ( power_power @ A @ A2 @ M ) @ ( power_power @ A @ A2 @ N ) )
% 0.34/0.50 => ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % power_le_imp_le_exp
% 0.34/0.50 thf(fact_210_strict__mono__less__eq,axiom,
% 0.34/0.50 ! [B: $tType,A: $tType] :
% 0.34/0.50 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 & ( order @ B @ ( type2 @ B ) ) )
% 0.34/0.50 => ! [F3: A > B,X: A,Y: A] :
% 0.34/0.50 ( ( order_strict_mono @ A @ B @ F3 )
% 0.34/0.50 => ( ( ord_less_eq @ B @ ( F3 @ X ) @ ( F3 @ Y ) )
% 0.34/0.50 = ( ord_less_eq @ A @ X @ Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % strict_mono_less_eq
% 0.34/0.50 thf(fact_211_abs__not__less__zero,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ~ ( ord_less @ A @ ( abs_abs @ A @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % abs_not_less_zero
% 0.34/0.50 thf(fact_212_abs__of__pos,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.50 => ( ( abs_abs @ A @ A2 )
% 0.34/0.50 = A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % abs_of_pos
% 0.34/0.50 thf(fact_213_complete__interval,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,P: A > $o] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( P @ A2 )
% 0.34/0.50 => ( ~ ( P @ B3 )
% 0.34/0.50 => ? [C3: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.34/0.50 & ( ord_less_eq @ A @ C3 @ B3 )
% 0.34/0.50 & ! [X6: A] :
% 0.34/0.50 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.34/0.50 & ( ord_less @ A @ X6 @ C3 ) )
% 0.34/0.50 => ( P @ X6 ) )
% 0.34/0.50 & ! [D3: A] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ( ( ord_less_eq @ A @ A2 @ X7 )
% 0.34/0.50 & ( ord_less @ A @ X7 @ D3 ) )
% 0.34/0.50 => ( P @ X7 ) )
% 0.34/0.50 => ( ord_less_eq @ A @ D3 @ C3 ) ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % complete_interval
% 0.34/0.50 thf(fact_214_order_Onot__eq__order__implies__strict,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( A2 != B3 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.not_eq_order_implies_strict
% 0.34/0.50 thf(fact_215_dual__order_Ostrict__implies__order,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less @ A @ B3 @ A2 )
% 0.34/0.50 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_implies_order
% 0.34/0.50 thf(fact_216_dual__order_Ostrict__iff__order,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less @ A )
% 0.34/0.50 = ( ^ [B4: A,A6: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.34/0.50 & ( A6 != B4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_iff_order
% 0.34/0.50 thf(fact_217_dual__order_Oorder__iff__strict,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less_eq @ A )
% 0.34/0.50 = ( ^ [B4: A,A6: A] :
% 0.34/0.50 ( ( ord_less @ A @ B4 @ A6 )
% 0.34/0.50 | ( A6 = B4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.order_iff_strict
% 0.34/0.50 thf(fact_218_order_Ostrict__implies__order,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_implies_order
% 0.34/0.50 thf(fact_219_dense__le__bounded,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,Z3: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ! [W: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ W )
% 0.34/0.50 => ( ( ord_less @ A @ W @ Y )
% 0.34/0.50 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dense_le_bounded
% 0.34/0.50 thf(fact_220_dense__ge__bounded,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Z3: A,X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z3 @ X )
% 0.34/0.50 => ( ! [W: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z3 @ W )
% 0.34/0.50 => ( ( ord_less @ A @ W @ X )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dense_ge_bounded
% 0.34/0.50 thf(fact_221_dual__order_Ostrict__trans2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ B3 @ A2 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_trans2
% 0.34/0.50 thf(fact_222_dual__order_Ostrict__trans1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A,C2: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.34/0.50 => ( ( ord_less @ A @ C2 @ B3 )
% 0.34/0.50 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.strict_trans1
% 0.34/0.50 thf(fact_223_order_Ostrict__iff__order,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less @ A )
% 0.34/0.50 = ( ^ [A6: A,B4: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.34/0.50 & ( A6 != B4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_iff_order
% 0.34/0.50 thf(fact_224_order_Oorder__iff__strict,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less_eq @ A )
% 0.34/0.50 = ( ^ [A6: A,B4: A] :
% 0.34/0.50 ( ( ord_less @ A @ A6 @ B4 )
% 0.34/0.50 | ( A6 = B4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.order_iff_strict
% 0.34/0.50 thf(fact_225_order_Ostrict__trans2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_trans2
% 0.34/0.50 thf(fact_226_order_Ostrict__trans1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A,C2: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less @ A @ B3 @ C2 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order.strict_trans1
% 0.34/0.50 thf(fact_227_not__le__imp__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Y: A,X: A] :
% 0.34/0.50 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.34/0.50 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_le_imp_less
% 0.34/0.50 thf(fact_228_less__le__not__le,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less @ A )
% 0.34/0.50 = ( ^ [X8: A,Y4: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X8 @ Y4 )
% 0.34/0.50 & ~ ( ord_less_eq @ A @ Y4 @ X8 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_le_not_le
% 0.34/0.50 thf(fact_229_le__imp__less__or__eq,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 | ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % le_imp_less_or_eq
% 0.34/0.50 thf(fact_230_le__less__linear,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.50 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % le_less_linear
% 0.34/0.50 thf(fact_231_dense__le,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Y: A,Z3: A] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Y )
% 0.34/0.50 => ( ord_less_eq @ A @ X7 @ Z3 ) )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dense_le
% 0.34/0.50 thf(fact_232_dense__ge,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Z3: A,Y: A] :
% 0.34/0.50 ( ! [X7: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z3 @ X7 )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ X7 ) )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dense_ge
% 0.34/0.50 thf(fact_233_less__le__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,Z3: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.34/0.50 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_le_trans
% 0.34/0.50 thf(fact_234_le__less__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A,Z3: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less @ A @ Y @ Z3 )
% 0.34/0.50 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % le_less_trans
% 0.34/0.50 thf(fact_235_antisym__conv2,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.50 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.34/0.50 = ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % antisym_conv2
% 0.34/0.50 thf(fact_236_antisym__conv1,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ~ ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.50 = ( X = Y ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % antisym_conv1
% 0.34/0.50 thf(fact_237_less__imp__le,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_imp_le
% 0.34/0.50 thf(fact_238_le__neq__trans,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( A2 != B3 )
% 0.34/0.50 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % le_neq_trans
% 0.34/0.50 thf(fact_239_not__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.34/0.50 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_less
% 0.34/0.50 thf(fact_240_not__le,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.34/0.50 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % not_le
% 0.34/0.50 thf(fact_241_order__less__le__subst2,axiom,
% 0.34/0.50 ! [A: $tType,C: $tType] :
% 0.34/0.50 ( ( ( order @ C @ ( type2 @ C ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less_eq @ C @ ( F3 @ B3 ) @ C2 )
% 0.34/0.50 => ( ! [X7: A,Y2: A] :
% 0.34/0.50 ( ( ord_less @ A @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_less_le_subst2
% 0.34/0.50 thf(fact_242_order__less__le__subst1,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( ( order @ B @ ( type2 @ B ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.34/0.50 ( ( ord_less @ A @ A2 @ ( F3 @ B3 ) )
% 0.34/0.50 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.34/0.50 => ( ! [X7: B,Y2: B] :
% 0.34/0.50 ( ( ord_less_eq @ B @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less_eq @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_less_le_subst1
% 0.34/0.50 thf(fact_243_order__le__less__subst2,axiom,
% 0.34/0.50 ! [A: $tType,C: $tType] :
% 0.34/0.50 ( ( ( order @ C @ ( type2 @ C ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.34/0.50 => ( ( ord_less @ C @ ( F3 @ B3 ) @ C2 )
% 0.34/0.50 => ( ! [X7: A,Y2: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less_eq @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_le_less_subst2
% 0.34/0.50 thf(fact_244_order__le__less__subst1,axiom,
% 0.34/0.50 ! [A: $tType,B: $tType] :
% 0.34/0.50 ( ( ( order @ B @ ( type2 @ B ) )
% 0.34/0.50 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.50 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.34/0.50 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B3 ) )
% 0.34/0.50 => ( ( ord_less @ B @ B3 @ C2 )
% 0.34/0.50 => ( ! [X7: B,Y2: B] :
% 0.34/0.50 ( ( ord_less @ B @ X7 @ Y2 )
% 0.34/0.50 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.34/0.50 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % order_le_less_subst1
% 0.34/0.50 thf(fact_245_less__le,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less @ A )
% 0.34/0.50 = ( ^ [X8: A,Y4: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ X8 @ Y4 )
% 0.34/0.50 & ( X8 != Y4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % less_le
% 0.34/0.50 thf(fact_246_le__less,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ( ( ord_less_eq @ A )
% 0.34/0.50 = ( ^ [X8: A,Y4: A] :
% 0.34/0.50 ( ( ord_less @ A @ X8 @ Y4 )
% 0.34/0.50 | ( X8 = Y4 ) ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % le_less
% 0.34/0.50 thf(fact_247_leI,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [X: A,Y: A] :
% 0.34/0.50 ( ~ ( ord_less @ A @ X @ Y )
% 0.34/0.50 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % leI
% 0.34/0.50 thf(fact_248_leD,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [Y: A,X: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.50 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % leD
% 0.34/0.50 thf(fact_249_pinf_I6_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ~ ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(6)
% 0.34/0.50 thf(fact_250_pinf_I8_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ Z @ X6 )
% 0.34/0.50 => ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % pinf(8)
% 0.34/0.50 thf(fact_251_minf_I6_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(6)
% 0.34/0.50 thf(fact_252_minf_I8_J,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [T: A] :
% 0.34/0.50 ? [Z: A] :
% 0.34/0.50 ! [X6: A] :
% 0.34/0.50 ( ( ord_less @ A @ X6 @ Z )
% 0.34/0.50 => ~ ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % minf(8)
% 0.34/0.50 thf(fact_253_abs__less__iff,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [A2: A,B3: A] :
% 0.34/0.50 ( ( ord_less @ A @ ( abs_abs @ A @ A2 ) @ B3 )
% 0.34/0.50 = ( ( ord_less @ A @ A2 @ B3 )
% 0.34/0.50 & ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % abs_less_iff
% 0.34/0.50 thf(fact_254_rbt_Orel__mono,axiom,
% 0.34/0.50 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 0.34/0.50 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 0.34/0.50 => ( ( ord_less_eq @ ( B > D > $o ) @ R22 @ R2a )
% 0.34/0.50 => ( ord_less_eq @ ( ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ C @ D ) > $o ) @ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 ) @ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % rbt.rel_mono
% 0.34/0.50 thf(fact_255_dual__order_Oantisym,axiom,
% 0.34/0.50 ! [A: $tType] :
% 0.34/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.50 => ! [B3: A,A2: A] :
% 0.34/0.50 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.34/0.50 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.34/0.50 => ( A2 = B3 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 % dual_order.antisym
% 0.34/0.50
% 0.34/0.50 %----Type constructors (28)
% 0.34/0.50 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.34/0.50 ! [A7: $tType,A8: $tType] :
% 0.34/0.50 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.34/0.50 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.34/0.50 ! [A7: $tType,A8: $tType] :
% 0.34/0.50 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.34/0.50 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_fun___Orderings_Oord,axiom,
% 0.34/0.50 ! [A7: $tType,A8: $tType] :
% 0.34/0.50 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.34/0.50 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.34/0.50 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.34/0.50 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.34/0.50 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.34/0.50 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.34/0.50 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.34/0.50 strict797366125id_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.34/0.50 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.34/0.50 linord1659791738miring @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 0.34/0.50 ordere216010020id_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.34/0.50 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 0.34/0.50 zero_less_one @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.34/0.50 wellorder @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.34/0.50 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.34/0.50 preorder @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.34/0.50 linorder @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.34/0.50 no_top @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.34/0.50 order @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.34/0.50 ord @ nat @ ( type2 @ nat ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.34/0.50 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.34/0.50 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.34/0.50 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.34/0.50 preorder @ $o @ ( type2 @ $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.34/0.50 linorder @ $o @ ( type2 @ $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.34/0.50 order @ $o @ ( type2 @ $o ) ).
% 0.34/0.50
% 0.34/0.50 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.34/0.50 ord @ $o @ ( type2 @ $o ) ).
% 0.34/0.50
% 0.34/0.50 %----Helper facts (3)
% 0.34/0.50 thf(help_If_3_1_T,axiom,
% 0.34/0.50 ! [P: $o] :
% 0.34/0.50 ( ( P = $true )
% 0.34/0.50 | ( P = $false ) ) ).
% 0.34/0.50
% 0.34/0.50 thf(help_If_2_1_T,axiom,
% 0.34/0.50 ! [A: $tType,X: A,Y: A] :
% 0.34/0.50 ( ( if @ A @ $false @ X @ Y )
% 0.34/0.50 = Y ) ).
% 0.34/0.50
% 0.34/0.50 thf(help_If_1_1_T,axiom,
% 0.34/0.50 ! [A: $tType,X: A,Y: A] :
% 0.34/0.50 ( ( if @ A @ $true @ X @ Y )
% 0.34/0.50 = X ) ).
% 0.34/0.50
% 0.34/0.50 %----Conjectures (2)
% 0.34/0.50 thf(conj_0,hypothesis,
% 0.34/0.50 rBT_Im1040612427e_inv1 @ a @ b @ t ).
% 0.34/0.50
% 0.34/0.50 thf(conj_1,conjecture,
% 0.34/0.50 rBT_Im1071879905_inv1l @ a @ b @ t ).
% 0.34/0.50
% 0.34/0.50 %------------------------------------------------------------------------------
% 0.34/0.50 ------------------------
% 0.35/1.50 ---- Embedded in THF ---
% 0.35/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.35/1.50 %%% Generated on Tue Feb 24 06:12:19 EST 2026
% 0.35/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.35/1.50 %%% Logic specification used:
% 0.35/1.50 %%% thf(spec, logic, $$dhol).
% 0.35/1.50
% 0.35/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2DTF28340.p
% 0.35/1.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor, type, rBT_Im1923302023_color: $tType).
% 0.35/1.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt, type, rBT_Im246033960le_rbt: ($tType > ($tType > $tType))).
% 0.35/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.35/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.35/1.50 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.35/1.50 thf(ty_tf_b, type, b: $tType).
% 0.35/1.50 thf(ty_tf_a, type, a: $tType).
% 0.35/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__ab__group__add__abs, type, ordere142940540dd_abs: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add, type, strict797366125id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.35/1.50 thf(sy_c_BNF__Def_Oeq__onp, type, bNF_eq_onp: (!> [A:$tType]: (((A > $o) > (A > (A > $o)))))).
% 0.35/1.50 thf(sy_c_Groups_Oabs__class_Oabs, type, abs_abs: (!> [A:$tType]: ((A > A)))).
% 0.35/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.35/1.50 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 0.35/1.50 thf(sy_c_Groups_Osgn__class_Osgn, type, sgn_sgn: (!> [A:$tType]: ((A > A)))).
% 0.35/1.50 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.35/1.50 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 0.35/1.50 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.35/1.50 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 0.35/1.50 thf(sy_c_Nat_Osemiring__1__class_Oof__nat, type, semiring_1_of_nat: (!> [A:$tType]: ((nat > A)))).
% 0.35/1.50 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 0.35/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.35/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.35/1.50 thf(sy_c_Orderings_Oorder__class_Ostrict__mono, type, order_strict_mono: (!> [A:$tType,B:$tType]: (((A > B) > $o)))).
% 0.35/1.50 thf(sy_c_Power_Opower__class_Opower, type, power_power: (!> [A:$tType]: ((A > (nat > A))))).
% 0.35/1.50 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obheight, type, rBT_Im315265182height: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > nat)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color, type, rBT_Im1975547051_color: (!> [A:$tType]: ((A > (A > (rBT_Im1923302023_color > A)))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color, type, rBT_Im1059957627_color: (!> [A:$tType]: ((A > (A > (rBT_Im1923302023_color > A)))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color, type, rBT_Im800559290_color: (rBT_Im1923302023_color > nat)).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of, type, rBT_Im1805589839lor_of: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > rBT_Im1923302023_color)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1, type, rBT_Im1040612427e_inv1: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1l, type, rBT_Im1071879905_inv1l: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater, type, rBT_Im1259024060reater: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less, type, rBT_Im2075124343t_less: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted, type, rBT_Im759614907sorted: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater, type, rBT_Im1332541288reater: (!> [A:$tType,B:$tType]: ((A > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less, type, rBT_Im903026891t_less: (!> [A:$tType,B:$tType]: ((A > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted, type, rBT_Im1183586831sorted: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch, type, rBT_Im480247531Branch: (!> [A:$tType,B:$tType]: ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty, type, rBT_Im418718756_Empty: (!> [A:$tType,B:$tType]: (((rBT_Im246033960le_rbt @ A) @ B)))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt, type, rBT_Im858806507se_rbt: (!> [C:$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)))))).
% 0.35/1.50 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) > $o)))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt, type, rBT_Im1947144893ec_rbt: (!> [E:$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)))))).
% 0.35/1.50 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) > $o))))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt, type, rBT_Im1178217900t1_rbt: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (set @ A))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt, type, rBT_Im1550225131t2_rbt: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (set @ B))))).
% 0.35/1.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt, type, rBT_Im1485196410ze_rbt: (!> [A:$tType,B:$tType]: (((A > nat) > ((B > nat) > (((rBT_Im246033960le_rbt @ A) @ B) > nat)))))).
% 0.35/1.50 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool, type, zero_neq_one_of_bool: (!> [A:$tType]: (($o > A)))).
% 0.35/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.35/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.35/1.50 thf(sy_v_t, type, t: ((rBT_Im246033960le_rbt @ a) @ b)).
% 0.35/1.50 thf(fact_0_inv1l_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,C2:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1071879905_inv1l @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ L) @ K) @ V) @ R)) = ((((rBT_Im1040612427e_inv1 @ A) @ B) @ L) & (((rBT_Im1040612427e_inv1 @ A) @ B) @ R)))))).
% 0.35/1.50 thf(fact_1_inv1l_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1071879905_inv1l @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_2_inv1_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1040612427e_inv1 @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_3_inv1_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,Rt:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1040612427e_inv1 @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ Lt) @ K) @ V) @ Rt)) = ((((rBT_Im1040612427e_inv1 @ A) @ B) @ Lt) & ((((rBT_Im1040612427e_inv1 @ A) @ B) @ Rt) & ((C2 = rBT_Impl_Mirabelle_B) | (((((rBT_Im1805589839lor_of @ A) @ B) @ Lt) = rBT_Impl_Mirabelle_B) & ((((rBT_Im1805589839lor_of @ A) @ B) @ Rt) = rBT_Impl_Mirabelle_B))))))))).
% 0.35/1.50 thf(fact_4_color_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F1:A,F2:A,Color:rBT_Im1923302023_color]: (((H @ ((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ Color)) = ((((rBT_Im1975547051_color @ B) @ (H @ F1)) @ (H @ F2)) @ Color))))).
% 0.35/1.50 thf(fact_5_rbt_Oinject, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25) = (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & ((X22 = Y22) & ((X23 = Y23) & ((X24 = Y24) & (X25 = Y25))))))))).
% 0.35/1.50 thf(fact_6_color_Osimps_I4_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_B) = F2)))).
% 0.35/1.50 thf(fact_7_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))))).
% 0.35/1.50 thf(fact_8_color__of_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,C2:rBT_Im1923302023_color,Uu:((rBT_Im246033960le_rbt @ A) @ B),Uv:A,Uw:B,Ux:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1805589839lor_of @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ Uu) @ Uv) @ Uw) @ Ux)) = C2)))).
% 0.35/1.50 thf(fact_9_color__of_Osimps_I1_J, axiom, (! [A:$tType,B:$tType]: (((((rBT_Im1805589839lor_of @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = rBT_Impl_Mirabelle_B)))).
% 0.35/1.50 thf(fact_10_rbt_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > $o),Rbt:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) => ((! [X1:rBT_Im1923302023_color,X2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,X4:B,X5:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ X2) => ((P @ X5) => (P @ (((((((rBT_Im480247531Branch @ A) @ B) @ X1) @ X2) @ X3) @ X4) @ X5)))))) => (P @ Rbt)))))).
% 0.35/1.50 thf(fact_11_rbt_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((rBT_Im246033960le_rbt @ A) @ B)]: (((Y != ((rBT_Im418718756_Empty @ A) @ B)) => (~ ((! [X212:rBT_Im1923302023_color,X222:((rBT_Im246033960le_rbt @ A) @ B),X232:A,X242:B,X252:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y != (((((((rBT_Im480247531Branch @ A) @ B) @ X212) @ X222) @ X232) @ X242) @ X252)))))))))).
% 0.35/1.50 thf(fact_12_rbt__cases, axiom, (! [B:$tType,A:$tType,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((T != ((rBT_Im418718756_Empty @ A) @ B)) => ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K2:A,V2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ K2) @ V2) @ R2)))) => (~ ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K2:A,V2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ K2) @ V2) @ R2))))))))))).
% 0.35/1.50 thf(fact_13_color_Osimps_I6_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1059957627_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_B) = F2)))).
% 0.35/1.50 thf(fact_14_ord_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_15_color_Osimps_I3_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1975547051_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_R) = F1)))).
% 0.35/1.50 thf(fact_16_rbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A]: (((((rBT_Im903026891t_less @ A) @ B) @ K) @ ((rBT_Im418718756_Empty @ A) @ B)))))))).
% 0.35/1.50 thf(fact_17_rbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A]: (((((rBT_Im1332541288reater @ A) @ B) @ K) @ ((rBT_Im418718756_Empty @ A) @ B)))))))).
% 0.35/1.50 thf(fact_18_color_Odistinct_I1_J, axiom, (rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B)).
% 0.35/1.50 thf(fact_19_color_Oinduct, axiom, (! [P:(rBT_Im1923302023_color > $o),Color:rBT_Im1923302023_color]: (((P @ rBT_Impl_Mirabelle_R) => ((P @ rBT_Impl_Mirabelle_B) => (P @ Color)))))).
% 0.35/1.50 thf(fact_20_color_Oexhaust, axiom, (! [Y:rBT_Im1923302023_color]: (((Y != rBT_Impl_Mirabelle_R) => (Y = rBT_Impl_Mirabelle_B))))).
% 0.35/1.50 thf(fact_21_rbt_Osimps_I4_J, axiom, (! [A:$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)))).
% 0.35/1.50 thf(fact_22_rbt_Osimps_I5_J, axiom, (! [C:$tType,B:$tType,A:$tType,F1:C,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > C))))),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im858806507se_rbt @ C) @ A) @ B) @ F1) @ F2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((((F2 @ X21) @ X22) @ X23) @ X24) @ X25))))).
% 0.35/1.50 thf(fact_23_color_Osimps_I5_J, axiom, (! [A:$tType,F1:A,F2:A]: ((((((rBT_Im1059957627_color @ A) @ F1) @ F2) @ rBT_Impl_Mirabelle_R) = F1)))).
% 0.35/1.50 thf(fact_24_rbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [C2:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1183586831sorted @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ L) @ K) @ V) @ R)) = (((((rBT_Im903026891t_less @ A) @ B) @ K) @ L) & (((((rBT_Im1332541288reater @ A) @ B) @ K) @ R) & ((((rBT_Im1183586831sorted @ A) @ B) @ L) & (((rBT_Im1183586831sorted @ A) @ B) @ R))))))))))).
% 0.35/1.50 thf(fact_25_rbt__greater__simps_I2_J, axiom, (! [C:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C),Kt:A,V:C,Rt:((rBT_Im246033960le_rbt @ A) @ C)]: ((((((rBT_Im1332541288reater @ A) @ C) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C) @ C2) @ Lt) @ Kt) @ V) @ Rt)) = ((((ord_less @ A) @ K) @ Kt) & (((((rBT_Im1332541288reater @ A) @ C) @ K) @ Lt) & ((((rBT_Im1332541288reater @ A) @ C) @ K) @ Rt)))))))))).
% 0.35/1.50 thf(fact_26_rbt__less__simps_I2_J, axiom, (! [C:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C),Kt:A,V:C,Rt:((rBT_Im246033960le_rbt @ A) @ C)]: ((((((rBT_Im903026891t_less @ A) @ C) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C) @ C2) @ Lt) @ Kt) @ V) @ Rt)) = ((((ord_less @ A) @ Kt) @ K) & (((((rBT_Im903026891t_less @ A) @ C) @ K) @ Lt) & ((((rBT_Im903026891t_less @ A) @ C) @ K) @ Rt)))))))))).
% 0.35/1.50 thf(fact_27_ord_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),C2:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im759614907sorted @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ L) @ K) @ V) @ R)) = ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ L) & ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ R) & (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ L) & ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ R)))))))).
% 0.35/1.50 thf(fact_28_ord_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_29_ord_Orbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_30_ord_Orbt__greater__simps_I2_J, axiom, (! [C:$tType,A:$tType,Less:(A > (A > $o)),K:A,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C),Kt:A,V:C,Rt:((rBT_Im246033960le_rbt @ A) @ C)]: (((((((rBT_Im1259024060reater @ A) @ C) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C) @ C2) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ A) @ C) @ Less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ A) @ C) @ Less) @ K) @ Rt))))))).
% 0.35/1.50 thf(fact_31_ord_Orbt__less__simps_I2_J, axiom, (! [C:$tType,A:$tType,Less:(A > (A > $o)),K:A,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C),Kt:A,V:C,Rt:((rBT_Im246033960le_rbt @ A) @ C)]: (((((((rBT_Im2075124343t_less @ A) @ C) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C) @ C2) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ A) @ C) @ Less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ A) @ C) @ Less) @ K) @ Rt))))))).
% 0.35/1.50 thf(fact_32_rbt_Osimps_I6_J, axiom, (! [A:$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)))).
% 0.35/1.50 thf(fact_33_rbt_Osimps_I7_J, axiom, (! [E:$tType,B:$tType,A:$tType,F1:E,F2:(rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > (E > (E > E))))))),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((((((F2 @ X21) @ X22) @ X23) @ X24) @ X25) @ ((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ X22)) @ ((((((rBT_Im1947144893ec_rbt @ E) @ A) @ B) @ F1) @ F2) @ X25)))))).
% 0.35/1.50 thf(fact_34_rbt__less__trans, axiom, (! [C:$tType,A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,T:((rBT_Im246033960le_rbt @ A) @ C),Y:A]: ((((((rBT_Im903026891t_less @ A) @ C) @ X) @ T) => ((((ord_less @ A) @ X) @ Y) => ((((rBT_Im903026891t_less @ A) @ C) @ Y) @ T))))))))).
