%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP029^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 08:54:58 AM UTC 2026
% Result : ContradictoryAxioms 2.78s 1.74s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 31 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 77 ( 8 ~; 0 |; 9 &; 60 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 10 con; 0-4 aty)
% Number of variables : 10 ( 10 ^; 0 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
binary594033953_set_a: $tType ).
thf(type_def_6,type,
set_a: $tType ).
thf(type_def_8,type,
binary1439146945Tree_a: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(type_def_10,type,
set_set_a: $tType ).
thf(type_def_11,type,
int: $tType ).
thf(type_def_12,type,
set_set_set_a: $tType ).
thf(func_def_0,type,
binary594033953_set_a: $tType ).
thf(func_def_1,type,
binary1439146945Tree_a: $tType ).
thf(func_def_2,type,
set_set_set_a: $tType ).
thf(func_def_3,type,
set_set_a: $tType ).
thf(func_def_4,type,
set_a: $tType ).
thf(func_def_5,type,
int: $tType ).
thf(func_def_6,type,
a: $tType ).
thf(func_def_7,type,
binary313540327_set_a: binary594033953_set_a > set_a > binary594033953_set_a > binary594033953_set_a ).
thf(func_def_8,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_9,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(func_def_10,type,
binary1613048283_set_a: binary594033953_set_a > set_set_a ).
thf(func_def_11,type,
binary256242811Tree_a: binary1439146945Tree_a > set_a ).
thf(func_def_12,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(func_def_13,type,
binary1001944660_set_a: binary594033953_set_a > set_set_a ).
thf(func_def_14,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(func_def_15,type,
binary512218034_set_a: ( set_a > int ) > binary594033953_set_a > $o ).
thf(func_def_16,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(func_def_17,type,
binary1524747315_set_a: ( set_a > int ) > set_a > set_a > binary594033953_set_a > $o ).
thf(func_def_18,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(func_def_19,type,
the_a: ( a > $o ) > a ).
thf(func_def_20,type,
semila1223476304_a_a_o: ( ( a > a > $o ) > ( a > a > $o ) > a > a > $o ) > ( a > a > $o ) > $o ).
thf(func_def_21,type,
semila980155549tr_a_o: ( ( a > $o ) > ( a > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(func_def_22,type,
semila1409648192_set_a: ( set_a > set_a > set_a ) > set_a > $o ).
thf(func_def_23,type,
sup_su198629954et_a_o: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > set_a > $o ).
thf(func_def_24,type,
sup_sup_set_a_o: ( set_a > $o ) > ( set_a > $o ) > set_a > $o ).
thf(func_def_25,type,
sup_sup_a_a_o: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_26,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_27,type,
sup_sup_int: int > int > int ).
thf(func_def_28,type,
sup_sup_set_set_a: set_set_a > set_set_a > set_set_a ).
thf(func_def_29,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_30,type,
bot_bot_set_a_o: set_a > $o ).
thf(func_def_31,type,
bot_bot_a_a_o: a > a > $o ).
thf(func_def_32,type,
bot_bot_a_o: a > $o ).
thf(func_def_34,type,
bot_bot_set_set_a: set_set_a ).
thf(func_def_35,type,
bot_bot_set_a: set_a ).
thf(func_def_36,type,
ord_less_set_a_o: ( set_a > $o ) > ( set_a > $o ) > $o ).
thf(func_def_37,type,
ord_less_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(func_def_38,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_39,type,
ord_less_int: int > int > $o ).
thf(func_def_40,type,
ord_less_set_set_a: set_set_a > set_set_a > $o ).
thf(func_def_41,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_42,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_43,type,
powp_set_a: ( set_a > $o ) > set_set_a > $o ).
thf(func_def_44,type,
powp_a: ( a > $o ) > set_a > $o ).
thf(func_def_45,type,
collect_set_set_a: ( set_set_a > $o ) > set_set_set_a ).
thf(func_def_46,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(func_def_47,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_48,type,
pow_set_a: set_set_a > set_set_set_a ).
thf(func_def_49,type,
pow_a: set_a > set_set_a ).
thf(func_def_50,type,
insert_set_a: set_a > set_set_a > set_set_a ).
thf(func_def_51,type,
insert_a: a > set_a > set_a ).
thf(func_def_52,type,
is_empty_a: set_a > $o ).
thf(func_def_53,type,
is_singleton_set_a: set_set_a > $o ).
thf(func_def_54,type,
is_singleton_a: set_a > $o ).
thf(func_def_55,type,
the_elem_a: set_a > a ).
thf(func_def_56,type,
chains_a: set_set_a > set_set_set_a ).
thf(func_def_57,type,
pred_chain_set_a: set_set_a > ( set_a > set_a > $o ) > set_set_a > $o ).
thf(func_def_58,type,
pred_chain_a: set_a > ( a > a > $o ) > set_a > $o ).
thf(func_def_59,type,
member_set_set_a: set_set_a > set_set_set_a > $o ).
thf(func_def_60,type,
member_set_a: set_a > set_set_a > $o ).
thf(func_def_61,type,
member_a: a > set_a > $o ).
thf(func_def_62,type,
a2: a ).
thf(func_def_63,type,
b: a ).
thf(func_def_64,type,
h: a > int ).
thf(func_def_65,type,
t1: binary1439146945Tree_a ).
thf(func_def_66,type,
t2: binary1439146945Tree_a ).
thf(func_def_67,type,
x: a ).
thf(f1987,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1986]) ).
thf(f1986,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f1985]) ).
thf(f1985,plain,
( $true
= ( ( ( sup_sup_int @ ( h @ a2 ) @ ( h @ a2 ) )
= ( h @ a2 ) )
& $false ) ),
inference(boolean_simplification,[status(thm)],[f1984]) ).
thf(f1984,plain,
( $true
= ( ( ( sup_sup_int @ ( h @ a2 ) @ ( h @ a2 ) )
= ( h @ a2 ) )
& ~ $true ) ),
inference(boolean_simplification,[status(thm)],[f1980]) ).
thf(f1980,plain,
( $true
= ( ( ( sup_sup_int @ ( h @ a2 ) @ ( h @ a2 ) )
= ( h @ a2 ) )
& ( ( h @ a2 )
!= ( h @ a2 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1893,f1180]) ).
thf(f1180,plain,
( ( h @ a2 )
= ( h @ b ) ),
inference(cnf_transformation,[status(thm)],[f485]) ).
thf(f485,plain,
( ( h @ a2 )
= ( h @ b ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( h @ a2 )
= ( h @ b ) ),
file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_0_hahb) ).
thf(f1893,plain,
( $true
= ( ( ( sup_sup_int @ ( h @ a2 ) @ ( h @ b ) )
= ( h @ a2 ) )
& ( ( h @ b )
!= ( h @ a2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1655]) ).
thf(f1655,plain,
( $true
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) )
@ ( h @ b )
@ ( h @ a2 ) ) ),
inference(definition_unfolding,[status(thm)],[f1374,f1096]) ).
thf(f1096,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f499]) ).
thf(f499,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f498]) ).
thf(f498,plain,
( ( ^ [X0: int,X1: int] :
( ( X0 != X1 )
& ( ( sup_sup_int @ X1 @ X0 )
= X1 ) ) )
= ord_less_int ),
inference(rectify,[status(thm)],[f310]) ).
thf(f310,axiom,
( ( ^ [X22: int,X21: int] :
( ( X21 != X22 )
& ( ( sup_sup_int @ X21 @ X22 )
= X21 ) ) )
= ord_less_int ),
file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_309_sup_Ostrict__order__iff) ).
thf(f1374,plain,
( ( ord_less_int @ ( h @ b ) @ ( h @ a2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f685]) ).
thf(f685,plain,
( ( ord_less_int @ ( h @ b ) @ ( h @ a2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f684]) ).
thf(f684,plain,
ord_less_int @ ( h @ b ) @ ( h @ a2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
ord_less_int @ ( h @ b ) @ ( h @ a2 ),
file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP029^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 08:23:45 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : ITP029^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.47 % Domain : Interactive Theorem Proving
% 0.29/0.47 % Problem : Sledgehammer BinaryTree problem prob_163__3251696_1
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Des21]
% 0.29/0.47 % Names : BinaryTree/prob_163__3251696_1 [Des21]
% 0.29/0.47
% 0.29/0.47 % Status : ContradictoryAxioms
% 0.29/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.27 v7.5.0
% 0.29/0.47 % Syntax : Number of formulae : 419 ( 158 unt; 68 typ; 0 def)
% 0.29/0.47 % Number of atoms : 1066 ( 355 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 10 ( 3 avg)
% 0.29/0.47 % Number of connectives : 2657 ( 136 ~; 30 |; 62 &;2013 @)
% 0.29/0.47 % ( 0 <=>; 416 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 15 ( 6 avg)
% 0.29/0.47 % Number of types : 8 ( 7 usr)
% 0.29/0.47 % Number of type conns : 462 ( 462 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 63 ( 61 usr; 10 con; 0-4 aty)
% 0.29/0.47 % Number of variables : 1000 ( 102 ^; 862 !; 36 ?;1000 :)
% 0.29/0.47 % SPC : TH0_CAX_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:03.251
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % Could-be-implicit typings (7)
% 0.29/0.47 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 binary594033953_set_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 0.29/0.47 binary1439146945Tree_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.29/0.47 set_set_set_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 set_set_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 set_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Int__Oint,type,
% 0.29/0.47 int: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_tf__a,type,
% 0.29/0.47 a: $tType ).
