%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP033^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:00 AM UTC 2026
% Result : Theorem 2.65s 1.68s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 85 ( 8 ~; 3 |; 0 &; 71 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 7 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
binary1439146945Tree_a: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_8,type,
int: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
produc376588196ee_a_a: $tType ).
thf(func_def_0,type,
produc376588196ee_a_a: $tType ).
thf(func_def_1,type,
binary1439146945Tree_a: $tType ).
thf(func_def_2,type,
set_a: $tType ).
thf(func_def_3,type,
int: $tType ).
thf(func_def_4,type,
a: $tType ).
thf(func_def_5,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_6,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(func_def_7,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_8,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(func_def_9,type,
binary1804682569move_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_10,type,
binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).
thf(func_def_11,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(func_def_12,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(func_def_13,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(func_def_14,type,
binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_15,type,
binary1774981152rmrm_a: ( a > int ) > binary1439146945Tree_a > produc376588196ee_a_a ).
thf(func_def_16,type,
bot_bot_a_o: a > $o ).
thf(func_def_18,type,
bot_bot_set_a: set_a ).
thf(func_def_19,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_20,type,
ord_less_int: int > int > $o ).
thf(func_def_21,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_22,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_23,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_24,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_25,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_26,type,
ordering_top_a_o: ( ( a > $o ) > ( a > $o ) > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > $o ) > $o ).
thf(func_def_27,type,
ordering_top_set_a: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > $o ).
thf(func_def_28,type,
produc374321428ee_a_a: binary1439146945Tree_a > a > produc376588196ee_a_a ).
thf(func_def_29,type,
produc1275654896Tree_a: ( binary1439146945Tree_a > a > binary1439146945Tree_a ) > produc376588196ee_a_a > binary1439146945Tree_a ).
thf(func_def_30,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_31,type,
member_a: a > set_a > $o ).
thf(func_def_32,type,
h: a > int ).
thf(func_def_33,type,
t1: binary1439146945Tree_a ).
thf(func_def_34,type,
t2: binary1439146945Tree_a ).
thf(func_def_35,type,
x: a ).
thf(func_def_51,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f1077,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1076,f1050]) ).
thf(f1050,plain,
( ( binary1721989714Tree_a @ h @ t1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1039]) ).
thf(f1039,plain,
( ( binary1721989714Tree_a @ h @ t1 )
!= $true ),
inference(flattening,[status(thm)],[f908]) ).
thf(f908,plain,
( ( binary1721989714Tree_a @ h @ t1 )
!= $true ),
inference(fool_elimination,[status(thm)],[f907]) ).
thf(f907,plain,
~ ( binary1721989714Tree_a @ h @ t1 ),
inference(rectify,[status(thm)],[f355]) ).
thf(f355,negated_conjecture,
~ ( binary1721989714Tree_a @ h @ t1 ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f354,conjecture,
binary1721989714Tree_a @ h @ t1,
file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',conj_0) ).
thf(f1076,plain,
( ( binary1721989714Tree_a @ h @ t1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1075]) ).
thf(f1075,plain,
( ( $true != $true )
| ( ( binary1721989714Tree_a @ h @ t1 )
= $true ) ),
inference(superposition,[status(thm)],[f1056,f1052]) ).
thf(f1052,plain,
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f788]) ).
thf(f788,plain,
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f787]) ).
thf(f787,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',fact_1_s) ).
thf(f1056,plain,
! [X2: a,X3: a > int,X0: binary1439146945Tree_a,X1: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a @ X3 @ ( binary717961607le_T_a @ X1 @ X2 @ X0 ) )
!= $true )
| ( ( binary1721989714Tree_a @ X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1042]) ).
thf(f1042,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a,X3: a > int] :
( ( ( binary1721989714Tree_a @ X3 @ X1 )
= $true )
| ( ( binary1721989714Tree_a @ X3 @ ( binary717961607le_T_a @ X1 @ X2 @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f416]) ).
thf(f416,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a,X3: a > int] :
( ( ( binary1721989714Tree_a @ X3 @ ( binary717961607le_T_a @ X1 @ X2 @ X0 ) )
= $true )
=> ( ( binary1721989714Tree_a @ X3 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f415]) ).
thf(f415,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a,X3: a > int] :
( ( binary1721989714Tree_a @ X3 @ ( binary717961607le_T_a @ X1 @ X2 @ X0 ) )
=> ( binary1721989714Tree_a @ X3 @ X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a,X0: a > int] :
( ( binary1721989714Tree_a @ X0 @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) )
=> ( binary1721989714Tree_a @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',fact_3_sortLemmaL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP033^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:09 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ITP033^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.47 % Domain : Interactive Theorem Proving
% 0.27/0.47 % Problem : Sledgehammer BinaryTree problem prob_508__3255320_1
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Des21]
% 0.27/0.47 % Names : BinaryTree/prob_508__3255320_1 [Des21]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.27/0.47 % Syntax : Number of formulae : 390 ( 96 unt; 36 typ; 0 def)
% 0.27/0.47 % Number of atoms : 1164 ( 241 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 10 ( 3 avg)
% 0.27/0.47 % Number of connectives : 3147 ( 123 ~; 18 |; 53 &;2350 @)
% 0.27/0.47 % ( 0 <=>; 603 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 18 ( 8 avg)
% 0.27/0.47 % Number of types : 6 ( 5 usr)
% 0.27/0.47 % Number of type conns : 570 ( 570 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 33 ( 31 usr; 7 con; 0-4 aty)
% 0.27/0.47 % Number of variables : 1135 ( 119 ^;1008 !; 8 ?;1135 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:27.980
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % Could-be-implicit typings (5)
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_Mtf__a_J,type,
% 0.27/0.47 produc376588196ee_a_a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 0.27/0.47 binary1439146945Tree_a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.27/0.47 set_a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Int__Oint,type,
% 0.27/0.47 int: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_tf__a,type,
% 0.27/0.47 a: $tType ).
% 0.27/0.47
% 0.27/0.47 % Explicit typings (31)
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 0.27/0.47 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 0.27/0.47 binary476621312_Tip_a: binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Obinsert_001tf__a,type,
% 0.27/0.47 binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Omemb_001tf__a,type,
% 0.27/0.47 binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oremove_001tf__a,type,
% 0.27/0.47 binary1804682569move_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Orm_001tf__a,type,
% 0.27/0.47 binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 0.27/0.47 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 0.27/0.47 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 0.27/0.47 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Owrm_001tf__a,type,
% 0.27/0.47 binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Owrmrm_001tf__a,type,
% 0.27/0.47 binary1774981152rmrm_a: ( a > int ) > binary1439146945Tree_a > produc376588196ee_a_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 0.27/0.47 bot_bot_a_o: a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.27/0.47 bot_bot_o: $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.47 bot_bot_set_a: set_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 0.27/0.47 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.27/0.47 ord_less_int: int > int > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.47 ord_less_set_a: set_a > set_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 0.27/0.47 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 0.27/0.47 ord_less_eq_o: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.27/0.47 ord_less_eq_int: int > int > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.47 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oordering__top_001_062_Itf__a_M_Eo_J,type,
% 0.27/0.47 ordering_top_a_o: ( ( a > $o ) > ( a > $o ) > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Orderings_Oordering__top_001t__Set__Oset_Itf__a_J,type,
% 0.27/0.47 ordering_top_set_a: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_001tf__a,type,
% 0.27/0.47 produc374321428ee_a_a: binary1439146945Tree_a > a > produc376588196ee_a_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_001tf__a_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 0.27/0.47 produc1275654896Tree_a: ( binary1439146945Tree_a > a > binary1439146945Tree_a ) > produc376588196ee_a_a > binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.27/0.47 collect_a: ( a > $o ) > set_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001tf__a,type,
% 0.27/0.47 member_a: a > set_a > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_h,type,
% 0.27/0.47 h: a > int ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_t1____,type,
% 0.27/0.47 t1: binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_t2____,type,
% 0.27/0.47 t2: binary1439146945Tree_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_x____,type,
% 0.27/0.47 x: a ).
% 0.27/0.47
% 0.27/0.47 % Relevant facts (353)
% 0.27/0.47 thf(fact_0_t2nTip,axiom,
% 0.27/0.47 t2 != binary476621312_Tip_a ).
% 0.27/0.47
% 0.27/0.47 % t2nTip
% 0.27/0.47 thf(fact_1_s,axiom,
% 0.27/0.47 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 0.27/0.47
% 0.27/0.47 % s
% 0.27/0.47 thf(fact_2_res,axiom,
% 0.27/0.47 ( ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
% 0.27/0.47 = ( binary717961607le_T_a @ t1 @ x @ ( binary1217730267_wrm_a @ h @ t2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % res
% 0.27/0.47 thf(fact_3_sortLemmaL,axiom,
% 0.27/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.27/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % sortLemmaL
% 0.27/0.47 thf(fact_4_sortLemmaR,axiom,
% 0.27/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.27/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % sortLemmaR
% 0.27/0.47 thf(fact_5_Tree_Oinject,axiom,
% 0.27/0.47 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 0.27/0.47 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 0.27/0.47 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X22 = Y22 )
% 0.27/0.47 & ( X23 = Y23 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Tree.inject
% 0.27/0.47 thf(fact_6_binsert__sorted,axiom,
% 0.27/0.47 ! [H: a > int,T: binary1439146945Tree_a,X: a] :
% 0.27/0.47 ( ( binary1721989714Tree_a @ H @ T )
% 0.27/0.47 => ( binary1721989714Tree_a @ H @ ( binary1226383794sert_a @ H @ X @ T ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % binsert_sorted
% 0.27/0.47 thf(fact_7_h1,axiom,
% 0.27/0.47 ( ( ( t1 != binary476621312_Tip_a )
% 0.27/0.47 & ( binary1721989714Tree_a @ h @ t1 ) )
% 0.27/0.47 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % h1
% 0.27/0.47 thf(fact_8_sortedTree_Osimps_I1_J,axiom,
% 0.27/0.47 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 0.27/0.47
% 0.27/0.47 % sortedTree.simps(1)
% 0.27/0.47 thf(fact_9_memb__spec,axiom,
% 0.27/0.47 ! [H: a > int,T: binary1439146945Tree_a,X: a] :
% 0.27/0.47 ( ( binary1721989714Tree_a @ H @ T )
% 0.27/0.47 => ( ( binary2053421120memb_a @ H @ X @ T )
% 0.27/0.47 = ( member_a @ X @ ( binary945792244etOf_a @ T ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % memb_spec
% 0.27/0.47 thf(fact_10_sorted__distinct__pred__def,axiom,
% 0.27/0.47 ( binary670562003pred_a
% 0.27/0.47 = ( ^ [H2: a > int,A: a,B: a,T3: binary1439146945Tree_a] :
% 0.27/0.47 ( ( ( binary1721989714Tree_a @ H2 @ T3 )
% 0.27/0.47 & ( member_a @ A @ ( binary945792244etOf_a @ T3 ) )
% 0.27/0.47 & ( member_a @ B @ ( binary945792244etOf_a @ T3 ) )
% 0.27/0.47 & ( ( H2 @ A )
% 0.27/0.47 = ( H2 @ B ) ) )
% 0.27/0.47 => ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_distinct_pred_def
% 0.27/0.47 thf(fact_11_h2,axiom,
% 0.27/0.47 ( ( ( t2 != binary476621312_Tip_a )
% 0.27/0.47 & ( binary1721989714Tree_a @ h @ t2 ) )
% 0.27/0.47 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % h2
% 0.27/0.47 thf(fact_12_sorted__distinct,axiom,
% 0.27/0.47 ! [H: a > int,A2: a,B2: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A2 @ B2 @ T ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_distinct
% 0.27/0.47 thf(fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062,axiom,
% 0.27/0.47 ( ( ( binary476621312_Tip_a != binary476621312_Tip_a )
% 0.27/0.47 & ( binary1721989714Tree_a @ h @ binary476621312_Tip_a ) )
% 0.27/0.47 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ binary476621312_Tip_a ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % \<open>Tip \<noteq> Tip \<and> sortedTree h Tip \<longrightarrow> sortedTree h (wrm h Tip)\<close>
% 0.27/0.47 thf(fact_14_Tree_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.27/0.47 ( binary476621312_Tip_a
% 0.27/0.47 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Tree.distinct(1)
% 0.27/0.47 thf(fact_15_binsert_Osimps_I1_J,axiom,
% 0.27/0.47 ! [H: a > int,E: a] :
% 0.27/0.47 ( ( binary1226383794sert_a @ H @ E @ binary476621312_Tip_a )
% 0.27/0.47 = ( binary717961607le_T_a @ binary476621312_Tip_a @ E @ binary476621312_Tip_a ) ) ).
% 0.27/0.47
% 0.27/0.47 % binsert.simps(1)
% 0.27/0.47 thf(fact_16_wrm_Osimps,axiom,
% 0.27/0.47 ! [T2: binary1439146945Tree_a,H: a > int,T1: binary1439146945Tree_a,X: a] :
% 0.27/0.47 ( ( ( T2 = binary476621312_Tip_a )
% 0.27/0.47 => ( ( binary1217730267_wrm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = T1 ) )
% 0.27/0.47 & ( ( T2 != binary476621312_Tip_a )
% 0.27/0.47 => ( ( binary1217730267_wrm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( binary717961607le_T_a @ T1 @ X @ ( binary1217730267_wrm_a @ H @ T2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % wrm.simps
% 0.27/0.47 thf(fact_17_Tree_Oinduct,axiom,
% 0.27/0.47 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 0.27/0.47 ( ( P @ binary476621312_Tip_a )
% 0.27/0.47 => ( ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
% 0.27/0.47 ( ( P @ X1 )
% 0.27/0.47 => ( ( P @ X3 )
% 0.27/0.47 => ( P @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) ) ) )
% 0.27/0.47 => ( P @ Tree ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Tree.induct
% 0.27/0.47 thf(fact_18_Tree_Oexhaust,axiom,
% 0.27/0.47 ! [Y: binary1439146945Tree_a] :
% 0.27/0.47 ( ( Y != binary476621312_Tip_a )
% 0.27/0.47 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Tree.exhaust
% 0.27/0.47 thf(fact_19_rm__set,axiom,
% 0.27/0.47 ! [T: binary1439146945Tree_a,H: a > int] :
% 0.27/0.47 ( ( ( T != binary476621312_Tip_a )
% 0.27/0.47 & ( binary1721989714Tree_a @ H @ T ) )
% 0.27/0.47 => ( member_a @ ( binary339557810e_rm_a @ H @ T ) @ ( binary945792244etOf_a @ T ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % rm_set
% 0.27/0.47 thf(fact_20_rm_Osimps,axiom,
% 0.27/0.47 ! [T2: binary1439146945Tree_a,H: a > int,T1: binary1439146945Tree_a,X: a] :
% 0.27/0.47 ( ( ( T2 = binary476621312_Tip_a )
% 0.27/0.47 => ( ( binary339557810e_rm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = X ) )
% 0.27/0.47 & ( ( T2 != binary476621312_Tip_a )
% 0.27/0.47 => ( ( binary339557810e_rm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( binary339557810e_rm_a @ H @ T2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % rm.simps
% 0.27/0.47 thf(fact_21_wrm__set1,axiom,
% 0.27/0.47 ! [T: binary1439146945Tree_a,H: a > int] :
% 0.27/0.47 ( ( ( T != binary476621312_Tip_a )
% 0.27/0.47 & ( binary1721989714Tree_a @ H @ T ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ H @ T ) ) @ ( binary945792244etOf_a @ T ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % wrm_set1
% 0.27/0.47 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 0.27/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.27/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( ( binary1721989714Tree_a @ H @ T1 )
% 0.27/0.47 & ! [X4: a] :
% 0.27/0.47 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 0.27/0.47 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X ) ) )
% 0.27/0.47 & ! [X4: a] :
% 0.27/0.47 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 0.27/0.47 => ( ord_less_int @ ( H @ X ) @ ( H @ X4 ) ) )
% 0.27/0.47 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sortedTree.simps(2)
% 0.27/0.47 thf(fact_23_remove_Osimps_I1_J,axiom,
% 0.27/0.47 ! [H: a > int,E: a] :
% 0.27/0.47 ( ( binary1804682569move_a @ H @ E @ binary476621312_Tip_a )
% 0.27/0.47 = binary476621312_Tip_a ) ).
% 0.27/0.47
% 0.27/0.47 % remove.simps(1)
% 0.27/0.47 thf(fact_24_binsert_Osimps_I2_J,axiom,
% 0.27/0.47 ! [H: a > int,E: a,X: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 0.27/0.47 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 0.27/0.47 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( binary717961607le_T_a @ ( binary1226383794sert_a @ H @ E @ T1 ) @ X @ T2 ) ) )
% 0.27/0.47 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 0.27/0.47 => ( ( ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 0.27/0.47 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( binary717961607le_T_a @ T1 @ X @ ( binary1226383794sert_a @ H @ E @ T2 ) ) ) )
% 0.27/0.47 & ( ~ ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 0.27/0.47 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.47 = ( binary717961607le_T_a @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % binsert.simps(2)
% 0.27/0.47 thf(fact_25_setOf_Osimps_I1_J,axiom,
% 0.27/0.47 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 0.27/0.47 = bot_bot_set_a ) ).
% 0.27/0.47
% 0.27/0.47 % setOf.simps(1)
% 0.27/0.47 thf(fact_26_empty__subsetI,axiom,
% 0.27/0.47 ! [A3: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A3 ) ).