% 0.35/1.50 thf(fact_35_rbt__greater__trans, axiom, (! [C:$tType,A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A,T:((rBT_Im246033960le_rbt @ A) @ C)]: (((((ord_less @ A) @ X) @ Y) => (((((rBT_Im1332541288reater @ A) @ C) @ Y) @ T) => ((((rBT_Im1332541288reater @ A) @ C) @ X) @ T))))))))).
% 0.35/1.50 thf(fact_36_rbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (((rBT_Im1183586831sorted @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 0.35/1.50 thf(fact_37_minf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X6:C]: (((((ord_less @ C) @ X6) @ Z) => (F = F)))))))))))).
% 0.35/1.50 thf(fact_38_minf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (~ ((((ord_less @ A) @ T) @ X6)))))))))))))).
% 0.35/1.50 thf(fact_39_minf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (((ord_less @ A) @ X6) @ T)))))))))))).
% 0.35/1.50 thf(fact_40_minf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (X6 != T)))))))))))).
% 0.35/1.50 thf(fact_41_minf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (X6 != T)))))))))))).
% 0.35/1.50 thf(fact_42_minf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z2) => ((P @ X7) = (P2 @ X7))))))) => ((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z2) => ((Q @ X7) = (Q2 @ X7))))))) => (? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (((P @ X6) | (Q @ X6)) = ((P2 @ X6) | (Q2 @ X6)))))))))))))))).
% 0.35/1.50 thf(fact_43_minf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z2) => ((P @ X7) = (P2 @ X7))))))) => ((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ X7) @ Z2) => ((Q @ X7) = (Q2 @ X7))))))) => (? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (((P @ X6) & (Q @ X6)) = ((P2 @ X6) & (Q2 @ X6)))))))))))))))).
% 0.35/1.50 thf(fact_44_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: ((((ord @ C) @ (type2 @ C)) => (! [F:D]: ((? [Z:C]: ((! [X6:C]: (((((ord_less @ C) @ Z) @ X6) => (F = F)))))))))))).
% 0.35/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.35/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X8:A]: ((((member @ A) @ X8) @ A3)))) = A3)))).
% 0.35/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X7:A]: (((P @ X7) = (Q @ X7)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.35/1.50 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G:(A > B)]: (((! [X7:A]: (((F3 @ X7) = (G @ X7)))) => (F3 = G))))).
% 0.35/1.50 thf(fact_49_pinf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (((ord_less @ A) @ T) @ X6)))))))))))).
% 0.35/1.50 thf(fact_50_pinf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ Z2) @ X7) => ((P @ X7) = (P2 @ X7))))))) => ((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ Z2) @ X7) => ((Q @ X7) = (Q2 @ X7))))))) => (? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (((P @ X6) & (Q @ X6)) = ((P2 @ X6) & (Q2 @ X6)))))))))))))))).
% 0.35/1.50 thf(fact_51_pinf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ Z2) @ X7) => ((P @ X7) = (P2 @ X7))))))) => ((? [Z2:A]: ((! [X7:A]: (((((ord_less @ A) @ Z2) @ X7) => ((Q @ X7) = (Q2 @ X7))))))) => (? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (((P @ X6) | (Q @ X6)) = ((P2 @ X6) | (Q2 @ X6)))))))))))))))).
% 0.35/1.50 thf(fact_52_pinf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (X6 != T)))))))))))).
% 0.35/1.50 thf(fact_53_pinf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (X6 != T)))))))))))).
% 0.35/1.50 thf(fact_54_pinf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (~ ((((ord_less @ A) @ X6) @ T)))))))))))))).
% 0.35/1.50 thf(fact_55_ex__gt__or__lt, axiom, (! [A:$tType]: ((((condit1656338222tinuum @ A) @ (type2 @ A)) => (! [A2:A]: ((? [B2:A]: (((((ord_less @ A) @ A2) @ B2) | (((ord_less @ A) @ B2) @ A2)))))))))).
% 0.35/1.50 thf(fact_56_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.35/1.50 thf(fact_57_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (A2 != B3)))))))).
% 0.35/1.50 thf(fact_58_linordered__field__no__ub, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X6:A]: ((? [X1:A]: ((((ord_less @ A) @ X6) @ X1))))))))).
% 0.35/1.50 thf(fact_59_linordered__field__no__lb, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [X6:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X6))))))))).
% 0.35/1.50 thf(fact_60_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (A2 != B3)))))))).
% 0.35/1.50 thf(fact_61_dependent__wellorder__choice, axiom, (! [B:$tType,A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:((A > B) > (A > (B > $o)))]: (((! [R2:B,F4:(A > B),G2:(A > B),X7:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X7) => ((F4 @ Y3) = (G2 @ Y3))))) => ((((P @ F4) @ X7) @ R2) = (((P @ G2) @ X7) @ R2))))) => ((! [X7:A,F4:(A > B)]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X7) => (((P @ F4) @ Y3) @ (F4 @ Y3))))) => (? [X12:B]: ((((P @ F4) @ X7) @ X12)))))) => (? [F4:(A > B)]: ((! [X6:A]: ((((P @ F4) @ X6) @ (F4 @ X6)))))))))))))).
% 0.35/1.50 thf(fact_62_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 0.35/1.50 thf(fact_63_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F3:(B > A),B3:B,C2:B]: (((A2 = (F3 @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X7:B,Y2:B]: (((((ord_less @ B) @ X7) @ Y2) => (((ord_less @ A) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.35/1.50 thf(fact_64_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F3:(A > B),C2:B]: (((((ord_less @ A) @ A2) @ B3) => (((F3 @ B3) = C2) => ((! [X7:A,Y2:A]: (((((ord_less @ A) @ X7) @ Y2) => (((ord_less @ B) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ B) @ (F3 @ A2)) @ C2)))))))))).
% 0.35/1.50 thf(fact_65_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F3:(B > A),B3:B,C2:B]: (((((ord_less @ A) @ A2) @ (F3 @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X7:B,Y2:B]: (((((ord_less @ B) @ X7) @ Y2) => (((ord_less @ A) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.35/1.50 thf(fact_66_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F3:(A > C),C2:C]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ C) @ (F3 @ B3)) @ C2) => ((! [X7:A,Y2:A]: (((((ord_less @ A) @ X7) @ Y2) => (((ord_less @ C) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ C) @ (F3 @ A2)) @ C2)))))))))).
% 0.35/1.50 thf(fact_67_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 0.35/1.50 thf(fact_68_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X1:A]: ((((ord_less @ A) @ X) @ X1))))))))).
% 0.35/1.50 thf(fact_69_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.35/1.50 thf(fact_70_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.35/1.50 thf(fact_71_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 0.35/1.50 thf(fact_72_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 0.35/1.50 thf(fact_73_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.35/1.50 thf(fact_74_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.35/1.50 thf(fact_75_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 0.35/1.50 thf(fact_76_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X) @ Z3))))))))).
% 0.35/1.50 thf(fact_77_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.35/1.50 thf(fact_78_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 0.35/1.50 thf(fact_79_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((A2 = B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 0.35/1.50 thf(fact_80_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ A2) @ B3) => ((B3 = C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 0.35/1.50 thf(fact_81_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (~ ((((ord_less @ A) @ A2) @ B3)))))))))).
% 0.35/1.50 thf(fact_82_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.35/1.50 thf(fact_83_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.35/1.50 thf(fact_84_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X7:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X7) => (P @ Y3)))) => (P @ X7)))) => (P @ A2)))))))).
% 0.35/1.50 thf(fact_85_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.35/1.50 thf(fact_86_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 0.35/1.50 thf(fact_87_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 0.35/1.50 thf(fact_88_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.35/1.50 thf(fact_89_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 0.35/1.50 thf(fact_90_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 0.35/1.50 thf(fact_91_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.35/1.50 thf(fact_92_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A2))))))))).
% 0.35/1.50 thf(fact_93_rbt_Opred__inject_I2_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P22:(B > $o),A2:rBT_Im1923302023_color,Aa:((rBT_Im246033960le_rbt @ A) @ B),Ab:A,Ac:B,Ad:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A2) @ Aa) @ Ab) @ Ac) @ Ad)) = ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ Aa) & ((P1 @ Ab) & ((P22 @ Ac) & (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ Ad)))))))).
% 0.35/1.50 thf(fact_94_rbt_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((~ (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) @ ((rBT_Im418718756_Empty @ C) @ D))))))).
% 0.35/1.50 thf(fact_95_rbt_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ C) @ D),Y23:C,Y24:D,Y25:((rBT_Im246033960le_rbt @ C) @ D)]: ((~ (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((rBT_Im418718756_Empty @ A) @ B)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25))))))).
% 0.35/1.50 thf(fact_96_strict__monoD, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F3:(A > B),X:A,Y:A]: (((((order_strict_mono @ A) @ B) @ F3) => ((((ord_less @ A) @ X) @ Y) => (((ord_less @ B) @ (F3 @ X)) @ (F3 @ Y)))))))))).
% 0.35/1.50 thf(fact_97_strict__monoI, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F3:(A > B)]: (((! [X7:A,Y2:A]: (((((ord_less @ A) @ X7) @ Y2) => (((ord_less @ B) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((order_strict_mono @ A) @ B) @ F3)))))))).
% 0.35/1.50 thf(fact_98_strict__mono__def, axiom, (! [B:$tType,A:$tType]: (((((order @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (((order_strict_mono @ A) @ B) = (^ [F5:(A > B)]: ((! [X8:A,Y4:A]: (((((ord_less @ A) @ X8) @ Y4) => (((ord_less @ B) @ (F5 @ X8)) @ (F5 @ Y4)))))))))))).
% 0.35/1.50 thf(fact_99_strict__mono__less, axiom, (! [B:$tType,A:$tType]: (((((linorder @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F3:(A > B),X:A,Y:A]: (((((order_strict_mono @ A) @ B) @ F3) => ((((ord_less @ B) @ (F3 @ X)) @ (F3 @ Y)) = (((ord_less @ A) @ X) @ Y))))))))).
% 0.35/1.50 thf(fact_100_strict__mono__eq, axiom, (! [B:$tType,A:$tType]: (((((linorder @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F3:(A > B),X:A,Y:A]: (((((order_strict_mono @ A) @ B) @ F3) => (((F3 @ X) = (F3 @ Y)) = (X = Y))))))))).
% 0.35/1.50 thf(fact_101_rbt_Orel__refl, axiom, (! [D:$tType,C:$tType,R1a:(C > (C > $o)),R2a:(D > (D > $o)),X:((rBT_Im246033960le_rbt @ C) @ D)]: (((! [X7:C]: (((R1a @ X7) @ X7))) => ((! [X7:D]: (((R2a @ X7) @ X7))) => ((((((((rBT_Im1000242676el_rbt @ C) @ C) @ D) @ D) @ R1a) @ R2a) @ X) @ X)))))).
% 0.35/1.50 thf(fact_102_rbt_Orel__eq, axiom, (! [B:$tType,A:$tType]: ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ (^ [Y5:A,Z4:A]: ((Y5 = Z4)))) @ (^ [Y5:B,Z4:B]: ((Y5 = Z4)))) = (^ [Y5:((rBT_Im246033960le_rbt @ A) @ B),Z4:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y5 = Z4))))))).
% 0.35/1.50 thf(fact_103_rbt_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,X21:rBT_Im1923302023_color,Y21:rBT_Im1923302023_color,R1:(A > (C > $o)),R22:(B > (D > $o)),X22:((rBT_Im246033960le_rbt @ A) @ B),Y22:((rBT_Im246033960le_rbt @ C) @ D),X23:A,Y23:C,X24:B,Y24:D,X25:((rBT_Im246033960le_rbt @ A) @ B),Y25:((rBT_Im246033960le_rbt @ C) @ D)]: (((X21 = Y21) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X22) @ Y22) => (((R1 @ X23) @ Y23) => (((R22 @ X24) @ Y24) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X25) @ Y25) => ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)))))))))).
% 0.35/1.50 thf(fact_104_rbt_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ C) @ D),Y23:C,Y24:D,Y25:((rBT_Im246033960le_rbt @ C) @ D)]: ((((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) @ (((((((rBT_Im480247531Branch @ C) @ D) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X22) @ Y22) & (((R1 @ X23) @ Y23) & (((R22 @ X24) @ Y24) & ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X25) @ Y25))))))))).
% 0.35/1.50 thf(fact_105_rbt_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o))]: (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ ((rBT_Im418718756_Empty @ A) @ B)) @ ((rBT_Im418718756_Empty @ C) @ D))))).
% 0.35/1.50 thf(fact_106_rbt_Opred__inject_I1_J, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P22:(B > $o)]: ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 0.35/1.50 thf(fact_107_rbt_Opred__rel, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1931894874ed_rbt @ A) @ B) = (^ [P12:(A > $o),P23:(B > $o),X8:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ ((bNF_eq_onp @ A) @ P12)) @ ((bNF_eq_onp @ B) @ P23)) @ X8) @ X8))))))).
% 0.35/1.50 thf(fact_108_bheight_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,C2:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,Rt:((rBT_Im246033960le_rbt @ A) @ B)]: ((((C2 = rBT_Impl_Mirabelle_B) => ((((rBT_Im315265182height @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ Lt) @ K) @ V) @ Rt)) = (suc @ (((rBT_Im315265182height @ A) @ B) @ Lt)))) & ((C2 != rBT_Impl_Mirabelle_B) => ((((rBT_Im315265182height @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C2) @ Lt) @ K) @ V) @ Rt)) = (((rBT_Im315265182height @ A) @ B) @ Lt))))))).
% 0.35/1.50 thf(fact_109_rbt_Oset__intros_I1_J, axiom, (! [B:$tType,A:$tType,X:A,A22:((rBT_Im246033960le_rbt @ A) @ B),A1:rBT_Im1923302023_color,A32:A,A4:B,A5:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ A) @ X) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A22)) => (((member @ A) @ X) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A32) @ A4) @ A5))))))).
% 0.35/1.50 thf(fact_110_rbt_Oset__intros_I2_J, axiom, (! [B:$tType,A:$tType,A32:A,A1:rBT_Im1923302023_color,A22:((rBT_Im246033960le_rbt @ A) @ B),A4:B,A5:((rBT_Im246033960le_rbt @ A) @ B)]: ((((member @ A) @ A32) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A32) @ A4) @ A5)))))).
% 0.35/1.50 thf(fact_111_rbt_Oset__intros_I3_J, axiom, (! [B:$tType,A:$tType,Xb:A,A5:((rBT_Im246033960le_rbt @ A) @ B),A1:rBT_Im1923302023_color,A22:((rBT_Im246033960le_rbt @ A) @ B),A32:A,A4:B]: (((((member @ A) @ Xb) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A5)) => (((member @ A) @ Xb) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1) @ A22) @ A32) @ A4) @ A5))))))).
% 0.35/1.50 thf(fact_112_rbt_Orel__eq__onp, axiom, (! [A:$tType,B:$tType,P1:(A > $o),P22:(B > $o)]: ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ ((bNF_eq_onp @ A) @ P1)) @ ((bNF_eq_onp @ B) @ P22)) = ((bNF_eq_onp @ ((rBT_Im246033960le_rbt @ A) @ B)) @ ((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22)))))).
% 0.35/1.50 thf(fact_113_rbt_Oset__cases_I1_J, axiom, (! [B:$tType,A:$tType,E2:A,A2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ A2)) => ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B)]: (((? [Z32:A,Z42:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ Z32) @ Z42) @ Z5)))) => (~ ((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Z22))))))) => ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B),Z42:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 != (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ E2) @ Z42) @ Z5)))) => (~ ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B),Z32:A,Z42:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: (((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ Z32) @ Z42) @ Z5)) => (~ ((((member @ A) @ E2) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Z5))))))))))))))).
% 0.35/1.50 thf(fact_114_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F3:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F3 @ N2)) @ (F3 @ (suc @ N2))))) => ((((ord_less @ A) @ (F3 @ N)) @ (F3 @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 0.35/1.50 thf(fact_115_lift__Suc__mono__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [F3:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F3 @ N2)) @ (F3 @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N3) => (((ord_less @ A) @ (F3 @ N)) @ (F3 @ N3)))))))))).
% 0.35/1.50 thf(fact_116_bheight_Osimps_I1_J, axiom, (! [A:$tType,B:$tType]: (((((rBT_Im315265182height @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (zero_zero @ nat))))).
% 0.35/1.50 thf(fact_117_rbt_Opred__mono__strong, axiom, (! [B:$tType,A:$tType,P1:(A > $o),P22:(B > $o),X:((rBT_Im246033960le_rbt @ A) @ B),P1a:(A > $o),P2a:(B > $o)]: (((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ X) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((P1 @ Z1) => (P1a @ Z1))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((P22 @ Z22) => (P2a @ Z22))))) => (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1a) @ P2a) @ X))))))).
% 0.35/1.50 thf(fact_118_rbt_Opred__cong, axiom, (! [B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),Ya:((rBT_Im246033960le_rbt @ A) @ B),P1:(A > $o),P1a:(A > $o),P22:(B > $o),P2a:(B > $o)]: (((X = Ya) => ((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Ya)) => ((P1 @ Z1) = (P1a @ Z1))))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Ya)) => ((P22 @ Z22) = (P2a @ Z22))))) => ((((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1) @ P22) @ X) = (((((rBT_Im1931894874ed_rbt @ A) @ B) @ P1a) @ P2a) @ Ya)))))))).
% 0.35/1.50 thf(fact_119_rbt_Oset__intros_I4_J, axiom, (! [B:$tType,A:$tType,Xe:B,A2a:((rBT_Im246033960le_rbt @ A) @ B),A1a:rBT_Im1923302023_color,A3a:A,A4a:B,A5a:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ B) @ Xe) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A2a)) => (((member @ B) @ Xe) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a))))))).
% 0.35/1.50 thf(fact_120_rbt_Oset__intros_I5_J, axiom, (! [B:$tType,A:$tType,A4a:B,A1a:rBT_Im1923302023_color,A2a:((rBT_Im246033960le_rbt @ A) @ B),A3a:A,A5a:((rBT_Im246033960le_rbt @ A) @ B)]: ((((member @ B) @ A4a) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a)))))).
% 0.35/1.50 thf(fact_121_rbt_Oset__intros_I6_J, axiom, (! [B:$tType,A:$tType,Xg:B,A5a:((rBT_Im246033960le_rbt @ A) @ B),A1a:rBT_Im1923302023_color,A2a:((rBT_Im246033960le_rbt @ A) @ B),A3a:A,A4a:B]: (((((member @ B) @ Xg) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A5a)) => (((member @ B) @ Xg) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ A1a) @ A2a) @ A3a) @ A4a) @ A5a))))))).
% 0.35/1.50 thf(fact_122_rbt_Oset__cases_I2_J, axiom, (! [B:$tType,A:$tType,E2:B,A2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ A2)) => ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B)]: (((? [Z32:A,Z42:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ Z32) @ Z42) @ Z5)))) => (~ ((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Z22))))))) => ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B),Z32:A,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: ((A2 != (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ Z32) @ E2) @ Z5)))) => (~ ((! [Z1:rBT_Im1923302023_color,Z22:((rBT_Im246033960le_rbt @ A) @ B),Z32:A,Z42:B,Z5:((rBT_Im246033960le_rbt @ A) @ B)]: (((A2 = (((((((rBT_Im480247531Branch @ A) @ B) @ Z1) @ Z22) @ Z32) @ Z42) @ Z5)) => (~ ((((member @ B) @ E2) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Z5))))))))))))))).
% 0.35/1.50 thf(fact_123_rbt_Orel__cong, axiom, (! [A:$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)),R22:(B > (D > $o)),R2a:(B > (D > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ Ya)) => ((((member @ C) @ Y1) @ (((rBT_Im1178217900t1_rbt @ C) @ D) @ Xa)) => (((R1 @ Z1) @ Y1) = ((R1a @ Z1) @ Y1)))))) => ((! [Z22:B,Y26:D]: (((((member @ B) @ Z22) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ Ya)) => ((((member @ D) @ Y26) @ (((rBT_Im1550225131t2_rbt @ C) @ D) @ Xa)) => (((R22 @ Z22) @ Y26) = ((R2a @ Z22) @ Y26)))))) => (((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X) @ Y) = ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ Ya) @ Xa))))))))).
% 0.35/1.50 thf(fact_124_rbt_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,R1:(A > (C > $o)),R22:(B > (D > $o)),X:((rBT_Im246033960le_rbt @ A) @ B),Y:((rBT_Im246033960le_rbt @ C) @ D),R1a:(A > (C > $o)),R2a:(B > (D > $o))]: ((((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22) @ X) @ Y) => ((! [Z1:A,Y1:C]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((((member @ C) @ Y1) @ (((rBT_Im1178217900t1_rbt @ C) @ D) @ Y)) => (((R1 @ Z1) @ Y1) => ((R1a @ Z1) @ Y1)))))) => ((! [Z22:B,Y26:D]: (((((member @ B) @ Z22) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((((member @ D) @ Y26) @ (((rBT_Im1550225131t2_rbt @ C) @ D) @ Y)) => (((R22 @ Z22) @ Y26) => ((R2a @ Z22) @ Y26)))))) => ((((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1a) @ R2a) @ X) @ Y))))))).
% 0.35/1.50 thf(fact_125_rbt_Orel__refl__strong, axiom, (! [B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B),R1a:(A > (A > $o)),R2a:(B > (B > $o))]: (((! [Z1:A]: (((((member @ A) @ Z1) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X)) => ((R1a @ Z1) @ Z1)))) => ((! [Z22:B]: (((((member @ B) @ Z22) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X)) => ((R2a @ Z22) @ Z22)))) => ((((((((rBT_Im1000242676el_rbt @ A) @ A) @ B) @ B) @ R1a) @ R2a) @ X) @ X)))))).
% 0.35/1.50 thf(fact_126_not__gr__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_127_color_Osize__gen_I1_J, axiom, ((rBT_Im800559290_color @ rBT_Impl_Mirabelle_R) = (zero_zero @ nat))).
% 0.35/1.50 thf(fact_128_color_Osize__gen_I2_J, axiom, ((rBT_Im800559290_color @ rBT_Impl_Mirabelle_B) = (zero_zero @ nat))).
% 0.35/1.50 thf(fact_129_less__numeral__extra_I3_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 0.35/1.50 thf(fact_130_zero__less__iff__neq__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_131_gr__implies__not__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_132_not__less__zero, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 0.35/1.50 thf(fact_133_gr__zeroI, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 0.35/1.50 thf(fact_134_color_Osize_I3_J, axiom, (((size_size @ rBT_Im1923302023_color) @ rBT_Impl_Mirabelle_R) = (zero_zero @ nat))).
% 0.35/1.50 thf(fact_135_color_Osize_I4_J, axiom, (((size_size @ rBT_Im1923302023_color) @ rBT_Impl_Mirabelle_B) = (zero_zero @ nat))).
% 0.35/1.50 thf(fact_136_rbt_Osize__gen_I1_J, axiom, (! [A:$tType,B:$tType,Xa:(A > nat),X:(B > nat)]: (((((((rBT_Im1485196410ze_rbt @ A) @ B) @ Xa) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = (zero_zero @ nat))))).
% 0.35/1.50 thf(fact_137_rbt_Osize_I3_J, axiom, (! [A:$tType,B:$tType]: ((((size_size @ ((rBT_Im246033960le_rbt @ A) @ B)) @ ((rBT_Im418718756_Empty @ A) @ B)) = (zero_zero @ nat))))).
% 0.35/1.50 thf(fact_138_rbt_Osize_I4_J, axiom, (! [A:$tType,B:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((size_size @ ((rBT_Im246033960le_rbt @ A) @ B)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25)) = (((plus_plus @ nat) @ (((plus_plus @ nat) @ ((size_size @ ((rBT_Im246033960le_rbt @ A) @ B)) @ X22)) @ ((size_size @ ((rBT_Im246033960le_rbt @ A) @ B)) @ X25))) @ (suc @ (zero_zero @ nat))))))).
% 0.35/1.50 thf(fact_139_of__nat__0__less__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((semiring_1_of_nat @ A) @ N)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))))).
% 0.35/1.50 thf(fact_140_sgn__greater, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((sgn_sgn @ A) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.35/1.50 thf(fact_141_sgn__less, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ ((sgn_sgn @ A) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_142_sgn__sgn, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: ((((sgn_sgn @ A) @ ((sgn_sgn @ A) @ A2)) = ((sgn_sgn @ A) @ A2)))))))).
% 0.35/1.50 thf(fact_143_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B3) @ C2)) = (((ord_less @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_144_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C2:A,A2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B3)) = (((ord_less @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_145_zero__less__double__add__iff__zero__less__single__add, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.35/1.50 thf(fact_146_double__add__less__zero__iff__single__add__less__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_147_less__add__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ B3) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B3)))))))).
% 0.35/1.50 thf(fact_148_less__add__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B3)) = (((ord_less @ A) @ (zero_zero @ A)) @ B3)))))))).
% 0.35/1.50 thf(fact_149_add__less__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ B3) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_150_add__less__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ B3) @ A2)) @ B3) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_151_of__nat__less__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:nat,N:nat]: (((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N)) = (((ord_less @ nat) @ M) @ N)))))))).
% 0.35/1.50 thf(fact_152_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ C2) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C2))))))))).
% 0.35/1.50 thf(fact_153_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A6:A,B4:A]: ((((plus_plus @ A) @ B4) @ A6)))))))).
% 0.35/1.50 thf(fact_154_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((plus_plus @ A) @ B3) @ (((plus_plus @ A) @ A2) @ C2)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B3) @ C2))))))))).
% 0.35/1.50 thf(fact_155_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B3) @ C2)) => (((ord_less @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_156_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C2:A,A2:A,B3:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B3)) => (((ord_less @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_157_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B3) @ C2))))))))).
% 0.35/1.50 thf(fact_158_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less @ A) @ (((plus_plus @ A) @ C2) @ A2)) @ (((plus_plus @ A) @ C2) @ B3))))))))).
% 0.35/1.50 thf(fact_159_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A,D2:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ C2) @ D2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C2)) @ (((plus_plus @ A) @ B3) @ D2)))))))))).
% 0.35/1.50 thf(fact_160_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.35/1.50 thf(fact_161_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.35/1.50 thf(fact_162_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.35/1.50 thf(fact_163_sgn__0__0, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((sgn_sgn @ A) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_164_of__nat__less__0__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:nat]: ((~ ((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ (zero_zero @ A)))))))))).
% 0.35/1.50 thf(fact_165_of__nat__less__imp__less, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:nat,N:nat]: (((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N)) => (((ord_less @ nat) @ M) @ N)))))))).
% 0.35/1.50 thf(fact_166_less__imp__of__nat__less, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N))))))))).