% 0.29/0.47
% 0.29/0.47 % Explicit typings (61)
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 binary313540327_set_a: binary594033953_set_a > set_a > binary594033953_set_a > binary594033953_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 0.29/0.47 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 0.29/0.47 binary476621312_Tip_a: binary1439146945Tree_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 binary1613048283_set_a: binary594033953_set_a > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001tf__a,type,
% 0.29/0.47 binary256242811Tree_a: binary1439146945Tree_a > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001tf__a,type,
% 0.29/0.47 binary504661350_eqs_a: ( a > int ) > a > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 binary1001944660_set_a: binary594033953_set_a > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 0.29/0.47 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 binary512218034_set_a: ( set_a > int ) > binary594033953_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 0.29/0.47 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 binary1524747315_set_a: ( set_a > int ) > set_a > set_a > binary594033953_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 0.29/0.47 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_HOL_OThe_001tf__a,type,
% 0.29/0.47 the_a: ( a > $o ) > a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osemilattice__neutr_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.29/0.47 semila1223476304_a_a_o: ( ( a > a > $o ) > ( a > a > $o ) > a > a > $o ) > ( a > a > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osemilattice__neutr_001_062_Itf__a_M_Eo_J,type,
% 0.29/0.47 semila980155549tr_a_o: ( ( a > $o ) > ( a > $o ) > a > $o ) > ( a > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 semila1409648192_set_a: ( set_a > set_a > set_a ) > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_Itf__a_J_M_062_It__Set__Oset_Itf__a_J_M_Eo_J_J,type,
% 0.29/0.47 sup_su198629954et_a_o: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 0.29/0.47 sup_sup_set_a_o: ( set_a > $o ) > ( set_a > $o ) > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.29/0.47 sup_sup_a_a_o: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
% 0.29/0.47 sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 0.29/0.47 sup_sup_int: int > int > int ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 sup_sup_set_set_a: set_set_a > set_set_a > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 sup_sup_set_a: set_a > set_a > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 0.29/0.47 bot_bot_set_a_o: set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.29/0.47 bot_bot_a_a_o: a > a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 0.29/0.47 bot_bot_a_o: a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.29/0.47 bot_bot_o: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 bot_bot_set_set_a: set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 bot_bot_set_a: set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 0.29/0.47 ord_less_set_a_o: ( set_a > $o ) > ( set_a > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 0.29/0.47 ord_less_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 0.29/0.47 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.29/0.47 ord_less_int: int > int > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 ord_less_set_set_a: set_set_a > set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 ord_less_set_a: set_a > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Relation_OPowp_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 powp_set_a: ( set_a > $o ) > set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Relation_OPowp_001tf__a,type,
% 0.29/0.47 powp_a: ( a > $o ) > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 collect_set_set_a: ( set_set_a > $o ) > set_set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 collect_set_a: ( set_a > $o ) > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.29/0.47 collect_a: ( a > $o ) > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OPow_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 pow_set_a: set_set_a > set_set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_OPow_001tf__a,type,
% 0.29/0.47 pow_a: set_a > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Oinsert_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 insert_set_a: set_a > set_set_a > set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.29/0.47 insert_a: a > set_a > set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Ois__empty_001tf__a,type,
% 0.29/0.47 is_empty_a: set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Ois__singleton_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 is_singleton_set_a: set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 0.29/0.47 is_singleton_a: set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Set_Othe__elem_001tf__a,type,
% 0.29/0.47 the_elem_a: set_a > a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Zorn_Ochains_001tf__a,type,
% 0.29/0.47 chains_a: set_set_a > set_set_set_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Zorn_Opred__on_Ochain_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 pred_chain_set_a: set_set_a > ( set_a > set_a > $o ) > set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Zorn_Opred__on_Ochain_001tf__a,type,
% 0.29/0.47 pred_chain_a: set_a > ( a > a > $o ) > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.29/0.47 member_set_set_a: set_set_a > set_set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 0.29/0.47 member_set_a: set_a > set_set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_member_001tf__a,type,
% 0.29/0.47 member_a: a > set_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_a,type,
% 0.29/0.47 a2: a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_b,type,
% 0.29/0.47 b: a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_h,type,
% 0.29/0.47 h: a > int ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_t1____,type,
% 0.29/0.47 t1: binary1439146945Tree_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_t2____,type,
% 0.29/0.47 t2: binary1439146945Tree_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_x____,type,
% 0.29/0.47 x: a ).
% 0.29/0.47
% 0.29/0.47 % Relevant facts (350)
% 0.29/0.47 thf(fact_0_hahb,axiom,
% 0.29/0.47 ( ( h @ a2 )
% 0.29/0.47 = ( h @ b ) ) ).
% 0.29/0.47
% 0.29/0.47 % hahb
% 0.29/0.47 thf(fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062,axiom,
% 0.29/0.47 ord_less_int @ ( h @ b ) @ ( h @ a2 ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>h b < h a\<close>
% 0.29/0.47 thf(fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 0.29/0.47 ( ( a2 = x )
% 0.29/0.47 => ( a2 = b ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>a = x \<Longrightarrow> a = b\<close>
% 0.29/0.47 thf(fact_3_adef1,axiom,
% 0.29/0.47 member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ).
% 0.29/0.47
% 0.29/0.47 % adef1
% 0.29/0.47 thf(fact_4_bdef1,axiom,
% 0.29/0.47 member_a @ b @ ( binary945792244etOf_a @ t1 ) ).
% 0.29/0.47
% 0.29/0.47 % bdef1
% 0.29/0.47 thf(fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 0.29/0.47 ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
% 0.29/0.47 => ( a2 = b ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>a \<in> setOf t1 \<Longrightarrow> a = b\<close>
% 0.29/0.47 thf(fact_6_o1,axiom,
% 0.29/0.47 ord_less_int @ ( h @ b ) @ ( h @ x ) ).
% 0.29/0.47
% 0.29/0.47 % o1
% 0.29/0.47 thf(fact_7_o2,axiom,
% 0.29/0.47 ord_less_int @ ( h @ x ) @ ( h @ a2 ) ).
% 0.29/0.47
% 0.29/0.47 % o2
% 0.29/0.47 thf(fact_8_h2,axiom,
% 0.29/0.47 binary670562003pred_a @ h @ a2 @ b @ t2 ).
% 0.29/0.47
% 0.29/0.47 % h2
% 0.29/0.47 thf(fact_9_h1,axiom,
% 0.29/0.47 binary670562003pred_a @ h @ a2 @ b @ t1 ).
% 0.29/0.47
% 0.29/0.47 % h1
% 0.29/0.47 thf(fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062,axiom,
% 0.29/0.47 binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a ).
% 0.29/0.47
% 0.29/0.47 % \<open>sorted_distinct_pred h a b Tip\<close>
% 0.29/0.47 thf(fact_11_calculation,axiom,
% 0.29/0.47 ( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
% 0.29/0.47 | ( b = x )
% 0.29/0.47 | ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % calculation
% 0.29/0.47 thf(fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062,axiom,
% 0.29/0.47 ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
% 0.29/0.47 | ( a2 = x )
% 0.29/0.47 | ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>a \<in> setOf t1 \<or> a = x \<or> a \<in> setOf t2\<close>
% 0.29/0.47 thf(fact_13_bdef,axiom,
% 0.29/0.47 member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % bdef
% 0.29/0.47 thf(fact_14_Tree_Oinject,axiom,
% 0.29/0.47 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 0.29/0.47 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 0.29/0.47 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 0.29/0.47 = ( ( X21 = Y21 )
% 0.29/0.47 & ( X22 = Y22 )
% 0.29/0.47 & ( X23 = Y23 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Tree.inject
% 0.29/0.47 thf(fact_15_adef,axiom,
% 0.29/0.47 member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % adef
% 0.29/0.47 thf(fact_16_s,axiom,
% 0.29/0.47 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 0.29/0.47
% 0.29/0.47 % s
% 0.29/0.47 thf(fact_17_Tree_Odistinct_I1_J,axiom,
% 0.29/0.47 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.29/0.47 ( binary476621312_Tip_a
% 0.29/0.47 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 0.29/0.47
% 0.29/0.47 % Tree.distinct(1)
% 0.29/0.47 thf(fact_18_Tree_Oinduct,axiom,
% 0.29/0.47 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 0.29/0.47 ( ( P @ binary476621312_Tip_a )
% 0.29/0.47 => ( ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
% 0.29/0.47 ( ( P @ X1 )
% 0.29/0.47 => ( ( P @ X3 )
% 0.29/0.47 => ( P @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) ) ) )
% 0.29/0.47 => ( P @ Tree ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Tree.induct
% 0.29/0.47 thf(fact_19_Tree_Oexhaust,axiom,
% 0.29/0.47 ! [Y: binary1439146945Tree_a] :
% 0.29/0.47 ( ( Y != binary476621312_Tip_a )
% 0.29/0.47 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 0.29/0.47 ( Y
% 0.29/0.47 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Tree.exhaust
% 0.29/0.47 thf(fact_20_s2,axiom,
% 0.29/0.47 binary1721989714Tree_a @ h @ t2 ).
% 0.29/0.47
% 0.29/0.47 % s2
% 0.29/0.47 thf(fact_21_s1,axiom,
% 0.29/0.47 binary1721989714Tree_a @ h @ t1 ).
% 0.29/0.47
% 0.29/0.47 % s1
% 0.29/0.47 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 0.29/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.29/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.29/0.47 = ( ( binary1721989714Tree_a @ H @ T1 )
% 0.29/0.47 & ! [X4: a] :
% 0.29/0.47 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 0.29/0.47 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X ) ) )
% 0.29/0.47 & ! [X4: a] :
% 0.29/0.47 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 0.29/0.47 => ( ord_less_int @ ( H @ X ) @ ( H @ X4 ) ) )
% 0.29/0.47 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sortedTree.simps(2)
% 0.29/0.47 thf(fact_23_sorted__distinct__pred__def,axiom,
% 0.29/0.47 ( binary1524747315_set_a
% 0.29/0.47 = ( ^ [H2: set_a > int,A: set_a,B: set_a,T: binary594033953_set_a] :
% 0.29/0.47 ( ( ( binary512218034_set_a @ H2 @ T )
% 0.29/0.47 & ( member_set_a @ A @ ( binary1001944660_set_a @ T ) )
% 0.29/0.47 & ( member_set_a @ B @ ( binary1001944660_set_a @ T ) )
% 0.29/0.47 & ( ( H2 @ A )
% 0.29/0.47 = ( H2 @ B ) ) )
% 0.29/0.47 => ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sorted_distinct_pred_def
% 0.29/0.47 thf(fact_24_sorted__distinct__pred__def,axiom,
% 0.29/0.47 ( binary670562003pred_a
% 0.29/0.47 = ( ^ [H2: a > int,A: a,B: a,T: binary1439146945Tree_a] :
% 0.29/0.47 ( ( ( binary1721989714Tree_a @ H2 @ T )
% 0.29/0.47 & ( member_a @ A @ ( binary945792244etOf_a @ T ) )
% 0.29/0.47 & ( member_a @ B @ ( binary945792244etOf_a @ T ) )
% 0.29/0.47 & ( ( H2 @ A )
% 0.29/0.47 = ( H2 @ B ) ) )
% 0.29/0.47 => ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sorted_distinct_pred_def
% 0.29/0.47 thf(fact_25_eqs__def,axiom,
% 0.29/0.47 ( binary504661350_eqs_a
% 0.29/0.47 = ( ^ [H2: a > int,X4: a] :
% 0.29/0.47 ( collect_a
% 0.29/0.47 @ ^ [Y2: a] :
% 0.29/0.47 ( ( H2 @ Y2 )
% 0.29/0.47 = ( H2 @ X4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eqs_def
% 0.29/0.47 thf(fact_26_minf_I7_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ~ ( ord_less_int @ T3 @ X5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(7)
% 0.29/0.47 thf(fact_27_minf_I5_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ( ord_less_int @ X5 @ T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(5)
% 0.29/0.47 thf(fact_28_minf_I4_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ( X5 != T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(4)
% 0.29/0.47 thf(fact_29_minf_I3_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ( X5 != T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(3)
% 0.29/0.47 thf(fact_30_minf_I2_J,axiom,
% 0.29/0.47 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.29/0.47 ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Z2 )
% 0.29/0.47 => ( ( P @ X6 )
% 0.29/0.47 = ( P2 @ X6 ) ) )
% 0.29/0.47 => ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Z2 )
% 0.29/0.47 => ( ( Q @ X6 )
% 0.29/0.47 = ( Q2 @ X6 ) ) )
% 0.29/0.47 => ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ( ( ( P @ X5 )
% 0.29/0.47 | ( Q @ X5 ) )
% 0.29/0.47 = ( ( P2 @ X5 )
% 0.29/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(2)
% 0.29/0.47 thf(fact_31_sortLemmaR,axiom,