% 0.27/0.47
% 0.27/0.47 % empty_subsetI
% 0.27/0.47 thf(fact_27_subset__empty,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ bot_bot_set_a )
% 0.27/0.47 = ( A3 = bot_bot_set_a ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_empty
% 0.27/0.47 thf(fact_28_subset__antisym,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.27/0.47 => ( A3 = B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_antisym
% 0.27/0.47 thf(fact_29_subsetI,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a] :
% 0.27/0.47 ( ! [X5: a] :
% 0.27/0.47 ( ( member_a @ X5 @ A3 )
% 0.27/0.47 => ( member_a @ X5 @ B3 ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetI
% 0.27/0.47 thf(fact_30_empty__Collect__eq,axiom,
% 0.27/0.47 ! [P: a > $o] :
% 0.27/0.47 ( ( bot_bot_set_a
% 0.27/0.47 = ( collect_a @ P ) )
% 0.27/0.47 = ( ! [X4: a] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % empty_Collect_eq
% 0.27/0.47 thf(fact_31_Collect__empty__eq,axiom,
% 0.27/0.47 ! [P: a > $o] :
% 0.27/0.47 ( ( ( collect_a @ P )
% 0.27/0.47 = bot_bot_set_a )
% 0.27/0.47 = ( ! [X4: a] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_empty_eq
% 0.27/0.47 thf(fact_32_all__not__in__conv,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( ! [X4: a] :
% 0.27/0.47 ~ ( member_a @ X4 @ A3 ) )
% 0.27/0.47 = ( A3 = bot_bot_set_a ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_33_empty__iff,axiom,
% 0.27/0.47 ! [C: a] :
% 0.27/0.47 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_34_bot__apply,axiom,
% 0.27/0.47 ( bot_bot_a_o
% 0.27/0.47 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_apply
% 0.27/0.47 thf(fact_35_order__refl,axiom,
% 0.27/0.47 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % order_refl
% 0.27/0.47 thf(fact_36_order__refl,axiom,
% 0.27/0.47 ! [X: a > $o] : ( ord_less_eq_a_o @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % order_refl
% 0.27/0.47 thf(fact_37_bot__set__def,axiom,
% 0.27/0.47 ( bot_bot_set_a
% 0.27/0.47 = ( collect_a @ bot_bot_a_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_set_def
% 0.27/0.47 thf(fact_38_le__funD,axiom,
% 0.27/0.47 ! [F: a > $o,G: a > $o,X: a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ F @ G )
% 0.27/0.47 => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funD
% 0.27/0.47 thf(fact_39_le__funE,axiom,
% 0.27/0.47 ! [F: a > $o,G: a > $o,X: a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ F @ G )
% 0.27/0.47 => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funE
% 0.27/0.47 thf(fact_40_le__funI,axiom,
% 0.27/0.47 ! [F: a > $o,G: a > $o] :
% 0.27/0.47 ( ! [X5: a] : ( ord_less_eq_o @ ( F @ X5 ) @ ( G @ X5 ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ F @ G ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_funI
% 0.27/0.47 thf(fact_41_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: a,P: a > $o] :
% 0.27/0.47 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_42_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( collect_a
% 0.27/0.47 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.27/0.47 = A3 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_43_Collect__cong,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ! [X5: a] :
% 0.27/0.47 ( ( P @ X5 )
% 0.27/0.47 = ( Q @ X5 ) )
% 0.27/0.47 => ( ( collect_a @ P )
% 0.27/0.47 = ( collect_a @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_cong
% 0.27/0.47 thf(fact_44_le__fun__def,axiom,
% 0.27/0.47 ( ord_less_eq_a_o
% 0.27/0.47 = ( ^ [F2: a > $o,G2: a > $o] :
% 0.27/0.47 ! [X4: a] : ( ord_less_eq_o @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_fun_def
% 0.27/0.47 thf(fact_45_order__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_46_order__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_47_order__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_48_order__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst1
% 0.27/0.47 thf(fact_49_order__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_50_order__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_51_order__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_52_order__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_subst2
% 0.27/0.47 thf(fact_53_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_54_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_55_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_56_ord__eq__le__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_subst
% 0.27/0.47 thf(fact_57_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_58_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_59_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_60_ord__le__eq__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_subst
% 0.27/0.47 thf(fact_61_eq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [X4: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 0.27/0.47 & ( ord_less_eq_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_iff
% 0.27/0.47 thf(fact_62_eq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [X4: a > $o,Y4: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 0.27/0.47 & ( ord_less_eq_a_o @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_iff
% 0.27/0.47 thf(fact_63_antisym,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ Y @ X )
% 0.27/0.47 => ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym
% 0.27/0.47 thf(fact_64_antisym,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ Y @ X )
% 0.27/0.47 => ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym
% 0.27/0.47 thf(fact_65_eq__refl,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_refl
% 0.27/0.47 thf(fact_66_eq__refl,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ord_less_eq_a_o @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_refl
% 0.27/0.47 thf(fact_67_order_Otrans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.trans
% 0.27/0.47 thf(fact_68_order_Otrans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.trans
% 0.27/0.47 thf(fact_69_antisym__conv,axiom,
% 0.27/0.47 ! [Y: set_a,X: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ Y @ X )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv
% 0.27/0.47 thf(fact_70_antisym__conv,axiom,
% 0.27/0.47 ! [Y: a > $o,X: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ Y @ X )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv
% 0.27/0.47 thf(fact_71_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [A: set_a,B: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.47 & ( ord_less_eq_set_a @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.eq_iff
% 0.27/0.47 thf(fact_72_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [A: a > $o,B: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A @ B )
% 0.27/0.47 & ( ord_less_eq_a_o @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.eq_iff
% 0.27/0.47 thf(fact_73_ord__eq__le__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_trans
% 0.27/0.47 thf(fact_74_ord__eq__le__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_le_trans
% 0.27/0.47 thf(fact_75_ord__le__eq__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C )
% 0.27/0.47 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_trans
% 0.27/0.47 thf(fact_76_ord__le__eq__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C )
% 0.27/0.47 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_le_eq_trans
% 0.27/0.47 thf(fact_77_order__class_Oorder_Oantisym,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.antisym
% 0.27/0.47 thf(fact_78_order__class_Oorder_Oantisym,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ A2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_class.order.antisym
% 0.27/0.47 thf(fact_79_order__trans,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_trans
% 0.27/0.47 thf(fact_80_order__trans,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_trans
% 0.27/0.47 thf(fact_81_dual__order_Orefl,axiom,
% 0.27/0.47 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.refl
% 0.27/0.47 thf(fact_82_dual__order_Orefl,axiom,
% 0.27/0.47 ! [A2: a > $o] : ( ord_less_eq_a_o @ A2 @ A2 ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.refl
% 0.27/0.47 thf(fact_83_dual__order_Otrans,axiom,
% 0.27/0.47 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ C @ B2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ C @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.trans
% 0.27/0.47 thf(fact_84_dual__order_Otrans,axiom,
% 0.27/0.47 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ C @ B2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ C @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.trans
% 0.27/0.47 thf(fact_85_dual__order_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [A: set_a,B: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.47 & ( ord_less_eq_set_a @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.eq_iff
% 0.27/0.47 thf(fact_86_dual__order_Oeq__iff,axiom,
% 0.27/0.47 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [A: a > $o,B: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ B @ A )
% 0.27/0.47 & ( ord_less_eq_a_o @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.eq_iff
% 0.27/0.47 thf(fact_87_dual__order_Oantisym,axiom,
% 0.27/0.47 ! [B2: set_a,A2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.antisym
% 0.27/0.47 thf(fact_88_dual__order_Oantisym,axiom,
% 0.27/0.47 ! [B2: a > $o,A2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( A2 = B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.antisym
% 0.27/0.47 thf(fact_89_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_90_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_91_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_92_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_93_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_94_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_95_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_96_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_97_ord__eq__less__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2
% 0.27/0.47 = ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_subst
% 0.27/0.47 thf(fact_98_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_99_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_100_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_101_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_102_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_103_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_104_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_105_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_106_ord__less__eq__subst,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ( F @ B2 )
% 0.27/0.47 = C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_subst
% 0.27/0.47 thf(fact_107_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_108_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_109_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_110_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_111_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_112_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_113_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_114_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_115_order__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst1
% 0.27/0.47 thf(fact_116_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_117_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_118_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_119_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_120_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_121_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_122_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_123_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_124_order__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_subst2
% 0.27/0.47 thf(fact_125_lt__ex,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 0.27/0.47
% 0.27/0.47 % lt_ex
% 0.27/0.47 thf(fact_126_gt__ex,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 0.27/0.47
% 0.27/0.47 % gt_ex
% 0.27/0.47 thf(fact_127_neqE,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( X != Y )
% 0.27/0.47 => ( ~ ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % neqE
% 0.27/0.47 thf(fact_128_neq__iff,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( X != Y )
% 0.27/0.47 = ( ( ord_less_int @ X @ Y )
% 0.27/0.47 | ( ord_less_int @ Y @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq_iff
% 0.27/0.47 thf(fact_129_order_Oasym,axiom,
% 0.27/0.47 ! [A2: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.asym
% 0.27/0.47 thf(fact_130_order_Oasym,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.asym
% 0.27/0.47 thf(fact_131_order_Oasym,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.asym
% 0.27/0.47 thf(fact_132_less__imp__neq,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_neq
% 0.27/0.47 thf(fact_133_less__imp__neq,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_neq
% 0.27/0.47 thf(fact_134_less__imp__neq,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_neq
% 0.27/0.47 thf(fact_135_less__asym,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym
% 0.27/0.47 thf(fact_136_less__asym,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym
% 0.27/0.47 thf(fact_137_less__asym,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym
% 0.27/0.47 thf(fact_138_less__asym_H,axiom,
% 0.27/0.47 ! [A2: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym'
% 0.27/0.47 thf(fact_139_less__asym_H,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym'
% 0.27/0.47 thf(fact_140_less__asym_H,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_asym'
% 0.27/0.47 thf(fact_141_less__trans,axiom,
% 0.27/0.47 ! [X: int,Y: int,Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ( ord_less_int @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_trans
% 0.27/0.47 thf(fact_142_less__trans,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_set_a @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_trans
% 0.27/0.47 thf(fact_143_less__trans,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( ( ord_less_a_o @ Y @ Z2 )
% 0.27/0.47 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_trans
% 0.27/0.47 thf(fact_144_less__linear,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 | ( X = Y )
% 0.27/0.47 | ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_linear
% 0.27/0.47 thf(fact_145_less__irrefl,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ~ ( ord_less_int @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % less_irrefl
% 0.27/0.47 thf(fact_146_less__irrefl,axiom,
% 0.27/0.47 ! [X: set_a] :
% 0.27/0.47 ~ ( ord_less_set_a @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % less_irrefl
% 0.27/0.47 thf(fact_147_less__irrefl,axiom,
% 0.27/0.47 ! [X: a > $o] :
% 0.27/0.47 ~ ( ord_less_a_o @ X @ X ) ).
% 0.27/0.47
% 0.27/0.47 % less_irrefl
% 0.27/0.47 thf(fact_148_ord__eq__less__trans,axiom,
% 0.27/0.47 ! [A2: int,B2: int,C: int] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_trans
% 0.27/0.47 thf(fact_149_ord__eq__less__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_trans
% 0.27/0.47 thf(fact_150_ord__eq__less__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( A2 = B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_eq_less_trans
% 0.27/0.47 thf(fact_151_ord__less__eq__trans,axiom,
% 0.27/0.47 ! [A2: int,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C )
% 0.27/0.47 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_trans
% 0.27/0.47 thf(fact_152_ord__less__eq__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_trans
% 0.27/0.47 thf(fact_153_ord__less__eq__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( B2 = C )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ord_less_eq_trans
% 0.27/0.47 thf(fact_154_dual__order_Oasym,axiom,
% 0.27/0.47 ! [B2: int,A2: int] :
% 0.27/0.47 ( ( ord_less_int @ B2 @ A2 )
% 0.27/0.47 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.asym
% 0.27/0.47 thf(fact_155_dual__order_Oasym,axiom,
% 0.27/0.47 ! [B2: set_a,A2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ B2 @ A2 )
% 0.27/0.47 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.asym
% 0.27/0.47 thf(fact_156_dual__order_Oasym,axiom,
% 0.27/0.47 ! [B2: a > $o,A2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ B2 @ A2 )
% 0.27/0.47 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.asym
% 0.27/0.47 thf(fact_157_less__imp__not__eq,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq
% 0.27/0.47 thf(fact_158_less__imp__not__eq,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq
% 0.27/0.47 thf(fact_159_less__imp__not__eq,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq
% 0.27/0.47 thf(fact_160_less__not__sym,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_sym
% 0.27/0.47 thf(fact_161_less__not__sym,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_sym
% 0.27/0.47 thf(fact_162_less__not__sym,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_sym
% 0.27/0.47 thf(fact_163_antisym__conv3,axiom,
% 0.27/0.47 ! [Y: int,X: int] :
% 0.27/0.47 ( ~ ( ord_less_int @ Y @ X )
% 0.27/0.47 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv3
% 0.27/0.47 thf(fact_164_less__imp__not__eq2,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( Y != X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq2
% 0.27/0.47 thf(fact_165_less__imp__not__eq2,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( Y != X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq2
% 0.27/0.47 thf(fact_166_less__imp__not__eq2,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( Y != X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_eq2
% 0.27/0.47 thf(fact_167_less__imp__triv,axiom,
% 0.27/0.47 ! [X: int,Y: int,P: $o] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ( ord_less_int @ Y @ X )
% 0.27/0.47 => P ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_triv
% 0.27/0.47 thf(fact_168_less__imp__triv,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a,P: $o] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_set_a @ Y @ X )
% 0.27/0.47 => P ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_triv
% 0.27/0.47 thf(fact_169_less__imp__triv,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o,P: $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( ( ord_less_a_o @ Y @ X )
% 0.27/0.47 => P ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_triv
% 0.27/0.47 thf(fact_170_linorder__cases,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ~ ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ( X != Y )
% 0.27/0.47 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % linorder_cases
% 0.27/0.47 thf(fact_171_dual__order_Oirrefl,axiom,
% 0.27/0.47 ! [A2: int] :
% 0.27/0.47 ~ ( ord_less_int @ A2 @ A2 ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.irrefl
% 0.27/0.47 thf(fact_172_dual__order_Oirrefl,axiom,
% 0.27/0.47 ! [A2: set_a] :
% 0.27/0.47 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.irrefl
% 0.27/0.47 thf(fact_173_dual__order_Oirrefl,axiom,
% 0.27/0.47 ! [A2: a > $o] :
% 0.27/0.47 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.irrefl
% 0.27/0.47 thf(fact_174_order_Ostrict__trans,axiom,
% 0.27/0.47 ! [A2: int,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_trans
% 0.27/0.47 thf(fact_175_order_Ostrict__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_trans
% 0.27/0.47 thf(fact_176_order_Ostrict__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_trans
% 0.27/0.47 thf(fact_177_less__imp__not__less,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_less
% 0.27/0.47 thf(fact_178_less__imp__not__less,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_less
% 0.27/0.47 thf(fact_179_less__imp__not__less,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_not_less
% 0.27/0.47 thf(fact_180_linorder__less__wlog,axiom,
% 0.27/0.47 ! [P: int > int > $o,A2: int,B2: int] :
% 0.27/0.47 ( ! [A4: int,B4: int] :
% 0.27/0.47 ( ( ord_less_int @ A4 @ B4 )
% 0.27/0.47 => ( P @ A4 @ B4 ) )
% 0.27/0.47 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 0.27/0.47 => ( ! [A4: int,B4: int] :
% 0.27/0.47 ( ( P @ B4 @ A4 )
% 0.27/0.47 => ( P @ A4 @ B4 ) )
% 0.27/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % linorder_less_wlog
% 0.27/0.47 thf(fact_181_dual__order_Ostrict__trans,axiom,
% 0.27/0.47 ! [B2: int,A2: int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_int @ C @ B2 )
% 0.27/0.47 => ( ord_less_int @ C @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_trans
% 0.27/0.47 thf(fact_182_dual__order_Ostrict__trans,axiom,
% 0.27/0.47 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_set_a @ C @ B2 )
% 0.27/0.47 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_trans
% 0.27/0.47 thf(fact_183_dual__order_Ostrict__trans,axiom,
% 0.27/0.47 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ B2 @ A2 )
% 0.27/0.47 => ( ( ord_less_a_o @ C @ B2 )
% 0.27/0.47 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_trans
% 0.27/0.47 thf(fact_184_not__less__iff__gr__or__eq,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.27/0.47 = ( ( ord_less_int @ Y @ X )
% 0.27/0.47 | ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_less_iff_gr_or_eq
% 0.27/0.47 thf(fact_185_order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [A2: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_implies_not_eq
% 0.27/0.47 thf(fact_186_order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_implies_not_eq
% 0.27/0.47 thf(fact_187_order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % order.strict_implies_not_eq
% 0.27/0.47 thf(fact_188_dual__order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [B2: int,A2: int] :
% 0.27/0.47 ( ( ord_less_int @ B2 @ A2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_implies_not_eq
% 0.27/0.47 thf(fact_189_dual__order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [B2: set_a,A2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ B2 @ A2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_implies_not_eq
% 0.27/0.47 thf(fact_190_dual__order_Ostrict__implies__not__eq,axiom,
% 0.27/0.47 ! [B2: a > $o,A2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ B2 @ A2 )
% 0.27/0.47 => ( A2 != B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % dual_order.strict_implies_not_eq
% 0.27/0.47 thf(fact_191_bot__fun__def,axiom,
% 0.27/0.47 ( bot_bot_a_o
% 0.27/0.47 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_fun_def
% 0.27/0.47 thf(fact_192_emptyE,axiom,
% 0.27/0.47 ! [A2: a] :
% 0.27/0.47 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_193_equals0D,axiom,
% 0.27/0.47 ! [A3: set_a,A2: a] :
% 0.27/0.47 ( ( A3 = bot_bot_set_a )
% 0.27/0.47 => ~ ( member_a @ A2 @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_194_equals0I,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ! [Y2: a] :
% 0.27/0.47 ~ ( member_a @ Y2 @ A3 )
% 0.27/0.47 => ( A3 = bot_bot_set_a ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_195_ex__in__conv,axiom,
% 0.27/0.47 ! [A3: set_a] :
% 0.27/0.47 ( ( ? [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.27/0.47 = ( A3 != bot_bot_set_a ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_196_in__mono,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a,X: a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.47 => ( ( member_a @ X @ A3 )
% 0.27/0.47 => ( member_a @ X @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_mono
% 0.27/0.47 thf(fact_197_subsetD,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a,C: a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.47 => ( ( member_a @ C @ A3 )
% 0.27/0.47 => ( member_a @ C @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subsetD
% 0.27/0.47 thf(fact_198_equalityE,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ~ ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.47 => ~ ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityE
% 0.27/0.47 thf(fact_199_subset__eq,axiom,
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ! [X4: a] :
% 0.27/0.47 ( ( member_a @ X4 @ A5 )
% 0.27/0.47 => ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_eq
% 0.27/0.47 thf(fact_200_equalityD1,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD1
% 0.27/0.47 thf(fact_201_equalityD2,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a] :
% 0.27/0.47 ( ( A3 = B3 )
% 0.27/0.47 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % equalityD2
% 0.27/0.47 thf(fact_202_subset__iff,axiom,
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ! [T3: a] :
% 0.27/0.47 ( ( member_a @ T3 @ A5 )
% 0.27/0.47 => ( member_a @ T3 @ B5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_iff
% 0.27/0.47 thf(fact_203_subset__refl,axiom,
% 0.27/0.47 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 0.27/0.47
% 0.27/0.47 % subset_refl
% 0.27/0.47 thf(fact_204_Collect__mono,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ! [X5: a] :
% 0.27/0.47 ( ( P @ X5 )
% 0.27/0.47 => ( Q @ X5 ) )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono
% 0.27/0.47 thf(fact_205_subset__trans,axiom,
% 0.27/0.47 ! [A3: set_a,B3: set_a,C2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ A3 @ C2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subset_trans
% 0.27/0.47 thf(fact_206_set__eq__subset,axiom,
% 0.27/0.47 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 0.27/0.47 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.27/0.47 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % set_eq_subset
% 0.27/0.47 thf(fact_207_Collect__mono__iff,axiom,
% 0.27/0.47 ! [P: a > $o,Q: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.27/0.47 = ( ! [X4: a] :
% 0.27/0.47 ( ( P @ X4 )
% 0.27/0.47 => ( Q @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mono_iff
% 0.27/0.47 thf(fact_208_empty__def,axiom,
% 0.27/0.47 ( bot_bot_set_a
% 0.27/0.47 = ( collect_a
% 0.27/0.47 @ ^ [X4: a] : $false ) ) ).