% 0.35/1.50 thf(fact_167_add__neg__neg, axiom, (! [A:$tType]: ((((ordere216010020id_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B3) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B3)) @ (zero_zero @ A)))))))))).
% 0.35/1.50 thf(fact_168_add__pos__pos, axiom, (! [A:$tType]: ((((ordere216010020id_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B3) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B3)))))))))).
% 0.35/1.50 thf(fact_169_pos__add__strict, axiom, (! [A:$tType]: ((((strict797366125id_add @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ B3) @ (((plus_plus @ A) @ A2) @ C2)))))))))).
% 0.35/1.50 thf(fact_170_sgn__pos, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((sgn_sgn @ A) @ A2) = (one_one @ A))))))))).
% 0.35/1.50 thf(fact_171_of__nat__zero__less__power__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [X:nat,N:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((power_power @ A) @ ((semiring_1_of_nat @ A) @ X)) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ X) | (N = (zero_zero @ nat)))))))))).
% 0.35/1.50 thf(fact_172_of__bool__eq_I1_J, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => (((zero_neq_one_of_bool @ A) @ $false) = (zero_zero @ A)))))).
% 0.35/1.50 thf(fact_173_rbt_Opred__set, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1931894874ed_rbt @ A) @ B) = (^ [P12:(A > $o),P23:(B > $o),X8:((rBT_Im246033960le_rbt @ A) @ B)]: (((! [Y4:A]: (((((member @ A) @ Y4) @ (((rBT_Im1178217900t1_rbt @ A) @ B) @ X8)) => (P12 @ Y4)))) & (! [Y4:B]: (((((member @ B) @ Y4) @ (((rBT_Im1550225131t2_rbt @ A) @ B) @ X8)) => (P23 @ Y4))))))))))).
% 0.35/1.50 thf(fact_174_of__bool__eq_I2_J, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => (((zero_neq_one_of_bool @ A) @ $true) = (one_one @ A)))))).
% 0.35/1.50 thf(fact_175_power__inject__exp, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,M:nat,N:nat]: (((((ord_less @ A) @ (one_one @ A)) @ A2) => (((((power_power @ A) @ A2) @ M) = (((power_power @ A) @ A2) @ N)) = (M = N))))))))).
% 0.35/1.50 thf(fact_176_power__strict__increasing__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [B3:A,X:nat,Y:nat]: (((((ord_less @ A) @ (one_one @ A)) @ B3) => ((((ord_less @ A) @ (((power_power @ A) @ B3) @ X)) @ (((power_power @ A) @ B3) @ Y)) = (((ord_less @ nat) @ X) @ Y))))))))).
% 0.35/1.50 thf(fact_177_power__Suc__less__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,N:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ A2) @ (one_one @ A)) => (((ord_less @ A) @ (((power_power @ A) @ A2) @ (suc @ N))) @ (one_one @ A)))))))))).
% 0.35/1.50 thf(fact_178_of__bool__def, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => ((zero_neq_one_of_bool @ A) = (^ [P3:$o]: (((((if @ A) @ P3) @ (one_one @ A)) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_179_zero__neq__one, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => ((zero_zero @ A) != (one_one @ A)))))).
% 0.35/1.50 thf(fact_180_split__of__bool, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => (! [P:(A > $o),P4:$o]: (((P @ ((zero_neq_one_of_bool @ A) @ P4)) = ((P4 => (P @ (one_one @ A))) & ((~ (P4)) => (P @ (zero_zero @ A))))))))))).
% 0.35/1.50 thf(fact_181_split__of__bool__asm, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => (! [P:(A > $o),P4:$o]: (((P @ ((zero_neq_one_of_bool @ A) @ P4)) = (~ (((P4 & (~ ((P @ (one_one @ A))))) | ((~ (P4)) & (~ ((P @ (zero_zero @ A))))))))))))))).
% 0.35/1.50 thf(fact_182_less__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 0.35/1.50 thf(fact_183_one__less__power, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,N:nat]: (((((ord_less @ A) @ (one_one @ A)) @ A2) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (((ord_less @ A) @ (one_one @ A)) @ (((power_power @ A) @ A2) @ N)))))))))).
% 0.35/1.50 thf(fact_184_zero__less__power, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,N:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((power_power @ A) @ A2) @ N))))))))).
% 0.35/1.50 thf(fact_185_power__strict__decreasing, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:nat,N4:nat,A2:A]: (((((ord_less @ nat) @ N) @ N4) => ((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ A2) @ (one_one @ A)) => (((ord_less @ A) @ (((power_power @ A) @ A2) @ N4)) @ (((power_power @ A) @ A2) @ N))))))))))).
% 0.35/1.50 thf(fact_186_of__bool__eq__iff, axiom, (! [A:$tType]: ((((zero_neq_one @ A) @ (type2 @ A)) => (! [P4:$o,Q3:$o]: (((((zero_neq_one_of_bool @ A) @ P4) = ((zero_neq_one_of_bool @ A) @ Q3)) = (P4 = Q3)))))))).
% 0.35/1.50 thf(fact_187_power__strict__increasing, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:nat,N4:nat,A2:A]: (((((ord_less @ nat) @ N) @ N4) => ((((ord_less @ A) @ (one_one @ A)) @ A2) => (((ord_less @ A) @ (((power_power @ A) @ A2) @ N)) @ (((power_power @ A) @ A2) @ N4)))))))))).
% 0.35/1.50 thf(fact_188_power__less__imp__less__exp, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,M:nat,N:nat]: (((((ord_less @ A) @ (one_one @ A)) @ A2) => ((((ord_less @ A) @ (((power_power @ A) @ A2) @ M)) @ (((power_power @ A) @ A2) @ N)) => (((ord_less @ nat) @ M) @ N))))))))).
% 0.35/1.50 thf(fact_189_power__gt1, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,N:nat]: (((((ord_less @ A) @ (one_one @ A)) @ A2) => (((ord_less @ A) @ (one_one @ A)) @ (((power_power @ A) @ A2) @ (suc @ N)))))))))).
% 0.35/1.50 thf(fact_190_not__one__less__zero, axiom, (! [A:$tType]: ((((linord1659791738miring @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 0.35/1.50 thf(fact_191_zero__less__one, axiom, (! [A:$tType]: ((((zero_less_one @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.35/1.50 thf(fact_192_less__numeral__extra_I1_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.35/1.50 thf(fact_193_less__numeral__extra_I2_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 0.35/1.50 thf(fact_194_less__add__one, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 0.35/1.50 thf(fact_195_zero__less__two, axiom, (! [A:$tType]: ((((linord1659791738miring @ A) @ (type2 @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A))))))).
% 0.35/1.50 thf(fact_196_sgn__1__pos, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((sgn_sgn @ A) @ A2) = (one_one @ A)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.35/1.50 thf(fact_197_power__strict__mono, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,B3:A,N:nat]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (((ord_less @ A) @ (((power_power @ A) @ A2) @ N)) @ (((power_power @ A) @ B3) @ N))))))))))).
% 0.35/1.50 thf(fact_198_sgn__neg, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => (((sgn_sgn @ A) @ A2) = ((uminus_uminus @ A) @ (one_one @ A)))))))))).
% 0.35/1.50 thf(fact_199_zero__less__power__abs__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A,N:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((power_power @ A) @ ((abs_abs @ A) @ A2)) @ N)) = ((A2 != (zero_zero @ A)) | (N = (zero_zero @ nat)))))))))).
% 0.35/1.50 thf(fact_200_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.35/1.50 thf(fact_201_neg__less__iff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B3)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_202_abs__one, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (((abs_abs @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 0.35/1.50 thf(fact_203_neg__less__0__iff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.35/1.50 thf(fact_204_neg__0__less__iff__less, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_205_neg__less__pos, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ A2) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.35/1.50 thf(fact_206_less__neg__neg, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ A2) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_207_zero__less__abs__iff, axiom, (! [A:$tType]: ((((ordere142940540dd_abs @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((abs_abs @ A) @ A2)) = (A2 != (zero_zero @ A))))))))).
% 0.35/1.50 thf(fact_208_power__increasing__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [B3:A,X:nat,Y:nat]: (((((ord_less @ A) @ (one_one @ A)) @ B3) => ((((ord_less_eq @ A) @ (((power_power @ A) @ B3) @ X)) @ (((power_power @ A) @ B3) @ Y)) = (((ord_less_eq @ nat) @ X) @ Y))))))))).
% 0.35/1.50 thf(fact_209_power__le__imp__le__exp, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [A2:A,M:nat,N:nat]: (((((ord_less @ A) @ (one_one @ A)) @ A2) => ((((ord_less_eq @ A) @ (((power_power @ A) @ A2) @ M)) @ (((power_power @ A) @ A2) @ N)) => (((ord_less_eq @ nat) @ M) @ N))))))))).
% 0.35/1.50 thf(fact_210_strict__mono__less__eq, axiom, (! [B:$tType,A:$tType]: (((((linorder @ A) @ (type2 @ A)) & ((order @ B) @ (type2 @ B))) => (! [F3:(A > B),X:A,Y:A]: (((((order_strict_mono @ A) @ B) @ F3) => ((((ord_less_eq @ B) @ (F3 @ X)) @ (F3 @ Y)) = (((ord_less_eq @ A) @ X) @ Y))))))))).
% 0.35/1.50 thf(fact_211_abs__not__less__zero, axiom, (! [A:$tType]: ((((ordere142940540dd_abs @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ ((abs_abs @ A) @ A2)) @ (zero_zero @ A)))))))))).
% 0.35/1.50 thf(fact_212_abs__of__pos, axiom, (! [A:$tType]: ((((ordere142940540dd_abs @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((abs_abs @ A) @ A2) = A2)))))))).
% 0.35/1.50 thf(fact_213_complete__interval, axiom, (! [A:$tType]: ((((condit1037483654norder @ A) @ (type2 @ A)) => (! [A2:A,B3:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B3) => ((P @ A2) => ((~ ((P @ B3))) => (? [C3:A]: (((((ord_less_eq @ A) @ A2) @ C3) & ((((ord_less_eq @ A) @ C3) @ B3) & ((! [X6:A]: ((((((ord_less_eq @ A) @ A2) @ X6) & (((ord_less @ A) @ X6) @ C3)) => (P @ X6)))) & (! [D3:A]: (((! [X7:A]: ((((((ord_less_eq @ A) @ A2) @ X7) & (((ord_less @ A) @ X7) @ D3)) => (P @ X7)))) => (((ord_less_eq @ A) @ D3) @ C3)))))))))))))))))).
% 0.35/1.50 thf(fact_214_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((A2 != B3) => ((((ord_less_eq @ A) @ A2) @ B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 0.35/1.50 thf(fact_215_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (((ord_less_eq @ A) @ B3) @ A2)))))))).
% 0.35/1.50 thf(fact_216_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B4:A,A6:A]: (((((ord_less_eq @ A) @ B4) @ A6) & (A6 != B4))))))))).
% 0.35/1.50 thf(fact_217_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B4:A,A6:A]: (((((ord_less @ A) @ B4) @ A6) | (A6 = B4))))))))).
% 0.35/1.50 thf(fact_218_order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (((ord_less_eq @ A) @ A2) @ B3)))))))).
% 0.35/1.50 thf(fact_219_dense__le__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((ord_less @ A) @ X) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 0.35/1.50 thf(fact_220_dense__ge__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z3:A,X:A,Y:A]: (((((ord_less @ A) @ Z3) @ X) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 0.35/1.50 thf(fact_221_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A2))))))))).
% 0.35/1.50 thf(fact_222_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A2))))))))).
% 0.35/1.50 thf(fact_223_order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [A6:A,B4:A]: (((((ord_less_eq @ A) @ A6) @ B4) & (A6 != B4))))))))).
% 0.35/1.50 thf(fact_224_order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A6:A,B4:A]: (((((ord_less @ A) @ A6) @ B4) | (A6 = B4))))))))).
% 0.35/1.50 thf(fact_225_order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 0.35/1.50 thf(fact_226_order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A2) @ C2))))))))).
% 0.35/1.50 thf(fact_227_not__le__imp__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X))) => (((ord_less @ A) @ X) @ Y)))))))).
% 0.35/1.50 thf(fact_228_less__le__not__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X8:A,Y4:A]: (((((ord_less_eq @ A) @ X8) @ Y4) & (~ ((((ord_less_eq @ A) @ Y4) @ X8))))))))))).
% 0.35/1.50 thf(fact_229_le__imp__less__or__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 0.35/1.50 thf(fact_230_le__less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X)))))))).
% 0.35/1.50 thf(fact_231_dense__le, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Y:A,Z3:A]: (((! [X7:A]: (((((ord_less @ A) @ X7) @ Y) => (((ord_less_eq @ A) @ X7) @ Z3)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 0.35/1.50 thf(fact_232_dense__ge, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z3:A,Y:A]: (((! [X7:A]: (((((ord_less @ A) @ Z3) @ X7) => (((ord_less_eq @ A) @ Y) @ X7)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 0.35/1.50 thf(fact_233_less__le__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less @ A) @ X) @ Z3))))))))).
% 0.35/1.50 thf(fact_234_le__less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X) @ Z3))))))))).
% 0.35/1.50 thf(fact_235_antisym__conv2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.35/1.50 thf(fact_236_antisym__conv1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.35/1.50 thf(fact_237_less__imp__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.35/1.50 thf(fact_238_le__neq__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((A2 != B3) => (((ord_less @ A) @ A2) @ B3))))))))).
% 0.35/1.50 thf(fact_239_not__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.35/1.50 thf(fact_240_not__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) = (((ord_less @ A) @ Y) @ X)))))))).
% 0.35/1.50 thf(fact_241_order__less__le__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F3:(A > C),C2:C]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F3 @ B3)) @ C2) => ((! [X7:A,Y2:A]: (((((ord_less @ A) @ X7) @ Y2) => (((ord_less @ C) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ C) @ (F3 @ A2)) @ C2)))))))))).
% 0.35/1.50 thf(fact_242_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F3:(B > A),B3:B,C2:B]: (((((ord_less @ A) @ A2) @ (F3 @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X7:B,Y2:B]: (((((ord_less_eq @ B) @ X7) @ Y2) => (((ord_less_eq @ A) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.35/1.50 thf(fact_243_order__le__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F3:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less @ C) @ (F3 @ B3)) @ C2) => ((! [X7:A,Y2:A]: (((((ord_less_eq @ A) @ X7) @ Y2) => (((ord_less_eq @ C) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ C) @ (F3 @ A2)) @ C2)))))))))).
% 0.35/1.50 thf(fact_244_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F3:(B > A),B3:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F3 @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X7:B,Y2:B]: (((((ord_less @ B) @ X7) @ Y2) => (((ord_less @ A) @ (F3 @ X7)) @ (F3 @ Y2))))) => (((ord_less @ A) @ A2) @ (F3 @ C2))))))))))).
% 0.35/1.50 thf(fact_245_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X8:A,Y4:A]: (((((ord_less_eq @ A) @ X8) @ Y4) & (X8 != Y4))))))))).
% 0.35/1.50 thf(fact_246_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X8:A,Y4:A]: (((((ord_less @ A) @ X8) @ Y4) | (X8 = Y4))))))))).
% 0.35/1.50 thf(fact_247_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.35/1.50 thf(fact_248_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less @ A) @ X) @ Y)))))))))).
% 0.35/1.50 thf(fact_249_pinf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (~ ((((ord_less_eq @ A) @ X6) @ T)))))))))))))).
% 0.35/1.50 thf(fact_250_pinf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ Z) @ X6) => (((ord_less_eq @ A) @ T) @ X6)))))))))))).
% 0.35/1.50 thf(fact_251_minf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (((ord_less_eq @ A) @ X6) @ T)))))))))))).
% 0.35/1.50 thf(fact_252_minf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:A]: ((? [Z:A]: ((! [X6:A]: (((((ord_less @ A) @ X6) @ Z) => (~ ((((ord_less_eq @ A) @ T) @ X6)))))))))))))).
% 0.35/1.50 thf(fact_253_abs__less__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less @ A) @ ((abs_abs @ A) @ A2)) @ B3) = ((((ord_less @ A) @ A2) @ B3) & (((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ B3))))))))).
% 0.35/1.50 thf(fact_254_rbt_Orel__mono, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (C > $o)),R1a:(A > (C > $o)),R22:(B > (D > $o)),R2a:(B > (D > $o))]: (((((ord_less_eq @ (A > (C > $o))) @ R1) @ R1a) => ((((ord_less_eq @ (B > (D > $o))) @ R22) @ R2a) => (((ord_less_eq @ (((rBT_Im246033960le_rbt @ A) @ B) > (((rBT_Im246033960le_rbt @ C) @ D) > $o))) @ ((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1) @ R22)) @ ((((((rBT_Im1000242676el_rbt @ A) @ C) @ B) @ D) @ R1a) @ R2a))))))).
% 0.35/1.50 thf(fact_255_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 0.35/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 0.35/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 0.35/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 0.35/1.50 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, ((condit1037483654norder @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, ((ordere516151231imp_le @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, ((ordere223160158up_add @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add, axiom, ((strict797366125id_add @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, ((linord1659791738miring @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add, axiom, ((ordere216010020id_add @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Rings_Ozero__less__one, axiom, ((zero_less_one @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, ((zero_neq_one @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 0.35/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 0.35/1.50 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 0.35/1.50 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 0.35/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 0.35/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_8, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 0.35/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, ((order @ $o) @ (type2 @ $o))).
% 0.35/1.50 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, ((ord @ $o) @ (type2 @ $o))).
% 0.35/1.50 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.35/1.50 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 0.35/1.50 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 0.35/1.50 thf(conj_0, hypothesis, (((rBT_Im1040612427e_inv1 @ a) @ b) @ t)).
% 0.35/1.50 thf(conj_1, conjecture, (((rBT_Im1071879905_inv1l @ a) @ b) @ t)).
% 0.35/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2DTF28340.p
% 0.35/1.50 ------------------------
% 0.35/1.55 ---- Cleaned THF ---
% 0.35/1.56 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.35/1.56 rBT_Im1923302023_color: $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.35/1.56 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_t_Set_Oset,type,
% 0.35/1.56 set: $tType > $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_t_Nat_Onat,type,
% 0.35/1.56 nat: $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_t_itself,type,
% 0.35/1.56 itself: $tType > $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_tf_b,type,
% 0.35/1.56 b: $tType ).
% 0.35/1.56
% 0.35/1.56 thf(ty_tf_a,type,
% 0.35/1.56 a: $tType ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_HOL_Otype,type,
% 0.35/1.56 type:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Oord,type,
% 0.35/1.56 ord:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Oorder,type,
% 0.35/1.56 order:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Ono__bot,type,
% 0.35/1.56 no_bot:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Ono__top,type,
% 0.35/1.56 no_top:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Olinorder,type,
% 0.35/1.56 linorder:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Opreorder,type,
% 0.35/1.56 preorder:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.35/1.56 zero_neq_one:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Owellorder,type,
% 0.35/1.56 wellorder:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.35/1.56 zero_less_one:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Odense__order,type,
% 0.35/1.56 dense_order:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.35/1.56 linordered_idom:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Fields_Olinordered__field,type,
% 0.35/1.56 linordered_field:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.35/1.56 dense_linorder:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.35/1.56 linordered_semidom:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.35/1.56 ordered_ab_group_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.35/1.56 linord219039673up_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.35/1.56 ordere216010020id_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.35/1.56 ordere142940540dd_abs:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.35/1.56 linord1659791738miring:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.35/1.56 canoni770627133id_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.35/1.56 strict797366125id_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.35/1.56 ordere236663937imp_le:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.35/1.56 ordere223160158up_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.35/1.56 strict2144017051up_add:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.35/1.56 ordere516151231imp_le:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.35/1.56 condit1656338222tinuum:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.35/1.56 condit1037483654norder:
% 0.35/1.56 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_BNF__Def_Oeq__onp,type,
% 0.35/1.56 bNF_eq_onp:
% 0.35/1.56 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.35/1.56 abs_abs:
% 0.35/1.56 !>[A: $tType] : ( A > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.35/1.56 one_one:
% 0.35/1.56 !>[A: $tType] : A ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.35/1.56 plus_plus:
% 0.35/1.56 !>[A: $tType] : ( A > A > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Osgn__class_Osgn,type,
% 0.35/1.56 sgn_sgn:
% 0.35/1.56 !>[A: $tType] : ( A > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.35/1.56 uminus_uminus:
% 0.35/1.56 !>[A: $tType] : ( A > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.35/1.56 zero_zero:
% 0.35/1.56 !>[A: $tType] : A ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_If,type,
% 0.35/1.56 if:
% 0.35/1.56 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Nat_OSuc,type,
% 0.35/1.56 suc: nat > nat ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Nat_Osemiring__1__class_Oof__nat,type,
% 0.35/1.56 semiring_1_of_nat:
% 0.35/1.56 !>[A: $tType] : ( nat > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.35/1.56 size_size:
% 0.35/1.56 !>[A: $tType] : ( A > nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.35/1.56 ord_less:
% 0.35/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.35/1.56 ord_less_eq:
% 0.35/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Orderings_Oorder__class_Ostrict__mono,type,
% 0.35/1.56 order_strict_mono:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Power_Opower__class_Opower,type,
% 0.35/1.56 power_power:
% 0.35/1.56 !>[A: $tType] : ( A > nat > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Pure_Otype,type,
% 0.35/1.56 type2:
% 0.35/1.56 !>[A: $tType] : ( itself @ A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obheight,type,
% 0.35/1.56 rBT_Im315265182height:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 0.35/1.56 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 0.35/1.56 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Ocase__color,type,
% 0.35/1.56 rBT_Im1975547051_color:
% 0.35/1.56 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Orec__color,type,
% 0.35/1.56 rBT_Im1059957627_color:
% 0.35/1.56 !>[A: $tType] : ( A > A > rBT_Im1923302023_color > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_Osize__color,type,
% 0.35/1.56 rBT_Im800559290_color: rBT_Im1923302023_color > nat ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor__of,type,
% 0.35/1.56 rBT_Im1805589839lor_of:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > rBT_Im1923302023_color ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1,type,
% 0.35/1.56 rBT_Im1040612427e_inv1:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oinv1l,type,
% 0.35/1.56 rBT_Im1071879905_inv1l:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 0.35/1.56 rBT_Im1259024060reater:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 0.35/1.56 rBT_Im2075124343t_less:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 0.35/1.56 rBT_Im759614907sorted:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater,type,
% 0.35/1.56 rBT_Im1332541288reater:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less,type,
% 0.35/1.56 rBT_Im903026891t_less:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted,type,
% 0.35/1.56 rBT_Im1183586831sorted:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.35/1.56 rBT_Im480247531Branch:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.35/1.56 rBT_Im418718756_Empty:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Ocase__rbt,type,
% 0.35/1.56 rBT_Im858806507se_rbt:
% 0.35/1.56 !>[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 ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Opred__rbt,type,
% 0.35/1.56 rBT_Im1931894874ed_rbt:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( B > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orec__rbt,type,
% 0.35/1.56 rBT_Im1947144893ec_rbt:
% 0.35/1.56 !>[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 ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Orel__rbt,type,
% 0.35/1.56 rBT_Im1000242676el_rbt:
% 0.35/1.56 !>[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 ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset1__rbt,type,
% 0.35/1.56 rBT_Im1178217900t1_rbt:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ A ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Oset2__rbt,type,
% 0.35/1.56 rBT_Im1550225131t2_rbt:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( set @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_Osize__rbt,type,
% 0.35/1.56 rBT_Im1485196410ze_rbt:
% 0.35/1.56 !>[A: $tType,B: $tType] : ( ( A > nat ) > ( B > nat ) > ( rBT_Im246033960le_rbt @ A @ B ) > nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool,type,
% 0.35/1.56 zero_neq_one_of_bool:
% 0.35/1.56 !>[A: $tType] : ( $o > A ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_Set_OCollect,type,
% 0.35/1.56 collect:
% 0.35/1.56 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_c_member,type,
% 0.35/1.56 member:
% 0.35/1.56 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(sy_v_t,type,
% 0.35/1.56 t: rBT_Im246033960le_rbt @ a @ b ).