% 0.29/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.29/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.29/0.47 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % sortLemmaR
% 0.29/0.47 thf(fact_32_sortLemmaL,axiom,
% 0.29/0.47 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.29/0.47 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.29/0.47 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 0.29/0.47
% 0.29/0.47 % sortLemmaL
% 0.29/0.47 thf(fact_33_sortedTree_Osimps_I1_J,axiom,
% 0.29/0.47 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 0.29/0.47
% 0.29/0.47 % sortedTree.simps(1)
% 0.29/0.47 thf(fact_34_pinf_I1_J,axiom,
% 0.29/0.47 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.29/0.47 ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ Z2 @ X6 )
% 0.29/0.47 => ( ( P @ X6 )
% 0.29/0.47 = ( P2 @ X6 ) ) )
% 0.29/0.47 => ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ Z2 @ X6 )
% 0.29/0.47 => ( ( Q @ X6 )
% 0.29/0.47 = ( Q2 @ X6 ) ) )
% 0.29/0.47 => ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ( ( ( P @ X5 )
% 0.29/0.47 & ( Q @ X5 ) )
% 0.29/0.47 = ( ( P2 @ X5 )
% 0.29/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(1)
% 0.29/0.47 thf(fact_35_pinf_I2_J,axiom,
% 0.29/0.47 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.29/0.47 ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ Z2 @ X6 )
% 0.29/0.47 => ( ( P @ X6 )
% 0.29/0.47 = ( P2 @ X6 ) ) )
% 0.29/0.47 => ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ Z2 @ X6 )
% 0.29/0.47 => ( ( Q @ X6 )
% 0.29/0.47 = ( Q2 @ X6 ) ) )
% 0.29/0.47 => ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ( ( ( P @ X5 )
% 0.29/0.47 | ( Q @ X5 ) )
% 0.29/0.47 = ( ( P2 @ X5 )
% 0.29/0.47 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(2)
% 0.29/0.47 thf(fact_36_pinf_I3_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ( X5 != T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(3)
% 0.29/0.47 thf(fact_37_pinf_I4_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ( X5 != T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(4)
% 0.29/0.47 thf(fact_38_pinf_I5_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ~ ( ord_less_int @ X5 @ T3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(5)
% 0.29/0.47 thf(fact_39_pinf_I7_J,axiom,
% 0.29/0.47 ! [T3: int] :
% 0.29/0.47 ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ Z @ X5 )
% 0.29/0.47 => ( ord_less_int @ T3 @ X5 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(7)
% 0.29/0.47 thf(fact_40_minf_I1_J,axiom,
% 0.29/0.47 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.29/0.47 ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Z2 )
% 0.29/0.47 => ( ( P @ X6 )
% 0.29/0.47 = ( P2 @ X6 ) ) )
% 0.29/0.47 => ( ? [Z2: int] :
% 0.29/0.47 ! [X6: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Z2 )
% 0.29/0.47 => ( ( Q @ X6 )
% 0.29/0.47 = ( Q2 @ X6 ) ) )
% 0.29/0.47 => ? [Z: int] :
% 0.29/0.47 ! [X5: int] :
% 0.29/0.47 ( ( ord_less_int @ X5 @ Z )
% 0.29/0.47 => ( ( ( P @ X5 )
% 0.29/0.47 & ( Q @ X5 ) )
% 0.29/0.47 = ( ( P2 @ X5 )
% 0.29/0.47 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(1)
% 0.29/0.47 thf(fact_41_linorder__neqE__linordered__idom,axiom,
% 0.29/0.47 ! [X: int,Y: int] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 => ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.47 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_neqE_linordered_idom
% 0.29/0.47 thf(fact_42_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [B2: set_a,A2: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ B2 @ A2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_not_eq
% 0.29/0.47 thf(fact_43_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [B2: a > $o,A2: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ B2 @ A2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_not_eq
% 0.29/0.47 thf(fact_44_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [B2: int,A2: int] :
% 0.29/0.47 ( ( ord_less_int @ B2 @ A2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_not_eq
% 0.29/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A2: set_a,P: set_a > $o] :
% 0.29/0.47 ( ( member_set_a @ A2 @ ( collect_set_a @ P ) )
% 0.29/0.47 = ( P @ A2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_46_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A2: a,P: a > $o] :
% 0.29/0.47 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.29/0.47 = ( P @ A2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_47_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A3: set_set_a] :
% 0.29/0.47 ( ( collect_set_a
% 0.29/0.47 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 0.29/0.47 = A3 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_48_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A3: set_a] :
% 0.29/0.47 ( ( collect_a
% 0.29/0.47 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.29/0.47 = A3 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_49_Collect__cong,axiom,
% 0.29/0.47 ! [P: a > $o,Q: a > $o] :
% 0.29/0.47 ( ! [X6: a] :
% 0.29/0.47 ( ( P @ X6 )
% 0.29/0.47 = ( Q @ X6 ) )
% 0.29/0.47 => ( ( collect_a @ P )
% 0.29/0.47 = ( collect_a @ Q ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_cong
% 0.29/0.47 thf(fact_50_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [A2: set_a,B2: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_not_eq
% 0.29/0.47 thf(fact_51_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [A2: a > $o,B2: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_not_eq
% 0.29/0.47 thf(fact_52_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [A2: int,B2: int] :
% 0.29/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.47 => ( A2 != B2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_not_eq
% 0.29/0.47 thf(fact_53_not__less__iff__gr__or__eq,axiom,
% 0.29/0.47 ! [X: int,Y: int] :
% 0.29/0.47 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.47 = ( ( ord_less_int @ Y @ X )
% 0.29/0.47 | ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_less_iff_gr_or_eq
% 0.29/0.47 thf(fact_54_dual__order_Ostrict__trans,axiom,
% 0.29/0.47 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ B2 @ A2 )
% 0.29/0.47 => ( ( ord_less_set_a @ C @ B2 )
% 0.29/0.47 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans
% 0.29/0.47 thf(fact_55_dual__order_Ostrict__trans,axiom,
% 0.29/0.47 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ B2 @ A2 )
% 0.29/0.47 => ( ( ord_less_a_o @ C @ B2 )
% 0.29/0.47 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans
% 0.29/0.47 thf(fact_56_dual__order_Ostrict__trans,axiom,
% 0.29/0.47 ! [B2: int,A2: int,C: int] :
% 0.29/0.47 ( ( ord_less_int @ B2 @ A2 )
% 0.29/0.47 => ( ( ord_less_int @ C @ B2 )
% 0.29/0.47 => ( ord_less_int @ C @ A2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans
% 0.29/0.47 thf(fact_57_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.47 => ( ! [X6: int,Y3: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_58_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.47 => ( ! [X6: int,Y3: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_59_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.47 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_60_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.47 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_61_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.47 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.47 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_62_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.47 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_63_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.47 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_64_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.47 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.47 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_65_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( F @ B2 ) )
% 0.29/0.47 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.47 => ( ! [X6: int,Y3: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_66_ord__less__eq__subst,axiom,
% 0.29/0.47 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.29/0.47 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.47 => ( ( ( F @ B2 )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X6: int,Y3: int] :
% 0.29/0.47 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.47 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_less_eq_subst
% 0.29/0.47 thf(fact_67_ord__less__eq__subst,axiom,
% 0.29/0.47 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_68_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_69_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_70_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_71_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_72_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_73_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_74_ord__less__eq__subst,axiom,
% 0.29/0.48 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ( F @ B2 )
% 0.29/0.48 = C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_subst
% 0.29/0.48 thf(fact_75_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_76_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_77_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_78_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_79_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_80_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_81_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_82_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_83_order__less__subst1,axiom,
% 0.29/0.48 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.29/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst1
% 0.29/0.48 thf(fact_84_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_85_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_86_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_87_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_88_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_89_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_90_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_91_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: a > $o,Y3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_92_order__less__subst2,axiom,
% 0.29/0.48 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.29/0.48 => ( ! [X6: int,Y3: int] :
% 0.29/0.48 ( ( ord_less_int @ X6 @ Y3 )
% 0.29/0.48 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 0.29/0.48 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order_less_subst2
% 0.29/0.48 thf(fact_93_lt__ex,axiom,
% 0.29/0.48 ! [X: int] :
% 0.29/0.48 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 0.29/0.48
% 0.29/0.48 % lt_ex
% 0.29/0.48 thf(fact_94_gt__ex,axiom,
% 0.29/0.48 ! [X: int] :
% 0.29/0.48 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 0.29/0.48
% 0.29/0.48 % gt_ex
% 0.29/0.48 thf(fact_95_neqE,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( X != Y )
% 0.29/0.48 => ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % neqE
% 0.29/0.48 thf(fact_96_neq__iff,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( X != Y )
% 0.29/0.48 = ( ( ord_less_int @ X @ Y )
% 0.29/0.48 | ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % neq_iff
% 0.29/0.48 thf(fact_97_order_Oasym,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.asym
% 0.29/0.48 thf(fact_98_order_Oasym,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.asym
% 0.29/0.48 thf(fact_99_order_Oasym,axiom,
% 0.29/0.48 ! [A2: int,B2: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.asym
% 0.29/0.48 thf(fact_100_less__imp__neq,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_neq
% 0.29/0.48 thf(fact_101_less__imp__neq,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_neq
% 0.29/0.48 thf(fact_102_less__imp__neq,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_neq
% 0.29/0.48 thf(fact_103_less__asym,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym
% 0.29/0.48 thf(fact_104_less__asym,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym
% 0.29/0.48 thf(fact_105_less__asym,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym
% 0.29/0.48 thf(fact_106_less__asym_H,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym'
% 0.29/0.48 thf(fact_107_less__asym_H,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym'
% 0.29/0.48 thf(fact_108_less__asym_H,axiom,
% 0.29/0.48 ! [A2: int,B2: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_asym'
% 0.29/0.48 thf(fact_109_less__trans,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a,Z3: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ( ( ord_less_set_a @ Y @ Z3 )
% 0.29/0.48 => ( ord_less_set_a @ X @ Z3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_trans
% 0.29/0.48 thf(fact_110_less__trans,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o,Z3: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ( ( ord_less_a_o @ Y @ Z3 )
% 0.29/0.48 => ( ord_less_a_o @ X @ Z3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_trans
% 0.29/0.48 thf(fact_111_less__trans,axiom,
% 0.29/0.48 ! [X: int,Y: int,Z3: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( ( ord_less_int @ Y @ Z3 )
% 0.29/0.48 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_trans
% 0.29/0.48 thf(fact_112_less__linear,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 | ( X = Y )
% 0.29/0.48 | ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_linear
% 0.29/0.48 thf(fact_113_less__irrefl,axiom,
% 0.29/0.48 ! [X: set_a] :
% 0.29/0.48 ~ ( ord_less_set_a @ X @ X ) ).
% 0.29/0.48
% 0.29/0.48 % less_irrefl
% 0.29/0.48 thf(fact_114_less__irrefl,axiom,
% 0.29/0.48 ! [X: a > $o] :
% 0.29/0.48 ~ ( ord_less_a_o @ X @ X ) ).