% 0.27/0.47
% 0.27/0.47 % empty_def
% 0.27/0.47 thf(fact_209_Collect__subset,axiom,
% 0.27/0.47 ! [A3: set_a,P: a > $o] :
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 @ ( collect_a
% 0.27/0.47 @ ^ [X4: a] :
% 0.27/0.47 ( ( member_a @ X4 @ A3 )
% 0.27/0.47 & ( P @ X4 ) ) )
% 0.27/0.47 @ A3 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_subset
% 0.27/0.47 thf(fact_210_leD,axiom,
% 0.27/0.47 ! [Y: int,X: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ Y @ X )
% 0.27/0.47 => ~ ( ord_less_int @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % leD
% 0.27/0.47 thf(fact_211_leD,axiom,
% 0.27/0.47 ! [Y: set_a,X: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ Y @ X )
% 0.27/0.47 => ~ ( ord_less_set_a @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % leD
% 0.27/0.47 thf(fact_212_leD,axiom,
% 0.27/0.47 ! [Y: a > $o,X: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ Y @ X )
% 0.27/0.47 => ~ ( ord_less_a_o @ X @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % leD
% 0.27/0.47 thf(fact_213_leI,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ~ ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % leI
% 0.27/0.47 thf(fact_214_le__less,axiom,
% 0.27/0.47 ( ord_less_eq_int
% 0.27/0.47 = ( ^ [X4: int,Y4: int] :
% 0.27/0.47 ( ( ord_less_int @ X4 @ Y4 )
% 0.27/0.47 | ( X4 = Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_less
% 0.27/0.47 thf(fact_215_le__less,axiom,
% 0.27/0.47 ( ord_less_eq_set_a
% 0.27/0.47 = ( ^ [X4: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.27/0.47 | ( X4 = Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_less
% 0.27/0.47 thf(fact_216_le__less,axiom,
% 0.27/0.47 ( ord_less_eq_a_o
% 0.27/0.47 = ( ^ [X4: a > $o,Y4: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.27/0.47 | ( X4 = Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_less
% 0.27/0.47 thf(fact_217_less__le,axiom,
% 0.27/0.47 ( ord_less_int
% 0.27/0.47 = ( ^ [X4: int,Y4: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.27/0.47 & ( X4 != Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_le
% 0.27/0.47 thf(fact_218_less__le,axiom,
% 0.27/0.47 ( ord_less_set_a
% 0.27/0.47 = ( ^ [X4: set_a,Y4: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 0.27/0.47 & ( X4 != Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_le
% 0.27/0.47 thf(fact_219_less__le,axiom,
% 0.27/0.47 ( ord_less_a_o
% 0.27/0.47 = ( ^ [X4: a > $o,Y4: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 0.27/0.47 & ( X4 != Y4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_le
% 0.27/0.47 thf(fact_220_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_221_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_222_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_223_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_224_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_225_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_226_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_227_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_228_order__le__less__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst1
% 0.27/0.47 thf(fact_229_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_230_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_231_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_232_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_233_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_234_order__le__less__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_le_less_subst2
% 0.27/0.47 thf(fact_235_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_236_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_237_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_238_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_239_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_240_order__less__le__subst1,axiom,
% 0.27/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst1
% 0.27/0.47 thf(fact_241_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_242_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_243_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_244_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_245_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_246_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_247_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: int,Y2: int] :
% 0.27/0.47 ( ( ord_less_int @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_248_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: set_a,Y2: set_a] :
% 0.27/0.47 ( ( ord_less_set_a @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_249_order__less__le__subst2,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 0.27/0.47 => ( ! [X5: a > $o,Y2: a > $o] :
% 0.27/0.47 ( ( ord_less_a_o @ X5 @ Y2 )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 0.27/0.47 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % order_less_le_subst2
% 0.27/0.47 thf(fact_250_not__le,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 0.27/0.47 = ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_le
% 0.27/0.47 thf(fact_251_not__less,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.27/0.47 = ( ord_less_eq_int @ Y @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_less
% 0.27/0.47 thf(fact_252_le__neq__trans,axiom,
% 0.27/0.47 ! [A2: int,B2: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ A2 @ B2 )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_neq_trans
% 0.27/0.47 thf(fact_253_le__neq__trans,axiom,
% 0.27/0.47 ! [A2: set_a,B2: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_neq_trans
% 0.27/0.47 thf(fact_254_le__neq__trans,axiom,
% 0.27/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( ord_less_a_o @ A2 @ B2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_neq_trans
% 0.27/0.47 thf(fact_255_antisym__conv1,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ~ ( ord_less_int @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_int @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv1
% 0.27/0.47 thf(fact_256_antisym__conv1,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ~ ( ord_less_set_a @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv1
% 0.27/0.47 thf(fact_257_antisym__conv1,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ~ ( ord_less_a_o @ X @ Y )
% 0.27/0.47 => ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv1
% 0.27/0.47 thf(fact_258_antisym__conv2,axiom,
% 0.27/0.47 ! [X: int,Y: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ X @ Y )
% 0.27/0.47 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv2
% 0.27/0.47 thf(fact_259_antisym__conv2,axiom,
% 0.27/0.47 ! [X: set_a,Y: set_a] :
% 0.27/0.47 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.47 => ( ( ~ ( ord_less_set_a @ X @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % antisym_conv2
% 0.27/0.47 thf(fact_260_antisym__conv2,axiom,
% 0.27/0.47 ! [X: a > $o,Y: a > $o] :
% 0.27/0.47 ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.47 => ( ( ~ ( ord_less_a_o @ X @ Y ) )
% 0.27/0.48 = ( X = Y ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % antisym_conv2
% 0.27/0.48 thf(fact_261_less__imp__le,axiom,
% 0.27/0.48 ! [X: int,Y: int] :
% 0.27/0.48 ( ( ord_less_int @ X @ Y )
% 0.27/0.48 => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_imp_le
% 0.27/0.48 thf(fact_262_less__imp__le,axiom,
% 0.27/0.48 ! [X: set_a,Y: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.48 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_imp_le
% 0.27/0.48 thf(fact_263_less__imp__le,axiom,
% 0.27/0.48 ! [X: a > $o,Y: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.48 => ( ord_less_eq_a_o @ X @ Y ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_imp_le
% 0.27/0.48 thf(fact_264_le__less__trans,axiom,
% 0.27/0.48 ! [X: int,Y: int,Z2: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ X @ Y )
% 0.27/0.48 => ( ( ord_less_int @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_less_trans
% 0.27/0.48 thf(fact_265_le__less__trans,axiom,
% 0.27/0.48 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.48 => ( ( ord_less_set_a @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_less_trans
% 0.27/0.48 thf(fact_266_le__less__trans,axiom,
% 0.27/0.48 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.48 => ( ( ord_less_a_o @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_less_trans
% 0.27/0.48 thf(fact_267_less__le__trans,axiom,
% 0.27/0.48 ! [X: int,Y: int,Z2: int] :
% 0.27/0.48 ( ( ord_less_int @ X @ Y )
% 0.27/0.48 => ( ( ord_less_eq_int @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_trans
% 0.27/0.48 thf(fact_268_less__le__trans,axiom,
% 0.27/0.48 ! [X: set_a,Y: set_a,Z2: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_trans
% 0.27/0.48 thf(fact_269_less__le__trans,axiom,
% 0.27/0.48 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.27/0.48 => ( ( ord_less_eq_a_o @ Y @ Z2 )
% 0.27/0.48 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_trans
% 0.27/0.48 thf(fact_270_le__less__linear,axiom,
% 0.27/0.48 ! [X: int,Y: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ X @ Y )
% 0.27/0.48 | ( ord_less_int @ Y @ X ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_less_linear
% 0.27/0.48 thf(fact_271_le__imp__less__or__eq,axiom,
% 0.27/0.48 ! [X: int,Y: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ X @ Y )
% 0.27/0.48 => ( ( ord_less_int @ X @ Y )
% 0.27/0.48 | ( X = Y ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_imp_less_or_eq
% 0.27/0.48 thf(fact_272_le__imp__less__or__eq,axiom,
% 0.27/0.48 ! [X: set_a,Y: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ X @ Y )
% 0.27/0.48 => ( ( ord_less_set_a @ X @ Y )
% 0.27/0.48 | ( X = Y ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_imp_less_or_eq
% 0.27/0.48 thf(fact_273_le__imp__less__or__eq,axiom,
% 0.27/0.48 ! [X: a > $o,Y: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ X @ Y )
% 0.27/0.48 => ( ( ord_less_a_o @ X @ Y )
% 0.27/0.48 | ( X = Y ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_imp_less_or_eq
% 0.27/0.48 thf(fact_274_less__le__not__le,axiom,
% 0.27/0.48 ( ord_less_int
% 0.27/0.48 = ( ^ [X4: int,Y4: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.27/0.48 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_not_le
% 0.27/0.48 thf(fact_275_less__le__not__le,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [X4: set_a,Y4: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 0.27/0.48 & ~ ( ord_less_eq_set_a @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_not_le
% 0.27/0.48 thf(fact_276_less__le__not__le,axiom,
% 0.27/0.48 ( ord_less_a_o
% 0.27/0.48 = ( ^ [X4: a > $o,Y4: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 0.27/0.48 & ~ ( ord_less_eq_a_o @ Y4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_le_not_le
% 0.27/0.48 thf(fact_277_not__le__imp__less,axiom,
% 0.27/0.48 ! [Y: int,X: int] :
% 0.27/0.48 ( ~ ( ord_less_eq_int @ Y @ X )
% 0.27/0.48 => ( ord_less_int @ X @ Y ) ) ).
% 0.27/0.48
% 0.27/0.48 % not_le_imp_less
% 0.27/0.48 thf(fact_278_order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [A2: int,B2: int,C: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.27/0.48 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans1
% 0.27/0.48 thf(fact_279_order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.27/0.48 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans1
% 0.27/0.48 thf(fact_280_order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.27/0.48 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans1
% 0.27/0.48 thf(fact_281_order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [A2: int,B2: int,C: int] :
% 0.27/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_eq_int @ B2 @ C )
% 0.27/0.48 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans2
% 0.27/0.48 thf(fact_282_order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.27/0.48 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans2
% 0.27/0.48 thf(fact_283_order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.48 => ( ( ord_less_eq_a_o @ B2 @ C )
% 0.27/0.48 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_trans2
% 0.27/0.48 thf(fact_284_order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_int
% 0.27/0.48 = ( ^ [A: int,B: int] :
% 0.27/0.48 ( ( ord_less_int @ A @ B )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.order_iff_strict
% 0.27/0.48 thf(fact_285_order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_set_a
% 0.27/0.48 = ( ^ [A: set_a,B: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A @ B )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.order_iff_strict
% 0.27/0.48 thf(fact_286_order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_a_o
% 0.27/0.48 = ( ^ [A: a > $o,B: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ A @ B )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.order_iff_strict
% 0.27/0.48 thf(fact_287_order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_int
% 0.27/0.48 = ( ^ [A: int,B: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ A @ B )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_iff_order
% 0.27/0.48 thf(fact_288_order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [A: set_a,B: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A @ B )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_iff_order
% 0.27/0.48 thf(fact_289_order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_a_o
% 0.27/0.48 = ( ^ [A: a > $o,B: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ A @ B )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_iff_order
% 0.27/0.48 thf(fact_290_dual__order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [B2: int,A2: int,C: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_int @ C @ B2 )
% 0.27/0.48 => ( ord_less_int @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans1
% 0.27/0.48 thf(fact_291_dual__order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_set_a @ C @ B2 )
% 0.27/0.48 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans1
% 0.27/0.48 thf(fact_292_dual__order_Ostrict__trans1,axiom,
% 0.27/0.48 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_a_o @ C @ B2 )
% 0.27/0.48 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans1
% 0.27/0.48 thf(fact_293_dual__order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [B2: int,A2: int,C: int] :
% 0.27/0.48 ( ( ord_less_int @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_eq_int @ C @ B2 )
% 0.27/0.48 => ( ord_less_int @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans2
% 0.27/0.48 thf(fact_294_dual__order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ C @ B2 )
% 0.27/0.48 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans2
% 0.27/0.48 thf(fact_295_dual__order_Ostrict__trans2,axiom,
% 0.27/0.48 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ B2 @ A2 )
% 0.27/0.48 => ( ( ord_less_eq_a_o @ C @ B2 )
% 0.27/0.48 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_trans2
% 0.27/0.48 thf(fact_296_order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [A2: int,B2: int] :
% 0.27/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_implies_order
% 0.27/0.48 thf(fact_297_order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [A2: set_a,B2: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_implies_order
% 0.27/0.48 thf(fact_298_order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_eq_a_o @ A2 @ B2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.strict_implies_order
% 0.27/0.48 thf(fact_299_dual__order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_int
% 0.27/0.48 = ( ^ [B: int,A: int] :
% 0.27/0.48 ( ( ord_less_int @ B @ A )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.order_iff_strict
% 0.27/0.48 thf(fact_300_dual__order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_set_a
% 0.27/0.48 = ( ^ [B: set_a,A: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ B @ A )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.order_iff_strict
% 0.27/0.48 thf(fact_301_dual__order_Oorder__iff__strict,axiom,
% 0.27/0.48 ( ord_less_eq_a_o
% 0.27/0.48 = ( ^ [B: a > $o,A: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ B @ A )
% 0.27/0.48 | ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.order_iff_strict
% 0.27/0.48 thf(fact_302_dual__order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_int
% 0.27/0.48 = ( ^ [B: int,A: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ B @ A )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_iff_order
% 0.27/0.48 thf(fact_303_dual__order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [B: set_a,A: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ B @ A )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_iff_order
% 0.27/0.48 thf(fact_304_dual__order_Ostrict__iff__order,axiom,
% 0.27/0.48 ( ord_less_a_o
% 0.27/0.48 = ( ^ [B: a > $o,A: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ B @ A )
% 0.27/0.48 & ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_iff_order
% 0.27/0.48 thf(fact_305_dual__order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [B2: int,A2: int] :
% 0.27/0.48 ( ( ord_less_int @ B2 @ A2 )
% 0.27/0.48 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_implies_order
% 0.27/0.48 thf(fact_306_dual__order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [B2: set_a,A2: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ B2 @ A2 )
% 0.27/0.48 => ( ord_less_eq_set_a @ B2 @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_implies_order
% 0.27/0.48 thf(fact_307_dual__order_Ostrict__implies__order,axiom,
% 0.27/0.48 ! [B2: a > $o,A2: a > $o] :
% 0.27/0.48 ( ( ord_less_a_o @ B2 @ A2 )
% 0.27/0.48 => ( ord_less_eq_a_o @ B2 @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.strict_implies_order
% 0.27/0.48 thf(fact_308_order_Onot__eq__order__implies__strict,axiom,
% 0.27/0.48 ! [A2: int,B2: int] :
% 0.27/0.48 ( ( A2 != B2 )
% 0.27/0.48 => ( ( ord_less_eq_int @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.not_eq_order_implies_strict
% 0.27/0.48 thf(fact_309_order_Onot__eq__order__implies__strict,axiom,
% 0.27/0.48 ! [A2: set_a,B2: set_a] :
% 0.27/0.48 ( ( A2 != B2 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.not_eq_order_implies_strict
% 0.27/0.48 thf(fact_310_order_Onot__eq__order__implies__strict,axiom,
% 0.27/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.27/0.48 ( ( A2 != B2 )
% 0.27/0.48 => ( ( ord_less_eq_a_o @ A2 @ B2 )
% 0.27/0.48 => ( ord_less_a_o @ A2 @ B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.not_eq_order_implies_strict
% 0.27/0.48 thf(fact_311_bot_Oextremum,axiom,
% 0.27/0.48 ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum
% 0.27/0.48 thf(fact_312_bot_Oextremum,axiom,
% 0.27/0.48 ! [A2: a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A2 ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum
% 0.27/0.48 thf(fact_313_bot_Oextremum__unique,axiom,
% 0.27/0.48 ! [A2: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 0.27/0.48 = ( A2 = bot_bot_set_a ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_unique
% 0.27/0.48 thf(fact_314_bot_Oextremum__unique,axiom,
% 0.27/0.48 ! [A2: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ A2 @ bot_bot_a_o )
% 0.27/0.48 = ( A2 = bot_bot_a_o ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_unique
% 0.27/0.48 thf(fact_315_bot_Oextremum__uniqueI,axiom,
% 0.27/0.48 ! [A2: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 0.27/0.48 => ( A2 = bot_bot_set_a ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_uniqueI
% 0.27/0.48 thf(fact_316_bot_Oextremum__uniqueI,axiom,
% 0.27/0.48 ! [A2: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ A2 @ bot_bot_a_o )
% 0.27/0.48 => ( A2 = bot_bot_a_o ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_uniqueI
% 0.27/0.48 thf(fact_317_bot_Oextremum__strict,axiom,
% 0.27/0.48 ! [A2: set_a] :
% 0.27/0.48 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_strict
% 0.27/0.48 thf(fact_318_bot_Oextremum__strict,axiom,
% 0.27/0.48 ! [A2: a > $o] :
% 0.27/0.48 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_strict
% 0.27/0.48 thf(fact_319_bot_Onot__eq__extremum,axiom,
% 0.27/0.48 ! [A2: set_a] :
% 0.27/0.48 ( ( A2 != bot_bot_set_a )
% 0.27/0.48 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.not_eq_extremum
% 0.27/0.48 thf(fact_320_bot_Onot__eq__extremum,axiom,
% 0.27/0.48 ! [A2: a > $o] :
% 0.27/0.48 ( ( A2 != bot_bot_a_o )
% 0.27/0.48 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.not_eq_extremum
% 0.27/0.48 thf(fact_321_subset__emptyI,axiom,
% 0.27/0.48 ! [A3: set_a] :
% 0.27/0.48 ( ! [X5: a] :
% 0.27/0.48 ~ ( member_a @ X5 @ A3 )
% 0.27/0.48 => ( ord_less_eq_set_a @ A3 @ bot_bot_set_a ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_emptyI
% 0.27/0.48 thf(fact_322_minf_I8_J,axiom,
% 0.27/0.48 ! [T: int] :
% 0.27/0.48 ? [Z3: int] :
% 0.27/0.48 ! [X6: int] :
% 0.27/0.48 ( ( ord_less_int @ X6 @ Z3 )
% 0.27/0.48 => ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% 0.27/0.48
% 0.27/0.48 % minf(8)
% 0.27/0.48 thf(fact_323_minf_I6_J,axiom,
% 0.27/0.48 ! [T: int] :
% 0.27/0.48 ? [Z3: int] :
% 0.27/0.48 ! [X6: int] :
% 0.27/0.48 ( ( ord_less_int @ X6 @ Z3 )
% 0.27/0.48 => ( ord_less_eq_int @ X6 @ T ) ) ).