% 0.35/1.56
% 0.35/1.56 thf(fact_0_inv1l_Osimps_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im1071879905_inv1l @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.35/1.56 = ( ( rBT_Im1040612427e_inv1 @ A @ B @ L )
% 0.35/1.56 & ( rBT_Im1040612427e_inv1 @ A @ B @ R ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_1_inv1l_Osimps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] : ( rBT_Im1071879905_inv1l @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_2_inv1_Osimps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] : ( rBT_Im1040612427e_inv1 @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_3_inv1_Osimps_I2_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,Rt: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im1040612427e_inv1 @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.35/1.56 = ( ( rBT_Im1040612427e_inv1 @ A @ B @ Lt )
% 0.35/1.56 & ( rBT_Im1040612427e_inv1 @ A @ B @ Rt )
% 0.35/1.56 & ( ( C2 = rBT_Impl_Mirabelle_B )
% 0.35/1.56 | ( ( ( rBT_Im1805589839lor_of @ A @ B @ Lt )
% 0.35/1.56 = rBT_Impl_Mirabelle_B )
% 0.35/1.56 & ( ( rBT_Im1805589839lor_of @ A @ B @ Rt )
% 0.35/1.56 = rBT_Impl_Mirabelle_B ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_4_color_Ocase__distrib,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,H: A > B,F1: A,F2: A,Color: rBT_Im1923302023_color] :
% 0.35/1.56 ( ( H @ ( rBT_Im1975547051_color @ A @ F1 @ F2 @ Color ) )
% 0.35/1.56 = ( rBT_Im1975547051_color @ B @ ( H @ F1 ) @ ( H @ F2 ) @ Color ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_5_rbt_Oinject,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 0.35/1.56 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.35/1.56 = ( ( X21 = Y21 )
% 0.35/1.56 & ( X22 = Y22 )
% 0.35/1.56 & ( X23 = Y23 )
% 0.35/1.56 & ( X24 = Y24 )
% 0.35/1.56 & ( X25 = Y25 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_6_color_Osimps_I4_J,axiom,
% 0.35/1.56 ! [A: $tType,F1: A,F2: A] :
% 0.35/1.56 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.35/1.56 = F2 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_7_rbt_Odistinct_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_8_color__of_Osimps_I2_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,C2: rBT_Im1923302023_color,Uu: rBT_Im246033960le_rbt @ A @ B,Uv: A,Uw: B,Ux: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im1805589839lor_of @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Uu @ Uv @ Uw @ Ux ) )
% 0.35/1.56 = C2 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_9_color__of_Osimps_I1_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( rBT_Im1805589839lor_of @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = rBT_Impl_Mirabelle_B ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_10_rbt_Oinduct,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 => ( ! [X1: rBT_Im1923302023_color,X2: rBT_Im246033960le_rbt @ A @ B,X3: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( P @ X2 )
% 0.35/1.56 => ( ( P @ X5 )
% 0.35/1.56 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) )
% 0.35/1.56 => ( P @ Rbt ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_11_rbt_Oexhaust,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( Y
% 0.35/1.56 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( Y
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_12_rbt__cases,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( T
% 0.35/1.56 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( T
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K2 @ V2 @ R2 ) )
% 0.35/1.56 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K2: A,V2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( T
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K2 @ V2 @ R2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_13_color_Osimps_I6_J,axiom,
% 0.35/1.56 ! [A: $tType,F1: A,F2: A] :
% 0.35/1.56 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_B )
% 0.35/1.56 = F2 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_14_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_15_color_Osimps_I3_J,axiom,
% 0.35/1.56 ! [A: $tType,F1: A,F2: A] :
% 0.35/1.56 ( ( rBT_Im1975547051_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.35/1.56 = F1 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_16_rbt__less__simps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [K: A] : ( rBT_Im903026891t_less @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_17_rbt__greater__simps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [K: A] : ( rBT_Im1332541288reater @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_18_color_Odistinct_I1_J,axiom,
% 0.35/1.56 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 0.35/1.56
% 0.35/1.56 thf(fact_19_color_Oinduct,axiom,
% 0.35/1.56 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 0.35/1.56 ( ( P @ rBT_Impl_Mirabelle_R )
% 0.35/1.56 => ( ( P @ rBT_Impl_Mirabelle_B )
% 0.35/1.56 => ( P @ Color ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_20_color_Oexhaust,axiom,
% 0.35/1.56 ! [Y: rBT_Im1923302023_color] :
% 0.35/1.56 ( ( Y != rBT_Impl_Mirabelle_R )
% 0.35/1.56 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_21_rbt_Osimps_I4_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = F1 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_22_rbt_Osimps_I5_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( rBT_Im858806507se_rbt @ C @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.35/1.56 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_23_color_Osimps_I5_J,axiom,
% 0.35/1.56 ! [A: $tType,F1: A,F2: A] :
% 0.35/1.56 ( ( rBT_Im1059957627_color @ A @ F1 @ F2 @ rBT_Impl_Mirabelle_R )
% 0.35/1.56 = F1 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_24_rbt__sorted_Osimps_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.35/1.56 = ( ( rBT_Im903026891t_less @ A @ B @ K @ L )
% 0.35/1.56 & ( rBT_Im1332541288reater @ A @ B @ K @ R )
% 0.35/1.56 & ( rBT_Im1183586831sorted @ A @ B @ L )
% 0.35/1.56 & ( rBT_Im1183586831sorted @ A @ B @ R ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_25_rbt__greater__simps_I2_J,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.35/1.56 ( ( rBT_Im1332541288reater @ A @ C @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.35/1.56 = ( ( ord_less @ A @ K @ Kt )
% 0.35/1.56 & ( rBT_Im1332541288reater @ A @ C @ K @ Lt )
% 0.35/1.56 & ( rBT_Im1332541288reater @ A @ C @ K @ Rt ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_26_rbt__less__simps_I2_J,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.35/1.56 ( ( rBT_Im903026891t_less @ A @ C @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.35/1.56 = ( ( ord_less @ A @ Kt @ K )
% 0.35/1.56 & ( rBT_Im903026891t_less @ A @ C @ K @ Lt )
% 0.35/1.56 & ( rBT_Im903026891t_less @ A @ C @ K @ Rt ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_27_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Less: A > A > $o,C2: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C2 @ L @ K @ V @ R ) )
% 0.35/1.56 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 0.35/1.56 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 0.35/1.56 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 0.35/1.56 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_28_ord_Orbt__greater__simps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_29_ord_Orbt__less__simps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_30_ord_Orbt__greater__simps_I2_J,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType,Less: A > A > $o,K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.35/1.56 ( ( rBT_Im1259024060reater @ A @ C @ Less @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.35/1.56 = ( ( Less @ K @ Kt )
% 0.35/1.56 & ( rBT_Im1259024060reater @ A @ C @ Less @ K @ Lt )
% 0.35/1.56 & ( rBT_Im1259024060reater @ A @ C @ Less @ K @ Rt ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_31_ord_Orbt__less__simps_I2_J,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType,Less: A > A > $o,K: A,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C,Kt: A,V: C,Rt: rBT_Im246033960le_rbt @ A @ C] :
% 0.35/1.56 ( ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ ( rBT_Im480247531Branch @ A @ C @ C2 @ Lt @ Kt @ V @ Rt ) )
% 0.35/1.56 = ( ( Less @ Kt @ K )
% 0.35/1.56 & ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ Lt )
% 0.35/1.56 & ( rBT_Im2075124343t_less @ A @ C @ Less @ K @ Rt ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_32_rbt_Osimps_I6_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = F1 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_33_rbt_Osimps_I7_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.35/1.56 = ( F2 @ X21 @ X22 @ X23 @ X24 @ X25 @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X22 ) @ ( rBT_Im1947144893ec_rbt @ E @ A @ B @ F1 @ F2 @ X25 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_34_rbt__less__trans,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,T: rBT_Im246033960le_rbt @ A @ C,Y: A] :
% 0.35/1.56 ( ( rBT_Im903026891t_less @ A @ C @ X @ T )
% 0.35/1.56 => ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( rBT_Im903026891t_less @ A @ C @ Y @ T ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_35_rbt__greater__trans,axiom,
% 0.35/1.56 ! [C: $tType,A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,T: rBT_Im246033960le_rbt @ A @ C] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( rBT_Im1332541288reater @ A @ C @ Y @ T )
% 0.35/1.56 => ( rBT_Im1332541288reater @ A @ C @ X @ T ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_36_rbt__sorted_Osimps_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_37_minf_I11_J,axiom,
% 0.35/1.56 ! [C: $tType,D: $tType] :
% 0.35/1.56 ( ( ord @ C @ ( type2 @ C ) )
% 0.35/1.56 => ! [F: D] :
% 0.35/1.56 ? [Z: C] :
% 0.35/1.56 ! [X6: C] :
% 0.35/1.56 ( ( ord_less @ C @ X6 @ Z )
% 0.35/1.56 => ( F = F ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_38_minf_I7_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ~ ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_39_minf_I5_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_40_minf_I4_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( X6 != T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_41_minf_I3_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( X6 != T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_42_minf_I2_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.35/1.56 ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Z2 )
% 0.35/1.56 => ( ( P @ X7 )
% 0.35/1.56 = ( P2 @ X7 ) ) )
% 0.35/1.56 => ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Z2 )
% 0.35/1.56 => ( ( Q @ X7 )
% 0.35/1.56 = ( Q2 @ X7 ) ) )
% 0.35/1.56 => ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( ( ( P @ X6 )
% 0.35/1.56 | ( Q @ X6 ) )
% 0.35/1.56 = ( ( P2 @ X6 )
% 0.35/1.56 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_43_minf_I1_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.35/1.56 ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Z2 )
% 0.35/1.56 => ( ( P @ X7 )
% 0.35/1.56 = ( P2 @ X7 ) ) )
% 0.35/1.56 => ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Z2 )
% 0.35/1.56 => ( ( Q @ X7 )
% 0.35/1.56 = ( Q2 @ X7 ) ) )
% 0.35/1.56 => ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( ( ( P @ X6 )
% 0.35/1.56 & ( Q @ X6 ) )
% 0.35/1.56 = ( ( P2 @ X6 )
% 0.35/1.56 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_44_pinf_I11_J,axiom,
% 0.35/1.56 ! [C: $tType,D: $tType] :
% 0.35/1.56 ( ( ord @ C @ ( type2 @ C ) )
% 0.35/1.56 => ! [F: D] :
% 0.35/1.56 ? [Z: C] :
% 0.35/1.56 ! [X6: C] :
% 0.35/1.56 ( ( ord_less @ C @ Z @ X6 )
% 0.35/1.56 => ( F = F ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_45_mem__Collect__eq,axiom,
% 0.35/1.56 ! [A: $tType,A2: A,P: A > $o] :
% 0.35/1.56 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.35/1.56 = ( P @ A2 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_46_Collect__mem__eq,axiom,
% 0.35/1.56 ! [A: $tType,A3: set @ A] :
% 0.35/1.56 ( ( collect @ A
% 0.35/1.56 @ ^ [X8: A] : ( member @ A @ X8 @ A3 ) )
% 0.35/1.56 = A3 ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_47_Collect__cong,axiom,
% 0.35/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ( P @ X7 )
% 0.35/1.56 = ( Q @ X7 ) )
% 0.35/1.56 => ( ( collect @ A @ P )
% 0.35/1.56 = ( collect @ A @ Q ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_48_ext,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ( F3 @ X7 )
% 0.35/1.56 = ( G @ X7 ) )
% 0.35/1.56 => ( F3 = G ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_49_pinf_I7_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( ord_less @ A @ T @ X6 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_50_pinf_I1_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.35/1.56 ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z2 @ X7 )
% 0.35/1.56 => ( ( P @ X7 )
% 0.35/1.56 = ( P2 @ X7 ) ) )
% 0.35/1.56 => ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z2 @ X7 )
% 0.35/1.56 => ( ( Q @ X7 )
% 0.35/1.56 = ( Q2 @ X7 ) ) )
% 0.35/1.56 => ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( ( ( P @ X6 )
% 0.35/1.56 & ( Q @ X6 ) )
% 0.35/1.56 = ( ( P2 @ X6 )
% 0.35/1.56 & ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_51_pinf_I2_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.35/1.56 ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z2 @ X7 )
% 0.35/1.56 => ( ( P @ X7 )
% 0.35/1.56 = ( P2 @ X7 ) ) )
% 0.35/1.56 => ( ? [Z2: A] :
% 0.35/1.56 ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z2 @ X7 )
% 0.35/1.56 => ( ( Q @ X7 )
% 0.35/1.56 = ( Q2 @ X7 ) ) )
% 0.35/1.56 => ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( ( ( P @ X6 )
% 0.35/1.56 | ( Q @ X6 ) )
% 0.35/1.56 = ( ( P2 @ X6 )
% 0.35/1.56 | ( Q2 @ X6 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_52_pinf_I3_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( X6 != T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_53_pinf_I4_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( X6 != T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_54_pinf_I5_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ~ ( ord_less @ A @ X6 @ T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_55_ex__gt__or__lt,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ? [B2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.35/1.56 | ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_56_linorder__neqE__linordered__idom,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( X != Y )
% 0.35/1.56 => ( ~ ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_57_dual__order_Ostrict__implies__not__eq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ B3 @ A2 )
% 0.35/1.56 => ( A2 != B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_58_linordered__field__no__ub,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X6: A] :
% 0.35/1.56 ? [X1: A] : ( ord_less @ A @ X6 @ X1 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_59_linordered__field__no__lb,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X6: A] :
% 0.35/1.56 ? [Y2: A] : ( ord_less @ A @ Y2 @ X6 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_60_order_Ostrict__implies__not__eq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( A2 != B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_61_dependent__wellorder__choice,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: ( A > B ) > A > B > $o] :
% 0.35/1.56 ( ! [R2: B,F4: A > B,G2: A > B,X7: A] :
% 0.35/1.56 ( ! [Y3: A] :
% 0.35/1.56 ( ( ord_less @ A @ Y3 @ X7 )
% 0.35/1.56 => ( ( F4 @ Y3 )
% 0.35/1.56 = ( G2 @ Y3 ) ) )
% 0.35/1.56 => ( ( P @ F4 @ X7 @ R2 )
% 0.35/1.56 = ( P @ G2 @ X7 @ R2 ) ) )
% 0.35/1.56 => ( ! [X7: A,F4: A > B] :
% 0.35/1.56 ( ! [Y3: A] :
% 0.35/1.56 ( ( ord_less @ A @ Y3 @ X7 )
% 0.35/1.56 => ( P @ F4 @ Y3 @ ( F4 @ Y3 ) ) )
% 0.35/1.56 => ? [X12: B] : ( P @ F4 @ X7 @ X12 ) )
% 0.35/1.56 => ? [F4: A > B] :
% 0.35/1.56 ! [X6: A] : ( P @ F4 @ X6 @ ( F4 @ X6 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_62_not__less__iff__gr__or__eq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.35/1.56 = ( ( ord_less @ A @ Y @ X )
% 0.35/1.56 | ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_63_ord__eq__less__subst,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.35/1.56 & ( ord @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.35/1.56 ( ( A2
% 0.35/1.56 = ( F3 @ B3 ) )
% 0.35/1.56 => ( ( ord_less @ B @ B3 @ C2 )
% 0.35/1.56 => ( ! [X7: B,Y2: B] :
% 0.35/1.56 ( ( ord_less @ B @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_64_ord__less__eq__subst,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.35/1.56 & ( ord @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,B3: A,F3: A > B,C2: B] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ( F3 @ B3 )
% 0.35/1.56 = C2 )
% 0.35/1.56 => ( ! [X7: A,Y2: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ B @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ B @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_65_order__less__subst1,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( ( order @ B @ ( type2 @ B ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( F3 @ B3 ) )
% 0.35/1.56 => ( ( ord_less @ B @ B3 @ C2 )
% 0.35/1.56 => ( ! [X7: B,Y2: B] :
% 0.35/1.56 ( ( ord_less @ B @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_66_order__less__subst2,axiom,
% 0.35/1.56 ! [A: $tType,C: $tType] :
% 0.35/1.56 ( ( ( order @ C @ ( type2 @ C ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less @ C @ ( F3 @ B3 ) @ C2 )
% 0.35/1.56 => ( ! [X7: A,Y2: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_67_lt__ex,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A] :
% 0.35/1.56 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_68_gt__ex,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( no_top @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A] :
% 0.35/1.56 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_69_neqE,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( X != Y )
% 0.35/1.56 => ( ~ ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_70_neq__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( X != Y )
% 0.35/1.56 = ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_71_order_Oasym,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_72_dense,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ? [Z: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Z )
% 0.35/1.56 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_73_less__imp__neq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( X != Y ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_74_less__asym,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_75_less__asym_H,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_76_less__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,Z3: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less @ A @ Y @ Z3 )
% 0.35/1.56 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_77_less__linear,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 | ( X = Y )
% 0.35/1.56 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_78_less__irrefl,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A] :
% 0.35/1.56 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_79_ord__eq__less__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( A2 = B3 )
% 0.35/1.56 => ( ( ord_less @ A @ B3 @ C2 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_80_ord__less__eq__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( B3 = C2 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_81_dual__order_Oasym,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ B3 @ A2 )
% 0.35/1.56 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_82_less__imp__not__eq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( X != Y ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_83_less__not__sym,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_84_less__induct,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,A2: A] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ! [Y3: A] :
% 0.35/1.56 ( ( ord_less @ A @ Y3 @ X7 )
% 0.35/1.56 => ( P @ Y3 ) )
% 0.35/1.56 => ( P @ X7 ) )
% 0.35/1.56 => ( P @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_85_antisym__conv3,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Y: A,X: A] :
% 0.35/1.56 ( ~ ( ord_less @ A @ Y @ X )
% 0.35/1.56 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.35/1.56 = ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_86_less__imp__not__eq2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( Y != X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_87_less__imp__triv,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,P: $o] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less @ A @ Y @ X )
% 0.35/1.56 => P ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_88_linorder__cases,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ~ ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( X != Y )
% 0.35/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_89_dual__order_Oirrefl,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_90_order_Ostrict__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less @ A @ B3 @ C2 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_91_less__imp__not__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_92_dual__order_Ostrict__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ B3 @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ C2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_93_rbt_Opred__inject_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,A2: rBT_Im1923302023_color,Aa: rBT_Im246033960le_rbt @ A @ B,Ab: A,Ac: B,Ad: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ ( rBT_Im480247531Branch @ A @ B @ A2 @ Aa @ Ab @ Ac @ Ad ) )
% 0.35/1.56 = ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ Aa )
% 0.35/1.56 & ( P1 @ Ab )
% 0.35/1.56 & ( P22 @ Ac )
% 0.35/1.56 & ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ Ad ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_94_rbt_Orel__distinct_I2_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_95_rbt_Orel__distinct_I1_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ C @ D,Y23: C,Y24: D,Y25: rBT_Im246033960le_rbt @ C @ D] :
% 0.35/1.56 ~ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_96_strict__monoD,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ! [F3: A > B,X: A,Y: A] :
% 0.35/1.56 ( ( order_strict_mono @ A @ B @ F3 )
% 0.35/1.56 => ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ord_less @ B @ ( F3 @ X ) @ ( F3 @ Y ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_97_strict__monoI,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ! [F3: A > B] :
% 0.35/1.56 ( ! [X7: A,Y2: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ B @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( order_strict_mono @ A @ B @ F3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_98_strict__mono__def,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ( ( order_strict_mono @ A @ B )
% 0.35/1.56 = ( ^ [F5: A > B] :
% 0.35/1.56 ! [X8: A,Y4: A] :
% 0.35/1.56 ( ( ord_less @ A @ X8 @ Y4 )
% 0.35/1.56 => ( ord_less @ B @ ( F5 @ X8 ) @ ( F5 @ Y4 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_99_strict__mono__less,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ! [F3: A > B,X: A,Y: A] :
% 0.35/1.56 ( ( order_strict_mono @ A @ B @ F3 )
% 0.35/1.56 => ( ( ord_less @ B @ ( F3 @ X ) @ ( F3 @ Y ) )
% 0.35/1.56 = ( ord_less @ A @ X @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_100_strict__mono__eq,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ! [F3: A > B,X: A,Y: A] :
% 0.35/1.56 ( ( order_strict_mono @ A @ B @ F3 )
% 0.35/1.56 => ( ( ( F3 @ X )
% 0.35/1.56 = ( F3 @ Y ) )
% 0.35/1.56 = ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_101_rbt_Orel__refl,axiom,
% 0.35/1.56 ! [D: $tType,C: $tType,R1a: C > C > $o,R2a: D > D > $o,X: rBT_Im246033960le_rbt @ C @ D] :
% 0.35/1.56 ( ! [X7: C] : ( R1a @ X7 @ X7 )
% 0.35/1.56 => ( ! [X7: D] : ( R2a @ X7 @ X7 )
% 0.35/1.56 => ( rBT_Im1000242676el_rbt @ C @ C @ D @ D @ R1a @ R2a @ X @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_102_rbt_Orel__eq,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B
% 0.35/1.56 @ ^ [Y5: A,Z4: A] : ( Y5 = Z4 )
% 0.35/1.56 @ ^ [Y5: B,Z4: B] : ( Y5 = Z4 ) )
% 0.35/1.56 = ( ^ [Y5: rBT_Im246033960le_rbt @ A @ B,Z4: rBT_Im246033960le_rbt @ A @ B] : ( Y5 = Z4 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_103_rbt_Orel__intros_I2_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,X21: rBT_Im1923302023_color,Y21: rBT_Im1923302023_color,R1: A > C > $o,R22: 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] :
% 0.35/1.56 ( ( X21 = Y21 )
% 0.35/1.56 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X22 @ Y22 )
% 0.35/1.56 => ( ( R1 @ X23 @ Y23 )
% 0.35/1.56 => ( ( R22 @ X24 @ Y24 )
% 0.35/1.56 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X25 @ Y25 )
% 0.35/1.56 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_104_rbt_Orel__inject_I2_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: 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] :
% 0.35/1.56 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) @ ( rBT_Im480247531Branch @ C @ D @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.35/1.56 = ( ( X21 = Y21 )
% 0.35/1.56 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X22 @ Y22 )
% 0.35/1.56 & ( R1 @ X23 @ Y23 )
% 0.35/1.56 & ( R22 @ X24 @ Y24 )
% 0.35/1.56 & ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X25 @ Y25 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_105_rbt_Octr__transfer_I1_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o] : ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ ( rBT_Im418718756_Empty @ A @ B ) @ ( rBT_Im418718756_Empty @ C @ D ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_106_rbt_Opred__inject_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o] : ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_107_rbt_Opred__rel,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.35/1.56 = ( ^ [P12: A > $o,P23: B > $o,X8: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P12 ) @ ( bNF_eq_onp @ B @ P23 ) @ X8 @ X8 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_108_bheight_Osimps_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,C2: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,Rt: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( ( C2 = rBT_Impl_Mirabelle_B )
% 0.35/1.56 => ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.35/1.56 = ( suc @ ( rBT_Im315265182height @ A @ B @ Lt ) ) ) )
% 0.35/1.56 & ( ( C2 != rBT_Impl_Mirabelle_B )
% 0.35/1.56 => ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C2 @ Lt @ K @ V @ Rt ) )
% 0.35/1.56 = ( rBT_Im315265182height @ A @ B @ Lt ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_109_rbt_Oset__intros_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,X: A,A22: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A32: A,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ A22 ) )
% 0.35/1.56 => ( member @ A @ X @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_110_rbt_Oset__intros_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,A32: A,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A4: B,A5: rBT_Im246033960le_rbt @ A @ B] : ( member @ A @ A32 @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_111_rbt_Oset__intros_I3_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,Xb: A,A5: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im1923302023_color,A22: rBT_Im246033960le_rbt @ A @ B,A32: A,A4: B] :
% 0.35/1.56 ( ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ A5 ) )
% 0.35/1.56 => ( member @ A @ Xb @ ( rBT_Im1178217900t1_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1 @ A22 @ A32 @ A4 @ A5 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_112_rbt_Orel__eq__onp,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,P1: A > $o,P22: B > $o] :
% 0.35/1.56 ( ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ ( bNF_eq_onp @ A @ P1 ) @ ( bNF_eq_onp @ B @ P22 ) )
% 0.35/1.56 = ( bNF_eq_onp @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_113_rbt_Oset__cases_I1_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,E2: A,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ A2 ) )
% 0.35/1.56 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ? [Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( A2
% 0.35/1.56 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.35/1.56 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z22 ) ) )
% 0.35/1.56 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( A2
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ E2 @ Z42 @ Z5 ) )
% 0.35/1.56 => ~ ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( A2
% 0.35/1.56 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.35/1.56 => ~ ( member @ A @ E2 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_114_lift__Suc__mono__less__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [F3: nat > A,N: nat,M: nat] :
% 0.35/1.56 ( ! [N2: nat] : ( ord_less @ A @ ( F3 @ N2 ) @ ( F3 @ ( suc @ N2 ) ) )
% 0.35/1.56 => ( ( ord_less @ A @ ( F3 @ N ) @ ( F3 @ M ) )
% 0.35/1.56 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_115_lift__Suc__mono__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [F3: nat > A,N: nat,N3: nat] :
% 0.35/1.56 ( ! [N2: nat] : ( ord_less @ A @ ( F3 @ N2 ) @ ( F3 @ ( suc @ N2 ) ) )
% 0.35/1.56 => ( ( ord_less @ nat @ N @ N3 )
% 0.35/1.56 => ( ord_less @ A @ ( F3 @ N ) @ ( F3 @ N3 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_116_bheight_Osimps_I1_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( rBT_Im315265182height @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_117_rbt_Opred__mono__strong,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,P1: A > $o,P22: B > $o,X: rBT_Im246033960le_rbt @ A @ B,P1a: A > $o,P2a: B > $o] :
% 0.35/1.56 ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ X )
% 0.35/1.56 => ( ! [Z1: A] :
% 0.35/1.56 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( ( P1 @ Z1 )
% 0.35/1.56 => ( P1a @ Z1 ) ) )
% 0.35/1.56 => ( ! [Z22: B] :
% 0.35/1.56 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( ( P22 @ Z22 )
% 0.35/1.56 => ( P2a @ Z22 ) ) )
% 0.35/1.56 => ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ X ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_118_rbt_Opred__cong,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,Ya: rBT_Im246033960le_rbt @ A @ B,P1: A > $o,P1a: A > $o,P22: B > $o,P2a: B > $o] :
% 0.35/1.56 ( ( X = Ya )
% 0.35/1.56 => ( ! [Z1: A] :
% 0.35/1.56 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.35/1.56 => ( ( P1 @ Z1 )
% 0.35/1.56 = ( P1a @ Z1 ) ) )
% 0.35/1.56 => ( ! [Z22: B] :
% 0.35/1.56 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.35/1.56 => ( ( P22 @ Z22 )
% 0.35/1.56 = ( P2a @ Z22 ) ) )
% 0.35/1.56 => ( ( rBT_Im1931894874ed_rbt @ A @ B @ P1 @ P22 @ X )
% 0.35/1.56 = ( rBT_Im1931894874ed_rbt @ A @ B @ P1a @ P2a @ Ya ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_119_rbt_Oset__intros_I4_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2a ) )
% 0.35/1.56 => ( member @ B @ Xe @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_120_rbt_Oset__intros_I5_J,axiom,
% 0.35/1.56 ! [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 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_121_rbt_Oset__intros_I6_J,axiom,
% 0.35/1.56 ! [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] :
% 0.35/1.56 ( ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ A5a ) )
% 0.35/1.56 => ( member @ B @ Xg @ ( rBT_Im1550225131t2_rbt @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ A1a @ A2a @ A3a @ A4a @ A5a ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_122_rbt_Oset__cases_I2_J,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,E2: B,A2: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ A2 ) )
% 0.35/1.56 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ? [Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( A2
% 0.35/1.56 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.35/1.56 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z22 ) ) )
% 0.35/1.56 => ( ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( A2
% 0.35/1.56 != ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ E2 @ Z5 ) )
% 0.35/1.56 => ~ ! [Z1: rBT_Im1923302023_color,Z22: rBT_Im246033960le_rbt @ A @ B,Z32: A,Z42: B,Z5: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( A2
% 0.35/1.56 = ( rBT_Im480247531Branch @ A @ B @ Z1 @ Z22 @ Z32 @ Z42 @ Z5 ) )
% 0.35/1.56 => ~ ( member @ B @ E2 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Z5 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_123_rbt_Orel__cong,axiom,
% 0.35/1.56 ! [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,R22: B > D > $o,R2a: B > D > $o] :
% 0.35/1.56 ( ( X = Ya )
% 0.35/1.56 => ( ( Y = Xa )
% 0.35/1.56 => ( ! [Z1: A,Y1: C] :
% 0.35/1.56 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ Ya ) )
% 0.35/1.56 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Xa ) )
% 0.35/1.56 => ( ( R1 @ Z1 @ Y1 )
% 0.35/1.56 = ( R1a @ Z1 @ Y1 ) ) ) )
% 0.35/1.56 => ( ! [Z22: B,Y26: D] :
% 0.35/1.56 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ Ya ) )
% 0.35/1.56 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Xa ) )
% 0.35/1.56 => ( ( R22 @ Z22 @ Y26 )
% 0.35/1.56 = ( R2a @ Z22 @ Y26 ) ) ) )