% 0.29/0.48
% 0.29/0.48 % less_irrefl
% 0.29/0.48 thf(fact_115_less__irrefl,axiom,
% 0.29/0.48 ! [X: int] :
% 0.29/0.48 ~ ( ord_less_int @ X @ X ) ).
% 0.29/0.48
% 0.29/0.48 % less_irrefl
% 0.29/0.48 thf(fact_116_ord__eq__less__trans,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( A2 = B2 )
% 0.29/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_eq_less_trans
% 0.29/0.48 thf(fact_117_ord__eq__less__trans,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( A2 = B2 )
% 0.29/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_eq_less_trans
% 0.29/0.48 thf(fact_118_ord__eq__less__trans,axiom,
% 0.29/0.48 ! [A2: int,B2: int,C: int] :
% 0.29/0.48 ( ( A2 = B2 )
% 0.29/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.48 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_eq_less_trans
% 0.29/0.48 thf(fact_119_ord__less__eq__trans,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( B2 = C )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_trans
% 0.29/0.48 thf(fact_120_ord__less__eq__trans,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( B2 = C )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_trans
% 0.29/0.48 thf(fact_121_ord__less__eq__trans,axiom,
% 0.29/0.48 ! [A2: int,B2: int,C: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( B2 = C )
% 0.29/0.48 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ord_less_eq_trans
% 0.29/0.48 thf(fact_122_dual__order_Oasym,axiom,
% 0.29/0.48 ! [B2: set_a,A2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.asym
% 0.29/0.48 thf(fact_123_dual__order_Oasym,axiom,
% 0.29/0.48 ! [B2: a > $o,A2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.asym
% 0.29/0.48 thf(fact_124_dual__order_Oasym,axiom,
% 0.29/0.48 ! [B2: int,A2: int] :
% 0.29/0.48 ( ( ord_less_int @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.asym
% 0.29/0.48 thf(fact_125_less__imp__not__eq,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq
% 0.29/0.48 thf(fact_126_less__imp__not__eq,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq
% 0.29/0.48 thf(fact_127_less__imp__not__eq,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( X != Y ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq
% 0.29/0.48 thf(fact_128_less__not__sym,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_not_sym
% 0.29/0.48 thf(fact_129_less__not__sym,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_not_sym
% 0.29/0.48 thf(fact_130_less__not__sym,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_not_sym
% 0.29/0.48 thf(fact_131_antisym__conv3,axiom,
% 0.29/0.48 ! [Y: int,X: int] :
% 0.29/0.48 ( ~ ( ord_less_int @ Y @ X )
% 0.29/0.48 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.48 = ( X = Y ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % antisym_conv3
% 0.29/0.48 thf(fact_132_less__imp__not__eq2,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ( Y != X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq2
% 0.29/0.48 thf(fact_133_less__imp__not__eq2,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ( Y != X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq2
% 0.29/0.48 thf(fact_134_less__imp__not__eq2,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( Y != X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_eq2
% 0.29/0.48 thf(fact_135_less__imp__triv,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a,P: $o] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ( ( ord_less_set_a @ Y @ X )
% 0.29/0.48 => P ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_triv
% 0.29/0.48 thf(fact_136_less__imp__triv,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o,P: $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ( ( ord_less_a_o @ Y @ X )
% 0.29/0.48 => P ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_triv
% 0.29/0.48 thf(fact_137_less__imp__triv,axiom,
% 0.29/0.48 ! [X: int,Y: int,P: $o] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( ( ord_less_int @ Y @ X )
% 0.29/0.48 => P ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_triv
% 0.29/0.48 thf(fact_138_linorder__cases,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.48 => ( ( X != Y )
% 0.29/0.48 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % linorder_cases
% 0.29/0.48 thf(fact_139_dual__order_Oirrefl,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.irrefl
% 0.29/0.48 thf(fact_140_dual__order_Oirrefl,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.irrefl
% 0.29/0.48 thf(fact_141_dual__order_Oirrefl,axiom,
% 0.29/0.48 ! [A2: int] :
% 0.29/0.48 ~ ( ord_less_int @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % dual_order.irrefl
% 0.29/0.48 thf(fact_142_order_Ostrict__trans,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_set_a @ B2 @ C )
% 0.29/0.48 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans
% 0.29/0.48 thf(fact_143_order_Ostrict__trans,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_a_o @ B2 @ C )
% 0.29/0.48 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans
% 0.29/0.48 thf(fact_144_order_Ostrict__trans,axiom,
% 0.29/0.48 ! [A2: int,B2: int,C: int] :
% 0.29/0.48 ( ( ord_less_int @ A2 @ B2 )
% 0.29/0.48 => ( ( ord_less_int @ B2 @ C )
% 0.29/0.48 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % order.strict_trans
% 0.29/0.48 thf(fact_145_less__imp__not__less,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_less
% 0.29/0.48 thf(fact_146_less__imp__not__less,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_less
% 0.29/0.48 thf(fact_147_less__imp__not__less,axiom,
% 0.29/0.48 ! [X: int,Y: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ Y )
% 0.29/0.48 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_imp_not_less
% 0.29/0.48 thf(fact_148_linorder__less__wlog,axiom,
% 0.29/0.48 ! [P: int > int > $o,A2: int,B2: int] :
% 0.29/0.48 ( ! [A4: int,B3: int] :
% 0.29/0.48 ( ( ord_less_int @ A4 @ B3 )
% 0.29/0.48 => ( P @ A4 @ B3 ) )
% 0.29/0.48 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 0.29/0.48 => ( ! [A4: int,B3: int] :
% 0.29/0.48 ( ( P @ B3 @ A4 )
% 0.29/0.48 => ( P @ A4 @ B3 ) )
% 0.29/0.48 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % linorder_less_wlog
% 0.29/0.48 thf(fact_149_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % verit_comp_simplify1(1)
% 0.29/0.48 thf(fact_150_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % verit_comp_simplify1(1)
% 0.29/0.48 thf(fact_151_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.48 ! [A2: int] :
% 0.29/0.48 ~ ( ord_less_int @ A2 @ A2 ) ).
% 0.29/0.48
% 0.29/0.48 % verit_comp_simplify1(1)
% 0.29/0.48 thf(fact_152_setOf_Osimps_I1_J,axiom,
% 0.29/0.48 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 0.29/0.48 = bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % setOf.simps(1)
% 0.29/0.48 thf(fact_153_bot__apply,axiom,
% 0.29/0.48 ( bot_bot_a_o
% 0.29/0.48 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_apply
% 0.29/0.48 thf(fact_154_bot__fun__def,axiom,
% 0.29/0.48 ( bot_bot_a_o
% 0.29/0.48 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_fun_def
% 0.29/0.48 thf(fact_155_bot_Oextremum__strict,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % bot.extremum_strict
% 0.29/0.48 thf(fact_156_bot_Oextremum__strict,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 0.29/0.48
% 0.29/0.48 % bot.extremum_strict
% 0.29/0.48 thf(fact_157_bot_Onot__eq__extremum,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ( ( A2 != bot_bot_set_a )
% 0.29/0.48 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot.not_eq_extremum
% 0.29/0.48 thf(fact_158_bot_Onot__eq__extremum,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ( ( A2 != bot_bot_a_o )
% 0.29/0.48 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot.not_eq_extremum
% 0.29/0.48 thf(fact_159_empty__Collect__eq,axiom,
% 0.29/0.48 ! [P: a > $o] :
% 0.29/0.48 ( ( bot_bot_set_a
% 0.29/0.48 = ( collect_a @ P ) )
% 0.29/0.48 = ( ! [X4: a] :
% 0.29/0.48 ~ ( P @ X4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % empty_Collect_eq
% 0.29/0.48 thf(fact_160_Collect__empty__eq,axiom,
% 0.29/0.48 ! [P: a > $o] :
% 0.29/0.48 ( ( ( collect_a @ P )
% 0.29/0.48 = bot_bot_set_a )
% 0.29/0.48 = ( ! [X4: a] :
% 0.29/0.48 ~ ( P @ X4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_empty_eq
% 0.29/0.48 thf(fact_161_all__not__in__conv,axiom,
% 0.29/0.48 ! [A3: set_set_a] :
% 0.29/0.48 ( ( ! [X4: set_a] :
% 0.29/0.48 ~ ( member_set_a @ X4 @ A3 ) )
% 0.29/0.48 = ( A3 = bot_bot_set_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % all_not_in_conv
% 0.29/0.48 thf(fact_162_all__not__in__conv,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( ! [X4: a] :
% 0.29/0.48 ~ ( member_a @ X4 @ A3 ) )
% 0.29/0.48 = ( A3 = bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % all_not_in_conv
% 0.29/0.48 thf(fact_163_empty__iff,axiom,
% 0.29/0.48 ! [C: set_a] :
% 0.29/0.48 ~ ( member_set_a @ C @ bot_bot_set_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % empty_iff
% 0.29/0.48 thf(fact_164_empty__iff,axiom,
% 0.29/0.48 ! [C: a] :
% 0.29/0.48 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % empty_iff
% 0.29/0.48 thf(fact_165_empty__def,axiom,
% 0.29/0.48 ( bot_bot_set_a
% 0.29/0.48 = ( collect_a
% 0.29/0.48 @ ^ [X4: a] : $false ) ) ).