% 0.27/0.48
% 0.27/0.48 % minf(6)
% 0.27/0.48 thf(fact_324_pinf_I8_J,axiom,
% 0.27/0.48 ! [T: int] :
% 0.27/0.48 ? [Z3: int] :
% 0.27/0.48 ! [X6: int] :
% 0.27/0.48 ( ( ord_less_int @ Z3 @ X6 )
% 0.27/0.48 => ( ord_less_eq_int @ T @ X6 ) ) ).
% 0.27/0.48
% 0.27/0.48 % pinf(8)
% 0.27/0.48 thf(fact_325_pinf_I6_J,axiom,
% 0.27/0.48 ! [T: int] :
% 0.27/0.48 ? [Z3: int] :
% 0.27/0.48 ! [X6: int] :
% 0.27/0.48 ( ( ord_less_int @ Z3 @ X6 )
% 0.27/0.48 => ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% 0.27/0.48
% 0.27/0.48 % pinf(6)
% 0.27/0.48 thf(fact_326_verit__comp__simplify1_I3_J,axiom,
% 0.27/0.48 ! [B6: int,A6: int] :
% 0.27/0.48 ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 0.27/0.48 = ( ord_less_int @ A6 @ B6 ) ) ).
% 0.27/0.48
% 0.27/0.48 % verit_comp_simplify1(3)
% 0.27/0.48 thf(fact_327_complete__interval,axiom,
% 0.27/0.48 ! [A2: int,B2: int,P: int > $o] :
% 0.27/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.27/0.48 => ( ( P @ A2 )
% 0.27/0.48 => ( ~ ( P @ B2 )
% 0.27/0.48 => ? [C3: int] :
% 0.27/0.48 ( ( ord_less_eq_int @ A2 @ C3 )
% 0.27/0.48 & ( ord_less_eq_int @ C3 @ B2 )
% 0.27/0.48 & ! [X6: int] :
% 0.27/0.48 ( ( ( ord_less_eq_int @ A2 @ X6 )
% 0.27/0.48 & ( ord_less_int @ X6 @ C3 ) )
% 0.27/0.48 => ( P @ X6 ) )
% 0.27/0.48 & ! [D: int] :
% 0.27/0.48 ( ! [X5: int] :
% 0.27/0.48 ( ( ( ord_less_eq_int @ A2 @ X5 )
% 0.27/0.48 & ( ord_less_int @ X5 @ D ) )
% 0.27/0.48 => ( P @ X5 ) )
% 0.27/0.48 => ( ord_less_eq_int @ D @ C3 ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % complete_interval
% 0.27/0.48 thf(fact_328_bot_Oordering__top__axioms,axiom,
% 0.27/0.48 ( ordering_top_set_a
% 0.27/0.48 @ ^ [X4: set_a,Y4: set_a] : ( ord_less_eq_set_a @ Y4 @ X4 )
% 0.27/0.48 @ ^ [X4: set_a,Y4: set_a] : ( ord_less_set_a @ Y4 @ X4 )
% 0.27/0.48 @ bot_bot_set_a ) ).
% 0.27/0.48
% 0.27/0.48 % bot.ordering_top_axioms
% 0.27/0.48 thf(fact_329_bot_Oordering__top__axioms,axiom,
% 0.27/0.48 ( ordering_top_a_o
% 0.27/0.48 @ ^ [X4: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ Y4 @ X4 )
% 0.27/0.48 @ ^ [X4: a > $o,Y4: a > $o] : ( ord_less_a_o @ Y4 @ X4 )
% 0.27/0.48 @ bot_bot_a_o ) ).
% 0.27/0.48
% 0.27/0.48 % bot.ordering_top_axioms
% 0.27/0.48 thf(fact_330_psubsetI,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ( A3 != B3 )
% 0.27/0.48 => ( ord_less_set_a @ A3 @ B3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubsetI
% 0.27/0.48 thf(fact_331_less__fun__def,axiom,
% 0.27/0.48 ( ord_less_a_o
% 0.27/0.48 = ( ^ [F2: a > $o,G2: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_a_o @ F2 @ G2 )
% 0.27/0.48 & ~ ( ord_less_eq_a_o @ G2 @ F2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_fun_def
% 0.27/0.48 thf(fact_332_not__psubset__empty,axiom,
% 0.27/0.48 ! [A3: set_a] :
% 0.27/0.48 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 0.27/0.48
% 0.27/0.48 % not_psubset_empty
% 0.27/0.48 thf(fact_333_subset__iff__psubset__eq,axiom,
% 0.27/0.48 ( ord_less_eq_set_a
% 0.27/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A5 @ B5 )
% 0.27/0.48 | ( A5 = B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_iff_psubset_eq
% 0.27/0.48 thf(fact_334_subset__psubset__trans,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a,C2: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ( ord_less_set_a @ B3 @ C2 )
% 0.27/0.48 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_psubset_trans
% 0.27/0.48 thf(fact_335_subset__not__subset__eq,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.27/0.48 & ~ ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_not_subset_eq
% 0.27/0.48 thf(fact_336_psubset__subset__trans,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a,C2: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 0.27/0.48 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubset_subset_trans
% 0.27/0.48 thf(fact_337_psubset__imp__subset,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubset_imp_subset
% 0.27/0.48 thf(fact_338_psubset__eq,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 0.27/0.48 & ( A5 != B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubset_eq
% 0.27/0.48 thf(fact_339_psubsetE,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a] :
% 0.27/0.48 ( ( ord_less_set_a @ A3 @ B3 )
% 0.27/0.48 => ~ ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubsetE
% 0.27/0.48 thf(fact_340_less__eq__set__def,axiom,
% 0.27/0.48 ( ord_less_eq_set_a
% 0.27/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.48 ( ord_less_eq_a_o
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_eq_set_def
% 0.27/0.48 thf(fact_341_verit__comp__simplify1_I1_J,axiom,
% 0.27/0.48 ! [A2: set_a] :
% 0.27/0.48 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.27/0.48
% 0.27/0.48 % verit_comp_simplify1(1)
% 0.27/0.48 thf(fact_342_verit__comp__simplify1_I1_J,axiom,
% 0.27/0.48 ! [A2: a > $o] :
% 0.27/0.48 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.27/0.48
% 0.27/0.48 % verit_comp_simplify1(1)
% 0.27/0.48 thf(fact_343_prop__restrict,axiom,
% 0.27/0.48 ! [X: a,Z4: set_a,X7: set_a,P: a > $o] :
% 0.27/0.48 ( ( member_a @ X @ Z4 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ Z4
% 0.27/0.48 @ ( collect_a
% 0.27/0.48 @ ^ [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ X7 )
% 0.27/0.48 & ( P @ X4 ) ) ) )
% 0.27/0.48 => ( P @ X ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prop_restrict
% 0.27/0.48 thf(fact_344_Collect__restrict,axiom,
% 0.27/0.48 ! [X7: set_a,P: a > $o] :
% 0.27/0.48 ( ord_less_eq_set_a
% 0.27/0.48 @ ( collect_a
% 0.27/0.48 @ ^ [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ X7 )
% 0.27/0.48 & ( P @ X4 ) ) )
% 0.27/0.48 @ X7 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_restrict
% 0.27/0.48 thf(fact_345_bot__empty__eq,axiom,
% 0.27/0.48 ( bot_bot_a_o
% 0.27/0.48 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot_empty_eq
% 0.27/0.48 thf(fact_346_less__set__def,axiom,
% 0.27/0.48 ( ord_less_set_a
% 0.27/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.27/0.48 ( ord_less_a_o
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % less_set_def
% 0.27/0.48 thf(fact_347_psubsetD,axiom,
% 0.27/0.48 ! [A3: set_a,B3: set_a,C: a] :
% 0.27/0.48 ( ( ord_less_set_a @ A3 @ B3 )
% 0.27/0.48 => ( ( member_a @ C @ A3 )
% 0.27/0.48 => ( member_a @ C @ B3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % psubsetD
% 0.27/0.48 thf(fact_348_pred__subset__eq,axiom,
% 0.27/0.48 ! [R: set_a,S: set_a] :
% 0.27/0.48 ( ( ord_less_eq_a_o
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 0.27/0.48 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 0.27/0.48 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 0.27/0.48
% 0.27/0.48 % pred_subset_eq
% 0.27/0.48 thf(fact_349_subset__Collect__iff,axiom,
% 0.27/0.48 ! [B3: set_a,A3: set_a,P: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.27/0.48 => ( ( ord_less_eq_set_a @ B3
% 0.27/0.48 @ ( collect_a
% 0.27/0.48 @ ^ [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ A3 )
% 0.27/0.48 & ( P @ X4 ) ) ) )
% 0.27/0.48 = ( ! [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ B3 )
% 0.27/0.48 => ( P @ X4 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_Collect_iff
% 0.27/0.48 thf(fact_350_subset__CollectI,axiom,
% 0.27/0.48 ! [B3: set_a,A3: set_a,Q: a > $o,P: a > $o] :
% 0.27/0.48 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 0.27/0.48 => ( ! [X5: a] :
% 0.27/0.48 ( ( member_a @ X5 @ B3 )
% 0.27/0.48 => ( ( Q @ X5 )
% 0.27/0.48 => ( P @ X5 ) ) )
% 0.27/0.48 => ( ord_less_eq_set_a
% 0.27/0.48 @ ( collect_a
% 0.27/0.48 @ ^ [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ B3 )
% 0.27/0.48 & ( Q @ X4 ) ) )
% 0.27/0.48 @ ( collect_a
% 0.27/0.48 @ ^ [X4: a] :
% 0.27/0.48 ( ( member_a @ X4 @ A3 )
% 0.27/0.48 & ( P @ X4 ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_CollectI
% 0.27/0.48 thf(fact_351_remove_Osimps_I2_J,axiom,
% 0.27/0.48 ! [H: a > int,E: a,X: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 0.27/0.48 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 0.27/0.48 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.48 = ( binary717961607le_T_a @ ( binary1804682569move_a @ H @ E @ T1 ) @ X @ T2 ) ) )
% 0.27/0.48 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 0.27/0.48 => ( ( ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 0.27/0.48 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.48 = ( binary717961607le_T_a @ T1 @ X @ ( binary1804682569move_a @ H @ E @ T2 ) ) ) )
% 0.27/0.48 & ( ~ ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 0.27/0.48 => ( ( ( T1 = binary476621312_Tip_a )
% 0.27/0.48 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.48 = T2 ) )
% 0.27/0.48 & ( ( T1 != binary476621312_Tip_a )
% 0.27/0.48 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.27/0.48 = ( produc1275654896Tree_a
% 0.27/0.48 @ ^ [T1p: binary1439146945Tree_a,R2: a] : ( binary717961607le_T_a @ T1p @ R2 @ T2 )
% 0.27/0.48 @ ( binary1774981152rmrm_a @ H @ T1 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % remove.simps(2)
% 0.27/0.48 thf(fact_352_wrmrm__decomp,axiom,
% 0.27/0.48 ! [T: binary1439146945Tree_a,H: a > int] :
% 0.27/0.48 ( ( T != binary476621312_Tip_a )
% 0.27/0.48 => ( ( binary1774981152rmrm_a @ H @ T )
% 0.27/0.48 = ( produc374321428ee_a_a @ ( binary1217730267_wrm_a @ H @ T ) @ ( binary339557810e_rm_a @ H @ T ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % wrmrm_decomp
% 0.27/0.48
% 0.27/0.48 % Conjectures (1)
% 0.27/0.48 thf(conj_0,conjecture,
% 0.27/0.48 binary1721989714Tree_a @ h @ t1 ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 2.59/1.52 ---- Embedded in THF ---
% 2.59/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.59/1.53 %%% Generated on Tue Feb 24 08:24:10 EST 2026
% 2.59/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.59/1.53 %%% Logic specification used:
% 2.59/1.53 %%% thf(spec, logic, $$dhol).
% 2.59/1.53
% 2.59/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2DTF21808.p
% See solution above
% 2.59/1.53 ------------------------
% 2.59/1.55 ---- Cleaned THF ---
% 2.59/1.55 thf(ty_n_t__Product____Type__Oprod_It__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_Mtf__a_J,type,
% 2.59/1.55 produc376588196ee_a_a: $tType ).
% 2.59/1.55
% 2.59/1.55 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 2.59/1.55 binary1439146945Tree_a: $tType ).
% 2.59/1.55
% 2.59/1.55 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.59/1.55 set_a: $tType ).
% 2.59/1.55
% 2.59/1.55 thf(ty_n_t__Int__Oint,type,
% 2.59/1.55 int: $tType ).
% 2.59/1.55
% 2.59/1.55 thf(ty_n_tf__a,type,
% 2.59/1.55 a: $tType ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 2.59/1.55 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 2.59/1.55 binary476621312_Tip_a: binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Obinsert_001tf__a,type,
% 2.59/1.55 binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Omemb_001tf__a,type,
% 2.59/1.55 binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oremove_001tf__a,type,
% 2.59/1.55 binary1804682569move_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Orm_001tf__a,type,
% 2.59/1.55 binary339557810e_rm_a: ( a > int ) > binary1439146945Tree_a > a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 2.59/1.55 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 2.59/1.55 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 2.59/1.55 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Owrm_001tf__a,type,
% 2.59/1.55 binary1217730267_wrm_a: ( a > int ) > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Owrmrm_001tf__a,type,
% 2.59/1.55 binary1774981152rmrm_a: ( a > int ) > binary1439146945Tree_a > produc376588196ee_a_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 2.59/1.55 bot_bot_a_o: a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 2.59/1.55 bot_bot_o: $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 2.59/1.55 bot_bot_set_a: set_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 2.59/1.55 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 2.59/1.55 ord_less_int: int > int > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 2.59/1.55 ord_less_set_a: set_a > set_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
% 2.59/1.55 ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
% 2.59/1.55 ord_less_eq_o: $o > $o > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 2.59/1.55 ord_less_eq_int: int > int > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.59/1.55 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oordering__top_001_062_Itf__a_M_Eo_J,type,
% 2.59/1.55 ordering_top_a_o: ( ( a > $o ) > ( a > $o ) > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > $o ) > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Orderings_Oordering__top_001t__Set__Oset_Itf__a_J,type,
% 2.59/1.55 ordering_top_set_a: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Product__Type_OPair_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_001tf__a,type,
% 2.59/1.55 produc374321428ee_a_a: binary1439146945Tree_a > a > produc376588196ee_a_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J_001tf__a_001t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 2.59/1.55 produc1275654896Tree_a: ( binary1439146945Tree_a > a > binary1439146945Tree_a ) > produc376588196ee_a_a > binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.59/1.55 collect_a: ( a > $o ) > set_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_c_member_001tf__a,type,
% 2.59/1.55 member_a: a > set_a > $o ).
% 2.59/1.55
% 2.59/1.55 thf(sy_v_h,type,
% 2.59/1.55 h: a > int ).
% 2.59/1.55
% 2.59/1.55 thf(sy_v_t1____,type,
% 2.59/1.55 t1: binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_v_t2____,type,
% 2.59/1.55 t2: binary1439146945Tree_a ).
% 2.59/1.55
% 2.59/1.55 thf(sy_v_x____,type,
% 2.59/1.55 x: a ).
% 2.59/1.55
% 2.59/1.55 thf(fact_0_t2nTip,axiom,
% 2.59/1.55 t2 != binary476621312_Tip_a ).