% 0.35/1.56 => ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X @ Y )
% 0.35/1.56 = ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_124_rbt_Orel__mono__strong,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,D: $tType,C: $tType,R1: A > C > $o,R22: B > D > $o,X: rBT_Im246033960le_rbt @ A @ B,Y: rBT_Im246033960le_rbt @ C @ D,R1a: A > C > $o,R2a: B > D > $o] :
% 0.35/1.56 ( ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 @ X @ Y )
% 0.35/1.56 => ( ! [Z1: A,Y1: C] :
% 0.35/1.56 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( ( member @ C @ Y1 @ ( rBT_Im1178217900t1_rbt @ C @ D @ Y ) )
% 0.35/1.56 => ( ( R1 @ Z1 @ Y1 )
% 0.35/1.56 => ( R1a @ Z1 @ Y1 ) ) ) )
% 0.35/1.56 => ( ! [Z22: B,Y26: D] :
% 0.35/1.56 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( ( member @ D @ Y26 @ ( rBT_Im1550225131t2_rbt @ C @ D @ Y ) )
% 0.35/1.56 => ( ( R22 @ Z22 @ Y26 )
% 0.35/1.56 => ( R2a @ Z22 @ Y26 ) ) ) )
% 0.35/1.56 => ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a @ X @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_125_rbt_Orel__refl__strong,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B,R1a: A > A > $o,R2a: B > B > $o] :
% 0.35/1.56 ( ! [Z1: A] :
% 0.35/1.56 ( ( member @ A @ Z1 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( R1a @ Z1 @ Z1 ) )
% 0.35/1.56 => ( ! [Z22: B] :
% 0.35/1.56 ( ( member @ B @ Z22 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X ) )
% 0.35/1.56 => ( R2a @ Z22 @ Z22 ) )
% 0.35/1.56 => ( rBT_Im1000242676el_rbt @ A @ A @ B @ B @ R1a @ R2a @ X @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_126_not__gr__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: A] :
% 0.35/1.56 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.35/1.56 = ( N
% 0.35/1.56 = ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_127_color_Osize__gen_I1_J,axiom,
% 0.35/1.56 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_R )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_128_color_Osize__gen_I2_J,axiom,
% 0.35/1.56 ( ( rBT_Im800559290_color @ rBT_Impl_Mirabelle_B )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_129_less__numeral__extra_I3_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_130_zero__less__iff__neq__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.35/1.56 = ( N
% 0.35/1.56 != ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_131_gr__implies__not__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [M: A,N: A] :
% 0.35/1.56 ( ( ord_less @ A @ M @ N )
% 0.35/1.56 => ( N
% 0.35/1.56 != ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_132_not__less__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: A] :
% 0.35/1.56 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_133_gr__zeroI,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: A] :
% 0.35/1.56 ( ( N
% 0.35/1.56 != ( zero_zero @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_134_color_Osize_I3_J,axiom,
% 0.35/1.56 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_R )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_135_color_Osize_I4_J,axiom,
% 0.35/1.56 ( ( size_size @ rBT_Im1923302023_color @ rBT_Impl_Mirabelle_B )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_136_rbt_Osize__gen_I1_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,Xa: A > nat,X: B > nat] :
% 0.35/1.56 ( ( rBT_Im1485196410ze_rbt @ A @ B @ Xa @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_137_rbt_Osize_I3_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.35/1.56 = ( zero_zero @ nat ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_138_rbt_Osize_I4_J,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) )
% 0.35/1.56 = ( plus_plus @ nat @ ( plus_plus @ nat @ ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ X22 ) @ ( size_size @ ( rBT_Im246033960le_rbt @ A @ B ) @ X25 ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_139_of__nat__0__less__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.35/1.56 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_140_sgn__greater,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( sgn_sgn @ A @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_141_sgn__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( sgn_sgn @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_142_sgn__sgn,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( sgn_sgn @ A @ ( sgn_sgn @ A @ A2 ) )
% 0.35/1.56 = ( sgn_sgn @ A @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_143_add__less__cancel__right,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,C2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_144_add__less__cancel__left,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [C2: A,A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_145_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_146_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_147_less__add__same__cancel2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B3 @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_148_less__add__same__cancel1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B3 ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_149_add__less__same__cancel2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B3 ) @ B3 )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_150_add__less__same__cancel1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ B3 @ A2 ) @ B3 )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_151_of__nat__less__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.35/1.56 = ( ord_less @ nat @ M @ N ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_152_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B3 ) @ C2 )
% 0.35/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_153_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( plus_plus @ A )
% 0.35/1.56 = ( ^ [A6: A,B4: A] : ( plus_plus @ A @ B4 @ A6 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_154_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A,C2: A] :
% 0.35/1.56 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A2 @ C2 ) )
% 0.35/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_155_add__less__imp__less__right,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,C2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_156_add__less__imp__less__left,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [C2: A,A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_157_add__strict__right__mono,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_158_add__strict__left__mono,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ C2 @ A2 ) @ ( plus_plus @ A @ C2 @ B3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_159_add__strict__mono,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A,D2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less @ A @ C2 @ D2 )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C2 ) @ ( plus_plus @ A @ B3 @ D2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_160_add__mono__thms__linordered__field_I1_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.35/1.56 ( ( ( ord_less @ A @ I @ J )
% 0.35/1.56 & ( K = L ) )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_161_add__mono__thms__linordered__field_I2_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.35/1.56 ( ( ( I = J )
% 0.35/1.56 & ( ord_less @ A @ K @ L ) )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_162_add__mono__thms__linordered__field_I5_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.35/1.56 ( ( ( ord_less @ A @ I @ J )
% 0.35/1.56 & ( ord_less @ A @ K @ L ) )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_163_sgn__0__0,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ( sgn_sgn @ A @ A2 )
% 0.35/1.56 = ( zero_zero @ A ) )
% 0.35/1.56 = ( A2
% 0.35/1.56 = ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_164_of__nat__less__0__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [M: nat] :
% 0.35/1.56 ~ ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_165_of__nat__less__imp__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) )
% 0.35/1.56 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_166_less__imp__of__nat__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ nat @ M @ N )
% 0.35/1.56 => ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_167_add__neg__neg,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.35/1.56 => ( ( ord_less @ A @ B3 @ ( zero_zero @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_168_add__pos__pos,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere216010020id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B3 )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_169_pos__add__strict,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( strict797366125id_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ B3 @ C2 )
% 0.35/1.56 => ( ord_less @ A @ B3 @ ( plus_plus @ A @ A2 @ C2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_170_sgn__pos,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( sgn_sgn @ A @ A2 )
% 0.35/1.56 = ( one_one @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_171_of__nat__zero__less__power__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ ( semiring_1_of_nat @ A @ X ) @ N ) )
% 0.35/1.56 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ X )
% 0.35/1.56 | ( N
% 0.35/1.56 = ( zero_zero @ nat ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_172_of__bool__eq_I1_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( zero_neq_one_of_bool @ A @ $false )
% 0.35/1.56 = ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_173_rbt_Opred__set,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( rBT_Im1931894874ed_rbt @ A @ B )
% 0.35/1.56 = ( ^ [P12: A > $o,P23: B > $o,X8: rBT_Im246033960le_rbt @ A @ B] :
% 0.35/1.56 ( ! [Y4: A] :
% 0.35/1.56 ( ( member @ A @ Y4 @ ( rBT_Im1178217900t1_rbt @ A @ B @ X8 ) )
% 0.35/1.56 => ( P12 @ Y4 ) )
% 0.35/1.56 & ! [Y4: B] :
% 0.35/1.56 ( ( member @ B @ Y4 @ ( rBT_Im1550225131t2_rbt @ A @ B @ X8 ) )
% 0.35/1.56 => ( P23 @ Y4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_174_of__bool__eq_I2_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( zero_neq_one_of_bool @ A @ $true )
% 0.35/1.56 = ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_175_power__inject__exp,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ( ( power_power @ A @ A2 @ M )
% 0.35/1.56 = ( power_power @ A @ A2 @ N ) )
% 0.35/1.56 = ( M = N ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_176_power__strict__increasing__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,X: nat,Y: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ B3 )
% 0.35/1.56 => ( ( ord_less @ A @ ( power_power @ A @ B3 @ X ) @ ( power_power @ A @ B3 @ Y ) )
% 0.35/1.56 = ( ord_less @ nat @ X @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_177_power__Suc__less__one,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ A2 @ ( one_one @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( power_power @ A @ A2 @ ( suc @ N ) ) @ ( one_one @ A ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_178_of__bool__def,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( zero_neq_one_of_bool @ A )
% 0.35/1.56 = ( ^ [P3: $o] : ( if @ A @ P3 @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_179_zero__neq__one,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( zero_zero @ A )
% 0.35/1.56 != ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_180_split__of__bool,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P4: $o] :
% 0.35/1.56 ( ( P @ ( zero_neq_one_of_bool @ A @ P4 ) )
% 0.35/1.56 = ( ( P4
% 0.35/1.56 => ( P @ ( one_one @ A ) ) )
% 0.35/1.56 & ( ~ P4
% 0.35/1.56 => ( P @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_181_split__of__bool__asm,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P: A > $o,P4: $o] :
% 0.35/1.56 ( ( P @ ( zero_neq_one_of_bool @ A @ P4 ) )
% 0.35/1.56 = ( ~ ( ( P4
% 0.35/1.56 & ~ ( P @ ( one_one @ A ) ) )
% 0.35/1.56 | ( ~ P4
% 0.35/1.56 & ~ ( P @ ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_182_less__numeral__extra_I4_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_183_one__less__power,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.35/1.56 => ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ A2 @ N ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_184_zero__less__power,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ A2 @ N ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_185_power__strict__decreasing,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: nat,N4: nat,A2: A] :
% 0.35/1.56 ( ( ord_less @ nat @ N @ N4 )
% 0.35/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ A2 @ ( one_one @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( power_power @ A @ A2 @ N4 ) @ ( power_power @ A @ A2 @ N ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_186_of__bool__eq__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_neq_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [P4: $o,Q3: $o] :
% 0.35/1.56 ( ( ( zero_neq_one_of_bool @ A @ P4 )
% 0.35/1.56 = ( zero_neq_one_of_bool @ A @ Q3 ) )
% 0.35/1.56 = ( P4 = Q3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_187_power__strict__increasing,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [N: nat,N4: nat,A2: A] :
% 0.35/1.56 ( ( ord_less @ nat @ N @ N4 )
% 0.35/1.56 => ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ord_less @ A @ ( power_power @ A @ A2 @ N ) @ ( power_power @ A @ A2 @ N4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_188_power__less__imp__less__exp,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ ( power_power @ A @ A2 @ M ) @ ( power_power @ A @ A2 @ N ) )
% 0.35/1.56 => ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_189_power__gt1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ord_less @ A @ ( one_one @ A ) @ ( power_power @ A @ A2 @ ( suc @ N ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_190_not__one__less__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.35/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_191_zero__less__one,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( zero_less_one @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_192_less__numeral__extra_I1_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_193_less__numeral__extra_I2_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_194_less__add__one,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_195_zero__less__two,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord1659791738miring @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_196_sgn__1__pos,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ( sgn_sgn @ A @ A2 )
% 0.35/1.56 = ( one_one @ A ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_197_power__strict__mono,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.35/1.56 => ( ord_less @ A @ ( power_power @ A @ A2 @ N ) @ ( power_power @ A @ B3 @ N ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_198_sgn__neg,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.35/1.56 => ( ( sgn_sgn @ A @ A2 )
% 0.35/1.56 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_199_zero__less__power__abs__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( power_power @ A @ ( abs_abs @ A @ A2 ) @ N ) )
% 0.35/1.56 = ( ( A2
% 0.35/1.56 != ( zero_zero @ A ) )
% 0.35/1.56 | ( N
% 0.35/1.56 = ( zero_zero @ nat ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_200_order__refl,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_201_neg__less__iff__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_202_abs__one,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.35/1.56 = ( one_one @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_203_neg__less__0__iff__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_204_neg__0__less__iff__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_205_neg__less__pos,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ A2 )
% 0.35/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_206_less__neg__neg,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ A2 ) )
% 0.35/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_207_zero__less__abs__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( abs_abs @ A @ A2 ) )
% 0.35/1.56 = ( A2
% 0.35/1.56 != ( zero_zero @ A ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_208_power__increasing__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,X: nat,Y: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ B3 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ ( power_power @ A @ B3 @ X ) @ ( power_power @ A @ B3 @ Y ) )
% 0.35/1.56 = ( ord_less_eq @ nat @ X @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_209_power__le__imp__le__exp,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,M: nat,N: nat] :
% 0.35/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ A2 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ ( power_power @ A @ A2 @ M ) @ ( power_power @ A @ A2 @ N ) )
% 0.35/1.56 => ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_210_strict__mono__less__eq,axiom,
% 0.35/1.56 ! [B: $tType,A: $tType] :
% 0.35/1.56 ( ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 & ( order @ B @ ( type2 @ B ) ) )
% 0.35/1.56 => ! [F3: A > B,X: A,Y: A] :
% 0.35/1.56 ( ( order_strict_mono @ A @ B @ F3 )
% 0.35/1.56 => ( ( ord_less_eq @ B @ ( F3 @ X ) @ ( F3 @ Y ) )
% 0.35/1.56 = ( ord_less_eq @ A @ X @ Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_211_abs__not__less__zero,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ~ ( ord_less @ A @ ( abs_abs @ A @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_212_abs__of__pos,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( ordere142940540dd_abs @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.35/1.56 => ( ( abs_abs @ A @ A2 )
% 0.35/1.56 = A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_213_complete__interval,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,P: A > $o] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( P @ A2 )
% 0.35/1.56 => ( ~ ( P @ B3 )
% 0.35/1.56 => ? [C3: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.35/1.56 & ( ord_less_eq @ A @ C3 @ B3 )
% 0.35/1.56 & ! [X6: A] :
% 0.35/1.56 ( ( ( ord_less_eq @ A @ A2 @ X6 )
% 0.35/1.56 & ( ord_less @ A @ X6 @ C3 ) )
% 0.35/1.56 => ( P @ X6 ) )
% 0.35/1.56 & ! [D3: A] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ( ( ord_less_eq @ A @ A2 @ X7 )
% 0.35/1.56 & ( ord_less @ A @ X7 @ D3 ) )
% 0.35/1.56 => ( P @ X7 ) )
% 0.35/1.56 => ( ord_less_eq @ A @ D3 @ C3 ) ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_214_order_Onot__eq__order__implies__strict,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( A2 != B3 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_215_dual__order_Ostrict__implies__order,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less @ A @ B3 @ A2 )
% 0.35/1.56 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_216_dual__order_Ostrict__iff__order,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less @ A )
% 0.35/1.56 = ( ^ [B4: A,A6: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ B4 @ A6 )
% 0.35/1.56 & ( A6 != B4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_217_dual__order_Oorder__iff__strict,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less_eq @ A )
% 0.35/1.56 = ( ^ [B4: A,A6: A] :
% 0.35/1.56 ( ( ord_less @ A @ B4 @ A6 )
% 0.35/1.56 | ( A6 = B4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_218_order_Ostrict__implies__order,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ord_less_eq @ A @ A2 @ B3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_219_dense__le__bounded,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,Z3: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ! [W: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ W )
% 0.35/1.56 => ( ( ord_less @ A @ W @ Y )
% 0.35/1.56 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_220_dense__ge__bounded,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Z3: A,X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z3 @ X )
% 0.35/1.56 => ( ! [W: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z3 @ W )
% 0.35/1.56 => ( ( ord_less @ A @ W @ X )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_221_dual__order_Ostrict__trans2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ B3 @ A2 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_222_dual__order_Ostrict__trans1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A,C2: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.35/1.56 => ( ( ord_less @ A @ C2 @ B3 )
% 0.35/1.56 => ( ord_less @ A @ C2 @ A2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_223_order_Ostrict__iff__order,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less @ A )
% 0.35/1.56 = ( ^ [A6: A,B4: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A6 @ B4 )
% 0.35/1.56 & ( A6 != B4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_224_order_Oorder__iff__strict,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less_eq @ A )
% 0.35/1.56 = ( ^ [A6: A,B4: A] :
% 0.35/1.56 ( ( ord_less @ A @ A6 @ B4 )
% 0.35/1.56 | ( A6 = B4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_225_order_Ostrict__trans2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_226_order_Ostrict__trans1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A,C2: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less @ A @ B3 @ C2 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ C2 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_227_not__le__imp__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Y: A,X: A] :
% 0.35/1.56 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.35/1.56 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_228_less__le__not__le,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less @ A )
% 0.35/1.56 = ( ^ [X8: A,Y4: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X8 @ Y4 )
% 0.35/1.56 & ~ ( ord_less_eq @ A @ Y4 @ X8 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_229_le__imp__less__or__eq,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 | ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_230_le__less__linear,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.35/1.56 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_231_dense__le,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Y: A,Z3: A] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Y )
% 0.35/1.56 => ( ord_less_eq @ A @ X7 @ Z3 ) )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_232_dense__ge,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Z3: A,Y: A] :
% 0.35/1.56 ( ! [X7: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z3 @ X7 )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ X7 ) )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_233_less__le__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,Z3: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.35/1.56 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_234_le__less__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A,Z3: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less @ A @ Y @ Z3 )
% 0.35/1.56 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_235_antisym__conv2,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.35/1.56 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.35/1.56 = ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_236_antisym__conv1,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ~ ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ( ord_less_eq @ A @ X @ Y )
% 0.35/1.56 = ( X = Y ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_237_less__imp__le,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( preorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_238_le__neq__trans,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( A2 != B3 )
% 0.35/1.56 => ( ord_less @ A @ A2 @ B3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_239_not__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.35/1.56 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_240_not__le,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.35/1.56 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_241_order__less__le__subst2,axiom,
% 0.35/1.56 ! [A: $tType,C: $tType] :
% 0.35/1.56 ( ( ( order @ C @ ( type2 @ C ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less_eq @ C @ ( F3 @ B3 ) @ C2 )
% 0.35/1.56 => ( ! [X7: A,Y2: A] :
% 0.35/1.56 ( ( ord_less @ A @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_242_order__less__le__subst1,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( ( order @ B @ ( type2 @ B ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.35/1.56 ( ( ord_less @ A @ A2 @ ( F3 @ B3 ) )
% 0.35/1.56 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.35/1.56 => ( ! [X7: B,Y2: B] :
% 0.35/1.56 ( ( ord_less_eq @ B @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less_eq @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_243_order__le__less__subst2,axiom,
% 0.35/1.56 ! [A: $tType,C: $tType] :
% 0.35/1.56 ( ( ( order @ C @ ( type2 @ C ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,B3: A,F3: A > C,C2: C] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.35/1.56 => ( ( ord_less @ C @ ( F3 @ B3 ) @ C2 )
% 0.35/1.56 => ( ! [X7: A,Y2: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less_eq @ C @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ C @ ( F3 @ A2 ) @ C2 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_244_order__le__less__subst1,axiom,
% 0.35/1.56 ! [A: $tType,B: $tType] :
% 0.35/1.56 ( ( ( order @ B @ ( type2 @ B ) )
% 0.35/1.56 & ( order @ A @ ( type2 @ A ) ) )
% 0.35/1.56 => ! [A2: A,F3: B > A,B3: B,C2: B] :
% 0.35/1.56 ( ( ord_less_eq @ A @ A2 @ ( F3 @ B3 ) )
% 0.35/1.56 => ( ( ord_less @ B @ B3 @ C2 )
% 0.35/1.56 => ( ! [X7: B,Y2: B] :
% 0.35/1.56 ( ( ord_less @ B @ X7 @ Y2 )
% 0.35/1.56 => ( ord_less @ A @ ( F3 @ X7 ) @ ( F3 @ Y2 ) ) )
% 0.35/1.56 => ( ord_less @ A @ A2 @ ( F3 @ C2 ) ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_245_less__le,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less @ A )
% 0.35/1.56 = ( ^ [X8: A,Y4: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ X8 @ Y4 )
% 0.35/1.56 & ( X8 != Y4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_246_le__less,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ( ( ord_less_eq @ A )
% 0.35/1.56 = ( ^ [X8: A,Y4: A] :
% 0.35/1.56 ( ( ord_less @ A @ X8 @ Y4 )
% 0.35/1.56 | ( X8 = Y4 ) ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_247_leI,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [X: A,Y: A] :
% 0.35/1.56 ( ~ ( ord_less @ A @ X @ Y )
% 0.35/1.56 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_248_leD,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [Y: A,X: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ Y @ X )
% 0.35/1.56 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_249_pinf_I6_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ~ ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_250_pinf_I8_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ Z @ X6 )
% 0.35/1.56 => ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_251_minf_I6_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ( ord_less_eq @ A @ X6 @ T ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_252_minf_I8_J,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [T: A] :
% 0.35/1.56 ? [Z: A] :
% 0.35/1.56 ! [X6: A] :
% 0.35/1.56 ( ( ord_less @ A @ X6 @ Z )
% 0.35/1.56 => ~ ( ord_less_eq @ A @ T @ X6 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_253_abs__less__iff,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [A2: A,B3: A] :
% 0.35/1.56 ( ( ord_less @ A @ ( abs_abs @ A @ A2 ) @ B3 )
% 0.35/1.56 = ( ( ord_less @ A @ A2 @ B3 )
% 0.35/1.56 & ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_254_rbt_Orel__mono,axiom,
% 0.35/1.56 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > C > $o,R1a: A > C > $o,R22: B > D > $o,R2a: B > D > $o] :
% 0.35/1.56 ( ( ord_less_eq @ ( A > C > $o ) @ R1 @ R1a )
% 0.35/1.56 => ( ( ord_less_eq @ ( B > D > $o ) @ R22 @ R2a )
% 0.35/1.56 => ( ord_less_eq @ ( ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ C @ D ) > $o ) @ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1 @ R22 ) @ ( rBT_Im1000242676el_rbt @ A @ C @ B @ D @ R1a @ R2a ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(fact_255_dual__order_Oantisym,axiom,
% 0.35/1.56 ! [A: $tType] :
% 0.35/1.56 ( ( order @ A @ ( type2 @ A ) )
% 0.35/1.56 => ! [B3: A,A2: A] :
% 0.35/1.56 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.35/1.56 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.35/1.56 => ( A2 = B3 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.35/1.56 ! [A7: $tType,A8: $tType] :
% 0.35/1.56 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.35/1.56 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.35/1.56 ! [A7: $tType,A8: $tType] :
% 0.35/1.56 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.35/1.56 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 0.35/1.56 ! [A7: $tType,A8: $tType] :
% 0.35/1.56 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.35/1.56 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.35/1.56 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.35/1.56 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.35/1.56 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.35/1.56 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.35/1.56 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.35/1.56 strict797366125id_add @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.35/1.56 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.35/1.56 linord1659791738miring @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 0.35/1.56 ordere216010020id_add @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.35/1.56 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 0.35/1.56 zero_less_one @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.35/1.56 wellorder @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.35/1.56 zero_neq_one @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.35/1.56 preorder @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.35/1.56 linorder @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.35/1.56 no_top @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.35/1.56 order @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.35/1.56 ord @ nat @ ( type2 @ nat ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.35/1.56 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.35/1.56 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.35/1.56 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.35/1.56 preorder @ $o @ ( type2 @ $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.35/1.56 linorder @ $o @ ( type2 @ $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.35/1.56 order @ $o @ ( type2 @ $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.35/1.56 ord @ $o @ ( type2 @ $o ) ).
% 0.35/1.56
% 0.35/1.56 thf(help_If_3_1_T,axiom,
% 0.35/1.56 ! [P: $o] :
% 0.35/1.56 ( ( P = $true )
% 0.35/1.56 | ( P = $false ) ) ).
% 0.35/1.56
% 0.35/1.56 thf(help_If_2_1_T,axiom,
% 0.35/1.56 ! [A: $tType,X: A,Y: A] :
% 0.35/1.56 ( ( if @ A @ $false @ X @ Y )
% 0.35/1.56 = Y ) ).
% 0.35/1.56
% 0.35/1.56 thf(help_If_1_1_T,axiom,
% 0.35/1.56 ! [A: $tType,X: A,Y: A] :
% 0.35/1.56 ( ( if @ A @ $true @ X @ Y )
% 0.35/1.56 = X ) ).
% 0.35/1.56
% 0.35/1.56 thf(conj_0,hypothesis,
% 0.35/1.56 rBT_Im1040612427e_inv1 @ a @ b @ t ).
% 0.35/1.56
% 0.35/1.56 thf(conj_1,conjecture,
% 0.35/1.56 rBT_Im1071879905_inv1l @ a @ b @ t ).
% 0.35/1.56 ------------------------
% 0.35/1.58 % (28671)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_28340 for (2999ds/4Mi)
% 0.35/1.58 % (28671)Instruction limit reached!
% 0.35/1.58 % (28671)------------------------------
% 0.35/1.58 % (28671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.58 % (28671)Termination reason: Unknown
% 0.35/1.58 % (28671)Termination phase: shuffling
% 0.35/1.58
% 0.35/1.58 % (28671)Memory used [KB]: 1535
% 0.35/1.58 % (28671)Time elapsed: 0.003 s
% 0.35/1.58 % (28671)Instructions burned: 5 (million)
% 0.35/1.58 % (28671)------------------------------
% 0.35/1.58 % (28671)------------------------------
% 0.35/1.58 % (28674)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_28340 for (2999ds/2Mi)
% 0.35/1.58 % (28674)Instruction limit reached!
% 0.35/1.58 % (28674)------------------------------
% 0.35/1.58 % (28674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.58 % (28674)Termination reason: Unknown
% 0.35/1.58 % (28674)Termination phase: shuffling
% 0.35/1.58
% 0.35/1.58 % (28674)Memory used [KB]: 1407
% 0.35/1.58 % (28674)Time elapsed: 0.003 s
% 0.35/1.58 % (28674)Instructions burned: 4 (million)
% 0.35/1.58 % (28674)------------------------------
% 0.35/1.58 % (28674)------------------------------
% 0.35/1.59 % (28670)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/183Mi)
% 0.35/1.59 % (28672)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_28340 for (2999ds/27Mi)
% 0.35/1.59 % (28673)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/2Mi)
% 0.35/1.59 % (28676)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/18Mi)
% 0.35/1.59 % (28675)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_28340 for (2999ds/275Mi)
% 0.35/1.59 % (28673)Instruction limit reached!