% 0.29/0.48
% 0.29/0.48 % empty_def
% 0.29/0.48 thf(fact_166_bot__set__def,axiom,
% 0.29/0.48 ( bot_bot_set_a
% 0.29/0.48 = ( collect_a @ bot_bot_a_o ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_set_def
% 0.29/0.48 thf(fact_167_not__psubset__empty,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % not_psubset_empty
% 0.29/0.48 thf(fact_168_emptyE,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ~ ( member_set_a @ A2 @ bot_bot_set_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % emptyE
% 0.29/0.48 thf(fact_169_emptyE,axiom,
% 0.29/0.48 ! [A2: a] :
% 0.29/0.48 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % emptyE
% 0.29/0.48 thf(fact_170_equals0D,axiom,
% 0.29/0.48 ! [A3: set_set_a,A2: set_a] :
% 0.29/0.48 ( ( A3 = bot_bot_set_set_a )
% 0.29/0.48 => ~ ( member_set_a @ A2 @ A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % equals0D
% 0.29/0.48 thf(fact_171_equals0D,axiom,
% 0.29/0.48 ! [A3: set_a,A2: a] :
% 0.29/0.48 ( ( A3 = bot_bot_set_a )
% 0.29/0.48 => ~ ( member_a @ A2 @ A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % equals0D
% 0.29/0.48 thf(fact_172_equals0I,axiom,
% 0.29/0.48 ! [A3: set_set_a] :
% 0.29/0.48 ( ! [Y3: set_a] :
% 0.29/0.48 ~ ( member_set_a @ Y3 @ A3 )
% 0.29/0.48 => ( A3 = bot_bot_set_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % equals0I
% 0.29/0.48 thf(fact_173_equals0I,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ! [Y3: a] :
% 0.29/0.48 ~ ( member_a @ Y3 @ A3 )
% 0.29/0.48 => ( A3 = bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % equals0I
% 0.29/0.48 thf(fact_174_ex__in__conv,axiom,
% 0.29/0.48 ! [A3: set_set_a] :
% 0.29/0.48 ( ( ? [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 0.29/0.48 = ( A3 != bot_bot_set_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % ex_in_conv
% 0.29/0.48 thf(fact_175_ex__in__conv,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( ? [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.29/0.48 = ( A3 != bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % ex_in_conv
% 0.29/0.48 thf(fact_176_Set_Ois__empty__def,axiom,
% 0.29/0.48 ( is_empty_a
% 0.29/0.48 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Set.is_empty_def
% 0.29/0.48 thf(fact_177_Collect__empty__eq__bot,axiom,
% 0.29/0.48 ! [P: a > $o] :
% 0.29/0.48 ( ( ( collect_a @ P )
% 0.29/0.48 = bot_bot_set_a )
% 0.29/0.48 = ( P = bot_bot_a_o ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_empty_eq_bot
% 0.29/0.48 thf(fact_178_bot__empty__eq,axiom,
% 0.29/0.48 ( bot_bot_set_a_o
% 0.29/0.48 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ bot_bot_set_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_empty_eq
% 0.29/0.48 thf(fact_179_bot__empty__eq,axiom,
% 0.29/0.48 ( bot_bot_a_o
% 0.29/0.48 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_empty_eq
% 0.29/0.48 thf(fact_180_Tree_Osimps_I14_J,axiom,
% 0.29/0.48 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 0.29/0.48 = bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.simps(14)
% 0.29/0.48 thf(fact_181_is__singletonI_H,axiom,
% 0.29/0.48 ! [A3: set_set_a] :
% 0.29/0.48 ( ( A3 != bot_bot_set_set_a )
% 0.29/0.48 => ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( member_set_a @ X6 @ A3 )
% 0.29/0.48 => ( ( member_set_a @ Y3 @ A3 )
% 0.29/0.48 => ( X6 = Y3 ) ) )
% 0.29/0.48 => ( is_singleton_set_a @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singletonI'
% 0.29/0.48 thf(fact_182_is__singletonI_H,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( A3 != bot_bot_set_a )
% 0.29/0.48 => ( ! [X6: a,Y3: a] :
% 0.29/0.48 ( ( member_a @ X6 @ A3 )
% 0.29/0.48 => ( ( member_a @ Y3 @ A3 )
% 0.29/0.48 => ( X6 = Y3 ) ) )
% 0.29/0.48 => ( is_singleton_a @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singletonI'
% 0.29/0.48 thf(fact_183_psubsetD,axiom,
% 0.29/0.48 ! [A3: set_set_a,B4: set_set_a,C: set_a] :
% 0.29/0.48 ( ( ord_less_set_set_a @ A3 @ B4 )
% 0.29/0.48 => ( ( member_set_a @ C @ A3 )
% 0.29/0.48 => ( member_set_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % psubsetD
% 0.29/0.48 thf(fact_184_psubsetD,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,C: a] :
% 0.29/0.48 ( ( ord_less_set_a @ A3 @ B4 )
% 0.29/0.48 => ( ( member_a @ C @ A3 )
% 0.29/0.48 => ( member_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % psubsetD
% 0.29/0.48 thf(fact_185_less__set__def,axiom,
% 0.29/0.48 ( ord_less_set_set_a
% 0.29/0.48 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 0.29/0.48 ( ord_less_set_a_o
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A5 )
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ B5 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_set_def
% 0.29/0.48 thf(fact_186_less__set__def,axiom,
% 0.29/0.48 ( ord_less_set_a
% 0.29/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.29/0.48 ( ord_less_a_o
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_set_def
% 0.29/0.48 thf(fact_187_psubset__trans,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ A3 @ B4 )
% 0.29/0.48 => ( ( ord_less_set_a @ B4 @ C2 )
% 0.29/0.48 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % psubset_trans
% 0.29/0.48 thf(fact_188_Tree_Oset__cases,axiom,
% 0.29/0.48 ! [E: set_a,A2: binary594033953_set_a] :
% 0.29/0.48 ( ( member_set_a @ E @ ( binary1613048283_set_a @ A2 ) )
% 0.29/0.48 => ( ! [Z1: binary594033953_set_a] :
% 0.29/0.48 ( ? [Z22: set_a,Z32: binary594033953_set_a] :
% 0.29/0.48 ( A2
% 0.29/0.48 = ( binary313540327_set_a @ Z1 @ Z22 @ Z32 ) )
% 0.29/0.48 => ~ ( member_set_a @ E @ ( binary1613048283_set_a @ Z1 ) ) )
% 0.29/0.48 => ( ! [Z1: binary594033953_set_a,Z32: binary594033953_set_a] :
% 0.29/0.48 ( A2
% 0.29/0.48 != ( binary313540327_set_a @ Z1 @ E @ Z32 ) )
% 0.29/0.48 => ~ ! [Z1: binary594033953_set_a,Z22: set_a,Z32: binary594033953_set_a] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( binary313540327_set_a @ Z1 @ Z22 @ Z32 ) )
% 0.29/0.48 => ~ ( member_set_a @ E @ ( binary1613048283_set_a @ Z32 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_cases
% 0.29/0.48 thf(fact_189_Tree_Oset__cases,axiom,
% 0.29/0.48 ! [E: a,A2: binary1439146945Tree_a] :
% 0.29/0.48 ( ( member_a @ E @ ( binary256242811Tree_a @ A2 ) )
% 0.29/0.48 => ( ! [Z1: binary1439146945Tree_a] :
% 0.29/0.48 ( ? [Z22: a,Z32: binary1439146945Tree_a] :
% 0.29/0.48 ( A2
% 0.29/0.48 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 0.29/0.48 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 0.29/0.48 => ( ! [Z1: binary1439146945Tree_a,Z32: binary1439146945Tree_a] :
% 0.29/0.48 ( A2
% 0.29/0.48 != ( binary717961607le_T_a @ Z1 @ E @ Z32 ) )
% 0.29/0.48 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z32: binary1439146945Tree_a] :
% 0.29/0.48 ( ( A2
% 0.29/0.48 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 0.29/0.48 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z32 ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_cases
% 0.29/0.48 thf(fact_190_Tree_Oset__intros_I1_J,axiom,
% 0.29/0.48 ! [Y: set_a,X21: binary594033953_set_a,X22: set_a,X23: binary594033953_set_a] :
% 0.29/0.48 ( ( member_set_a @ Y @ ( binary1613048283_set_a @ X21 ) )
% 0.29/0.48 => ( member_set_a @ Y @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(1)
% 0.29/0.48 thf(fact_191_Tree_Oset__intros_I1_J,axiom,
% 0.29/0.48 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.29/0.48 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 0.29/0.48 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(1)
% 0.29/0.48 thf(fact_192_Tree_Oset__intros_I2_J,axiom,
% 0.29/0.48 ! [X22: set_a,X21: binary594033953_set_a,X23: binary594033953_set_a] : ( member_set_a @ X22 @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(2)
% 0.29/0.48 thf(fact_193_Tree_Oset__intros_I2_J,axiom,
% 0.29/0.48 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(2)
% 0.29/0.48 thf(fact_194_Tree_Oset__intros_I3_J,axiom,
% 0.29/0.48 ! [Ya: set_a,X23: binary594033953_set_a,X21: binary594033953_set_a,X22: set_a] :
% 0.29/0.48 ( ( member_set_a @ Ya @ ( binary1613048283_set_a @ X23 ) )
% 0.29/0.48 => ( member_set_a @ Ya @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(3)
% 0.29/0.48 thf(fact_195_Tree_Oset__intros_I3_J,axiom,
% 0.29/0.48 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 0.29/0.48 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 0.29/0.48 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.set_intros(3)
% 0.29/0.48 thf(fact_196_is__singletonI,axiom,
% 0.29/0.48 ! [X: a] : ( is_singleton_a @ ( insert_a @ X @ bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singletonI
% 0.29/0.48 thf(fact_197_is__singleton__def,axiom,
% 0.29/0.48 ( is_singleton_a
% 0.29/0.48 = ( ^ [A5: set_a] :
% 0.29/0.48 ? [X4: a] :
% 0.29/0.48 ( A5
% 0.29/0.48 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singleton_def
% 0.29/0.48 thf(fact_198_is__singletonE,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( is_singleton_a @ A3 )
% 0.29/0.48 => ~ ! [X6: a] :
% 0.29/0.48 ( A3
% 0.29/0.48 != ( insert_a @ X6 @ bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singletonE
% 0.29/0.48 thf(fact_199_insert__absorb2,axiom,
% 0.29/0.48 ! [X: a,A3: set_a] :
% 0.29/0.48 ( ( insert_a @ X @ ( insert_a @ X @ A3 ) )
% 0.29/0.48 = ( insert_a @ X @ A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_absorb2
% 0.29/0.48 thf(fact_200_insert__iff,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ A2 @ ( insert_set_a @ B2 @ A3 ) )
% 0.29/0.48 = ( ( A2 = B2 )
% 0.29/0.48 | ( member_set_a @ A2 @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_iff
% 0.29/0.48 thf(fact_201_insert__iff,axiom,
% 0.29/0.48 ! [A2: a,B2: a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 0.29/0.48 = ( ( A2 = B2 )
% 0.29/0.48 | ( member_a @ A2 @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_iff
% 0.29/0.48 thf(fact_202_insertCI,axiom,
% 0.29/0.48 ! [A2: set_a,B4: set_set_a,B2: set_a] :
% 0.29/0.48 ( ( ~ ( member_set_a @ A2 @ B4 )
% 0.29/0.48 => ( A2 = B2 ) )
% 0.29/0.48 => ( member_set_a @ A2 @ ( insert_set_a @ B2 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertCI
% 0.29/0.48 thf(fact_203_insertCI,axiom,
% 0.29/0.48 ! [A2: a,B4: set_a,B2: a] :
% 0.29/0.48 ( ( ~ ( member_a @ A2 @ B4 )
% 0.29/0.48 => ( A2 = B2 ) )
% 0.29/0.48 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertCI
% 0.29/0.48 thf(fact_204_singletonI,axiom,
% 0.29/0.48 ! [A2: set_a] : ( member_set_a @ A2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % singletonI
% 0.29/0.48 thf(fact_205_singletonI,axiom,
% 0.29/0.48 ! [A2: a] : ( member_a @ A2 @ ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % singletonI
% 0.29/0.48 thf(fact_206_singleton__conv,axiom,
% 0.29/0.48 ! [A2: a] :
% 0.29/0.48 ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] : ( X4 = A2 ) )
% 0.29/0.48 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_conv
% 0.29/0.48 thf(fact_207_singleton__conv2,axiom,
% 0.29/0.48 ! [A2: a] :
% 0.29/0.48 ( ( collect_a
% 0.29/0.48 @ ( ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 0.29/0.48 @ A2 ) )
% 0.29/0.48 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_conv2
% 0.29/0.48 thf(fact_208_singleton__inject,axiom,
% 0.29/0.48 ! [A2: a,B2: a] :
% 0.29/0.48 ( ( ( insert_a @ A2 @ bot_bot_set_a )
% 0.29/0.48 = ( insert_a @ B2 @ bot_bot_set_a ) )
% 0.29/0.48 => ( A2 = B2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_inject
% 0.29/0.48 thf(fact_209_insert__not__empty,axiom,
% 0.29/0.48 ! [A2: a,A3: set_a] :
% 0.29/0.48 ( ( insert_a @ A2 @ A3 )
% 0.29/0.48 != bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % insert_not_empty
% 0.29/0.48 thf(fact_210_doubleton__eq__iff,axiom,
% 0.29/0.48 ! [A2: a,B2: a,C: a,D: a] :
% 0.29/0.48 ( ( ( insert_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) )
% 0.29/0.48 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 0.29/0.48 = ( ( ( A2 = C )
% 0.29/0.48 & ( B2 = D ) )
% 0.29/0.48 | ( ( A2 = D )
% 0.29/0.48 & ( B2 = C ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % doubleton_eq_iff
% 0.29/0.48 thf(fact_211_singleton__iff,axiom,
% 0.29/0.48 ! [B2: set_a,A2: set_a] :
% 0.29/0.48 ( ( member_set_a @ B2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) )
% 0.29/0.48 = ( B2 = A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_iff
% 0.29/0.48 thf(fact_212_singleton__iff,axiom,
% 0.29/0.48 ! [B2: a,A2: a] :
% 0.29/0.48 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 0.29/0.48 = ( B2 = A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_iff
% 0.29/0.48 thf(fact_213_singletonD,axiom,
% 0.29/0.48 ! [B2: set_a,A2: set_a] :
% 0.29/0.48 ( ( member_set_a @ B2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) )
% 0.29/0.48 => ( B2 = A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % singletonD
% 0.29/0.48 thf(fact_214_singletonD,axiom,
% 0.29/0.48 ! [B2: a,A2: a] :
% 0.29/0.48 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 0.29/0.48 => ( B2 = A2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % singletonD
% 0.29/0.48 thf(fact_215_insert__compr,axiom,
% 0.29/0.48 ( insert_set_a
% 0.29/0.48 = ( ^ [A: set_a,B5: set_set_a] :
% 0.29/0.48 ( collect_set_a
% 0.29/0.48 @ ^ [X4: set_a] :
% 0.29/0.48 ( ( X4 = A )
% 0.29/0.48 | ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_compr
% 0.29/0.48 thf(fact_216_insert__compr,axiom,
% 0.29/0.48 ( insert_a
% 0.29/0.48 = ( ^ [A: a,B5: set_a] :
% 0.29/0.48 ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( X4 = A )
% 0.29/0.48 | ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_compr
% 0.29/0.48 thf(fact_217_insert__Collect,axiom,
% 0.29/0.48 ! [A2: a,P: a > $o] :
% 0.29/0.48 ( ( insert_a @ A2 @ ( collect_a @ P ) )
% 0.29/0.48 = ( collect_a
% 0.29/0.48 @ ^ [U: a] :
% 0.29/0.48 ( ( U != A2 )
% 0.29/0.48 => ( P @ U ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_Collect
% 0.29/0.48 thf(fact_218_mk__disjoint__insert,axiom,
% 0.29/0.48 ! [A2: set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ A2 @ A3 )
% 0.29/0.48 => ? [B6: set_set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_set_a @ A2 @ B6 ) )
% 0.29/0.48 & ~ ( member_set_a @ A2 @ B6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % mk_disjoint_insert
% 0.29/0.48 thf(fact_219_mk__disjoint__insert,axiom,
% 0.29/0.48 ! [A2: a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ A2 @ A3 )
% 0.29/0.48 => ? [B6: set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_a @ A2 @ B6 ) )
% 0.29/0.48 & ~ ( member_a @ A2 @ B6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % mk_disjoint_insert
% 0.29/0.48 thf(fact_220_insert__commute,axiom,
% 0.29/0.48 ! [X: a,Y: a,A3: set_a] :
% 0.29/0.48 ( ( insert_a @ X @ ( insert_a @ Y @ A3 ) )
% 0.29/0.48 = ( insert_a @ Y @ ( insert_a @ X @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_commute
% 0.29/0.48 thf(fact_221_insert__eq__iff,axiom,
% 0.29/0.48 ! [A2: set_a,A3: set_set_a,B2: set_a,B4: set_set_a] :
% 0.29/0.48 ( ~ ( member_set_a @ A2 @ A3 )
% 0.29/0.48 => ( ~ ( member_set_a @ B2 @ B4 )
% 0.29/0.48 => ( ( ( insert_set_a @ A2 @ A3 )
% 0.29/0.48 = ( insert_set_a @ B2 @ B4 ) )
% 0.29/0.48 = ( ( ( A2 = B2 )
% 0.29/0.48 => ( A3 = B4 ) )
% 0.29/0.48 & ( ( A2 != B2 )
% 0.29/0.48 => ? [C3: set_set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_set_a @ B2 @ C3 ) )
% 0.29/0.48 & ~ ( member_set_a @ B2 @ C3 )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_set_a @ A2 @ C3 ) )
% 0.29/0.48 & ~ ( member_set_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_eq_iff
% 0.29/0.48 thf(fact_222_insert__eq__iff,axiom,
% 0.29/0.48 ! [A2: a,A3: set_a,B2: a,B4: set_a] :
% 0.29/0.48 ( ~ ( member_a @ A2 @ A3 )
% 0.29/0.48 => ( ~ ( member_a @ B2 @ B4 )
% 0.29/0.48 => ( ( ( insert_a @ A2 @ A3 )
% 0.29/0.48 = ( insert_a @ B2 @ B4 ) )
% 0.29/0.48 = ( ( ( A2 = B2 )
% 0.29/0.48 => ( A3 = B4 ) )
% 0.29/0.48 & ( ( A2 != B2 )
% 0.29/0.48 => ? [C3: set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_a @ B2 @ C3 ) )
% 0.29/0.48 & ~ ( member_a @ B2 @ C3 )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_a @ A2 @ C3 ) )
% 0.29/0.48 & ~ ( member_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_eq_iff
% 0.29/0.48 thf(fact_223_insert__absorb,axiom,
% 0.29/0.48 ! [A2: set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ A2 @ A3 )
% 0.29/0.48 => ( ( insert_set_a @ A2 @ A3 )
% 0.29/0.48 = A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_absorb
% 0.29/0.48 thf(fact_224_insert__absorb,axiom,
% 0.29/0.48 ! [A2: a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ A2 @ A3 )
% 0.29/0.48 => ( ( insert_a @ A2 @ A3 )
% 0.29/0.48 = A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_absorb
% 0.29/0.48 thf(fact_225_insert__ident,axiom,
% 0.29/0.48 ! [X: set_a,A3: set_set_a,B4: set_set_a] :
% 0.29/0.48 ( ~ ( member_set_a @ X @ A3 )
% 0.29/0.48 => ( ~ ( member_set_a @ X @ B4 )
% 0.29/0.48 => ( ( ( insert_set_a @ X @ A3 )
% 0.29/0.48 = ( insert_set_a @ X @ B4 ) )
% 0.29/0.48 = ( A3 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_ident
% 0.29/0.48 thf(fact_226_insert__ident,axiom,
% 0.29/0.48 ! [X: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ~ ( member_a @ X @ A3 )
% 0.29/0.48 => ( ~ ( member_a @ X @ B4 )
% 0.29/0.48 => ( ( ( insert_a @ X @ A3 )
% 0.29/0.48 = ( insert_a @ X @ B4 ) )
% 0.29/0.48 = ( A3 = B4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_ident
% 0.29/0.48 thf(fact_227_Set_Oset__insert,axiom,
% 0.29/0.48 ! [X: set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ X @ A3 )
% 0.29/0.48 => ~ ! [B6: set_set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_set_a @ X @ B6 ) )
% 0.29/0.48 => ( member_set_a @ X @ B6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Set.set_insert
% 0.29/0.48 thf(fact_228_Set_Oset__insert,axiom,
% 0.29/0.48 ! [X: a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ X @ A3 )
% 0.29/0.48 => ~ ! [B6: set_a] :
% 0.29/0.48 ( ( A3
% 0.29/0.48 = ( insert_a @ X @ B6 ) )
% 0.29/0.48 => ( member_a @ X @ B6 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Set.set_insert
% 0.29/0.48 thf(fact_229_insertI2,axiom,
% 0.29/0.48 ! [A2: set_a,B4: set_set_a,B2: set_a] :
% 0.29/0.48 ( ( member_set_a @ A2 @ B4 )
% 0.29/0.48 => ( member_set_a @ A2 @ ( insert_set_a @ B2 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI2
% 0.29/0.48 thf(fact_230_insertI2,axiom,
% 0.29/0.48 ! [A2: a,B4: set_a,B2: a] :
% 0.29/0.48 ( ( member_a @ A2 @ B4 )
% 0.29/0.48 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI2
% 0.29/0.48 thf(fact_231_insertI1,axiom,
% 0.29/0.48 ! [A2: set_a,B4: set_set_a] : ( member_set_a @ A2 @ ( insert_set_a @ A2 @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI1
% 0.29/0.48 thf(fact_232_insertI1,axiom,
% 0.29/0.48 ! [A2: a,B4: set_a] : ( member_a @ A2 @ ( insert_a @ A2 @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertI1
% 0.29/0.48 thf(fact_233_insertE,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ A2 @ ( insert_set_a @ B2 @ A3 ) )
% 0.29/0.48 => ( ( A2 != B2 )
% 0.29/0.48 => ( member_set_a @ A2 @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertE
% 0.29/0.48 thf(fact_234_insertE,axiom,
% 0.29/0.48 ! [A2: a,B2: a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 0.29/0.48 => ( ( A2 != B2 )
% 0.29/0.48 => ( member_a @ A2 @ A3 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insertE
% 0.29/0.48 thf(fact_235_Collect__conv__if,axiom,
% 0.29/0.48 ! [P: a > $o,A2: a] :
% 0.29/0.48 ( ( ( P @ A2 )
% 0.29/0.48 => ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( X4 = A2 )
% 0.29/0.48 & ( P @ X4 ) ) )
% 0.29/0.48 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.29/0.48 & ( ~ ( P @ A2 )
% 0.29/0.48 => ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( X4 = A2 )
% 0.29/0.48 & ( P @ X4 ) ) )
% 0.29/0.48 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_conv_if
% 0.29/0.48 thf(fact_236_Collect__conv__if2,axiom,
% 0.29/0.48 ! [P: a > $o,A2: a] :
% 0.29/0.48 ( ( ( P @ A2 )
% 0.29/0.48 => ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( A2 = X4 )
% 0.29/0.48 & ( P @ X4 ) ) )
% 0.29/0.48 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.29/0.48 & ( ~ ( P @ A2 )
% 0.29/0.48 => ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( A2 = X4 )