% 2.59/1.55
% 2.59/1.55 thf(fact_1_s,axiom,
% 2.59/1.55 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_2_res,axiom,
% 2.59/1.55 ( ( binary1217730267_wrm_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
% 2.59/1.55 = ( binary717961607le_T_a @ t1 @ x @ ( binary1217730267_wrm_a @ h @ t2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_3_sortLemmaL,axiom,
% 2.59/1.55 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.59/1.55 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_4_sortLemmaR,axiom,
% 2.59/1.55 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.59/1.55 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_5_Tree_Oinject,axiom,
% 2.59/1.55 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 2.59/1.55 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 2.59/1.55 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 2.59/1.55 = ( ( X21 = Y21 )
% 2.59/1.55 & ( X22 = Y22 )
% 2.59/1.55 & ( X23 = Y23 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_6_binsert__sorted,axiom,
% 2.59/1.55 ! [H: a > int,T: binary1439146945Tree_a,X: a] :
% 2.59/1.55 ( ( binary1721989714Tree_a @ H @ T )
% 2.59/1.55 => ( binary1721989714Tree_a @ H @ ( binary1226383794sert_a @ H @ X @ T ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_7_h1,axiom,
% 2.59/1.55 ( ( ( t1 != binary476621312_Tip_a )
% 2.59/1.55 & ( binary1721989714Tree_a @ h @ t1 ) )
% 2.59/1.55 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t1 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_8_sortedTree_Osimps_I1_J,axiom,
% 2.59/1.55 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_9_memb__spec,axiom,
% 2.59/1.55 ! [H: a > int,T: binary1439146945Tree_a,X: a] :
% 2.59/1.55 ( ( binary1721989714Tree_a @ H @ T )
% 2.59/1.55 => ( ( binary2053421120memb_a @ H @ X @ T )
% 2.59/1.55 = ( member_a @ X @ ( binary945792244etOf_a @ T ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_10_sorted__distinct__pred__def,axiom,
% 2.59/1.55 ( binary670562003pred_a
% 2.59/1.55 = ( ^ [H2: a > int,A: a,B: a,T3: binary1439146945Tree_a] :
% 2.59/1.55 ( ( ( binary1721989714Tree_a @ H2 @ T3 )
% 2.59/1.55 & ( member_a @ A @ ( binary945792244etOf_a @ T3 ) )
% 2.59/1.55 & ( member_a @ B @ ( binary945792244etOf_a @ T3 ) )
% 2.59/1.55 & ( ( H2 @ A )
% 2.59/1.55 = ( H2 @ B ) ) )
% 2.59/1.55 => ( A = B ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_11_h2,axiom,
% 2.59/1.55 ( ( ( t2 != binary476621312_Tip_a )
% 2.59/1.55 & ( binary1721989714Tree_a @ h @ t2 ) )
% 2.59/1.55 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ t2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_12_sorted__distinct,axiom,
% 2.59/1.55 ! [H: a > int,A2: a,B2: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A2 @ B2 @ T ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_13__092_060open_062Tip_A_092_060noteq_062_ATip_A_092_060and_062_AsortedTree_Ah_ATip_A_092_060longrightarrow_062_AsortedTree_Ah_A_Iwrm_Ah_ATip_J_092_060close_062,axiom,
% 2.59/1.55 ( ( ( binary476621312_Tip_a != binary476621312_Tip_a )
% 2.59/1.55 & ( binary1721989714Tree_a @ h @ binary476621312_Tip_a ) )
% 2.59/1.55 => ( binary1721989714Tree_a @ h @ ( binary1217730267_wrm_a @ h @ binary476621312_Tip_a ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_14_Tree_Odistinct_I1_J,axiom,
% 2.59/1.55 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.59/1.55 ( binary476621312_Tip_a
% 2.59/1.55 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_15_binsert_Osimps_I1_J,axiom,
% 2.59/1.55 ! [H: a > int,E: a] :
% 2.59/1.55 ( ( binary1226383794sert_a @ H @ E @ binary476621312_Tip_a )
% 2.59/1.55 = ( binary717961607le_T_a @ binary476621312_Tip_a @ E @ binary476621312_Tip_a ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_16_wrm_Osimps,axiom,
% 2.59/1.55 ! [T2: binary1439146945Tree_a,H: a > int,T1: binary1439146945Tree_a,X: a] :
% 2.59/1.55 ( ( ( T2 = binary476621312_Tip_a )
% 2.59/1.55 => ( ( binary1217730267_wrm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = T1 ) )
% 2.59/1.55 & ( ( T2 != binary476621312_Tip_a )
% 2.59/1.55 => ( ( binary1217730267_wrm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( binary717961607le_T_a @ T1 @ X @ ( binary1217730267_wrm_a @ H @ T2 ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_17_Tree_Oinduct,axiom,
% 2.59/1.55 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 2.59/1.55 ( ( P @ binary476621312_Tip_a )
% 2.59/1.55 => ( ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
% 2.59/1.55 ( ( P @ X1 )
% 2.59/1.55 => ( ( P @ X3 )
% 2.59/1.55 => ( P @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) ) ) )
% 2.59/1.55 => ( P @ Tree ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_18_Tree_Oexhaust,axiom,
% 2.59/1.55 ! [Y: binary1439146945Tree_a] :
% 2.59/1.55 ( ( Y != binary476621312_Tip_a )
% 2.59/1.55 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 2.59/1.55 ( Y
% 2.59/1.55 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_19_rm__set,axiom,
% 2.59/1.55 ! [T: binary1439146945Tree_a,H: a > int] :
% 2.59/1.55 ( ( ( T != binary476621312_Tip_a )
% 2.59/1.55 & ( binary1721989714Tree_a @ H @ T ) )
% 2.59/1.55 => ( member_a @ ( binary339557810e_rm_a @ H @ T ) @ ( binary945792244etOf_a @ T ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_20_rm_Osimps,axiom,
% 2.59/1.55 ! [T2: binary1439146945Tree_a,H: a > int,T1: binary1439146945Tree_a,X: a] :
% 2.59/1.55 ( ( ( T2 = binary476621312_Tip_a )
% 2.59/1.55 => ( ( binary339557810e_rm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = X ) )
% 2.59/1.55 & ( ( T2 != binary476621312_Tip_a )
% 2.59/1.55 => ( ( binary339557810e_rm_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( binary339557810e_rm_a @ H @ T2 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_21_wrm__set1,axiom,
% 2.59/1.55 ! [T: binary1439146945Tree_a,H: a > int] :
% 2.59/1.55 ( ( ( T != binary476621312_Tip_a )
% 2.59/1.55 & ( binary1721989714Tree_a @ H @ T ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( binary945792244etOf_a @ ( binary1217730267_wrm_a @ H @ T ) ) @ ( binary945792244etOf_a @ T ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 2.59/1.55 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.59/1.55 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( ( binary1721989714Tree_a @ H @ T1 )
% 2.59/1.55 & ! [X4: a] :
% 2.59/1.55 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 2.59/1.55 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X ) ) )
% 2.59/1.55 & ! [X4: a] :
% 2.59/1.55 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 2.59/1.55 => ( ord_less_int @ ( H @ X ) @ ( H @ X4 ) ) )
% 2.59/1.55 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_23_remove_Osimps_I1_J,axiom,
% 2.59/1.55 ! [H: a > int,E: a] :
% 2.59/1.55 ( ( binary1804682569move_a @ H @ E @ binary476621312_Tip_a )
% 2.59/1.55 = binary476621312_Tip_a ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_24_binsert_Osimps_I2_J,axiom,
% 2.59/1.55 ! [H: a > int,E: a,X: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 2.59/1.55 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 2.59/1.55 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( binary717961607le_T_a @ ( binary1226383794sert_a @ H @ E @ T1 ) @ X @ T2 ) ) )
% 2.59/1.55 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 2.59/1.55 => ( ( ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 2.59/1.55 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( binary717961607le_T_a @ T1 @ X @ ( binary1226383794sert_a @ H @ E @ T2 ) ) ) )
% 2.59/1.55 & ( ~ ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 2.59/1.55 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.55 = ( binary717961607le_T_a @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_25_setOf_Osimps_I1_J,axiom,
% 2.59/1.55 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 2.59/1.55 = bot_bot_set_a ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_26_empty__subsetI,axiom,
% 2.59/1.55 ! [A3: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A3 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_27_subset__empty,axiom,
% 2.59/1.55 ! [A3: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A3 @ bot_bot_set_a )
% 2.59/1.55 = ( A3 = bot_bot_set_a ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_28_subset__antisym,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B3 @ A3 )
% 2.59/1.55 => ( A3 = B3 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_29_subsetI,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a] :
% 2.59/1.55 ( ! [X5: a] :
% 2.59/1.55 ( ( member_a @ X5 @ A3 )
% 2.59/1.55 => ( member_a @ X5 @ B3 ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_30_empty__Collect__eq,axiom,
% 2.59/1.55 ! [P: a > $o] :
% 2.59/1.55 ( ( bot_bot_set_a
% 2.59/1.55 = ( collect_a @ P ) )
% 2.59/1.55 = ( ! [X4: a] :
% 2.59/1.55 ~ ( P @ X4 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_31_Collect__empty__eq,axiom,
% 2.59/1.55 ! [P: a > $o] :
% 2.59/1.55 ( ( ( collect_a @ P )
% 2.59/1.55 = bot_bot_set_a )
% 2.59/1.55 = ( ! [X4: a] :
% 2.59/1.55 ~ ( P @ X4 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_32_all__not__in__conv,axiom,
% 2.59/1.55 ! [A3: set_a] :
% 2.59/1.55 ( ( ! [X4: a] :
% 2.59/1.55 ~ ( member_a @ X4 @ A3 ) )
% 2.59/1.55 = ( A3 = bot_bot_set_a ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_33_empty__iff,axiom,
% 2.59/1.55 ! [C: a] :
% 2.59/1.55 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_34_bot__apply,axiom,
% 2.59/1.55 ( bot_bot_a_o
% 2.59/1.55 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_35_order__refl,axiom,
% 2.59/1.55 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_36_order__refl,axiom,
% 2.59/1.55 ! [X: a > $o] : ( ord_less_eq_a_o @ X @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_37_bot__set__def,axiom,
% 2.59/1.55 ( bot_bot_set_a
% 2.59/1.55 = ( collect_a @ bot_bot_a_o ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_38_le__funD,axiom,
% 2.59/1.55 ! [F: a > $o,G: a > $o,X: a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ F @ G )
% 2.59/1.55 => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_39_le__funE,axiom,
% 2.59/1.55 ! [F: a > $o,G: a > $o,X: a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ F @ G )
% 2.59/1.55 => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_40_le__funI,axiom,
% 2.59/1.55 ! [F: a > $o,G: a > $o] :
% 2.59/1.55 ( ! [X5: a] : ( ord_less_eq_o @ ( F @ X5 ) @ ( G @ X5 ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ F @ G ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_41_mem__Collect__eq,axiom,
% 2.59/1.55 ! [A2: a,P: a > $o] :
% 2.59/1.55 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 2.59/1.55 = ( P @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_42_Collect__mem__eq,axiom,
% 2.59/1.55 ! [A3: set_a] :
% 2.59/1.55 ( ( collect_a
% 2.59/1.55 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.59/1.55 = A3 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_43_Collect__cong,axiom,
% 2.59/1.55 ! [P: a > $o,Q: a > $o] :
% 2.59/1.55 ( ! [X5: a] :
% 2.59/1.55 ( ( P @ X5 )
% 2.59/1.55 = ( Q @ X5 ) )
% 2.59/1.55 => ( ( collect_a @ P )
% 2.59/1.55 = ( collect_a @ Q ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_44_le__fun__def,axiom,
% 2.59/1.55 ( ord_less_eq_a_o
% 2.59/1.55 = ( ^ [F2: a > $o,G2: a > $o] :
% 2.59/1.55 ! [X4: a] : ( ord_less_eq_o @ ( F2 @ X4 ) @ ( G2 @ X4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_45_order__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_46_order__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_47_order__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_48_order__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_49_order__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_50_order__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_51_order__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_52_order__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_53_ord__eq__le__subst,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_54_ord__eq__le__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_55_ord__eq__le__subst,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_56_ord__eq__le__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_57_ord__le__eq__subst,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_58_ord__le__eq__subst,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_59_ord__le__eq__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_60_ord__le__eq__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_61_eq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [X4: set_a,Y4: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 2.59/1.55 & ( ord_less_eq_set_a @ Y4 @ X4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_62_eq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [X4: a > $o,Y4: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 2.59/1.55 & ( ord_less_eq_a_o @ Y4 @ X4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_63_antisym,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ Y @ X )
% 2.59/1.55 => ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_64_antisym,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ Y @ X )
% 2.59/1.55 => ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_65_eq__refl,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( X = Y )
% 2.59/1.55 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_66_eq__refl,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( X = Y )
% 2.59/1.55 => ( ord_less_eq_a_o @ X @ Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_67_order_Otrans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_68_order_Otrans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_69_antisym__conv,axiom,
% 2.59/1.55 ! [Y: set_a,X: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ Y @ X )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.55 = ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_70_antisym__conv,axiom,
% 2.59/1.55 ! [Y: a > $o,X: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ Y @ X )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.55 = ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_71_order__class_Oorder_Oeq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [A: set_a,B: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A @ B )
% 2.59/1.55 & ( ord_less_eq_set_a @ B @ A ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_72_order__class_Oorder_Oeq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [A: a > $o,B: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A @ B )
% 2.59/1.55 & ( ord_less_eq_a_o @ B @ A ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_73_ord__eq__le__trans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2 = B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_74_ord__eq__le__trans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2 = B2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_75_ord__le__eq__trans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( B2 = C )
% 2.59/1.55 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_76_ord__le__eq__trans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( B2 = C )
% 2.59/1.55 => ( ord_less_eq_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_77_order__class_Oorder_Oantisym,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.59/1.55 => ( A2 = B2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_78_order__class_Oorder_Oantisym,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ A2 )
% 2.59/1.55 => ( A2 = B2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_79_order__trans,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_80_order__trans,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ Y @ Z2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ X @ Z2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_81_dual__order_Orefl,axiom,
% 2.59/1.55 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_82_dual__order_Orefl,axiom,
% 2.59/1.55 ! [A2: a > $o] : ( ord_less_eq_a_o @ A2 @ A2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_83_dual__order_Otrans,axiom,
% 2.59/1.55 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ C @ B2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ C @ A2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_84_dual__order_Otrans,axiom,
% 2.59/1.55 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ C @ B2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ C @ A2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_85_dual__order_Oeq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [A: set_a,B: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ B @ A )
% 2.59/1.55 & ( ord_less_eq_set_a @ A @ B ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_86_dual__order_Oeq__iff,axiom,
% 2.59/1.55 ( ( ^ [Y3: a > $o,Z: a > $o] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [A: a > $o,B: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ B @ A )
% 2.59/1.55 & ( ord_less_eq_a_o @ A @ B ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_87_dual__order_Oantisym,axiom,
% 2.59/1.55 ! [B2: set_a,A2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( A2 = B2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_88_dual__order_Oantisym,axiom,
% 2.59/1.55 ! [B2: a > $o,A2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( A2 = B2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_89_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_90_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_91_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_92_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_93_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_94_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_95_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_96_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_97_ord__eq__less__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2
% 2.59/1.55 = ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_98_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_99_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_100_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_101_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_102_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_103_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_104_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_105_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_106_ord__less__eq__subst,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ( F @ B2 )
% 2.59/1.55 = C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_107_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_108_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_109_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_110_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_111_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_112_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_113_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_114_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_115_order__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_116_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_117_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_118_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_119_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_120_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_121_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_122_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_123_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_124_order__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_125_lt__ex,axiom,
% 2.59/1.55 ! [X: int] :
% 2.59/1.55 ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_126_gt__ex,axiom,
% 2.59/1.55 ! [X: int] :
% 2.59/1.55 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_127_neqE,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( X != Y )
% 2.59/1.55 => ( ~ ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_128_neq__iff,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( X != Y )
% 2.59/1.55 = ( ( ord_less_int @ X @ Y )
% 2.59/1.55 | ( ord_less_int @ Y @ X ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_129_order_Oasym,axiom,
% 2.59/1.55 ! [A2: int,B2: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_130_order_Oasym,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_131_order_Oasym,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_132_less__imp__neq,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_133_less__imp__neq,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_134_less__imp__neq,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_135_less__asym,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_136_less__asym,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_137_less__asym,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_138_less__asym_H,axiom,
% 2.59/1.55 ! [A2: int,B2: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_139_less__asym_H,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_140_less__asym_H,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_141_less__trans,axiom,
% 2.59/1.55 ! [X: int,Y: int,Z2: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( ( ord_less_int @ Y @ Z2 )
% 2.59/1.55 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_142_less__trans,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ( ( ord_less_set_a @ Y @ Z2 )
% 2.59/1.55 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_143_less__trans,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ( ( ord_less_a_o @ Y @ Z2 )
% 2.59/1.55 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_144_less__linear,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 | ( X = Y )
% 2.59/1.55 | ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_145_less__irrefl,axiom,
% 2.59/1.55 ! [X: int] :