% 0.35/1.59 % (28673)------------------------------
% 0.35/1.59 % (28673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.59 % (28673)Termination reason: Unknown
% 0.35/1.59 % (28673)Termination phase: shuffling
% 0.35/1.59
% 0.35/1.59 % (28673)Memory used [KB]: 1407
% 0.35/1.59 % (28673)Time elapsed: 0.004 s
% 0.35/1.59 % (28673)Instructions burned: 3 (million)
% 0.35/1.59 % (28673)------------------------------
% 0.35/1.59 % (28673)------------------------------
% 0.35/1.59 % (28677)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/3Mi)
% 0.35/1.59 % (28677)Instruction limit reached!
% 0.35/1.59 % (28677)------------------------------
% 0.35/1.59 % (28677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.35/1.59 % (28677)Termination reason: Unknown
% 0.35/1.59 % (28677)Termination phase: shuffling
% 0.35/1.59
% 0.35/1.59 % (28677)Memory used [KB]: 1407
% 0.35/1.59 % (28677)Time elapsed: 0.002 s
% 0.35/1.59 % (28677)Instructions burned: 3 (million)
% 0.35/1.59 % (28677)------------------------------
% 0.35/1.59 % (28677)------------------------------
% 2.88/1.60 % (28678)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_28340 for (2999ds/37Mi)
% 2.88/1.60 % (28676)Instruction limit reached!
% 2.88/1.60 % (28676)------------------------------
% 2.88/1.60 % (28676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (28676)Termination reason: Unknown
% 2.88/1.60 % (28676)Termination phase: shuffling
% 2.88/1.60
% 2.88/1.60 % (28676)Memory used [KB]: 1791
% 2.88/1.60 % (28676)Time elapsed: 0.014 s
% 2.88/1.60 % (28676)Instructions burned: 19 (million)
% 2.88/1.60 % (28676)------------------------------
% 2.88/1.60 % (28676)------------------------------
% 2.88/1.60 % (28680)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_28340 for (2999ds/3Mi)
% 2.88/1.60 % (28680)Instruction limit reached!
% 2.88/1.60 % (28680)------------------------------
% 2.88/1.60 % (28680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (28680)Termination reason: Unknown
% 2.88/1.60 % (28680)Termination phase: shuffling
% 2.88/1.60
% 2.88/1.60 % (28680)Memory used [KB]: 1407
% 2.88/1.60 % (28680)Time elapsed: 0.002 s
% 2.88/1.60 % (28680)Instructions burned: 3 (million)
% 2.88/1.60 % (28680)------------------------------
% 2.88/1.60 % (28680)------------------------------
% 2.88/1.60 % (28672)Instruction limit reached!
% 2.88/1.60 % (28672)------------------------------
% 2.88/1.60 % (28672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.60 % (28672)Termination reason: Unknown
% 2.88/1.60 % (28672)Termination phase: Property scanning
% 2.88/1.60
% 2.88/1.60 % (28672)Memory used [KB]: 2046
% 2.88/1.60 % (28672)Time elapsed: 0.019 s
% 2.88/1.60 % (28672)Instructions burned: 27 (million)
% 2.88/1.60 % (28672)------------------------------
% 2.88/1.60 % (28672)------------------------------
% 2.88/1.61 % (28679)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_28340 for (2999ds/15Mi)
% 2.88/1.61 % (28678)Instruction limit reached!
% 2.88/1.61 % (28678)------------------------------
% 2.88/1.61 % (28678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.61 % (28678)Termination reason: Unknown
% 2.88/1.61 % (28678)Termination phase: shuffling
% 2.88/1.61
% 2.88/1.61 % (28678)Memory used [KB]: 2174
% 2.88/1.61 % (28678)Time elapsed: 0.014 s
% 2.88/1.61 % (28678)Instructions burned: 40 (million)
% 2.88/1.61 % (28678)------------------------------
% 2.88/1.61 % (28678)------------------------------
% 2.88/1.61 % (28682)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/7Mi)
% 2.88/1.61 % (28682)Instruction limit reached!
% 2.88/1.61 % (28682)------------------------------
% 2.88/1.61 % (28682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.61 % (28682)Termination reason: Unknown
% 2.88/1.61 % (28682)Termination phase: shuffling
% 2.88/1.61
% 2.88/1.61 % (28682)Memory used [KB]: 1535
% 2.88/1.61 % (28682)Time elapsed: 0.004 s
% 2.88/1.61 % (28682)Instructions burned: 9 (million)
% 2.88/1.61 % (28682)------------------------------
% 2.88/1.61 % (28682)------------------------------
% 2.88/1.62 % (28675)Refutation not found, incomplete strategy
% 2.88/1.62 % (28675)------------------------------
% 2.88/1.62 % (28675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (28675)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.62
% 2.88/1.62
% 2.88/1.62 % (28675)Memory used [KB]: 6524
% 2.88/1.62 % (28675)Time elapsed: 0.030 s
% 2.88/1.62 % (28675)Instructions burned: 46 (million)
% 2.88/1.62 % (28675)------------------------------
% 2.88/1.62 % (28675)------------------------------
% 2.88/1.62 % (28679)Instruction limit reached!
% 2.88/1.62 % (28679)------------------------------
% 2.88/1.62 % (28679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (28679)Termination reason: Unknown
% 2.88/1.62 % (28679)Termination phase: shuffling
% 2.88/1.62
% 2.88/1.62 % (28679)Memory used [KB]: 1791
% 2.88/1.62 % (28679)Time elapsed: 0.012 s
% 2.88/1.62 % (28679)Instructions burned: 16 (million)
% 2.88/1.62 % (28679)------------------------------
% 2.88/1.62 % (28679)------------------------------
% 2.88/1.62 % (28681)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_28340 for (2999ds/1041Mi)
% 2.88/1.62 % (28684)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_28340 for (2999ds/3Mi)
% 2.88/1.62 % (28683)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/16Mi)
% 2.88/1.62 % (28684)Instruction limit reached!
% 2.88/1.62 % (28684)------------------------------
% 2.88/1.62 % (28684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (28684)Termination reason: Unknown
% 2.88/1.62 % (28684)Termination phase: shuffling
% 2.88/1.62
% 2.88/1.62 % (28684)Memory used [KB]: 1407
% 2.88/1.62 % (28684)Time elapsed: 0.003 s
% 2.88/1.62 % (28684)Instructions burned: 3 (million)
% 2.88/1.62 % (28684)------------------------------
% 2.88/1.62 % (28684)------------------------------
% 2.88/1.62 % (28685)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_28340 for (2999ds/3Mi)
% 2.88/1.62 % (28685)Instruction limit reached!
% 2.88/1.62 % (28685)------------------------------
% 2.88/1.62 % (28685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.62 % (28685)Termination reason: Unknown
% 2.88/1.62 % (28685)Termination phase: shuffling
% 2.88/1.62
% 2.88/1.62 % (28685)Memory used [KB]: 1407
% 2.88/1.62 % (28685)Time elapsed: 0.002 s
% 2.88/1.62 % (28685)Instructions burned: 3 (million)
% 2.88/1.62 % (28685)------------------------------
% 2.88/1.62 % (28685)------------------------------
% 2.88/1.63 % (28683)Instruction limit reached!
% 2.88/1.63 % (28683)------------------------------
% 2.88/1.63 % (28683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (28683)Termination reason: Unknown
% 2.88/1.63 % (28683)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (28683)Memory used [KB]: 1791
% 2.88/1.63 % (28683)Time elapsed: 0.012 s
% 2.88/1.63 % (28683)Instructions burned: 16 (million)
% 2.88/1.63 % (28683)------------------------------
% 2.88/1.63 % (28683)------------------------------
% 2.88/1.63 % (28688)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/4Mi)
% 2.88/1.63 % (28688)Instruction limit reached!
% 2.88/1.63 % (28688)------------------------------
% 2.88/1.63 % (28688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.63 % (28688)Termination reason: Unknown
% 2.88/1.63 % (28688)Termination phase: shuffling
% 2.88/1.63
% 2.88/1.63 % (28688)Memory used [KB]: 1535
% 2.88/1.63 % (28688)Time elapsed: 0.003 s
% 2.88/1.63 % (28688)Instructions burned: 4 (million)
% 2.88/1.63 % (28688)------------------------------
% 2.88/1.63 % (28688)------------------------------
% 2.88/1.63 % (28687)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/3Mi)
% 2.88/1.63 % (28689)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/18Mi)
% 2.88/1.63 % (28686)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/7Mi)
% 2.88/1.64 % (28687)Instruction limit reached!
% 2.88/1.64 % (28687)------------------------------
% 2.88/1.64 % (28687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (28687)Termination reason: Unknown
% 2.88/1.64 % (28687)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (28687)Memory used [KB]: 1407
% 2.88/1.64 % (28687)Time elapsed: 0.004 s
% 2.88/1.64 % (28687)Instructions burned: 4 (million)
% 2.88/1.64 % (28687)------------------------------
% 2.88/1.64 % (28687)------------------------------
% 2.88/1.64 % (28686)Instruction limit reached!
% 2.88/1.64 % (28686)------------------------------
% 2.88/1.64 % (28686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (28686)Termination reason: Unknown
% 2.88/1.64 % (28686)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (28686)Memory used [KB]: 1535
% 2.88/1.64 % (28686)Time elapsed: 0.007 s
% 2.88/1.64 % (28686)Instructions burned: 8 (million)
% 2.88/1.64 % (28686)------------------------------
% 2.88/1.64 % (28686)------------------------------
% 2.88/1.64 % (28689)Instruction limit reached!
% 2.88/1.64 % (28689)------------------------------
% 2.88/1.64 % (28689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.64 % (28689)Termination reason: Unknown
% 2.88/1.64 % (28689)Termination phase: shuffling
% 2.88/1.64
% 2.88/1.64 % (28689)Memory used [KB]: 1918
% 2.88/1.64 % (28689)Time elapsed: 0.007 s
% 2.88/1.64 % (28689)Instructions burned: 18 (million)
% 2.88/1.64 % (28689)------------------------------
% 2.88/1.64 % (28689)------------------------------
% 2.88/1.64 % (28690)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/710Mi)
% 2.88/1.64 % (28691)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/6Mi)
% 2.88/1.65 % (28691)Instruction limit reached!
% 2.88/1.65 % (28691)------------------------------
% 2.88/1.65 % (28691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.65 % (28691)Termination reason: Unknown
% 2.88/1.65 % (28691)Termination phase: shuffling
% 2.88/1.65
% 2.88/1.65 % (28691)Memory used [KB]: 1535
% 2.88/1.65 % (28691)Time elapsed: 0.004 s
% 2.88/1.65 % (28691)Instructions burned: 6 (million)
% 2.88/1.65 % (28691)------------------------------
% 2.88/1.65 % (28691)------------------------------
% 2.88/1.65 % (28692)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_28340 for (2999ds/902Mi)
% 2.88/1.65 % (28694)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/5Mi)
% 2.88/1.65 % (28694)Instruction limit reached!
% 2.88/1.65 % (28694)------------------------------
% 2.88/1.65 % (28694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.65 % (28694)Termination reason: Unknown
% 2.88/1.65 % (28694)Termination phase: shuffling
% 2.88/1.65
% 2.88/1.65 % (28694)Memory used [KB]: 1535
% 2.88/1.65 % (28694)Time elapsed: 0.003 s
% 2.88/1.65 % (28694)Instructions burned: 6 (million)
% 2.88/1.65 % (28694)------------------------------
% 2.88/1.65 % (28694)------------------------------
% 2.88/1.66 % (28695)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_28340 for (2999ds/6Mi)
% 2.88/1.66 % (28693)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_28340 for (2999ds/21Mi)
% 2.88/1.66 % (28695)Instruction limit reached!
% 2.88/1.66 % (28695)------------------------------
% 2.88/1.66 % (28695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.66 % (28695)Termination reason: Unknown
% 2.88/1.66 % (28695)Termination phase: shuffling
% 2.88/1.66
% 2.88/1.66 % (28695)Memory used [KB]: 1535
% 2.88/1.66 % (28695)Time elapsed: 0.004 s
% 2.88/1.66 % (28695)Instructions burned: 7 (million)
% 2.88/1.66 % (28695)------------------------------
% 2.88/1.66 % (28695)------------------------------
% 2.88/1.66 % (28696)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28340 for (2999ds/377Mi)
% 2.88/1.67 % (28697)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_28340 for (2999ds/779Mi)
% 2.88/1.67 % (28693)Instruction limit reached!
% 2.88/1.67 % (28693)------------------------------
% 2.88/1.67 % (28693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.67 % (28693)Termination reason: Unknown
% 2.88/1.67 % (28693)Termination phase: shuffling
% 2.88/1.67
% 2.88/1.67 % (28693)Memory used [KB]: 1918
% 2.88/1.67 % (28693)Time elapsed: 0.016 s
% 2.88/1.67 % (28693)Instructions burned: 22 (million)
% 2.88/1.67 % (28693)------------------------------
% 2.88/1.67 % (28693)------------------------------
% 2.88/1.67 % (28670)Instruction limit reached!
% 2.88/1.67 % (28670)------------------------------
% 2.88/1.67 % (28670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.67 % (28670)Termination reason: Unknown
% 2.88/1.67 % (28670)Termination phase: Saturation
% 2.88/1.67
% 2.88/1.67 % (28670)Memory used [KB]: 7419
% 2.88/1.67 % (28670)Time elapsed: 0.087 s
% 2.88/1.67 % (28670)Instructions burned: 185 (million)
% 2.88/1.67 % (28670)------------------------------
% 2.88/1.67 % (28670)------------------------------
% 2.88/1.68 % (28699)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/879Mi)
% 2.88/1.69 % (28698)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_28340 for (2999ds/19Mi)
% 2.88/1.70 % (28692)Refutation not found, incomplete strategy
% 2.88/1.70 % (28692)------------------------------
% 2.88/1.70 % (28692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.70 % (28692)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.70
% 2.88/1.70
% 2.88/1.70 % (28692)Memory used [KB]: 7547
% 2.88/1.70 % (28692)Time elapsed: 0.048 s
% 2.88/1.70 % (28692)Instructions burned: 156 (million)
% 2.88/1.70 % (28692)------------------------------
% 2.88/1.70 % (28692)------------------------------
% 2.88/1.70 % (28698)Instruction limit reached!
% 2.88/1.70 % (28698)------------------------------
% 2.88/1.70 % (28698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.70 % (28698)Termination reason: Unknown
% 2.88/1.70 % (28698)Termination phase: shuffling
% 2.88/1.70
% 2.88/1.70 % (28698)Memory used [KB]: 1791
% 2.88/1.70 % (28698)Time elapsed: 0.011 s
% 2.88/1.70 % (28698)Instructions burned: 20 (million)
% 2.88/1.70 % (28698)------------------------------
% 2.88/1.70 % (28698)------------------------------
% 2.88/1.71 % (28700)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/17Mi)
% 2.88/1.71 % (28701)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/3Mi)
% 2.88/1.71 % (28701)Instruction limit reached!
% 2.88/1.71 % (28701)------------------------------
% 2.88/1.71 % (28701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (28701)Termination reason: Unknown
% 2.88/1.71 % (28701)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (28701)Memory used [KB]: 1407
% 2.88/1.71 % (28701)Time elapsed: 0.003 s
% 2.88/1.71 % (28701)Instructions burned: 3 (million)
% 2.88/1.71 % (28701)------------------------------
% 2.88/1.71 % (28701)------------------------------
% 2.88/1.71 % (28700)Instruction limit reached!
% 2.88/1.71 % (28700)------------------------------
% 2.88/1.71 % (28700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (28700)Termination reason: Unknown
% 2.88/1.71 % (28700)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (28700)Memory used [KB]: 1918
% 2.88/1.71 % (28700)Time elapsed: 0.007 s
% 2.88/1.71 % (28700)Instructions burned: 18 (million)
% 2.88/1.71 % (28700)------------------------------
% 2.88/1.71 % (28700)------------------------------
% 2.88/1.72 % (28702)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/30Mi)
% 2.88/1.72 % (28703)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/127Mi)
% 2.88/1.73 % (28702)Instruction limit reached!
% 2.88/1.73 % (28702)------------------------------
% 2.88/1.73 % (28702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.73 % (28702)Termination reason: Unknown
% 2.88/1.73 % (28702)Termination phase: Property scanning
% 2.88/1.73
% 2.88/1.73 % (28702)Memory used [KB]: 2046
% 2.88/1.73 % (28702)Time elapsed: 0.013 s
% 2.88/1.73 % (28702)Instructions burned: 32 (million)
% 2.88/1.73 % (28702)------------------------------
% 2.88/1.73 % (28702)------------------------------
% 2.88/1.74 % (28704)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28340 for (2998ds/100Mi)
% 2.88/1.76 % (28703)Instruction limit reached!
% 2.88/1.76 % (28703)------------------------------
% 2.88/1.76 % (28703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.76 % (28703)Termination reason: Unknown
% 2.88/1.76 % (28703)Termination phase: Saturation
% 2.88/1.76
% 2.88/1.76 % (28703)Memory used [KB]: 7036
% 2.88/1.76 % (28703)Time elapsed: 0.039 s
% 2.88/1.76 % (28703)Instructions burned: 130 (million)
% 2.88/1.76 % (28703)------------------------------
% 2.88/1.76 % (28703)------------------------------
% 2.88/1.77 % (28705)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_28340 for (2997ds/3Mi)
% 2.88/1.77 % (28705)Instruction limit reached!
% 2.88/1.77 % (28705)------------------------------
% 2.88/1.77 % (28705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.77 % (28705)Termination reason: Unknown
% 2.88/1.77 % (28705)Termination phase: shuffling
% 2.88/1.77
% 2.88/1.77 % (28705)Memory used [KB]: 1535
% 2.88/1.77 % (28705)Time elapsed: 0.003 s
% 2.88/1.77 % (28705)Instructions burned: 6 (million)
% 2.88/1.77 % (28705)------------------------------
% 2.88/1.77 % (28705)------------------------------
% 2.88/1.77 % (28704)Instruction limit reached!
% 2.88/1.77 % (28704)------------------------------
% 2.88/1.77 % (28704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.77 % (28704)Termination reason: Unknown
% 2.88/1.77 % (28704)Termination phase: Property scanning
% 2.88/1.77
% 2.88/1.77 % (28704)Memory used [KB]: 2686
% 2.88/1.77 % (28704)Time elapsed: 0.032 s
% 2.88/1.77 % (28704)Instructions burned: 103 (million)
% 2.88/1.77 % (28704)------------------------------
% 2.88/1.77 % (28704)------------------------------
% 2.88/1.78 % (28696)Instruction limit reached!
% 2.88/1.78 % (28696)------------------------------
% 2.88/1.78 % (28696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.78 % (28696)Termination reason: Unknown
% 2.88/1.78 % (28696)Termination phase: Saturation
% 2.88/1.78
% 2.88/1.78 % (28696)Memory used [KB]: 7931
% 2.88/1.78 % (28696)Time elapsed: 0.116 s
% 2.88/1.78 % (28696)Instructions burned: 378 (million)
% 2.88/1.78 % (28696)------------------------------
% 2.88/1.78 % (28696)------------------------------
% 2.88/1.78 % (28706)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/20Mi)
% 2.88/1.78 % (28707)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/86Mi)
% 2.88/1.79 % (28708)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/107Mi)
% 2.88/1.79 % (28706)Instruction limit reached!
% 2.88/1.79 % (28706)------------------------------
% 2.88/1.79 % (28706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.79 % (28706)Termination reason: Unknown
% 2.88/1.79 % (28706)Termination phase: shuffling
% 2.88/1.79
% 2.88/1.79 % (28706)Memory used [KB]: 1918
% 2.88/1.79 % (28706)Time elapsed: 0.008 s
% 2.88/1.79 % (28706)Instructions burned: 21 (million)
% 2.88/1.79 % (28706)------------------------------
% 2.88/1.79 % (28706)------------------------------
% 2.88/1.80 % (28709)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/39Mi)
% 2.88/1.81 % (28709)Instruction limit reached!
% 2.88/1.81 % (28709)------------------------------
% 2.88/1.81 % (28709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.81 % (28709)Termination reason: Unknown
% 2.88/1.81 % (28709)Termination phase: shuffling
% 2.88/1.81
% 2.88/1.81 % (28709)Memory used [KB]: 2174
% 2.88/1.81 % (28709)Time elapsed: 0.012 s
% 2.88/1.81 % (28709)Instructions burned: 40 (million)
% 2.88/1.81 % (28709)------------------------------
% 2.88/1.81 % (28709)------------------------------
% 2.88/1.81 % (28707)Instruction limit reached!
% 2.88/1.81 % (28707)------------------------------
% 2.88/1.81 % (28707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.81 % (28707)Termination reason: Unknown
% 2.88/1.81 % (28707)Termination phase: Property scanning
% 2.88/1.81
% 2.88/1.81 % (28707)Memory used [KB]: 2430
% 2.88/1.81 % (28707)Time elapsed: 0.029 s
% 2.88/1.81 % (28707)Instructions burned: 86 (million)
% 2.88/1.81 % (28707)------------------------------
% 2.88/1.81 % (28707)------------------------------
% 2.88/1.82 % (28710)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/448Mi)
% 2.88/1.82 % (28708)Instruction limit reached!
% 2.88/1.82 % (28708)------------------------------
% 2.88/1.82 % (28708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.82 % (28708)Termination reason: Unknown
% 2.88/1.82 % (28708)Termination phase: Saturation
% 2.88/1.82
% 2.88/1.82 % (28708)Memory used [KB]: 6908
% 2.88/1.82 % (28708)Time elapsed: 0.033 s
% 2.88/1.82 % (28708)Instructions burned: 107 (million)
% 2.88/1.82 % (28708)------------------------------
% 2.88/1.82 % (28708)------------------------------
% 2.88/1.82 % (28711)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/46Mi)
% 2.88/1.83 % (28712)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/98Mi)
% 2.88/1.84 % (28711)Instruction limit reached!
% 2.88/1.84 % (28711)------------------------------
% 2.88/1.84 % (28711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.84 % (28711)Termination reason: Unknown
% 2.88/1.84 % (28711)Termination phase: Preprocessing 1
% 2.88/1.84
% 2.88/1.84 % (28711)Memory used [KB]: 2046
% 2.88/1.84 % (28711)Time elapsed: 0.017 s
% 2.88/1.84 % (28711)Instructions burned: 46 (million)
% 2.88/1.84 % (28711)------------------------------
% 2.88/1.84 % (28711)------------------------------
% 2.88/1.85 % (28713)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/507Mi)
% 2.88/1.85 % (28690)Instruction limit reached!
% 2.88/1.85 % (28690)------------------------------
% 2.88/1.85 % (28690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.85 % (28690)Termination reason: Unknown
% 2.88/1.85 % (28690)Termination phase: Saturation
% 2.88/1.85
% 2.88/1.85 % (28690)Memory used [KB]: 7931
% 2.88/1.85 % (28690)Time elapsed: 0.209 s
% 2.88/1.85 % (28690)Instructions burned: 713 (million)
% 2.88/1.85 % (28690)------------------------------
% 2.88/1.85 % (28690)------------------------------
% 2.88/1.85 % (28712)Instruction limit reached!
% 2.88/1.85 % (28712)------------------------------
% 2.88/1.85 % (28712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.85 % (28712)Termination reason: Unknown
% 2.88/1.85 % (28712)Termination phase: Property scanning
% 2.88/1.85
% 2.88/1.85 % (28712)Memory used [KB]: 2686
% 2.88/1.85 % (28712)Time elapsed: 0.028 s
% 2.88/1.85 % (28712)Instructions burned: 99 (million)
% 2.88/1.85 % (28712)------------------------------
% 2.88/1.85 % (28712)------------------------------
% 2.88/1.86 % (28714)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/149Mi)
% 2.88/1.86 % (28715)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_28340 for (2997ds/39Mi)
% 2.88/1.87 % (28715)Instruction limit reached!
% 2.88/1.87 % (28715)------------------------------
% 2.88/1.87 % (28715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.87 % (28715)Termination reason: Unknown
% 2.88/1.87 % (28715)Termination phase: Preprocessing 1
% 2.88/1.87
% 2.88/1.87 % (28715)Memory used [KB]: 2046
% 2.88/1.87 % (28715)Time elapsed: 0.013 s
% 2.88/1.87 % (28715)Instructions burned: 40 (million)
% 2.88/1.87 % (28715)------------------------------
% 2.88/1.87 % (28715)------------------------------
% 2.88/1.88 % (28716)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/6Mi)
% 2.88/1.89 % (28716)Instruction limit reached!
% 2.88/1.89 % (28716)------------------------------
% 2.88/1.89 % (28716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.89 % (28716)Termination reason: Unknown
% 2.88/1.89 % (28716)Termination phase: shuffling
% 2.88/1.89
% 2.88/1.89 % (28716)Memory used [KB]: 1535
% 2.88/1.89 % (28716)Time elapsed: 0.003 s
% 2.88/1.89 % (28716)Instructions burned: 6 (million)
% 2.88/1.89 % (28716)------------------------------
% 2.88/1.89 % (28716)------------------------------
% 2.88/1.90 % (28717)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/1087Mi)
% 2.88/1.90 % (28714)Instruction limit reached!
% 2.88/1.90 % (28714)------------------------------
% 2.88/1.90 % (28714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.90 % (28714)Termination reason: Unknown
% 2.88/1.90 % (28714)Termination phase: Saturation
% 2.88/1.90
% 2.88/1.90 % (28714)Memory used [KB]: 7164
% 2.88/1.90 % (28714)Time elapsed: 0.044 s
% 2.88/1.90 % (28714)Instructions burned: 151 (million)
% 2.88/1.90 % (28714)------------------------------
% 2.88/1.90 % (28714)------------------------------
% 2.88/1.91 % (28697)Instruction limit reached!
% 2.88/1.91 % (28697)------------------------------
% 2.88/1.91 % (28697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.91 % (28697)Termination reason: Unknown
% 2.88/1.91 % (28697)Termination phase: Saturation
% 2.88/1.91
% 2.88/1.91 % (28697)Memory used [KB]: 7675
% 2.88/1.91 % (28697)Time elapsed: 0.240 s
% 2.88/1.91 % (28697)Instructions burned: 780 (million)
% 2.88/1.91 % (28697)------------------------------
% 2.88/1.91 % (28697)------------------------------
% 2.88/1.91 % (28718)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/47Mi)
% 2.88/1.92 % (28719)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/44Mi)
% 2.88/1.93 % (28718)Instruction limit reached!
% 2.88/1.93 % (28718)------------------------------
% 2.88/1.93 % (28718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.93 % (28718)Termination reason: Unknown
% 2.88/1.93 % (28718)Termination phase: Preprocessing 3
% 2.88/1.93
% 2.88/1.93 % (28718)Memory used [KB]: 2302
% 2.88/1.93 % (28718)Time elapsed: 0.016 s
% 2.88/1.93 % (28718)Instructions burned: 47 (million)
% 2.88/1.93 % (28718)------------------------------
% 2.88/1.93 % (28718)------------------------------
% 2.88/1.93 % (28719)Instruction limit reached!