% 0.29/0.48 & ( P @ X4 ) ) )
% 0.29/0.48 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_conv_if2
% 0.29/0.48 thf(fact_237_is__singleton__the__elem,axiom,
% 0.29/0.48 ( is_singleton_a
% 0.29/0.48 = ( ^ [A5: set_a] :
% 0.29/0.48 ( A5
% 0.29/0.48 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % is_singleton_the_elem
% 0.29/0.48 thf(fact_238_the__elem__eq,axiom,
% 0.29/0.48 ! [X: a] :
% 0.29/0.48 ( ( the_elem_a @ ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % the_elem_eq
% 0.29/0.48 thf(fact_239_setOf_Osimps_I2_J,axiom,
% 0.29/0.48 ! [T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 0.29/0.48 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 0.29/0.48 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T2 ) ) @ ( insert_a @ X @ bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % setOf.simps(2)
% 0.29/0.48 thf(fact_240_Tree_Osimps_I15_J,axiom,
% 0.29/0.48 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.29/0.48 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 0.29/0.48 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Tree.simps(15)
% 0.29/0.48 thf(fact_241_UnCI,axiom,
% 0.29/0.48 ! [C: set_a,B4: set_set_a,A3: set_set_a] :
% 0.29/0.48 ( ( ~ ( member_set_a @ C @ B4 )
% 0.29/0.48 => ( member_set_a @ C @ A3 ) )
% 0.29/0.48 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnCI
% 0.29/0.48 thf(fact_242_UnCI,axiom,
% 0.29/0.48 ! [C: a,B4: set_a,A3: set_a] :
% 0.29/0.48 ( ( ~ ( member_a @ C @ B4 )
% 0.29/0.48 => ( member_a @ C @ A3 ) )
% 0.29/0.48 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnCI
% 0.29/0.48 thf(fact_243_Un__iff,axiom,
% 0.29/0.48 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) )
% 0.29/0.48 = ( ( member_set_a @ C @ A3 )
% 0.29/0.48 | ( member_set_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_iff
% 0.29/0.48 thf(fact_244_Un__iff,axiom,
% 0.29/0.48 ! [C: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 = ( ( member_a @ C @ A3 )
% 0.29/0.48 | ( member_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_iff
% 0.29/0.48 thf(fact_245_Un__empty,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 0.29/0.48 = bot_bot_set_a )
% 0.29/0.48 = ( ( A3 = bot_bot_set_a )
% 0.29/0.48 & ( B4 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_empty
% 0.29/0.48 thf(fact_246_Un__insert__right,axiom,
% 0.29/0.48 ! [A3: set_a,A2: a,B4: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 0.29/0.48 = ( insert_a @ A2 @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_insert_right
% 0.29/0.48 thf(fact_247_Un__insert__left,axiom,
% 0.29/0.48 ! [A2: a,B4: set_a,C2: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ ( insert_a @ A2 @ B4 ) @ C2 )
% 0.29/0.48 = ( insert_a @ A2 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_insert_left
% 0.29/0.48 thf(fact_248_UnE,axiom,
% 0.29/0.48 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) )
% 0.29/0.48 => ( ~ ( member_set_a @ C @ A3 )
% 0.29/0.48 => ( member_set_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnE
% 0.29/0.48 thf(fact_249_UnE,axiom,
% 0.29/0.48 ! [C: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 => ( ~ ( member_a @ C @ A3 )
% 0.29/0.48 => ( member_a @ C @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnE
% 0.29/0.48 thf(fact_250_UnI1,axiom,
% 0.29/0.48 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ C @ A3 )
% 0.29/0.48 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnI1
% 0.29/0.48 thf(fact_251_UnI1,axiom,
% 0.29/0.48 ! [C: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( member_a @ C @ A3 )
% 0.29/0.48 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnI1
% 0.29/0.48 thf(fact_252_UnI2,axiom,
% 0.29/0.48 ! [C: set_a,B4: set_set_a,A3: set_set_a] :
% 0.29/0.48 ( ( member_set_a @ C @ B4 )
% 0.29/0.48 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnI2
% 0.29/0.48 thf(fact_253_UnI2,axiom,
% 0.29/0.48 ! [C: a,B4: set_a,A3: set_a] :
% 0.29/0.48 ( ( member_a @ C @ B4 )
% 0.29/0.48 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % UnI2
% 0.29/0.48 thf(fact_254_bex__Un,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,P: a > $o] :
% 0.29/0.48 ( ( ? [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 & ( P @ X4 ) ) )
% 0.29/0.48 = ( ? [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ A3 )
% 0.29/0.48 & ( P @ X4 ) )
% 0.29/0.48 | ? [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ B4 )
% 0.29/0.48 & ( P @ X4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bex_Un
% 0.29/0.48 thf(fact_255_ball__Un,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,P: a > $o] :
% 0.29/0.48 ( ( ! [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 => ( P @ X4 ) ) )
% 0.29/0.48 = ( ! [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ A3 )
% 0.29/0.48 => ( P @ X4 ) )
% 0.29/0.48 & ! [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ B4 )
% 0.29/0.48 => ( P @ X4 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ball_Un
% 0.29/0.48 thf(fact_256_Un__assoc,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 0.29/0.48 = ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_assoc
% 0.29/0.48 thf(fact_257_Un__absorb,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A3 @ A3 )
% 0.29/0.48 = A3 ) ).
% 0.29/0.48
% 0.29/0.48 % Un_absorb
% 0.29/0.48 thf(fact_258_Un__commute,axiom,
% 0.29/0.48 ( sup_sup_set_a
% 0.29/0.48 = ( ^ [A5: set_a,B5: set_a] : ( sup_sup_set_a @ B5 @ A5 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_commute
% 0.29/0.48 thf(fact_259_Un__left__absorb,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_left_absorb
% 0.29/0.48 thf(fact_260_Un__left__commute,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 0.29/0.48 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_left_commute
% 0.29/0.48 thf(fact_261_Collect__disj__eq,axiom,
% 0.29/0.48 ! [P: a > $o,Q: a > $o] :
% 0.29/0.48 ( ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( P @ X4 )
% 0.29/0.48 | ( Q @ X4 ) ) )
% 0.29/0.48 = ( sup_sup_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Collect_disj_eq
% 0.29/0.48 thf(fact_262_Un__def,axiom,
% 0.29/0.48 ( sup_sup_set_set_a
% 0.29/0.48 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 0.29/0.48 ( collect_set_a
% 0.29/0.48 @ ^ [X4: set_a] :
% 0.29/0.48 ( ( member_set_a @ X4 @ A5 )
% 0.29/0.48 | ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_def
% 0.29/0.48 thf(fact_263_Un__def,axiom,
% 0.29/0.48 ( sup_sup_set_a
% 0.29/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.29/0.48 ( collect_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( ( member_a @ X4 @ A5 )
% 0.29/0.48 | ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_def
% 0.29/0.48 thf(fact_264_Un__empty__left,axiom,
% 0.29/0.48 ! [B4: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ bot_bot_set_a @ B4 )
% 0.29/0.48 = B4 ) ).
% 0.29/0.48
% 0.29/0.48 % Un_empty_left
% 0.29/0.48 thf(fact_265_Un__empty__right,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A3 @ bot_bot_set_a )
% 0.29/0.48 = A3 ) ).
% 0.29/0.48
% 0.29/0.48 % Un_empty_right
% 0.29/0.48 thf(fact_266_insert__def,axiom,
% 0.29/0.48 ( insert_a
% 0.29/0.48 = ( ^ [A: a] :
% 0.29/0.48 ( sup_sup_set_a
% 0.29/0.48 @ ( collect_a
% 0.29/0.48 @ ^ [X4: a] : ( X4 = A ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_def
% 0.29/0.48 thf(fact_267_insert__is__Un,axiom,
% 0.29/0.48 ( insert_a
% 0.29/0.48 = ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_is_Un
% 0.29/0.48 thf(fact_268_Un__singleton__iff,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a,X: a] :
% 0.29/0.48 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 = ( ( ( A3 = bot_bot_set_a )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) ) )
% 0.29/0.48 | ( ( A3
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 & ( B4 = bot_bot_set_a ) )
% 0.29/0.48 | ( ( A3
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Un_singleton_iff
% 0.29/0.48 thf(fact_269_singleton__Un__iff,axiom,
% 0.29/0.48 ! [X: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( ( insert_a @ X @ bot_bot_set_a )
% 0.29/0.48 = ( sup_sup_set_a @ A3 @ B4 ) )
% 0.29/0.48 = ( ( ( A3 = bot_bot_set_a )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) ) )
% 0.29/0.48 | ( ( A3
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 & ( B4 = bot_bot_set_a ) )
% 0.29/0.48 | ( ( A3
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) )
% 0.29/0.48 & ( B4
% 0.29/0.48 = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % singleton_Un_iff
% 0.29/0.48 thf(fact_270_sup__bot__left,axiom,
% 0.29/0.48 ! [X: a > a > $o] :
% 0.29/0.48 ( ( sup_sup_a_a_o @ bot_bot_a_a_o @ X )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_left
% 0.29/0.48 thf(fact_271_sup__bot__left,axiom,
% 0.29/0.48 ! [X: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ bot_bot_set_a @ X )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_left
% 0.29/0.48 thf(fact_272_sup__bot__left,axiom,
% 0.29/0.48 ! [X: a > $o] :
% 0.29/0.48 ( ( sup_sup_a_o @ bot_bot_a_o @ X )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_left
% 0.29/0.48 thf(fact_273_sup__bot__right,axiom,
% 0.29/0.48 ! [X: a > a > $o] :
% 0.29/0.48 ( ( sup_sup_a_a_o @ X @ bot_bot_a_a_o )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_right
% 0.29/0.48 thf(fact_274_sup__bot__right,axiom,
% 0.29/0.48 ! [X: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ X @ bot_bot_set_a )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_right
% 0.29/0.48 thf(fact_275_sup__bot__right,axiom,
% 0.29/0.48 ! [X: a > $o] :
% 0.29/0.48 ( ( sup_sup_a_o @ X @ bot_bot_a_o )
% 0.29/0.48 = X ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot_right
% 0.29/0.48 thf(fact_276_bot__eq__sup__iff,axiom,
% 0.29/0.48 ! [X: a > a > $o,Y: a > a > $o] :
% 0.29/0.48 ( ( bot_bot_a_a_o
% 0.29/0.48 = ( sup_sup_a_a_o @ X @ Y ) )
% 0.29/0.48 = ( ( X = bot_bot_a_a_o )
% 0.29/0.48 & ( Y = bot_bot_a_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_eq_sup_iff
% 0.29/0.48 thf(fact_277_bot__eq__sup__iff,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( bot_bot_set_a