% 2.59/1.55 ~ ( ord_less_int @ X @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_146_less__irrefl,axiom,
% 2.59/1.55 ! [X: set_a] :
% 2.59/1.55 ~ ( ord_less_set_a @ X @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_147_less__irrefl,axiom,
% 2.59/1.55 ! [X: a > $o] :
% 2.59/1.55 ~ ( ord_less_a_o @ X @ X ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_148_ord__eq__less__trans,axiom,
% 2.59/1.55 ! [A2: int,B2: int,C: int] :
% 2.59/1.55 ( ( A2 = B2 )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_149_ord__eq__less__trans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( A2 = B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_150_ord__eq__less__trans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( A2 = B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_151_ord__less__eq__trans,axiom,
% 2.59/1.55 ! [A2: int,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( B2 = C )
% 2.59/1.55 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_152_ord__less__eq__trans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( B2 = C )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_153_ord__less__eq__trans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( B2 = C )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_154_dual__order_Oasym,axiom,
% 2.59/1.55 ! [B2: int,A2: int] :
% 2.59/1.55 ( ( ord_less_int @ B2 @ A2 )
% 2.59/1.55 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_155_dual__order_Oasym,axiom,
% 2.59/1.55 ! [B2: set_a,A2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ B2 @ A2 )
% 2.59/1.55 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_156_dual__order_Oasym,axiom,
% 2.59/1.55 ! [B2: a > $o,A2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ B2 @ A2 )
% 2.59/1.55 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_157_less__imp__not__eq,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_158_less__imp__not__eq,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_159_less__imp__not__eq,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ( X != Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_160_less__not__sym,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_161_less__not__sym,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_162_less__not__sym,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_163_antisym__conv3,axiom,
% 2.59/1.55 ! [Y: int,X: int] :
% 2.59/1.55 ( ~ ( ord_less_int @ Y @ X )
% 2.59/1.55 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.59/1.55 = ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_164_less__imp__not__eq2,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( Y != X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_165_less__imp__not__eq2,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ( Y != X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_166_less__imp__not__eq2,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ( Y != X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_167_less__imp__triv,axiom,
% 2.59/1.55 ! [X: int,Y: int,P: $o] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( ( ord_less_int @ Y @ X )
% 2.59/1.55 => P ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_168_less__imp__triv,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a,P: $o] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ( ( ord_less_set_a @ Y @ X )
% 2.59/1.55 => P ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_169_less__imp__triv,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o,P: $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ( ( ord_less_a_o @ Y @ X )
% 2.59/1.55 => P ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_170_linorder__cases,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ~ ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( ( X != Y )
% 2.59/1.55 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_171_dual__order_Oirrefl,axiom,
% 2.59/1.55 ! [A2: int] :
% 2.59/1.55 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_172_dual__order_Oirrefl,axiom,
% 2.59/1.55 ! [A2: set_a] :
% 2.59/1.55 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_173_dual__order_Oirrefl,axiom,
% 2.59/1.55 ! [A2: a > $o] :
% 2.59/1.55 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_174_order_Ostrict__trans,axiom,
% 2.59/1.55 ! [A2: int,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_175_order_Ostrict__trans,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_176_order_Ostrict__trans,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_177_less__imp__not__less,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ord_less_int @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_178_less__imp__not__less,axiom,
% 2.59/1.55 ! [X: set_a,Y: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_179_less__imp__not__less,axiom,
% 2.59/1.55 ! [X: a > $o,Y: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.55 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_180_linorder__less__wlog,axiom,
% 2.59/1.55 ! [P: int > int > $o,A2: int,B2: int] :
% 2.59/1.55 ( ! [A4: int,B4: int] :
% 2.59/1.55 ( ( ord_less_int @ A4 @ B4 )
% 2.59/1.55 => ( P @ A4 @ B4 ) )
% 2.59/1.55 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 2.59/1.55 => ( ! [A4: int,B4: int] :
% 2.59/1.55 ( ( P @ B4 @ A4 )
% 2.59/1.55 => ( P @ A4 @ B4 ) )
% 2.59/1.55 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_181_dual__order_Ostrict__trans,axiom,
% 2.59/1.55 ! [B2: int,A2: int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_int @ C @ B2 )
% 2.59/1.55 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_182_dual__order_Ostrict__trans,axiom,
% 2.59/1.55 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_set_a @ C @ B2 )
% 2.59/1.55 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_183_dual__order_Ostrict__trans,axiom,
% 2.59/1.55 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ B2 @ A2 )
% 2.59/1.55 => ( ( ord_less_a_o @ C @ B2 )
% 2.59/1.55 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_184_not__less__iff__gr__or__eq,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.59/1.55 = ( ( ord_less_int @ Y @ X )
% 2.59/1.55 | ( X = Y ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_185_order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [A2: int,B2: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_186_order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_187_order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_188_dual__order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [B2: int,A2: int] :
% 2.59/1.55 ( ( ord_less_int @ B2 @ A2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_189_dual__order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [B2: set_a,A2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ B2 @ A2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_190_dual__order_Ostrict__implies__not__eq,axiom,
% 2.59/1.55 ! [B2: a > $o,A2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ B2 @ A2 )
% 2.59/1.55 => ( A2 != B2 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_191_bot__fun__def,axiom,
% 2.59/1.55 ( bot_bot_a_o
% 2.59/1.55 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_192_emptyE,axiom,
% 2.59/1.55 ! [A2: a] :
% 2.59/1.55 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_193_equals0D,axiom,
% 2.59/1.55 ! [A3: set_a,A2: a] :
% 2.59/1.55 ( ( A3 = bot_bot_set_a )
% 2.59/1.55 => ~ ( member_a @ A2 @ A3 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_194_equals0I,axiom,
% 2.59/1.55 ! [A3: set_a] :
% 2.59/1.55 ( ! [Y2: a] :
% 2.59/1.55 ~ ( member_a @ Y2 @ A3 )
% 2.59/1.55 => ( A3 = bot_bot_set_a ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_195_ex__in__conv,axiom,
% 2.59/1.55 ! [A3: set_a] :
% 2.59/1.55 ( ( ? [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.59/1.55 = ( A3 != bot_bot_set_a ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_196_in__mono,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a,X: a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.55 => ( ( member_a @ X @ A3 )
% 2.59/1.55 => ( member_a @ X @ B3 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_197_subsetD,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a,C: a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.55 => ( ( member_a @ C @ A3 )
% 2.59/1.55 => ( member_a @ C @ B3 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_198_equalityE,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a] :
% 2.59/1.55 ( ( A3 = B3 )
% 2.59/1.55 => ~ ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.55 => ~ ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_199_subset__eq,axiom,
% 2.59/1.55 ( ord_less_eq_set_a
% 2.59/1.55 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.55 ! [X4: a] :
% 2.59/1.55 ( ( member_a @ X4 @ A5 )
% 2.59/1.55 => ( member_a @ X4 @ B5 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_200_equalityD1,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a] :
% 2.59/1.55 ( ( A3 = B3 )
% 2.59/1.55 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_201_equalityD2,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a] :
% 2.59/1.55 ( ( A3 = B3 )
% 2.59/1.55 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_202_subset__iff,axiom,
% 2.59/1.55 ( ord_less_eq_set_a
% 2.59/1.55 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.55 ! [T3: a] :
% 2.59/1.55 ( ( member_a @ T3 @ A5 )
% 2.59/1.55 => ( member_a @ T3 @ B5 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_203_subset__refl,axiom,
% 2.59/1.55 ! [A3: set_a] : ( ord_less_eq_set_a @ A3 @ A3 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_204_Collect__mono,axiom,
% 2.59/1.55 ! [P: a > $o,Q: a > $o] :
% 2.59/1.55 ( ! [X5: a] :
% 2.59/1.55 ( ( P @ X5 )
% 2.59/1.55 => ( Q @ X5 ) )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_205_subset__trans,axiom,
% 2.59/1.55 ! [A3: set_a,B3: set_a,C2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ A3 @ C2 ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_206_set__eq__subset,axiom,
% 2.59/1.55 ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
% 2.59/1.55 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.59/1.55 & ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_207_Collect__mono__iff,axiom,
% 2.59/1.55 ! [P: a > $o,Q: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 2.59/1.55 = ( ! [X4: a] :
% 2.59/1.55 ( ( P @ X4 )
% 2.59/1.55 => ( Q @ X4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_208_empty__def,axiom,
% 2.59/1.55 ( bot_bot_set_a
% 2.59/1.55 = ( collect_a
% 2.59/1.55 @ ^ [X4: a] : $false ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_209_Collect__subset,axiom,
% 2.59/1.55 ! [A3: set_a,P: a > $o] :
% 2.59/1.55 ( ord_less_eq_set_a
% 2.59/1.55 @ ( collect_a
% 2.59/1.55 @ ^ [X4: a] :
% 2.59/1.55 ( ( member_a @ X4 @ A3 )
% 2.59/1.55 & ( P @ X4 ) ) )
% 2.59/1.55 @ A3 ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_210_leD,axiom,
% 2.59/1.55 ! [Y: int,X: int] :
% 2.59/1.55 ( ( ord_less_eq_int @ Y @ X )
% 2.59/1.55 => ~ ( ord_less_int @ X @ Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_211_leD,axiom,
% 2.59/1.55 ! [Y: set_a,X: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ Y @ X )
% 2.59/1.55 => ~ ( ord_less_set_a @ X @ Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_212_leD,axiom,
% 2.59/1.55 ! [Y: a > $o,X: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ Y @ X )
% 2.59/1.55 => ~ ( ord_less_a_o @ X @ Y ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_213_leI,axiom,
% 2.59/1.55 ! [X: int,Y: int] :
% 2.59/1.55 ( ~ ( ord_less_int @ X @ Y )
% 2.59/1.55 => ( ord_less_eq_int @ Y @ X ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_214_le__less,axiom,
% 2.59/1.55 ( ord_less_eq_int
% 2.59/1.55 = ( ^ [X4: int,Y4: int] :
% 2.59/1.55 ( ( ord_less_int @ X4 @ Y4 )
% 2.59/1.55 | ( X4 = Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_215_le__less,axiom,
% 2.59/1.55 ( ord_less_eq_set_a
% 2.59/1.55 = ( ^ [X4: set_a,Y4: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X4 @ Y4 )
% 2.59/1.55 | ( X4 = Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_216_le__less,axiom,
% 2.59/1.55 ( ord_less_eq_a_o
% 2.59/1.55 = ( ^ [X4: a > $o,Y4: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X4 @ Y4 )
% 2.59/1.55 | ( X4 = Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_217_less__le,axiom,
% 2.59/1.55 ( ord_less_int
% 2.59/1.55 = ( ^ [X4: int,Y4: int] :
% 2.59/1.55 ( ( ord_less_eq_int @ X4 @ Y4 )
% 2.59/1.55 & ( X4 != Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_218_less__le,axiom,
% 2.59/1.55 ( ord_less_set_a
% 2.59/1.55 = ( ^ [X4: set_a,Y4: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 2.59/1.55 & ( X4 != Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_219_less__le,axiom,
% 2.59/1.55 ( ord_less_a_o
% 2.59/1.55 = ( ^ [X4: a > $o,Y4: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 2.59/1.55 & ( X4 != Y4 ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_220_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_221_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_222_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_223_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_224_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_225_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_226_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_227_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_228_order__le__less__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_229_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_230_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_231_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_232_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_233_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_234_order__le__less__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_235_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_236_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_237_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_eq_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_238_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_239_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_240_order__less__le__subst1,axiom,
% 2.59/1.55 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.59/1.55 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_eq_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_eq_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_241_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_242_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_243_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.55 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_244_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: int,Y2: int] :
% 2.59/1.55 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_245_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 2.59/1.55 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.55 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.55 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.55
% 2.59/1.55 thf(fact_246_order__less__le__subst2,axiom,
% 2.59/1.55 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.59/1.55 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.55 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 2.59/1.56 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.56 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.56 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_247_order__less__le__subst2,axiom,
% 2.59/1.56 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 2.59/1.56 => ( ! [X5: int,Y2: int] :
% 2.59/1.56 ( ( ord_less_int @ X5 @ Y2 )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_248_order__less__le__subst2,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 2.59/1.56 => ( ! [X5: set_a,Y2: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ X5 @ Y2 )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_249_order__less__le__subst2,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ ( F @ B2 ) @ C )
% 2.59/1.56 => ( ! [X5: a > $o,Y2: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ X5 @ Y2 )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ X5 ) @ ( F @ Y2 ) ) )
% 2.59/1.56 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_250_not__le,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 2.59/1.56 = ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_251_not__less,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.59/1.56 = ( ord_less_eq_int @ Y @ X ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_252_le__neq__trans,axiom,
% 2.59/1.56 ! [A2: int,B2: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.59/1.56 => ( ( A2 != B2 )
% 2.59/1.56 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_253_le__neq__trans,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ( A2 != B2 )
% 2.59/1.56 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_254_le__neq__trans,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ( A2 != B2 )
% 2.59/1.56 => ( ord_less_a_o @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_255_antisym__conv1,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ~ ( ord_less_int @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_int @ X @ Y )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_256_antisym__conv1,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a] :
% 2.59/1.56 ( ~ ( ord_less_set_a @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_257_antisym__conv1,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o] :
% 2.59/1.56 ( ~ ( ord_less_a_o @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_258_antisym__conv2,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ X @ Y )
% 2.59/1.56 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_259_antisym__conv2,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.56 => ( ( ~ ( ord_less_set_a @ X @ Y ) )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_260_antisym__conv2,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.56 => ( ( ~ ( ord_less_a_o @ X @ Y ) )
% 2.59/1.56 = ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_261_less__imp__le,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ord_less_int @ X @ Y )
% 2.59/1.56 => ( ord_less_eq_int @ X @ Y ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_262_less__imp__le,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.56 => ( ord_less_eq_set_a @ X @ Y ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_263_less__imp__le,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.56 => ( ord_less_eq_a_o @ X @ Y ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_264_le__less__trans,axiom,
% 2.59/1.56 ! [X: int,Y: int,Z2: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ X @ Y )
% 2.59/1.56 => ( ( ord_less_int @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_265_le__less__trans,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.56 => ( ( ord_less_set_a @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_266_le__less__trans,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.56 => ( ( ord_less_a_o @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_267_less__le__trans,axiom,
% 2.59/1.56 ! [X: int,Y: int,Z2: int] :
% 2.59/1.56 ( ( ord_less_int @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_int @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_268_less__le__trans,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a,Z2: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_set_a @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_269_less__le__trans,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o,Z2: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ X @ Y )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ Y @ Z2 )
% 2.59/1.56 => ( ord_less_a_o @ X @ Z2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_270_le__less__linear,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ X @ Y )
% 2.59/1.56 | ( ord_less_int @ Y @ X ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_271_le__imp__less__or__eq,axiom,
% 2.59/1.56 ! [X: int,Y: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ X @ Y )
% 2.59/1.56 => ( ( ord_less_int @ X @ Y )
% 2.59/1.56 | ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_272_le__imp__less__or__eq,axiom,
% 2.59/1.56 ! [X: set_a,Y: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ X @ Y )
% 2.59/1.56 => ( ( ord_less_set_a @ X @ Y )
% 2.59/1.56 | ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_273_le__imp__less__or__eq,axiom,
% 2.59/1.56 ! [X: a > $o,Y: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ X @ Y )
% 2.59/1.56 => ( ( ord_less_a_o @ X @ Y )
% 2.59/1.56 | ( X = Y ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_274_less__le__not__le,axiom,
% 2.59/1.56 ( ord_less_int
% 2.59/1.56 = ( ^ [X4: int,Y4: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ X4 @ Y4 )
% 2.59/1.56 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_275_less__le__not__le,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [X4: set_a,Y4: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ X4 @ Y4 )
% 2.59/1.56 & ~ ( ord_less_eq_set_a @ Y4 @ X4 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_276_less__le__not__le,axiom,
% 2.59/1.56 ( ord_less_a_o
% 2.59/1.56 = ( ^ [X4: a > $o,Y4: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ X4 @ Y4 )
% 2.59/1.56 & ~ ( ord_less_eq_a_o @ Y4 @ X4 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_277_not__le__imp__less,axiom,
% 2.59/1.56 ! [Y: int,X: int] :
% 2.59/1.56 ( ~ ( ord_less_eq_int @ Y @ X )
% 2.59/1.56 => ( ord_less_int @ X @ Y ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_278_order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [A2: int,B2: int,C: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_int @ B2 @ C )
% 2.59/1.56 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_279_order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_set_a @ B2 @ C )