% 2.88/1.93 % (28719)------------------------------
% 2.88/1.93 % (28719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.93 % (28719)Termination reason: Unknown
% 2.88/1.93 % (28719)Termination phase: Property scanning
% 2.88/1.93
% 2.88/1.93 % (28719)Memory used [KB]: 2302
% 2.88/1.93 % (28719)Time elapsed: 0.014 s
% 2.88/1.93 % (28719)Instructions burned: 46 (million)
% 2.88/1.93 % (28719)------------------------------
% 2.88/1.93 % (28719)------------------------------
% 2.88/1.94 % (28720)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/432Mi)
% 2.88/1.94 % (28721)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/62Mi)
% 2.88/1.95 % (28710)Instruction limit reached!
% 2.88/1.95 % (28710)------------------------------
% 2.88/1.95 % (28710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.95 % (28710)Termination reason: Unknown
% 2.88/1.95 % (28710)Termination phase: Saturation
% 2.88/1.95
% 2.88/1.95 % (28710)Memory used [KB]: 7931
% 2.88/1.95 % (28710)Time elapsed: 0.135 s
% 2.88/1.95 % (28710)Instructions burned: 450 (million)
% 2.88/1.95 % (28710)------------------------------
% 2.88/1.95 % (28710)------------------------------
% 2.88/1.96 % (28721)Instruction limit reached!
% 2.88/1.96 % (28721)------------------------------
% 2.88/1.96 % (28721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.96 % (28721)Termination reason: Unknown
% 2.88/1.96 % (28721)Termination phase: Property scanning
% 2.88/1.96
% 2.88/1.96 % (28721)Memory used [KB]: 2302
% 2.88/1.96 % (28721)Time elapsed: 0.018 s
% 2.88/1.96 % (28721)Instructions burned: 63 (million)
% 2.88/1.96 % (28721)------------------------------
% 2.88/1.96 % (28721)------------------------------
% 2.88/1.96 % (28722)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/31Mi)
% 2.88/1.96 % (28681)Instruction limit reached!
% 2.88/1.96 % (28681)------------------------------
% 2.88/1.96 % (28681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.96 % (28681)Termination reason: Unknown
% 2.88/1.96 % (28681)Termination phase: Saturation
% 2.88/1.96
% 2.88/1.96 % (28681)Memory used [KB]: 9594
% 2.88/1.96 % (28681)Time elapsed: 0.348 s
% 2.88/1.96 % (28681)Instructions burned: 1042 (million)
% 2.88/1.96 % (28681)------------------------------
% 2.88/1.96 % (28681)------------------------------
% 2.88/1.96 % (28723)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/96Mi)
% 2.88/1.97 % (28722)Instruction limit reached!
% 2.88/1.97 % (28722)------------------------------
% 2.88/1.97 % (28722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.97 % (28722)Termination reason: Unknown
% 2.88/1.97 % (28722)Termination phase: Property scanning
% 2.88/1.97
% 2.88/1.97 % (28722)Memory used [KB]: 2046
% 2.88/1.97 % (28722)Time elapsed: 0.011 s
% 2.88/1.97 % (28722)Instructions burned: 32 (million)
% 2.88/1.97 % (28722)------------------------------
% 2.88/1.97 % (28722)------------------------------
% 2.88/1.97 % (28699)Instruction limit reached!
% 2.88/1.97 % (28699)------------------------------
% 2.88/1.97 % (28699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.97 % (28699)Termination reason: Unknown
% 2.88/1.97 % (28699)Termination phase: Saturation
% 2.88/1.97
% 2.88/1.97 % (28699)Memory used [KB]: 7164
% 2.88/1.97 % (28699)Time elapsed: 0.312 s
% 2.88/1.97 % (28699)Instructions burned: 880 (million)
% 2.88/1.97 % (28699)------------------------------
% 2.88/1.97 % (28699)------------------------------
% 2.88/1.97 % (28724)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_28340 for (2996ds/453Mi)
% 2.88/1.98 % (28725)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/71Mi)
% 2.88/1.98 % (28726)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/83Mi)
% 2.88/1.99 % (28723)Instruction limit reached!
% 2.88/1.99 % (28723)------------------------------
% 2.88/1.99 % (28723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.99 % (28723)Termination reason: Unknown
% 2.88/1.99 % (28723)Termination phase: Property scanning
% 2.88/1.99
% 2.88/1.99 % (28723)Memory used [KB]: 2430
% 2.88/1.99 % (28723)Time elapsed: 0.030 s
% 2.88/1.99 % (28723)Instructions burned: 98 (million)
% 2.88/1.99 % (28723)------------------------------
% 2.88/1.99 % (28723)------------------------------
% 2.88/2.00 % (28725)Instruction limit reached!
% 2.88/2.00 % (28725)------------------------------
% 2.88/2.00 % (28725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/2.00 % (28725)Termination reason: Unknown
% 2.88/2.00 % (28725)Termination phase: Property scanning
% 2.88/2.00
% 2.88/2.00 % (28725)Memory used [KB]: 2558
% 2.88/2.00 % (28725)Time elapsed: 0.024 s
% 2.88/2.00 % (28725)Instructions burned: 74 (million)
% 2.88/2.00 % (28725)------------------------------
% 2.88/2.00 % (28725)------------------------------
% 2.88/2.00 % (28727)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/11Mi)
% 2.88/2.01 % (28727)Instruction limit reached!
% 2.88/2.01 % (28727)------------------------------
% 2.88/2.01 % (28727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/2.01 % (28727)Termination reason: Unknown
% 2.88/2.01 % (28727)Termination phase: shuffling
% 2.88/2.01
% 2.88/2.01 % (28727)Memory used [KB]: 1663
% 2.88/2.01 % (28727)Time elapsed: 0.004 s
% 2.88/2.01 % (28727)Instructions burned: 11 (million)
% 2.88/2.01 % (28727)------------------------------
% 2.88/2.01 % (28727)------------------------------
% 2.88/2.01 % (28713)Instruction limit reached!
% 2.88/2.01 % (28713)------------------------------
% 2.88/2.01 % (28713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/2.01 % (28713)Termination reason: Unknown
% 2.88/2.01 % (28713)Termination phase: Saturation
% 2.88/2.01
% 2.88/2.01 % (28713)Memory used [KB]: 8827
% 2.88/2.01 % (28713)Time elapsed: 0.167 s
% 2.88/2.01 % (28713)Instructions burned: 508 (million)
% 2.88/2.01 % (28713)------------------------------
% 2.88/2.01 % (28713)------------------------------
% 5.76/2.01 % (28728)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/41Mi)
% 5.76/2.02 % (28729)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/6Mi)
% 5.76/2.02 % (28729)Instruction limit reached!
% 5.76/2.02 % (28729)------------------------------
% 5.76/2.02 % (28729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.02 % (28729)Termination reason: Unknown
% 5.76/2.02 % (28729)Termination phase: shuffling
% 5.76/2.02
% 5.76/2.02 % (28729)Memory used [KB]: 1535
% 5.76/2.02 % (28729)Time elapsed: 0.003 s
% 5.76/2.02 % (28729)Instructions burned: 6 (million)
% 5.76/2.02 % (28729)------------------------------
% 5.76/2.02 % (28729)------------------------------
% 5.76/2.02 % (28730)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/150Mi)
% 5.76/2.02 % (28726)Instruction limit reached!
% 5.76/2.02 % (28726)------------------------------
% 5.76/2.02 % (28726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.02 % (28726)Termination reason: Unknown
% 5.76/2.02 % (28726)Termination phase: Saturation
% 5.76/2.02
% 5.76/2.02 % (28726)Memory used [KB]: 6780
% 5.76/2.02 % (28726)Time elapsed: 0.041 s
% 5.76/2.02 % (28726)Instructions burned: 83 (million)
% 5.76/2.02 % (28726)------------------------------
% 5.76/2.02 % (28726)------------------------------
% 5.76/2.02 % (28728)Instruction limit reached!
% 5.76/2.02 % (28728)------------------------------
% 5.76/2.02 % (28728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.02 % (28728)Termination reason: Unknown
% 5.76/2.02 % (28728)Termination phase: shuffling
% 5.76/2.02
% 5.76/2.02 % (28728)Memory used [KB]: 2302
% 5.76/2.02 % (28728)Time elapsed: 0.013 s
% 5.76/2.02 % (28728)Instructions burned: 42 (million)
% 5.76/2.02 % (28728)------------------------------
% 5.76/2.02 % (28728)------------------------------
% 5.76/2.03 % (28731)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/343Mi)
% 5.76/2.03 % (28733)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/253Mi)
% 5.76/2.04 % (28732)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_28340 for (2995ds/109Mi)
% 5.76/2.07 % (28730)Instruction limit reached!
% 5.76/2.07 % (28730)------------------------------
% 5.76/2.07 % (28730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.07 % (28730)Termination reason: Unknown
% 5.76/2.07 % (28730)Termination phase: Saturation
% 5.76/2.07
% 5.76/2.07 % (28730)Memory used [KB]: 7164
% 5.76/2.07 % (28730)Time elapsed: 0.047 s
% 5.76/2.07 % (28730)Instructions burned: 152 (million)
% 5.76/2.07 % (28730)------------------------------
% 5.76/2.07 % (28730)------------------------------
% 5.76/2.07 % (28720)Instruction limit reached!
% 5.76/2.07 % (28720)------------------------------
% 5.76/2.07 % (28720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.07 % (28720)Termination reason: Unknown
% 5.76/2.07 % (28720)Termination phase: Saturation
% 5.76/2.07
% 5.76/2.07 % (28720)Memory used [KB]: 4477
% 5.76/2.07 % (28720)Time elapsed: 0.136 s
% 5.76/2.07 % (28720)Instructions burned: 433 (million)
% 5.76/2.07 % (28720)------------------------------
% 5.76/2.07 % (28720)------------------------------
% 5.76/2.08 % (28734)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/140Mi)
% 5.76/2.08 % (28735)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/614Mi)
% 5.76/2.10 % (28732)Instruction limit reached!
% 5.76/2.10 % (28732)------------------------------
% 5.76/2.10 % (28732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.10 % (28732)Termination reason: Unknown
% 5.76/2.10 % (28732)Termination phase: Saturation
% 5.76/2.10
% 5.76/2.10 % (28732)Memory used [KB]: 6908
% 5.76/2.10 % (28732)Time elapsed: 0.062 s
% 5.76/2.10 % (28732)Instructions burned: 109 (million)
% 5.76/2.10 % (28732)------------------------------
% 5.76/2.10 % (28732)------------------------------
% 5.76/2.11 % (28724)Instruction limit reached!
% 5.76/2.11 % (28724)------------------------------
% 5.76/2.11 % (28724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.11 % (28724)Termination reason: Unknown
% 5.76/2.11 % (28724)Termination phase: Saturation
% 5.76/2.11
% 5.76/2.11 % (28724)Memory used [KB]: 8699
% 5.76/2.11 % (28724)Time elapsed: 0.136 s
% 5.76/2.11 % (28724)Instructions burned: 455 (million)
% 5.76/2.11 % (28724)------------------------------
% 5.76/2.11 % (28724)------------------------------
% 6.39/2.11 % (28733)Instruction limit reached!
% 6.39/2.11 % (28733)------------------------------
% 6.39/2.11 % (28733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.11 % (28733)Termination reason: Unknown
% 6.39/2.11 % (28733)Termination phase: Saturation
% 6.39/2.11
% 6.39/2.11 % (28733)Memory used [KB]: 6908
% 6.39/2.11 % (28733)Time elapsed: 0.081 s
% 6.39/2.11 % (28733)Instructions burned: 254 (million)
% 6.39/2.11 % (28733)------------------------------
% 6.39/2.11 % (28733)------------------------------
% 6.39/2.12 % (28736)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/202Mi)
% 6.39/2.12 % (28737)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/339Mi)
% 6.39/2.12 % (28734)Instruction limit reached!
% 6.39/2.12 % (28734)------------------------------
% 6.39/2.12 % (28734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.12 % (28734)Termination reason: Unknown
% 6.39/2.12 % (28734)Termination phase: Saturation
% 6.39/2.12
% 6.39/2.12 % (28734)Memory used [KB]: 7164
% 6.39/2.12 % (28734)Time elapsed: 0.044 s
% 6.39/2.12 % (28734)Instructions burned: 141 (million)
% 6.39/2.12 % (28734)------------------------------
% 6.39/2.12 % (28734)------------------------------
% 6.39/2.12 % (28738)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/283Mi)
% 6.39/2.13 % (28739)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/134Mi)
% 6.39/2.13 % (28731)Instruction limit reached!
% 6.39/2.13 % (28731)------------------------------
% 6.39/2.13 % (28731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.13 % (28731)Termination reason: Unknown
% 6.39/2.13 % (28731)Termination phase: Saturation
% 6.39/2.13
% 6.39/2.13 % (28731)Memory used [KB]: 7419
% 6.39/2.13 % (28731)Time elapsed: 0.105 s
% 6.39/2.13 % (28731)Instructions burned: 343 (million)
% 6.39/2.13 % (28731)------------------------------
% 6.39/2.13 % (28731)------------------------------
% 6.39/2.14 % (28736)Refutation not found, incomplete strategy
% 6.39/2.14 % (28736)------------------------------
% 6.39/2.14 % (28736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (28736)Termination reason: Refutation not found, incomplete strategy
% 6.39/2.14
% 6.39/2.14
% 6.39/2.14 % (28736)Memory used [KB]: 6524
% 6.39/2.14 % (28736)Time elapsed: 0.022 s
% 6.39/2.14 % (28736)Instructions burned: 47 (million)
% 6.39/2.14 % (28736)------------------------------
% 6.39/2.14 % (28736)------------------------------
% 6.39/2.14 % (28740)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/298Mi)
% 6.39/2.15 % (28741)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_28340 for (2994ds/192Mi)
% 6.39/2.17 % (28739)Instruction limit reached!
% 6.39/2.17 % (28739)------------------------------
% 6.39/2.17 % (28739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.17 % (28739)Termination reason: Unknown
% 6.39/2.17 % (28739)Termination phase: Saturation
% 6.39/2.17
% 6.39/2.17 % (28739)Memory used [KB]: 7036
% 6.39/2.17 % (28739)Time elapsed: 0.041 s
% 6.39/2.17 % (28739)Instructions burned: 136 (million)
% 6.39/2.17 % (28739)------------------------------
% 6.39/2.17 % (28739)------------------------------
% 6.39/2.18 % (28742)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/258Mi)
% 6.81/2.21 % (28738)Instruction limit reached!
% 6.81/2.21 % (28738)------------------------------
% 6.81/2.21 % (28738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (28738)Termination reason: Unknown
% 6.81/2.21 % (28738)Termination phase: Saturation
% 6.81/2.21
% 6.81/2.21 % (28738)Memory used [KB]: 7803
% 6.81/2.21 % (28738)Time elapsed: 0.088 s
% 6.81/2.21 % (28738)Instructions burned: 285 (million)
% 6.81/2.21 % (28738)------------------------------
% 6.81/2.21 % (28738)------------------------------
% 6.81/2.21 % (28741)Instruction limit reached!
% 6.81/2.21 % (28741)------------------------------
% 6.81/2.21 % (28741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (28741)Termination reason: Unknown
% 6.81/2.21 % (28741)Termination phase: Saturation
% 6.81/2.21
% 6.81/2.21 % (28741)Memory used [KB]: 8187
% 6.81/2.21 % (28741)Time elapsed: 0.064 s
% 6.81/2.21 % (28741)Instructions burned: 192 (million)
% 6.81/2.21 % (28741)------------------------------
% 6.81/2.21 % (28741)------------------------------
% 6.81/2.22 % (28737)Instruction limit reached!
% 6.81/2.22 % (28737)------------------------------
% 6.81/2.22 % (28737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (28737)Termination reason: Unknown
% 6.81/2.22 % (28737)Termination phase: Saturation
% 6.81/2.22
% 6.81/2.22 % (28737)Memory used [KB]: 7675
% 6.81/2.22 % (28737)Time elapsed: 0.100 s
% 6.81/2.22 % (28737)Instructions burned: 339 (million)
% 6.81/2.22 % (28737)------------------------------
% 6.81/2.22 % (28737)------------------------------
% 6.81/2.22 % (28743)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/90Mi)
% 6.81/2.22 % (28744)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/231Mi)
% 6.81/2.22 % (28717)Instruction limit reached!
% 6.81/2.22 % (28717)------------------------------
% 6.81/2.22 % (28717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (28717)Termination reason: Unknown
% 6.81/2.22 % (28717)Termination phase: Saturation
% 6.81/2.22
% 6.81/2.22 % (28717)Memory used [KB]: 7547
% 6.81/2.22 % (28717)Time elapsed: 0.328 s
% 6.81/2.22 % (28717)Instructions burned: 1088 (million)
% 6.81/2.22 % (28717)------------------------------
% 6.81/2.22 % (28717)------------------------------
% 6.81/2.22 % (28740)Instruction limit reached!
% 6.81/2.22 % (28740)------------------------------
% 6.81/2.22 % (28740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (28740)Termination reason: Unknown
% 6.81/2.22 % (28740)Termination phase: Saturation
% 6.81/2.22
% 6.81/2.22 % (28740)Memory used [KB]: 8443
% 6.81/2.22 % (28740)Time elapsed: 0.084 s
% 6.81/2.22 % (28740)Instructions burned: 300 (million)
% 6.81/2.22 % (28740)------------------------------
% 6.81/2.22 % (28740)------------------------------
% 6.81/2.23 % (28745)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/458Mi)
% 6.81/2.23 % (28746)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/31Mi)
% 6.81/2.23 % (28747)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/297Mi)
% 6.81/2.24 % (28746)Instruction limit reached!
% 6.81/2.24 % (28746)------------------------------
% 6.81/2.24 % (28746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.24 % (28746)Termination reason: Unknown
% 6.81/2.24 % (28746)Termination phase: Property scanning
% 6.81/2.24
% 6.81/2.24 % (28746)Memory used [KB]: 2046
% 6.81/2.24 % (28746)Time elapsed: 0.012 s
% 6.81/2.24 % (28746)Instructions burned: 34 (million)
% 6.81/2.24 % (28746)------------------------------
% 6.81/2.24 % (28746)------------------------------
% 6.81/2.25 % (28743)Instruction limit reached!
% 6.81/2.25 % (28743)------------------------------
% 6.81/2.25 % (28743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (28743)Termination reason: Unknown
% 6.81/2.25 % (28743)Termination phase: Property scanning
% 6.81/2.25
% 6.81/2.25 % (28743)Memory used [KB]: 2430
% 6.81/2.25 % (28743)Time elapsed: 0.028 s
% 6.81/2.25 % (28743)Instructions burned: 92 (million)
% 6.81/2.25 % (28743)------------------------------
% 6.81/2.25 % (28743)------------------------------
% 6.81/2.25 % (28748)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/987Mi)
% 6.81/2.25 % (28742)Instruction limit reached!
% 6.81/2.25 % (28742)------------------------------
% 6.81/2.25 % (28742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (28742)Termination reason: Unknown
% 6.81/2.25 % (28742)Termination phase: Saturation
% 6.81/2.25
% 6.81/2.25 % (28742)Memory used [KB]: 7675
% 6.81/2.25 % (28742)Time elapsed: 0.077 s
% 6.81/2.25 % (28742)Instructions burned: 259 (million)
% 6.81/2.25 % (28742)------------------------------
% 6.81/2.25 % (28742)------------------------------
% 6.81/2.26 % (28749)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/182Mi)
% 6.81/2.26 % (28750)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_28340 for (2993ds/182Mi)
% 6.81/2.27 % (28735)Instruction limit reached!
% 6.81/2.27 % (28735)------------------------------
% 6.81/2.27 % (28735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (28735)Termination reason: Unknown
% 6.81/2.27 % (28735)Termination phase: Saturation
% 6.81/2.27
% 6.81/2.27 % (28735)Memory used [KB]: 8827
% 6.81/2.27 % (28735)Time elapsed: 0.188 s
% 6.81/2.27 % (28735)Instructions burned: 616 (million)
% 6.81/2.27 % (28735)------------------------------
% 6.81/2.27 % (28735)------------------------------
% 6.81/2.28 % (28751)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/154Mi)
% 6.81/2.29 % (28744)Instruction limit reached!
% 6.81/2.29 % (28744)------------------------------
% 6.81/2.29 % (28744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.29 % (28744)Termination reason: Unknown
% 6.81/2.29 % (28744)Termination phase: Saturation
% 6.81/2.29
% 6.81/2.29 % (28744)Memory used [KB]: 7291
% 6.81/2.29 % (28744)Time elapsed: 0.068 s
% 6.81/2.29 % (28744)Instructions burned: 234 (million)
% 6.81/2.29 % (28744)------------------------------
% 6.81/2.29 % (28744)------------------------------
% 7.63/2.30 % (28752)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/79Mi)
% 7.63/2.31 % (28749)Instruction limit reached!
% 7.63/2.31 % (28749)------------------------------
% 7.63/2.31 % (28749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.31 % (28749)Termination reason: Unknown
% 7.63/2.31 % (28749)Termination phase: Saturation
% 7.63/2.31
% 7.63/2.31 % (28749)Memory used [KB]: 7291
% 7.63/2.31 % (28749)Time elapsed: 0.054 s
% 7.63/2.31 % (28749)Instructions burned: 183 (million)
% 7.63/2.31 % (28749)------------------------------
% 7.63/2.31 % (28749)------------------------------
% 7.63/2.32 % (28753)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/216Mi)
% 7.63/2.32 % (28750)Instruction limit reached!
% 7.63/2.32 % (28750)------------------------------
% 7.63/2.32 % (28750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (28750)Termination reason: Unknown
% 7.63/2.32 % (28750)Termination phase: Saturation
% 7.63/2.32
% 7.63/2.32 % (28750)Memory used [KB]: 7419
% 7.63/2.32 % (28750)Time elapsed: 0.057 s
% 7.63/2.32 % (28750)Instructions burned: 183 (million)
% 7.63/2.32 % (28750)------------------------------
% 7.63/2.32 % (28750)------------------------------
% 7.63/2.32 % (28751)Instruction limit reached!
% 7.63/2.32 % (28751)------------------------------
% 7.63/2.32 % (28751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (28751)Termination reason: Unknown
% 7.63/2.32 % (28751)Termination phase: Saturation
% 7.63/2.32
% 7.63/2.32 % (28751)Memory used [KB]: 2942
% 7.63/2.32 % (28751)Time elapsed: 0.044 s
% 7.63/2.32 % (28751)Instructions burned: 154 (million)
% 7.63/2.32 % (28751)------------------------------
% 7.63/2.32 % (28751)------------------------------
% 7.63/2.32 % (28747)Instruction limit reached!
% 7.63/2.32 % (28747)------------------------------
% 7.63/2.32 % (28747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (28747)Termination reason: Unknown
% 7.63/2.32 % (28747)Termination phase: Saturation
% 7.63/2.32
% 7.63/2.32 % (28747)Memory used [KB]: 7803
% 7.63/2.32 % (28747)Time elapsed: 0.090 s
% 7.63/2.32 % (28747)Instructions burned: 299 (million)
% 7.63/2.32 % (28747)------------------------------
% 7.63/2.32 % (28747)------------------------------
% 7.63/2.32 % (28752)Instruction limit reached!
% 7.63/2.32 % (28752)------------------------------
% 7.63/2.32 % (28752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.32 % (28752)Termination reason: Unknown
% 7.63/2.32 % (28752)Termination phase: Function definition elimination
% 7.63/2.32
% 7.63/2.32 % (28752)Memory used [KB]: 2430
% 7.63/2.32 % (28752)Time elapsed: 0.027 s
% 7.63/2.32 % (28752)Instructions burned: 79 (million)
% 7.63/2.32 % (28752)------------------------------
% 7.63/2.32 % (28752)------------------------------
% 7.63/2.33 % (28754)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/114Mi)
% 7.63/2.33 % (28755)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/922Mi)
% 7.63/2.33 % (28756)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/182Mi)
% 7.63/2.33 % (28757)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/164Mi)
% 7.63/2.36 % (28754)Instruction limit reached!
% 7.63/2.36 % (28754)------------------------------
% 7.63/2.36 % (28754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.36 % (28754)Termination reason: Unknown
% 7.63/2.36 % (28754)Termination phase: Saturation
% 7.63/2.36
% 7.63/2.36 % (28754)Memory used [KB]: 7036
% 7.63/2.36 % (28754)Time elapsed: 0.034 s
% 7.63/2.36 % (28754)Instructions burned: 115 (million)
% 7.63/2.36 % (28754)------------------------------
% 7.63/2.36 % (28754)------------------------------
% 7.63/2.37 % (28745)Instruction limit reached!
% 7.63/2.37 % (28745)------------------------------
% 7.63/2.37 % (28745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.37 % (28745)Termination reason: Unknown
% 7.63/2.37 % (28745)Termination phase: Saturation
% 7.63/2.37
% 7.63/2.37 % (28745)Memory used [KB]: 7931
% 7.63/2.37 % (28745)Time elapsed: 0.142 s
% 7.63/2.37 % (28745)Instructions burned: 459 (million)
% 7.63/2.37 % (28745)------------------------------
% 7.63/2.37 % (28745)------------------------------
% 7.63/2.37 % (28758)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/50Mi)
% 7.63/2.38 % (28759)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_28340 for (2992ds/368Mi)
% 7.63/2.38 % (28753)Instruction limit reached!
% 7.63/2.38 % (28753)------------------------------
% 7.63/2.38 % (28753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.38 % (28753)Termination reason: Unknown
% 7.63/2.38 % (28753)Termination phase: Saturation
% 7.63/2.38
% 7.63/2.38 % (28753)Memory used [KB]: 7547
% 7.63/2.38 % (28753)Time elapsed: 0.064 s
% 7.63/2.38 % (28753)Instructions burned: 219 (million)
% 7.63/2.38 % (28753)------------------------------
% 7.63/2.38 % (28753)------------------------------
% 7.63/2.38 % (28756)Instruction limit reached!
% 7.63/2.38 % (28756)------------------------------
% 7.63/2.38 % (28756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.38 % (28756)Termination reason: Unknown
% 7.63/2.38 % (28756)Termination phase: Saturation
% 7.63/2.38
% 7.63/2.38 % (28756)Memory used [KB]: 7291
% 7.63/2.38 % (28756)Time elapsed: 0.051 s
% 7.63/2.38 % (28756)Instructions burned: 182 (million)
% 7.63/2.38 % (28756)------------------------------
% 7.63/2.38 % (28756)------------------------------
% 7.63/2.38 % (28757)Instruction limit reached!