% 2.59/1.56 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_280_order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_a_o @ B2 @ C )
% 2.59/1.56 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_281_order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [A2: int,B2: int,C: int] :
% 2.59/1.56 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_int @ B2 @ C )
% 2.59/1.56 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_282_order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ B2 @ C )
% 2.59/1.56 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_283_order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ B2 @ C )
% 2.59/1.56 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_284_order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_int
% 2.59/1.56 = ( ^ [A: int,B: int] :
% 2.59/1.56 ( ( ord_less_int @ A @ B )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_285_order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_set_a
% 2.59/1.56 = ( ^ [A: set_a,B: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A @ B )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_286_order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_a_o
% 2.59/1.56 = ( ^ [A: a > $o,B: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ A @ B )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_287_order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_int
% 2.59/1.56 = ( ^ [A: int,B: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ A @ B )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_288_order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [A: set_a,B: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A @ B )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_289_order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_a_o
% 2.59/1.56 = ( ^ [A: a > $o,B: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ A @ B )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_290_dual__order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [B2: int,A2: int,C: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_int @ C @ B2 )
% 2.59/1.56 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_291_dual__order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_set_a @ C @ B2 )
% 2.59/1.56 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_292_dual__order_Ostrict__trans1,axiom,
% 2.59/1.56 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_a_o @ C @ B2 )
% 2.59/1.56 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_293_dual__order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [B2: int,A2: int,C: int] :
% 2.59/1.56 ( ( ord_less_int @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_eq_int @ C @ B2 )
% 2.59/1.56 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_294_dual__order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ C @ B2 )
% 2.59/1.56 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_295_dual__order_Ostrict__trans2,axiom,
% 2.59/1.56 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ B2 @ A2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ C @ B2 )
% 2.59/1.56 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_296_order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [A2: int,B2: int] :
% 2.59/1.56 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_eq_int @ A2 @ B2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_297_order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_298_order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_eq_a_o @ A2 @ B2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_299_dual__order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_int
% 2.59/1.56 = ( ^ [B: int,A: int] :
% 2.59/1.56 ( ( ord_less_int @ B @ A )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_300_dual__order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_set_a
% 2.59/1.56 = ( ^ [B: set_a,A: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ B @ A )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_301_dual__order_Oorder__iff__strict,axiom,
% 2.59/1.56 ( ord_less_eq_a_o
% 2.59/1.56 = ( ^ [B: a > $o,A: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ B @ A )
% 2.59/1.56 | ( A = B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_302_dual__order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_int
% 2.59/1.56 = ( ^ [B: int,A: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ B @ A )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_303_dual__order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [B: set_a,A: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ B @ A )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_304_dual__order_Ostrict__iff__order,axiom,
% 2.59/1.56 ( ord_less_a_o
% 2.59/1.56 = ( ^ [B: a > $o,A: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ B @ A )
% 2.59/1.56 & ( A != B ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_305_dual__order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [B2: int,A2: int] :
% 2.59/1.56 ( ( ord_less_int @ B2 @ A2 )
% 2.59/1.56 => ( ord_less_eq_int @ B2 @ A2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_306_dual__order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [B2: set_a,A2: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ B2 @ A2 )
% 2.59/1.56 => ( ord_less_eq_set_a @ B2 @ A2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_307_dual__order_Ostrict__implies__order,axiom,
% 2.59/1.56 ! [B2: a > $o,A2: a > $o] :
% 2.59/1.56 ( ( ord_less_a_o @ B2 @ A2 )
% 2.59/1.56 => ( ord_less_eq_a_o @ B2 @ A2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_308_order_Onot__eq__order__implies__strict,axiom,
% 2.59/1.56 ! [A2: int,B2: int] :
% 2.59/1.56 ( ( A2 != B2 )
% 2.59/1.56 => ( ( ord_less_eq_int @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_int @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_309_order_Onot__eq__order__implies__strict,axiom,
% 2.59/1.56 ! [A2: set_a,B2: set_a] :
% 2.59/1.56 ( ( A2 != B2 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_310_order_Onot__eq__order__implies__strict,axiom,
% 2.59/1.56 ! [A2: a > $o,B2: a > $o] :
% 2.59/1.56 ( ( A2 != B2 )
% 2.59/1.56 => ( ( ord_less_eq_a_o @ A2 @ B2 )
% 2.59/1.56 => ( ord_less_a_o @ A2 @ B2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_311_bot_Oextremum,axiom,
% 2.59/1.56 ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_312_bot_Oextremum,axiom,
% 2.59/1.56 ! [A2: a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A2 ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_313_bot_Oextremum__unique,axiom,
% 2.59/1.56 ! [A2: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 2.59/1.56 = ( A2 = bot_bot_set_a ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_314_bot_Oextremum__unique,axiom,
% 2.59/1.56 ! [A2: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ A2 @ bot_bot_a_o )
% 2.59/1.56 = ( A2 = bot_bot_a_o ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_315_bot_Oextremum__uniqueI,axiom,
% 2.59/1.56 ! [A2: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
% 2.59/1.56 => ( A2 = bot_bot_set_a ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_316_bot_Oextremum__uniqueI,axiom,
% 2.59/1.56 ! [A2: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ A2 @ bot_bot_a_o )
% 2.59/1.56 => ( A2 = bot_bot_a_o ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_317_bot_Oextremum__strict,axiom,
% 2.59/1.56 ! [A2: set_a] :
% 2.59/1.56 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_318_bot_Oextremum__strict,axiom,
% 2.59/1.56 ! [A2: a > $o] :
% 2.59/1.56 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_319_bot_Onot__eq__extremum,axiom,
% 2.59/1.56 ! [A2: set_a] :
% 2.59/1.56 ( ( A2 != bot_bot_set_a )
% 2.59/1.56 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_320_bot_Onot__eq__extremum,axiom,
% 2.59/1.56 ! [A2: a > $o] :
% 2.59/1.56 ( ( A2 != bot_bot_a_o )
% 2.59/1.56 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_321_subset__emptyI,axiom,
% 2.59/1.56 ! [A3: set_a] :
% 2.59/1.56 ( ! [X5: a] :
% 2.59/1.56 ~ ( member_a @ X5 @ A3 )
% 2.59/1.56 => ( ord_less_eq_set_a @ A3 @ bot_bot_set_a ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_322_minf_I8_J,axiom,
% 2.59/1.56 ! [T: int] :
% 2.59/1.56 ? [Z3: int] :
% 2.59/1.56 ! [X6: int] :
% 2.59/1.56 ( ( ord_less_int @ X6 @ Z3 )
% 2.59/1.56 => ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_323_minf_I6_J,axiom,
% 2.59/1.56 ! [T: int] :
% 2.59/1.56 ? [Z3: int] :
% 2.59/1.56 ! [X6: int] :
% 2.59/1.56 ( ( ord_less_int @ X6 @ Z3 )
% 2.59/1.56 => ( ord_less_eq_int @ X6 @ T ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_324_pinf_I8_J,axiom,
% 2.59/1.56 ! [T: int] :
% 2.59/1.56 ? [Z3: int] :
% 2.59/1.56 ! [X6: int] :
% 2.59/1.56 ( ( ord_less_int @ Z3 @ X6 )
% 2.59/1.56 => ( ord_less_eq_int @ T @ X6 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_325_pinf_I6_J,axiom,
% 2.59/1.56 ! [T: int] :
% 2.59/1.56 ? [Z3: int] :
% 2.59/1.56 ! [X6: int] :
% 2.59/1.56 ( ( ord_less_int @ Z3 @ X6 )
% 2.59/1.56 => ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_326_verit__comp__simplify1_I3_J,axiom,
% 2.59/1.56 ! [B6: int,A6: int] :
% 2.59/1.56 ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 2.59/1.56 = ( ord_less_int @ A6 @ B6 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_327_complete__interval,axiom,
% 2.59/1.56 ! [A2: int,B2: int,P: int > $o] :
% 2.59/1.56 ( ( ord_less_int @ A2 @ B2 )
% 2.59/1.56 => ( ( P @ A2 )
% 2.59/1.56 => ( ~ ( P @ B2 )
% 2.59/1.56 => ? [C3: int] :
% 2.59/1.56 ( ( ord_less_eq_int @ A2 @ C3 )
% 2.59/1.56 & ( ord_less_eq_int @ C3 @ B2 )
% 2.59/1.56 & ! [X6: int] :
% 2.59/1.56 ( ( ( ord_less_eq_int @ A2 @ X6 )
% 2.59/1.56 & ( ord_less_int @ X6 @ C3 ) )
% 2.59/1.56 => ( P @ X6 ) )
% 2.59/1.56 & ! [D: int] :
% 2.59/1.56 ( ! [X5: int] :
% 2.59/1.56 ( ( ( ord_less_eq_int @ A2 @ X5 )
% 2.59/1.56 & ( ord_less_int @ X5 @ D ) )
% 2.59/1.56 => ( P @ X5 ) )
% 2.59/1.56 => ( ord_less_eq_int @ D @ C3 ) ) ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_328_bot_Oordering__top__axioms,axiom,
% 2.59/1.56 ( ordering_top_set_a
% 2.59/1.56 @ ^ [X4: set_a,Y4: set_a] : ( ord_less_eq_set_a @ Y4 @ X4 )
% 2.59/1.56 @ ^ [X4: set_a,Y4: set_a] : ( ord_less_set_a @ Y4 @ X4 )
% 2.59/1.56 @ bot_bot_set_a ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_329_bot_Oordering__top__axioms,axiom,
% 2.59/1.56 ( ordering_top_a_o
% 2.59/1.56 @ ^ [X4: a > $o,Y4: a > $o] : ( ord_less_eq_a_o @ Y4 @ X4 )
% 2.59/1.56 @ ^ [X4: a > $o,Y4: a > $o] : ( ord_less_a_o @ Y4 @ X4 )
% 2.59/1.56 @ bot_bot_a_o ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_330_psubsetI,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ( A3 != B3 )
% 2.59/1.56 => ( ord_less_set_a @ A3 @ B3 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_331_less__fun__def,axiom,
% 2.59/1.56 ( ord_less_a_o
% 2.59/1.56 = ( ^ [F2: a > $o,G2: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_a_o @ F2 @ G2 )
% 2.59/1.56 & ~ ( ord_less_eq_a_o @ G2 @ F2 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_332_not__psubset__empty,axiom,
% 2.59/1.56 ! [A3: set_a] :
% 2.59/1.56 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_333_subset__iff__psubset__eq,axiom,
% 2.59/1.56 ( ord_less_eq_set_a
% 2.59/1.56 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A5 @ B5 )
% 2.59/1.56 | ( A5 = B5 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_334_subset__psubset__trans,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a,C2: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ( ord_less_set_a @ B3 @ C2 )
% 2.59/1.56 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_335_subset__not__subset__eq,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.59/1.56 & ~ ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_336_psubset__subset__trans,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a,C2: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ B3 @ C2 )
% 2.59/1.56 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_337_psubset__imp__subset,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_338_psubset__eq,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ A5 @ B5 )
% 2.59/1.56 & ( A5 != B5 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_339_psubsetE,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a] :
% 2.59/1.56 ( ( ord_less_set_a @ A3 @ B3 )
% 2.59/1.56 => ~ ( ( ord_less_eq_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_340_less__eq__set__def,axiom,
% 2.59/1.56 ( ord_less_eq_set_a
% 2.59/1.56 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.56 ( ord_less_eq_a_o
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_341_verit__comp__simplify1_I1_J,axiom,
% 2.59/1.56 ! [A2: set_a] :
% 2.59/1.56 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_342_verit__comp__simplify1_I1_J,axiom,
% 2.59/1.56 ! [A2: a > $o] :
% 2.59/1.56 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_343_prop__restrict,axiom,
% 2.59/1.56 ! [X: a,Z4: set_a,X7: set_a,P: a > $o] :
% 2.59/1.56 ( ( member_a @ X @ Z4 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ Z4
% 2.59/1.56 @ ( collect_a
% 2.59/1.56 @ ^ [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ X7 )
% 2.59/1.56 & ( P @ X4 ) ) ) )
% 2.59/1.56 => ( P @ X ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_344_Collect__restrict,axiom,
% 2.59/1.56 ! [X7: set_a,P: a > $o] :
% 2.59/1.56 ( ord_less_eq_set_a
% 2.59/1.56 @ ( collect_a
% 2.59/1.56 @ ^ [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ X7 )
% 2.59/1.56 & ( P @ X4 ) ) )
% 2.59/1.56 @ X7 ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_345_bot__empty__eq,axiom,
% 2.59/1.56 ( bot_bot_a_o
% 2.59/1.56 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_346_less__set__def,axiom,
% 2.59/1.56 ( ord_less_set_a
% 2.59/1.56 = ( ^ [A5: set_a,B5: set_a] :
% 2.59/1.56 ( ord_less_a_o
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_347_psubsetD,axiom,
% 2.59/1.56 ! [A3: set_a,B3: set_a,C: a] :
% 2.59/1.56 ( ( ord_less_set_a @ A3 @ B3 )
% 2.59/1.56 => ( ( member_a @ C @ A3 )
% 2.59/1.56 => ( member_a @ C @ B3 ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_348_pred__subset__eq,axiom,
% 2.59/1.56 ! [R: set_a,S: set_a] :
% 2.59/1.56 ( ( ord_less_eq_a_o
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 2.59/1.56 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 2.59/1.56 = ( ord_less_eq_set_a @ R @ S ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_349_subset__Collect__iff,axiom,
% 2.59/1.56 ! [B3: set_a,A3: set_a,P: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 2.59/1.56 => ( ( ord_less_eq_set_a @ B3
% 2.59/1.56 @ ( collect_a
% 2.59/1.56 @ ^ [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ A3 )
% 2.59/1.56 & ( P @ X4 ) ) ) )
% 2.59/1.56 = ( ! [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ B3 )
% 2.59/1.56 => ( P @ X4 ) ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_350_subset__CollectI,axiom,
% 2.59/1.56 ! [B3: set_a,A3: set_a,Q: a > $o,P: a > $o] :
% 2.59/1.56 ( ( ord_less_eq_set_a @ B3 @ A3 )
% 2.59/1.56 => ( ! [X5: a] :
% 2.59/1.56 ( ( member_a @ X5 @ B3 )
% 2.59/1.56 => ( ( Q @ X5 )
% 2.59/1.56 => ( P @ X5 ) ) )
% 2.59/1.56 => ( ord_less_eq_set_a
% 2.59/1.56 @ ( collect_a
% 2.59/1.56 @ ^ [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ B3 )
% 2.59/1.56 & ( Q @ X4 ) ) )
% 2.59/1.56 @ ( collect_a
% 2.59/1.56 @ ^ [X4: a] :
% 2.59/1.56 ( ( member_a @ X4 @ A3 )
% 2.59/1.56 & ( P @ X4 ) ) ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_351_remove_Osimps_I2_J,axiom,
% 2.59/1.56 ! [H: a > int,E: a,X: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 2.59/1.56 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 2.59/1.56 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.56 = ( binary717961607le_T_a @ ( binary1804682569move_a @ H @ E @ T1 ) @ X @ T2 ) ) )
% 2.59/1.56 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X ) )
% 2.59/1.56 => ( ( ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 2.59/1.56 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.56 = ( binary717961607le_T_a @ T1 @ X @ ( binary1804682569move_a @ H @ E @ T2 ) ) ) )
% 2.59/1.56 & ( ~ ( ord_less_int @ ( H @ X ) @ ( H @ E ) )
% 2.59/1.56 => ( ( ( T1 = binary476621312_Tip_a )
% 2.59/1.56 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.56 = T2 ) )
% 2.59/1.56 & ( ( T1 != binary476621312_Tip_a )
% 2.59/1.56 => ( ( binary1804682569move_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.59/1.56 = ( produc1275654896Tree_a
% 2.59/1.56 @ ^ [T1p: binary1439146945Tree_a,R2: a] : ( binary717961607le_T_a @ T1p @ R2 @ T2 )
% 2.59/1.56 @ ( binary1774981152rmrm_a @ H @ T1 ) ) ) ) ) ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(fact_352_wrmrm__decomp,axiom,
% 2.59/1.56 ! [T: binary1439146945Tree_a,H: a > int] :
% 2.59/1.56 ( ( T != binary476621312_Tip_a )
% 2.59/1.56 => ( ( binary1774981152rmrm_a @ H @ T )
% 2.59/1.56 = ( produc374321428ee_a_a @ ( binary1217730267_wrm_a @ H @ T ) @ ( binary339557810e_rm_a @ H @ T ) ) ) ) ).
% 2.59/1.56
% 2.59/1.56 thf(conj_0,conjecture,
% 2.59/1.56 binary1721989714Tree_a @ h @ t1 ).
% 2.59/1.56 ------------------------
% 2.59/1.59 % (22382)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_21808 for (2999ds/4Mi)
% 2.59/1.59 % (22383)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_21808 for (2999ds/27Mi)
% 2.59/1.59 % (22381)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/183Mi)
% 2.59/1.59 % (22382)Instruction limit reached!
% 2.59/1.59 % (22382)------------------------------
% 2.59/1.59 % (22382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.59 % (22382)Termination reason: Unknown
% 2.59/1.59 % (22382)Termination phase: shuffling
% 2.59/1.59
% 2.59/1.59 % (22382)Memory used [KB]: 1407
% 2.59/1.59 % (22382)Time elapsed: 0.003 s
% 2.59/1.59 % (22382)Instructions burned: 5 (million)
% 2.59/1.59 % (22382)------------------------------
% 2.59/1.59 % (22382)------------------------------
% 2.59/1.60 % (22384)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/2Mi)
% 2.59/1.60 % (22385)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_21808 for (2999ds/2Mi)
% 2.59/1.60 % (22386)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_21808 for (2999ds/275Mi)
% 2.59/1.60 % (22387)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/18Mi)
% 2.65/1.60 % (22383)Instruction limit reached!
% 2.65/1.60 % (22383)------------------------------
% 2.65/1.60 % (22383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (22383)Termination reason: Unknown
% 2.65/1.60 % (22383)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (22383)Memory used [KB]: 1918
% 2.65/1.60 % (22383)Time elapsed: 0.011 s
% 2.65/1.60 % (22383)Instructions burned: 28 (million)
% 2.65/1.60 % (22383)------------------------------
% 2.65/1.60 % (22383)------------------------------
% 2.65/1.60 % (22384)Instruction limit reached!
% 2.65/1.60 % (22384)------------------------------
% 2.65/1.60 % (22384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (22384)Termination reason: Unknown
% 2.65/1.60 % (22384)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (22384)Memory used [KB]: 1407
% 2.65/1.60 % (22384)Time elapsed: 0.004 s
% 2.65/1.60 % (22384)Instructions burned: 3 (million)
% 2.65/1.60 % (22384)------------------------------
% 2.65/1.60 % (22384)------------------------------
% 2.65/1.60 % (22385)Instruction limit reached!
% 2.65/1.60 % (22385)------------------------------
% 2.65/1.60 % (22385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (22385)Termination reason: Unknown
% 2.65/1.60 % (22385)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (22385)Memory used [KB]: 1407
% 2.65/1.60 % (22385)Time elapsed: 0.004 s
% 2.65/1.60 % (22385)Instructions burned: 3 (million)
% 2.65/1.60 % (22385)------------------------------
% 2.65/1.60 % (22385)------------------------------
% 2.65/1.60 % (22392)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/3Mi)
% 2.65/1.60 % (22392)Instruction limit reached!
% 2.65/1.60 % (22392)------------------------------
% 2.65/1.60 % (22392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (22392)Termination reason: Unknown
% 2.65/1.60 % (22392)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (22392)Memory used [KB]: 1407
% 2.65/1.60 % (22392)Time elapsed: 0.002 s
% 2.65/1.60 % (22392)Instructions burned: 3 (million)
% 2.65/1.60 % (22392)------------------------------
% 2.65/1.60 % (22392)------------------------------
% 2.65/1.61 % (22387)Instruction limit reached!
% 2.65/1.61 % (22387)------------------------------
% 2.65/1.61 % (22387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.61 % (22387)Termination reason: Unknown
% 2.65/1.61 % (22387)Termination phase: shuffling
% 2.65/1.61
% 2.65/1.61 % (22387)Memory used [KB]: 1663
% 2.65/1.61 % (22387)Time elapsed: 0.014 s
% 2.65/1.61 % (22387)Instructions burned: 19 (million)
% 2.65/1.61 % (22387)------------------------------
% 2.65/1.61 % (22387)------------------------------
% 2.65/1.61 % (22401)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_21808 for (2999ds/1041Mi)
% 2.65/1.61 % (22397)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_21808 for (2999ds/37Mi)
% 2.65/1.61 % (22398)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_21808 for (2999ds/15Mi)
% 2.65/1.61 % (22399)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_21808 for (2999ds/3Mi)
% 2.65/1.62 % (22399)Instruction limit reached!
% 2.65/1.62 % (22399)------------------------------
% 2.65/1.62 % (22399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.62 % (22399)Termination reason: Unknown
% 2.65/1.62 % (22399)Termination phase: shuffling
% 2.65/1.62
% 2.65/1.62 % (22399)Memory used [KB]: 1407
% 2.65/1.62 % (22399)Time elapsed: 0.004 s
% 2.65/1.62 % (22399)Instructions burned: 3 (million)
% 2.65/1.62 % (22399)------------------------------
% 2.65/1.62 % (22399)------------------------------
% 2.65/1.62 % (22398)Instruction limit reached!