% 7.63/2.38 % (28757)------------------------------
% 7.63/2.38 % (28757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.38 % (28757)Termination reason: Unknown
% 7.63/2.38 % (28757)Termination phase: Saturation
% 7.63/2.38
% 7.63/2.38 % (28757)Memory used [KB]: 2814
% 7.63/2.38 % (28757)Time elapsed: 0.052 s
% 7.63/2.38 % (28757)Instructions burned: 164 (million)
% 7.63/2.38 % (28757)------------------------------
% 7.63/2.38 % (28757)------------------------------
% 7.63/2.39 % (28758)Instruction limit reached!
% 7.63/2.39 % (28758)------------------------------
% 7.63/2.39 % (28758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.39 % (28758)Termination reason: Unknown
% 7.63/2.39 % (28758)Termination phase: Property scanning
% 7.63/2.39
% 7.63/2.39 % (28758)Memory used [KB]: 2302
% 7.63/2.39 % (28758)Time elapsed: 0.015 s
% 7.63/2.39 % (28758)Instructions burned: 50 (million)
% 7.63/2.39 % (28758)------------------------------
% 7.63/2.39 % (28758)------------------------------
% 7.63/2.39 % (28761)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/267Mi)
% 7.63/2.39 % (28762)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/204Mi)
% 7.63/2.39 % (28763)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/26Mi)
% 8.36/2.40 % (28760)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/1021Mi)
% 8.36/2.40 % (28763)Instruction limit reached!
% 8.36/2.40 % (28763)------------------------------
% 8.36/2.40 % (28763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.40 % (28763)Termination reason: Unknown
% 8.36/2.40 % (28763)Termination phase: shuffling
% 8.36/2.40
% 8.36/2.40 % (28763)Memory used [KB]: 2046
% 8.36/2.40 % (28763)Time elapsed: 0.009 s
% 8.36/2.40 % (28763)Instructions burned: 29 (million)
% 8.36/2.40 % (28763)------------------------------
% 8.36/2.40 % (28763)------------------------------
% 8.36/2.41 % (28764)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/53Mi)
% 8.36/2.43 % (28764)Instruction limit reached!
% 8.36/2.43 % (28764)------------------------------
% 8.36/2.43 % (28764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.43 % (28764)Termination reason: Unknown
% 8.36/2.43 % (28764)Termination phase: Property scanning
% 8.36/2.43
% 8.36/2.43 % (28764)Memory used [KB]: 2302
% 8.36/2.43 % (28764)Time elapsed: 0.017 s
% 8.36/2.43 % (28764)Instructions burned: 55 (million)
% 8.36/2.43 % (28764)------------------------------
% 8.36/2.43 % (28764)------------------------------
% 8.36/2.44 % (28765)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_28340 for (2991ds/4436Mi)
% 8.36/2.46 % (28762)Instruction limit reached!
% 8.36/2.46 % (28762)------------------------------
% 8.36/2.46 % (28762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.46 % (28762)Termination reason: Unknown
% 8.36/2.46 % (28762)Termination phase: Saturation
% 8.36/2.46
% 8.36/2.46 % (28762)Memory used [KB]: 7419
% 8.36/2.46 % (28762)Time elapsed: 0.065 s
% 8.36/2.46 % (28762)Instructions burned: 207 (million)
% 8.36/2.46 % (28762)------------------------------
% 8.36/2.46 % (28762)------------------------------
% 8.36/2.46 % (28755)First to succeed.
% 8.36/2.47 % (28755)Refutation found. Thanks to Tanya!
% 8.36/2.47 % SZS status Theorem for DTF2THF_28340
% 8.36/2.47 % SZS output start Proof for DTF2THF_28340
% 8.36/2.47 thf(type_def_5, type, itself: ($tType) > $tType).
% 8.36/2.47 thf(type_def_7, type, nat: $tType).
% 8.36/2.47 thf(type_def_8, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 8.36/2.47 thf(type_def_9, type, rBT_Im1923302023_color: $tType).
% 8.36/2.47 thf(type_def_10, type, set: ($tType) > $tType).
% 8.36/2.47 thf(type_def_11, type, a: $tType).
% 8.36/2.47 thf(type_def_12, type, b: $tType).
% 8.36/2.47 thf(func_def_0, type, rBT_Im1923302023_color: $tType).
% 8.36/2.47 thf(func_def_1, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 8.36/2.47 thf(func_def_2, type, set: ($tType) > $tType).
% 8.36/2.47 thf(func_def_3, type, nat: $tType).
% 8.36/2.47 thf(func_def_4, type, itself: ($tType) > $tType).
% 8.36/2.47 thf(func_def_5, type, b: $tType).
% 8.36/2.47 thf(func_def_6, type, a: $tType).
% 8.36/2.47 thf(func_def_7, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_8, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_9, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_10, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_11, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_12, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_13, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_14, type, zero_neq_one: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_15, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_16, type, zero_less_one: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_17, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_18, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_19, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_20, type, dense_linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_21, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_23, type, linord219039673up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_24, type, ordere216010020id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_25, type, ordere142940540dd_abs: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_26, type, linord1659791738miring: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_27, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_28, type, strict797366125id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_29, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_30, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_31, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_32, type, ordere516151231imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_33, type, condit1656338222tinuum: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_34, type, condit1037483654norder: !>[X0: $tType]:(itself @ X0 > $o)).
% 8.36/2.47 thf(func_def_35, type, bNF_eq_onp: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 8.36/2.47 thf(func_def_36, type, abs_abs: !>[X0: $tType]:(X0 > X0)).
% 8.36/2.47 thf(func_def_37, type, one_one: !>[X0: $tType]:(X0)).
% 8.36/2.47 thf(func_def_38, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 8.36/2.47 thf(func_def_39, type, sgn_sgn: !>[X0: $tType]:(X0 > X0)).
% 8.36/2.47 thf(func_def_40, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 8.36/2.47 thf(func_def_41, type, zero_zero: !>[X0: $tType]:(X0)).
% 8.36/2.47 thf(func_def_42, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 8.36/2.47 thf(func_def_43, type, suc: nat > nat).
% 8.36/2.47 thf(func_def_44, type, semiring_1_of_nat: !>[X0: $tType]:(nat > X0)).
% 8.36/2.47 thf(func_def_45, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 8.36/2.47 thf(func_def_46, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 8.36/2.47 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 8.36/2.47 thf(func_def_48, type, order_strict_mono: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 8.36/2.47 thf(func_def_49, type, power_power: !>[X0: $tType]:(X0 > nat > X0)).
% 8.36/2.47 thf(func_def_50, type, type2: !>[X0: $tType]:(itself @ X0)).
% 8.36/2.47 thf(func_def_51, type, rBT_Im315265182height: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > nat)).
% 8.36/2.47 thf(func_def_52, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 8.36/2.47 thf(func_def_53, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 8.36/2.47 thf(func_def_54, type, rBT_Im1975547051_color: !>[X0: $tType]:(X0 > X0 > rBT_Im1923302023_color > X0)).
% 8.36/2.47 thf(func_def_55, type, rBT_Im1059957627_color: !>[X0: $tType]:(X0 > X0 > rBT_Im1923302023_color > X0)).
% 8.36/2.47 thf(func_def_56, type, rBT_Im800559290_color: rBT_Im1923302023_color > nat).
% 8.36/2.47 thf(func_def_57, type, rBT_Im1805589839lor_of: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im1923302023_color)).
% 8.36/2.47 thf(func_def_58, type, rBT_Im1040612427e_inv1: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_59, type, rBT_Im1071879905_inv1l: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_60, type, rBT_Im1259024060reater: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_61, type, rBT_Im2075124343t_less: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_62, type, rBT_Im759614907sorted: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_63, type, rBT_Im1332541288reater: !>[X0: $tType, X1: $tType]:(X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_64, type, rBT_Im903026891t_less: !>[X0: $tType, X1: $tType]:(X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_65, type, rBT_Im1183586831sorted: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_66, 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)).
% 8.36/2.47 thf(func_def_67, type, rBT_Im418718756_Empty: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1)).
% 8.36/2.47 thf(func_def_68, 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)).
% 8.36/2.47 thf(func_def_69, type, rBT_Im1931894874ed_rbt: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 8.36/2.47 thf(func_def_70, 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)).
% 8.36/2.47 thf(func_def_71, 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)).
% 8.36/2.47 thf(func_def_72, type, rBT_Im1178217900t1_rbt: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > set @ X0)).
% 8.36/2.47 thf(func_def_73, type, rBT_Im1550225131t2_rbt: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > set @ X1)).
% 8.36/2.47 thf(func_def_74, type, rBT_Im1485196410ze_rbt: !>[X0: $tType, X1: $tType]:((X0 > nat) > (X1 > nat) > rBT_Im246033960le_rbt @ X0 @ X1 > nat)).
% 8.36/2.47 thf(func_def_75, type, zero_neq_one_of_bool: !>[X0: $tType]:($o > X0)).
% 8.36/2.47 thf(func_def_76, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 8.36/2.47 thf(func_def_77, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 8.36/2.47 thf(func_def_78, type, t: rBT_Im246033960le_rbt @ a @ b).
% 8.36/2.47 thf(func_def_93, type, sK0: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im1923302023_color)).
% 8.36/2.47 thf(func_def_94, type, sK1: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 8.36/2.47 thf(func_def_95, type, sK2: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X1)).
% 8.36/2.47 thf(func_def_96, type, sK3: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X0)).
% 8.36/2.47 thf(func_def_97, type, sK4: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 8.36/2.47 thf(func_def_98, type, sK5: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im1923302023_color)).
% 8.36/2.47 thf(func_def_99, type, sK6: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 8.36/2.47 thf(func_def_100, type, sK7: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 8.36/2.47 thf(func_def_101, type, sK8: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 8.36/2.47 thf(func_def_102, type, sK9: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 8.36/2.47 thf(func_def_103, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 8.36/2.47 thf(func_def_105, type, ph12: !>[X0: $tType]:(X0)).
% 8.36/2.47 thf(f1553,plain,(
% 8.36/2.47 $false),
% 8.36/2.47 inference(avatar_sat_refutation,[status(thm)],[f874,f879,f1520,f1552])).
% 8.36/2.47 thf(f1552,plain,(
% 8.36/2.47 spl11_2 | ~spl11_3),
% 8.36/2.47 inference(avatar_contradiction_clause,[status(thm)],[f1551])).
% 8.36/2.47 thf(f1551,plain,(
% 8.36/2.47 $false | (spl11_2 | ~spl11_3)),
% 8.36/2.47 inference(subsumption_resolution,[status(thm)],[f1534,f878])).
% 8.36/2.47 thf(f878,plain,(
% 8.36/2.47 ((rBT_Im1071879905_inv1l @ a @ b @ t) != $true) | spl11_2),
% 8.36/2.47 inference(avatar_component_clause,[status(thm)],[f876])).
% 8.36/2.47 thf(f876,definition,(
% 8.36/2.47 spl11_2 <=> ((rBT_Im1071879905_inv1l @ a @ b @ t) = $true)),
% 8.36/2.47 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 8.36/2.47 thf(f1534,plain,(
% 8.36/2.47 ((rBT_Im1071879905_inv1l @ a @ b @ t) = $true) | ~spl11_3),
% 8.36/2.47 inference(superposition,[status(thm)],[f856,f1519])).
% 8.36/2.47 thf(f1519,plain,(
% 8.36/2.47 (t = rBT_Im418718756_Empty @ a @ b) | ~spl11_3),
% 8.36/2.47 inference(avatar_component_clause,[status(thm)],[f1517])).
% 8.36/2.47 thf(f1517,definition,(
% 8.36/2.47 spl11_3 <=> (t = rBT_Im418718756_Empty @ a @ b)),
% 8.36/2.47 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 8.36/2.47 thf(f856,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType] : (($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ rBT_Im418718756_Empty @ X1 @ X0))) )),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f807])).
% 8.36/2.47 thf(f807,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType] : ($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ rBT_Im418718756_Empty @ X1 @ X0))),
% 8.36/2.47 inference(fool_elimination,[status(thm)],[f806])).
% 8.36/2.47 thf(f806,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType] : (rBT_Im1071879905_inv1l @ X1 @ X0 @ rBT_Im418718756_Empty @ X1 @ X0)),
% 8.36/2.47 inference(rectify,[status(thm)],[f2])).
% 8.36/2.47 thf(f2,axiom,(
% 8.36/2.47 ! [X1 : $tType,X0 : $tType] : (rBT_Im1071879905_inv1l @ X0 @ X1 @ rBT_Im418718756_Empty @ X0 @ X1)),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',fact_1_inv1l_Osimps_I1_J)).
% 8.36/2.47 thf(f1520,plain,(
% 8.36/2.47 spl11_3 | ~spl11_1 | spl11_2),
% 8.36/2.47 inference(avatar_split_clause,[status(thm)],[f1515,f876,f871,f1517])).
% 8.36/2.47 thf(f871,definition,(
% 8.36/2.47 spl11_1 <=> ((rBT_Im1040612427e_inv1 @ a @ b @ t) = $true)),
% 8.36/2.47 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 8.36/2.47 thf(f1515,plain,(
% 8.36/2.47 (t = rBT_Im418718756_Empty @ a @ b) | (~spl11_1 | spl11_2)),
% 8.36/2.47 inference(subsumption_resolution,[status(thm)],[f1507,f873])).
% 8.36/2.47 thf(f873,plain,(
% 8.36/2.47 ((rBT_Im1040612427e_inv1 @ a @ b @ t) = $true) | ~spl11_1),
% 8.36/2.47 inference(avatar_component_clause,[status(thm)],[f871])).
% 8.36/2.47 thf(f1507,plain,(
% 8.36/2.47 (t = rBT_Im418718756_Empty @ a @ b) | ((rBT_Im1040612427e_inv1 @ a @ b @ t) != $true) | spl11_2),
% 8.36/2.47 inference(trivial_inequality_removal,[status(thm)],[f1491])).
% 8.36/2.47 thf(f1491,plain,(
% 8.36/2.47 (t = rBT_Im418718756_Empty @ a @ b) | ((rBT_Im1040612427e_inv1 @ a @ b @ t) != $true) | ($true != $true) | spl11_2),
% 8.36/2.47 inference(superposition,[status(thm)],[f878,f1486])).
% 8.36/2.47 thf(f1486,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true = (rBT_Im1071879905_inv1l @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2))) )),
% 8.36/2.47 inference(subsumption_resolution,[status(thm)],[f1483,f1302])).
% 8.36/2.47 thf(f1302,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK6 @ X1 @ X0 @ X2))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2)) )),
% 8.36/2.47 inference(superposition,[status(thm)],[f837,f845])).
% 8.36/2.47 thf(f845,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : (((rBT_Im480247531Branch @ X1 @ X0 @ (sK5 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X1 @ X2) @ (sK7 @ X0 @ X1 @ X2) @ (sK8 @ X0 @ X1 @ X2) @ (sK9 @ X0 @ X1 @ X2)) = X2) | (rBT_Im418718756_Empty @ X1 @ X0 = X2)) )),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f828])).
% 8.36/2.47 thf(f828,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im418718756_Empty @ X1 @ X0 = X2) | ((rBT_Im480247531Branch @ X1 @ X0 @ (sK5 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X1 @ X2) @ (sK7 @ X0 @ X1 @ X2) @ (sK8 @ X0 @ X1 @ X2) @ (sK9 @ X0 @ X1 @ X2)) = X2))),
% 8.36/2.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f822,f827])).
% 8.36/2.47 thf(f827,plain,(
% 8.36/2.47 ! [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 @ (sK5 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X1 @ X2) @ (sK7 @ X0 @ X1 @ X2) @ (sK8 @ X0 @ X1 @ X2) @ (sK9 @ X0 @ X1 @ X2)) = X2))),
% 8.36/2.47 introduced(definition,[],[choice_axiom])).
% 8.36/2.47 thf(f822,plain,(
% 8.36/2.47 ! [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))),
% 8.36/2.47 inference(ennf_transformation,[status(thm)],[f817])).
% 8.36/2.47 thf(f817,plain,(
% 8.36/2.47 ! [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))),
% 8.36/2.47 inference(rectify,[status(thm)],[f12])).
% 8.36/2.47 thf(f12,axiom,(
% 8.36/2.47 ! [X1 : $tType,X0 : $tType,X37 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im418718756_Empty @ X0 @ X1 != X37) => ~! [X38 : rBT_Im1923302023_color,X39 : rBT_Im246033960le_rbt @ X0 @ X1,X40 : X0,X41 : X1,X42 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im480247531Branch @ X0 @ X1 @ X38 @ X39 @ X40 @ X41 @ X42) != X37))),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',fact_11_rbt_Oexhaust)).
% 8.36/2.47 thf(f837,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1] : (($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6))) | ($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3))) )),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f824])).
% 8.36/2.47 thf(f824,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1] : (((((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) = $true) & ((rBT_Impl_Mirabelle_B = X2) | ((rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X6)) & (rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)))) & ($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6)))) & (($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6))) | ((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) != $true) | ((rBT_Impl_Mirabelle_B != X2) & ((rBT_Impl_Mirabelle_B != (rBT_Im1805589839lor_of @ X0 @ X1 @ X6)) | (rBT_Impl_Mirabelle_B != (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3))))),
% 8.36/2.47 inference(flattening,[status(thm)],[f823])).
% 8.36/2.47 thf(f823,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1] : (((((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) = $true) & ((rBT_Impl_Mirabelle_B = X2) | ((rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X6)) & (rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)))) & ($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6)))) & (($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6))) | (((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) != $true) | ((rBT_Impl_Mirabelle_B != X2) & ((rBT_Impl_Mirabelle_B != (rBT_Im1805589839lor_of @ X0 @ X1 @ X6)) | (rBT_Impl_Mirabelle_B != (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3)))))),
% 8.36/2.47 inference(nnf_transformation,[status(thm)],[f679])).
% 8.36/2.47 thf(f679,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1] : ((((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) = $true) & ((rBT_Impl_Mirabelle_B = X2) | ((rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X6)) & (rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)))) & ($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3))) <=> ($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6))))),
% 8.36/2.47 inference(fool_elimination,[status(thm)],[f678])).
% 8.36/2.47 thf(f678,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6)) = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X3) & (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) & (((rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X3)) & (rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X6))) | (rBT_Impl_Mirabelle_B = X2)))),
% 8.36/2.47 inference(rectify,[status(thm)],[f4])).
% 8.36/2.47 thf(f4,axiom,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X5 : rBT_Im1923302023_color,X10 : rBT_Im246033960le_rbt @ X0 @ X1,X7 : X0,X8 : X1,X11 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X5 @ X10 @ X7 @ X8 @ X11)) = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X10) & (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X11) & (((rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X10)) & (rBT_Impl_Mirabelle_B = (rBT_Im1805589839lor_of @ X0 @ X1 @ X11))) | (rBT_Impl_Mirabelle_B = X5)))),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',fact_3_inv1_Osimps_I2_J)).
% 8.36/2.47 thf(f1483,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im418718756_Empty @ X0 @ X1 = X2) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK6 @ X1 @ X0 @ X2))) | ($true = (rBT_Im1071879905_inv1l @ X0 @ X1 @ X2)) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2))) )),
% 8.36/2.47 inference(trivial_inequality_removal,[status(thm)],[f1482])).
% 8.36/2.47 thf(f1482,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK6 @ X1 @ X0 @ X2))) | ($true != $true) | (rBT_Im418718756_Empty @ X0 @ X1 = X2) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2)) | ($true = (rBT_Im1071879905_inv1l @ X0 @ X1 @ X2))) )),
% 8.36/2.47 inference(duplicate_literal_removal,[status(thm)],[f1476])).
% 8.36/2.47 thf(f1476,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK6 @ X1 @ X0 @ X2))) | ($true = (rBT_Im1071879905_inv1l @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2) | ($true != $true) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2)) )),
% 8.36/2.47 inference(superposition,[status(thm)],[f1308,f1305])).
% 8.36/2.47 thf(f1305,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK9 @ X1 @ X0 @ X2))) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2)) )),
% 8.36/2.47 inference(superposition,[status(thm)],[f840,f845])).
% 8.36/2.47 thf(f840,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X0 @ X1,X6 : rBT_Im246033960le_rbt @ X0 @ X1,X4 : X0,X5 : X1] : (($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6))) | ((rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) = $true)) )),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f824])).
% 8.36/2.47 thf(f1308,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im246033960le_rbt @ X0 @ X1] : (($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK9 @ X1 @ X0 @ X2))) | ($true = (rBT_Im1071879905_inv1l @ X0 @ X1 @ X2)) | (rBT_Im418718756_Empty @ X0 @ X1 = X2) | ($true != (rBT_Im1040612427e_inv1 @ X0 @ X1 @ (sK6 @ X1 @ X0 @ X2)))) )),
% 8.36/2.47 inference(superposition,[status(thm)],[f860,f845])).
% 8.36/2.47 thf(f860,plain,(
% 8.36/2.47 ( ! [X1 : $tType,X0 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X1 @ X0,X6 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : X1,X5 : X0] : (($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | ($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) | ($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))) )),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f834])).
% 8.36/2.47 thf(f834,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : X1,X5 : X0,X6 : rBT_Im246033960le_rbt @ X1 @ X0] : (((($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) & ($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))) | ($true != (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)))) & (($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | ($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) | ($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))))),
% 8.36/2.47 inference(flattening,[status(thm)],[f833])).
% 8.36/2.47 thf(f833,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : X1,X5 : X0,X6 : rBT_Im246033960le_rbt @ X1 @ X0] : (((($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) & ($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))) | ($true != (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)))) & (($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))) | (($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) | ($true != (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6)))))),
% 8.36/2.47 inference(nnf_transformation,[status(thm)],[f295])).
% 8.36/2.47 thf(f295,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : X1,X5 : X0,X6 : rBT_Im246033960le_rbt @ X1 @ X0] : ((($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3)) & ($true = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))) <=> ($true = (rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6))))),
% 8.36/2.47 inference(fool_elimination,[status(thm)],[f294])).
% 8.36/2.47 thf(f294,plain,(
% 8.36/2.47 ! [X0 : $tType,X1 : $tType,X2 : rBT_Im1923302023_color,X3 : rBT_Im246033960le_rbt @ X1 @ X0,X4 : X1,X5 : X0,X6 : rBT_Im246033960le_rbt @ X1 @ X0] : ((rBT_Im1071879905_inv1l @ X1 @ X0 @ (rBT_Im480247531Branch @ X1 @ X0 @ X2 @ X3 @ X4 @ X5 @ X6)) = (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X3) & (rBT_Im1040612427e_inv1 @ X1 @ X0 @ X6))),
% 8.36/2.47 inference(rectify,[status(thm)],[f1])).
% 8.36/2.47 thf(f1,axiom,(
% 8.36/2.47 ! [X1 : $tType,X0 : $tType,X5 : rBT_Im1923302023_color,X6 : rBT_Im246033960le_rbt @ X0 @ X1,X7 : X0,X8 : X1,X9 : rBT_Im246033960le_rbt @ X0 @ X1] : ((rBT_Im1071879905_inv1l @ X0 @ X1 @ (rBT_Im480247531Branch @ X0 @ X1 @ X5 @ X6 @ X7 @ X8 @ X9)) = (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X6) & (rBT_Im1040612427e_inv1 @ X0 @ X1 @ X9))),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',fact_0_inv1l_Osimps_I2_J)).
% 8.36/2.47 thf(f879,plain,(
% 8.36/2.47 ~spl11_2),
% 8.36/2.47 inference(avatar_split_clause,[status(thm)],[f846,f876])).
% 8.36/2.47 thf(f846,plain,(
% 8.36/2.47 ((rBT_Im1071879905_inv1l @ a @ b @ t) != $true)),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f812])).
% 8.36/2.47 thf(f812,plain,(
% 8.36/2.47 ((rBT_Im1071879905_inv1l @ a @ b @ t) != $true)),
% 8.36/2.47 inference(flattening,[status(thm)],[f683])).
% 8.36/2.47 thf(f683,plain,(
% 8.36/2.47 ~((rBT_Im1071879905_inv1l @ a @ b @ t) = $true)),
% 8.36/2.47 inference(fool_elimination,[status(thm)],[f682])).
% 8.36/2.47 thf(f682,plain,(
% 8.36/2.47 ~(rBT_Im1071879905_inv1l @ a @ b @ t)),
% 8.36/2.47 inference(rectify,[status(thm)],[f290])).
% 8.36/2.47 thf(f290,negated_conjecture,(
% 8.36/2.47 ~(rBT_Im1071879905_inv1l @ a @ b @ t)),
% 8.36/2.47 inference(negated_conjecture,[status(cth)],[f289])).
% 8.36/2.47 thf(f289,conjecture,(
% 8.36/2.47 (rBT_Im1071879905_inv1l @ a @ b @ t)),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',conj_1)).
% 8.36/2.47 thf(f874,plain,(
% 8.36/2.47 spl11_1),
% 8.36/2.47 inference(avatar_split_clause,[status(thm)],[f844,f871])).
% 8.36/2.47 thf(f844,plain,(
% 8.36/2.47 ((rBT_Im1040612427e_inv1 @ a @ b @ t) = $true)),
% 8.36/2.47 inference(cnf_transformation,[status(thm)],[f471])).
% 8.36/2.47 thf(f471,plain,(
% 8.36/2.47 ((rBT_Im1040612427e_inv1 @ a @ b @ t) = $true)),
% 8.36/2.47 inference(fool_elimination,[status(thm)],[f470])).
% 8.36/2.47 thf(f470,plain,(
% 8.36/2.47 (rBT_Im1040612427e_inv1 @ a @ b @ t)),
% 8.36/2.47 inference(rectify,[status(thm)],[f288])).
% 8.36/2.47 thf(f288,axiom,(
% 8.36/2.47 (rBT_Im1040612427e_inv1 @ a @ b @ t)),
% 8.36/2.47 file('/export/starexec/sandbox/tmp/tmp.VuMszqUTZw/DTF2THF_28340.p',conj_0)).
% 8.36/2.47 % SZS output end Proof for DTF2THF_28340
% 8.36/2.47 % (28755)------------------------------
% 8.36/2.47 % (28755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.47 % (28755)Termination reason: Refutation
% 8.36/2.47
% 8.36/2.47 % (28755)Memory used [KB]: 7164
% 8.36/2.47 % (28755)Time elapsed: 0.137 s
% 8.36/2.47 % (28755)Instructions burned: 453 (million)
% 8.36/2.47 % (28755)------------------------------
% 8.36/2.47 % (28755)------------------------------
% 8.36/2.47 % (28669)Success in time 0.897 s
%------------------------------------------------------------------------------