% 2.65/1.62 % (22398)------------------------------
% 2.65/1.62 % (22398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.62 % (22398)Termination reason: Unknown
% 2.65/1.62 % (22398)Termination phase: shuffling
% 2.65/1.62
% 2.65/1.62 % (22398)Memory used [KB]: 1663
% 2.65/1.62 % (22398)Time elapsed: 0.011 s
% 2.65/1.62 % (22398)Instructions burned: 15 (million)
% 2.65/1.62 % (22398)------------------------------
% 2.65/1.62 % (22398)------------------------------
% 2.65/1.63 % (22406)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/7Mi)
% 2.65/1.63 % (22386)Refutation not found, incomplete strategy
% 2.65/1.63 % (22386)------------------------------
% 2.65/1.63 % (22386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (22386)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.63
% 2.65/1.63
% 2.65/1.63 % (22386)Memory used [KB]: 6524
% 2.65/1.63 % (22386)Time elapsed: 0.033 s
% 2.65/1.63 % (22386)Instructions burned: 54 (million)
% 2.65/1.63 % (22386)------------------------------
% 2.65/1.63 % (22386)------------------------------
% 2.65/1.63 % (22406)Instruction limit reached!
% 2.65/1.63 % (22406)------------------------------
% 2.65/1.63 % (22406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (22406)Termination reason: Unknown
% 2.65/1.63 % (22406)Termination phase: shuffling
% 2.65/1.63
% 2.65/1.63 % (22406)Memory used [KB]: 1535
% 2.65/1.63 % (22406)Time elapsed: 0.007 s
% 2.65/1.63 % (22406)Instructions burned: 8 (million)
% 2.65/1.63 % (22406)------------------------------
% 2.65/1.63 % (22406)------------------------------
% 2.65/1.63 % (22397)Instruction limit reached!
% 2.65/1.63 % (22397)------------------------------
% 2.65/1.63 % (22397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (22397)Termination reason: Unknown
% 2.65/1.63 % (22397)Termination phase: shuffling
% 2.65/1.63
% 2.65/1.63 % (22397)Memory used [KB]: 2174
% 2.65/1.63 % (22397)Time elapsed: 0.021 s
% 2.65/1.63 % (22397)Instructions burned: 37 (million)
% 2.65/1.63 % (22397)------------------------------
% 2.65/1.63 % (22397)------------------------------
% 2.65/1.63 % (22410)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/16Mi)
% 2.65/1.64 % (22381)Instruction limit reached!
% 2.65/1.64 % (22381)------------------------------
% 2.65/1.64 % (22381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (22381)Termination reason: Unknown
% 2.65/1.64 % (22381)Termination phase: Property scanning
% 2.65/1.64
% 2.65/1.64 % (22381)Memory used [KB]: 2814
% 2.65/1.64 % (22381)Time elapsed: 0.050 s
% 2.65/1.64 % (22381)Instructions burned: 183 (million)
% 2.65/1.64 % (22381)------------------------------
% 2.65/1.64 % (22381)------------------------------
% 2.65/1.64 % (22410)Instruction limit reached!
% 2.65/1.64 % (22410)------------------------------
% 2.65/1.64 % (22410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (22410)Termination reason: Unknown
% 2.65/1.64 % (22410)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (22410)Memory used [KB]: 1663
% 2.65/1.64 % (22410)Time elapsed: 0.010 s
% 2.65/1.64 % (22410)Instructions burned: 17 (million)
% 2.65/1.64 % (22410)------------------------------
% 2.65/1.64 % (22410)------------------------------
% 2.65/1.64 % (22414)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_21808 for (2999ds/3Mi)
% 2.65/1.64 % (22414)Instruction limit reached!
% 2.65/1.64 % (22414)------------------------------
% 2.65/1.64 % (22414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (22414)Termination reason: Unknown
% 2.65/1.64 % (22414)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (22414)Memory used [KB]: 1407
% 2.65/1.64 % (22414)Time elapsed: 0.004 s
% 2.65/1.64 % (22414)Instructions burned: 3 (million)
% 2.65/1.64 % (22414)------------------------------
% 2.65/1.64 % (22414)------------------------------
% 2.65/1.64 % (22415)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_21808 for (2999ds/3Mi)
% 2.65/1.65 % (22423)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/4Mi)
% 2.65/1.65 % (22415)Instruction limit reached!
% 2.65/1.65 % (22415)------------------------------
% 2.65/1.65 % (22415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (22415)Termination reason: Unknown
% 2.65/1.65 % (22415)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (22415)Memory used [KB]: 1407
% 2.65/1.65 % (22415)Time elapsed: 0.004 s
% 2.65/1.65 % (22415)Instructions burned: 3 (million)
% 2.65/1.65 % (22415)------------------------------
% 2.65/1.65 % (22415)------------------------------
% 2.65/1.65 % (22417)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/7Mi)
% 2.65/1.65 % (22423)Instruction limit reached!
% 2.65/1.65 % (22423)------------------------------
% 2.65/1.65 % (22423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (22423)Termination reason: Unknown
% 2.65/1.65 % (22423)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (22423)Memory used [KB]: 1407
% 2.65/1.65 % (22423)Time elapsed: 0.003 s
% 2.65/1.65 % (22423)Instructions burned: 6 (million)
% 2.65/1.65 % (22423)------------------------------
% 2.65/1.65 % (22423)------------------------------
% 2.65/1.65 % (22420)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/3Mi)
% 2.65/1.65 % (22425)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/18Mi)
% 2.65/1.65 % (22417)Instruction limit reached!
% 2.65/1.65 % (22417)------------------------------
% 2.65/1.65 % (22417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (22417)Termination reason: Unknown
% 2.65/1.65 % (22417)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (22417)Memory used [KB]: 1535
% 2.65/1.65 % (22417)Time elapsed: 0.007 s
% 2.65/1.65 % (22417)Instructions burned: 8 (million)
% 2.65/1.65 % (22417)------------------------------
% 2.65/1.65 % (22417)------------------------------
% 2.65/1.65 % (22420)Instruction limit reached!
% 2.65/1.65 % (22420)------------------------------
% 2.65/1.65 % (22420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (22420)Termination reason: Unknown
% 2.65/1.65 % (22420)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (22420)Memory used [KB]: 1407
% 2.65/1.65 % (22420)Time elapsed: 0.004 s
% 2.65/1.65 % (22420)Instructions burned: 4 (million)
% 2.65/1.65 % (22420)------------------------------
% 2.65/1.65 % (22420)------------------------------
% 2.65/1.66 % (22430)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_21808 for (2999ds/902Mi)
% 2.65/1.66 % (22427)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/710Mi)
% 2.65/1.66 % (22425)Instruction limit reached!
% 2.65/1.66 % (22425)------------------------------
% 2.65/1.66 % (22425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.66 % (22425)Termination reason: Unknown
% 2.65/1.66 % (22425)Termination phase: shuffling
% 2.65/1.66
% 2.65/1.66 % (22425)Memory used [KB]: 1663
% 2.65/1.66 % (22425)Time elapsed: 0.008 s
% 2.65/1.66 % (22425)Instructions burned: 19 (million)
% 2.65/1.66 % (22425)------------------------------
% 2.65/1.66 % (22425)------------------------------
% 2.65/1.66 % (22429)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/6Mi)
% 2.65/1.67 % (22429)Instruction limit reached!
% 2.65/1.67 % (22429)------------------------------
% 2.65/1.67 % (22429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (22429)Termination reason: Unknown
% 2.65/1.67 % (22429)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (22429)Memory used [KB]: 1535
% 2.65/1.67 % (22429)Time elapsed: 0.006 s
% 2.65/1.67 % (22429)Instructions burned: 6 (million)
% 2.65/1.67 % (22429)------------------------------
% 2.65/1.67 % (22429)------------------------------
% 2.65/1.67 % (22438)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_21808 for (2999ds/6Mi)
% 2.65/1.67 % (22433)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_21808 for (2999ds/21Mi)
% 2.65/1.67 % (22434)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/5Mi)
% 2.65/1.67 % (22438)Instruction limit reached!
% 2.65/1.67 % (22438)------------------------------
% 2.65/1.67 % (22438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (22438)Termination reason: Unknown
% 2.65/1.67 % (22438)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (22438)Memory used [KB]: 1535
% 2.65/1.67 % (22438)Time elapsed: 0.004 s
% 2.65/1.67 % (22438)Instructions burned: 7 (million)
% 2.65/1.67 % (22438)------------------------------
% 2.65/1.67 % (22438)------------------------------
% 2.65/1.67 % (22434)Instruction limit reached!
% 2.65/1.67 % (22434)------------------------------
% 2.65/1.67 % (22434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (22434)Termination reason: Unknown
% 2.65/1.67 % (22434)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (22434)Memory used [KB]: 1407
% 2.65/1.67 % (22434)Time elapsed: 0.005 s
% 2.65/1.67 % (22434)Instructions burned: 6 (million)
% 2.65/1.67 % (22434)------------------------------
% 2.65/1.67 % (22434)------------------------------
% 2.65/1.68 % (22427)First to succeed.
% 2.65/1.68 % (22443)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21808 for (2999ds/377Mi)
% 2.65/1.68 % (22427)Refutation found. Thanks to Tanya!
% 2.65/1.68 % SZS status Theorem for DTF2THF_21808
% 2.65/1.68 % SZS output start Proof for DTF2THF_21808
% 2.65/1.68 thf(type_def_5, type, binary1439146945Tree_a: $tType).
% 2.65/1.68 thf(type_def_6, type, a: $tType).
% 2.65/1.68 thf(type_def_8, type, int: $tType).
% 2.65/1.68 thf(type_def_9, type, set_a: $tType).
% 2.65/1.68 thf(type_def_10, type, produc376588196ee_a_a: $tType).
% 2.65/1.68 thf(func_def_0, type, produc376588196ee_a_a: $tType).
% 2.65/1.68 thf(func_def_1, type, binary1439146945Tree_a: $tType).
% 2.65/1.68 thf(func_def_2, type, set_a: $tType).
% 2.65/1.68 thf(func_def_3, type, int: $tType).
% 2.65/1.68 thf(func_def_4, type, a: $tType).
% 2.65/1.68 thf(func_def_5, type, binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_6, type, binary476621312_Tip_a: binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_7, type, binary1226383794sert_a: (a > int) > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_8, type, binary2053421120memb_a: (a > int) > a > binary1439146945Tree_a > $o).
% 2.65/1.68 thf(func_def_9, type, binary1804682569move_a: (a > int) > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_10, type, binary339557810e_rm_a: (a > int) > binary1439146945Tree_a > a).
% 2.65/1.68 thf(func_def_11, type, binary945792244etOf_a: binary1439146945Tree_a > set_a).
% 2.65/1.68 thf(func_def_12, type, binary1721989714Tree_a: (a > int) > binary1439146945Tree_a > $o).
% 2.65/1.68 thf(func_def_13, type, binary670562003pred_a: (a > int) > a > a > binary1439146945Tree_a > $o).
% 2.65/1.68 thf(func_def_14, type, binary1217730267_wrm_a: (a > int) > binary1439146945Tree_a > binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_15, type, binary1774981152rmrm_a: (a > int) > binary1439146945Tree_a > produc376588196ee_a_a).
% 2.65/1.68 thf(func_def_16, type, bot_bot_a_o: a > $o).
% 2.65/1.68 thf(func_def_18, type, bot_bot_set_a: set_a).
% 2.65/1.68 thf(func_def_19, type, ord_less_a_o: (a > $o) > (a > $o) > $o).
% 2.65/1.68 thf(func_def_20, type, ord_less_int: int > int > $o).
% 2.65/1.68 thf(func_def_21, type, ord_less_set_a: set_a > set_a > $o).
% 2.65/1.68 thf(func_def_22, type, ord_less_eq_a_o: (a > $o) > (a > $o) > $o).
% 2.65/1.68 thf(func_def_23, type, ord_less_eq_o: $o > $o > $o).
% 2.65/1.68 thf(func_def_24, type, ord_less_eq_int: int > int > $o).
% 2.65/1.68 thf(func_def_25, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.65/1.68 thf(func_def_26, type, ordering_top_a_o: ((a > $o) > (a > $o) > $o) > ((a > $o) > (a > $o) > $o) > (a > $o) > $o).
% 2.65/1.68 thf(func_def_27, type, ordering_top_set_a: (set_a > set_a > $o) > (set_a > set_a > $o) > set_a > $o).
% 2.65/1.68 thf(func_def_28, type, produc374321428ee_a_a: binary1439146945Tree_a > a > produc376588196ee_a_a).
% 2.65/1.68 thf(func_def_29, type, produc1275654896Tree_a: (binary1439146945Tree_a > a > binary1439146945Tree_a) > produc376588196ee_a_a > binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_30, type, collect_a: (a > $o) > set_a).
% 2.65/1.68 thf(func_def_31, type, member_a: a > set_a > $o).
% 2.65/1.68 thf(func_def_32, type, h: a > int).
% 2.65/1.68 thf(func_def_33, type, t1: binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_34, type, t2: binary1439146945Tree_a).
% 2.65/1.68 thf(func_def_35, type, x: a).
% 2.65/1.68 thf(func_def_51, type, ph1: !>[X0: $tType]:(X0)).
% 2.65/1.68 thf(f1077,plain,(
% 2.65/1.68 $false),
% 2.65/1.68 inference(subsumption_resolution,[status(thm)],[f1076,f1050])).
% 2.65/1.68 thf(f1050,plain,(
% 2.65/1.68 ((binary1721989714Tree_a @ h @ t1) != $true)),
% 2.65/1.68 inference(cnf_transformation,[status(thm)],[f1039])).
% 2.65/1.68 thf(f1039,plain,(
% 2.65/1.68 ((binary1721989714Tree_a @ h @ t1) != $true)),
% 2.65/1.68 inference(flattening,[status(thm)],[f908])).
% 2.65/1.68 thf(f908,plain,(
% 2.65/1.68 ~((binary1721989714Tree_a @ h @ t1) = $true)),
% 2.65/1.68 inference(fool_elimination,[status(thm)],[f907])).
% 2.65/1.68 thf(f907,plain,(
% 2.65/1.68 ~(binary1721989714Tree_a @ h @ t1)),
% 2.65/1.68 inference(rectify,[status(thm)],[f355])).
% 2.65/1.68 thf(f355,negated_conjecture,(
% 2.65/1.68 ~(binary1721989714Tree_a @ h @ t1)),
% 2.65/1.68 inference(negated_conjecture,[status(cth)],[f354])).
% 2.65/1.68 thf(f354,conjecture,(
% 2.65/1.68 (binary1721989714Tree_a @ h @ t1)),
% 2.65/1.68 file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',conj_0)).
% 2.65/1.68 thf(f1076,plain,(
% 2.65/1.68 ((binary1721989714Tree_a @ h @ t1) = $true)),
% 2.65/1.68 inference(trivial_inequality_removal,[status(thm)],[f1075])).
% 2.65/1.68 thf(f1075,plain,(
% 2.65/1.68 ($true != $true) | ((binary1721989714Tree_a @ h @ t1) = $true)),
% 2.65/1.68 inference(superposition,[status(thm)],[f1056,f1052])).
% 2.65/1.68 thf(f1052,plain,(
% 2.65/1.68 ((binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = $true)),
% 2.65/1.68 inference(cnf_transformation,[status(thm)],[f788])).
% 2.65/1.68 thf(f788,plain,(
% 2.65/1.68 ((binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = $true)),
% 2.65/1.68 inference(fool_elimination,[status(thm)],[f787])).
% 2.65/1.68 thf(f787,plain,(
% 2.65/1.68 (binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))),
% 2.65/1.68 inference(rectify,[status(thm)],[f2])).
% 2.65/1.68 thf(f2,axiom,(
% 2.65/1.68 (binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))),
% 2.65/1.68 file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',fact_1_s)).
% 2.65/1.68 thf(f1056,plain,(
% 2.65/1.68 ( ! [X2 : a,X3 : a > int,X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a] : (((binary1721989714Tree_a @ X3 @ (binary717961607le_T_a @ X1 @ X2 @ X0)) != $true) | ((binary1721989714Tree_a @ X3 @ X1) = $true)) )),
% 2.65/1.68 inference(cnf_transformation,[status(thm)],[f1042])).
% 2.65/1.68 thf(f1042,plain,(
% 2.65/1.68 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a,X3 : a > int] : (((binary1721989714Tree_a @ X3 @ X1) = $true) | ((binary1721989714Tree_a @ X3 @ (binary717961607le_T_a @ X1 @ X2 @ X0)) != $true))),
% 2.65/1.68 inference(ennf_transformation,[status(thm)],[f416])).
% 2.65/1.68 thf(f416,plain,(
% 2.65/1.68 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a,X3 : a > int] : (((binary1721989714Tree_a @ X3 @ (binary717961607le_T_a @ X1 @ X2 @ X0)) = $true) => ((binary1721989714Tree_a @ X3 @ X1) = $true))),
% 2.65/1.68 inference(fool_elimination,[status(thm)],[f415])).
% 2.65/1.68 thf(f415,plain,(
% 2.65/1.68 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a,X3 : a > int] : ((binary1721989714Tree_a @ X3 @ (binary717961607le_T_a @ X1 @ X2 @ X0)) => (binary1721989714Tree_a @ X3 @ X1))),
% 2.65/1.68 inference(rectify,[status(thm)],[f4])).
% 2.65/1.68 thf(f4,axiom,(
% 2.65/1.68 ! [X3 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a,X0 : a > int] : ((binary1721989714Tree_a @ X0 @ (binary717961607le_T_a @ X1 @ X2 @ X3)) => (binary1721989714Tree_a @ X0 @ X1))),
% 2.65/1.68 file('/export/starexec/sandbox/tmp/tmp.1n6v1RiTxc/DTF2THF_21808.p',fact_3_sortLemmaL)).
% 2.65/1.68 % SZS output end Proof for DTF2THF_21808
% 2.65/1.68 % (22427)------------------------------
% 2.65/1.68 % (22427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.68 % (22427)Termination reason: Refutation
% 2.65/1.68
% 2.65/1.68 % (22427)Memory used [KB]: 6524
% 2.65/1.68 % (22427)Time elapsed: 0.021 s
% 2.65/1.68 % (22427)Instructions burned: 53 (million)
% 2.65/1.68 % (22427)------------------------------
% 2.65/1.68 % (22427)------------------------------
% 2.65/1.68 % (22370)Success in time 0.109 s
%------------------------------------------------------------------------------