% 0.29/0.48 = ( sup_sup_set_a @ X @ Y ) )
% 0.29/0.48 = ( ( X = bot_bot_set_a )
% 0.29/0.48 & ( Y = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_eq_sup_iff
% 0.29/0.48 thf(fact_278_bot__eq__sup__iff,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( bot_bot_a_o
% 0.29/0.48 = ( sup_sup_a_o @ X @ Y ) )
% 0.29/0.48 = ( ( X = bot_bot_a_o )
% 0.29/0.48 & ( Y = bot_bot_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % bot_eq_sup_iff
% 0.29/0.48 thf(fact_279_sup__bot_Oright__neutral,axiom,
% 0.29/0.48 ! [A2: a > a > $o] :
% 0.29/0.48 ( ( sup_sup_a_a_o @ A2 @ bot_bot_a_a_o )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.right_neutral
% 0.29/0.48 thf(fact_280_sup__bot_Oright__neutral,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ A2 @ bot_bot_set_a )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.right_neutral
% 0.29/0.48 thf(fact_281_sup__bot_Oright__neutral,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ( ( sup_sup_a_o @ A2 @ bot_bot_a_o )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.right_neutral
% 0.29/0.48 thf(fact_282_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48 ! [A2: a > a > $o,B2: a > a > $o] :
% 0.29/0.48 ( ( bot_bot_a_a_o
% 0.29/0.48 = ( sup_sup_a_a_o @ A2 @ B2 ) )
% 0.29/0.48 = ( ( A2 = bot_bot_a_a_o )
% 0.29/0.48 & ( B2 = bot_bot_a_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.neutr_eq_iff
% 0.29/0.48 thf(fact_283_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( bot_bot_set_a
% 0.29/0.48 = ( sup_sup_set_a @ A2 @ B2 ) )
% 0.29/0.48 = ( ( A2 = bot_bot_set_a )
% 0.29/0.48 & ( B2 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.neutr_eq_iff
% 0.29/0.48 thf(fact_284_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( bot_bot_a_o
% 0.29/0.48 = ( sup_sup_a_o @ A2 @ B2 ) )
% 0.29/0.48 = ( ( A2 = bot_bot_a_o )
% 0.29/0.48 & ( B2 = bot_bot_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.neutr_eq_iff
% 0.29/0.48 thf(fact_285_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48 ! [A2: a > a > $o] :
% 0.29/0.48 ( ( sup_sup_a_a_o @ bot_bot_a_a_o @ A2 )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.left_neutral
% 0.29/0.48 thf(fact_286_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48 ! [A2: set_a] :
% 0.29/0.48 ( ( sup_sup_set_a @ bot_bot_set_a @ A2 )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.left_neutral
% 0.29/0.48 thf(fact_287_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48 ! [A2: a > $o] :
% 0.29/0.48 ( ( sup_sup_a_o @ bot_bot_a_o @ A2 )
% 0.29/0.48 = A2 ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.left_neutral
% 0.29/0.48 thf(fact_288_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48 ! [A2: a > a > $o,B2: a > a > $o] :
% 0.29/0.48 ( ( ( sup_sup_a_a_o @ A2 @ B2 )
% 0.29/0.48 = bot_bot_a_a_o )
% 0.29/0.48 = ( ( A2 = bot_bot_a_a_o )
% 0.29/0.48 & ( B2 = bot_bot_a_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.eq_neutr_iff
% 0.29/0.48 thf(fact_289_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48 ! [A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( ( sup_sup_set_a @ A2 @ B2 )
% 0.29/0.48 = bot_bot_set_a )
% 0.29/0.48 = ( ( A2 = bot_bot_set_a )
% 0.29/0.48 & ( B2 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.eq_neutr_iff
% 0.29/0.48 thf(fact_290_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48 ! [A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( ( sup_sup_a_o @ A2 @ B2 )
% 0.29/0.48 = bot_bot_a_o )
% 0.29/0.48 = ( ( A2 = bot_bot_a_o )
% 0.29/0.48 & ( B2 = bot_bot_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.eq_neutr_iff
% 0.29/0.48 thf(fact_291_sup__eq__bot__iff,axiom,
% 0.29/0.48 ! [X: a > a > $o,Y: a > a > $o] :
% 0.29/0.48 ( ( ( sup_sup_a_a_o @ X @ Y )
% 0.29/0.48 = bot_bot_a_a_o )
% 0.29/0.48 = ( ( X = bot_bot_a_a_o )
% 0.29/0.48 & ( Y = bot_bot_a_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_eq_bot_iff
% 0.29/0.48 thf(fact_292_sup__eq__bot__iff,axiom,
% 0.29/0.48 ! [X: set_a,Y: set_a] :
% 0.29/0.48 ( ( ( sup_sup_set_a @ X @ Y )
% 0.29/0.48 = bot_bot_set_a )
% 0.29/0.48 = ( ( X = bot_bot_set_a )
% 0.29/0.48 & ( Y = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_eq_bot_iff
% 0.29/0.48 thf(fact_293_sup__eq__bot__iff,axiom,
% 0.29/0.48 ! [X: a > $o,Y: a > $o] :
% 0.29/0.48 ( ( ( sup_sup_a_o @ X @ Y )
% 0.29/0.48 = bot_bot_a_o )
% 0.29/0.48 = ( ( X = bot_bot_a_o )
% 0.29/0.48 & ( Y = bot_bot_a_o ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_eq_bot_iff
% 0.29/0.48 thf(fact_294_sup__set__def,axiom,
% 0.29/0.48 ( sup_sup_set_set_a
% 0.29/0.48 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 0.29/0.48 ( collect_set_a
% 0.29/0.48 @ ( sup_sup_set_a_o
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A5 )
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_set_def
% 0.29/0.48 thf(fact_295_sup__set__def,axiom,
% 0.29/0.48 ( sup_sup_set_a
% 0.29/0.48 = ( ^ [A5: set_a,B5: set_a] :
% 0.29/0.48 ( collect_a
% 0.29/0.48 @ ( sup_sup_a_o
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_set_def
% 0.29/0.48 thf(fact_296_sup__Un__eq,axiom,
% 0.29/0.48 ! [R: set_set_a,S: set_set_a] :
% 0.29/0.48 ( ( sup_sup_set_a_o
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ R )
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ S ) )
% 0.29/0.48 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ ( sup_sup_set_set_a @ R @ S ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_Un_eq
% 0.29/0.48 thf(fact_297_sup__Un__eq,axiom,
% 0.29/0.48 ! [R: set_a,S: set_a] :
% 0.29/0.48 ( ( sup_sup_a_o
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 0.29/0.48 = ( ^ [X4: a] : ( member_a @ X4 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup_Un_eq
% 0.29/0.48 thf(fact_298_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.48 ! [C: a > a > $o,B2: a > a > $o,A2: a > a > $o] :
% 0.29/0.48 ( ( ord_less_a_a_o @ C @ B2 )
% 0.29/0.48 => ( ord_less_a_a_o @ C @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI2
% 0.29/0.48 thf(fact_299_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.48 ! [C: set_a,B2: set_a,A2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ C @ B2 )
% 0.29/0.48 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI2
% 0.29/0.48 thf(fact_300_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.48 ! [C: a > $o,B2: a > $o,A2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ C @ B2 )
% 0.29/0.48 => ( ord_less_a_o @ C @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI2
% 0.29/0.48 thf(fact_301_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.48 ! [C: int,B2: int,A2: int] :
% 0.29/0.48 ( ( ord_less_int @ C @ B2 )
% 0.29/0.48 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI2
% 0.29/0.48 thf(fact_302_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.48 ! [C: a > a > $o,A2: a > a > $o,B2: a > a > $o] :
% 0.29/0.48 ( ( ord_less_a_a_o @ C @ A2 )
% 0.29/0.48 => ( ord_less_a_a_o @ C @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI1
% 0.29/0.48 thf(fact_303_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.48 ! [C: set_a,A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ C @ A2 )
% 0.29/0.48 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI1
% 0.29/0.48 thf(fact_304_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.48 ! [C: a > $o,A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ C @ A2 )
% 0.29/0.48 => ( ord_less_a_o @ C @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI1
% 0.29/0.48 thf(fact_305_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.48 ! [C: int,A2: int,B2: int] :
% 0.29/0.48 ( ( ord_less_int @ C @ A2 )
% 0.29/0.48 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_coboundedI1
% 0.29/0.48 thf(fact_306_sup_Ostrict__order__iff,axiom,
% 0.29/0.48 ( ord_less_a_a_o
% 0.29/0.48 = ( ^ [B: a > a > $o,A: a > a > $o] :
% 0.29/0.48 ( ( A
% 0.29/0.48 = ( sup_sup_a_a_o @ A @ B ) )
% 0.29/0.48 & ( A != B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_order_iff
% 0.29/0.48 thf(fact_307_sup_Ostrict__order__iff,axiom,
% 0.29/0.48 ( ord_less_set_a
% 0.29/0.48 = ( ^ [B: set_a,A: set_a] :
% 0.29/0.48 ( ( A
% 0.29/0.48 = ( sup_sup_set_a @ A @ B ) )
% 0.29/0.48 & ( A != B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_order_iff
% 0.29/0.48 thf(fact_308_sup_Ostrict__order__iff,axiom,
% 0.29/0.48 ( ord_less_a_o
% 0.29/0.48 = ( ^ [B: a > $o,A: a > $o] :
% 0.29/0.48 ( ( A
% 0.29/0.48 = ( sup_sup_a_o @ A @ B ) )
% 0.29/0.48 & ( A != B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_order_iff
% 0.29/0.48 thf(fact_309_sup_Ostrict__order__iff,axiom,
% 0.29/0.48 ( ord_less_int
% 0.29/0.48 = ( ^ [B: int,A: int] :
% 0.29/0.48 ( ( A
% 0.29/0.48 = ( sup_sup_int @ A @ B ) )
% 0.29/0.48 & ( A != B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_order_iff
% 0.29/0.48 thf(fact_310_sup_Ostrict__boundedE,axiom,
% 0.29/0.48 ! [B2: a > a > $o,C: a > a > $o,A2: a > a > $o] :
% 0.29/0.48 ( ( ord_less_a_a_o @ ( sup_sup_a_a_o @ B2 @ C ) @ A2 )
% 0.29/0.48 => ~ ( ( ord_less_a_a_o @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_a_a_o @ C @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_boundedE
% 0.29/0.48 thf(fact_311_sup_Ostrict__boundedE,axiom,
% 0.29/0.48 ! [B2: set_a,C: set_a,A2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ ( sup_sup_set_a @ B2 @ C ) @ A2 )
% 0.29/0.48 => ~ ( ( ord_less_set_a @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_boundedE
% 0.29/0.48 thf(fact_312_sup_Ostrict__boundedE,axiom,
% 0.29/0.48 ! [B2: a > $o,C: a > $o,A2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ ( sup_sup_a_o @ B2 @ C ) @ A2 )
% 0.29/0.48 => ~ ( ( ord_less_a_o @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_boundedE
% 0.29/0.48 thf(fact_313_sup_Ostrict__boundedE,axiom,
% 0.29/0.48 ! [B2: int,C: int,A2: int] :
% 0.29/0.48 ( ( ord_less_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 0.29/0.48 => ~ ( ( ord_less_int @ B2 @ A2 )
% 0.29/0.48 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % sup.strict_boundedE
% 0.29/0.48 thf(fact_314_less__supI2,axiom,
% 0.29/0.48 ! [X: a > a > $o,B2: a > a > $o,A2: a > a > $o] :
% 0.29/0.48 ( ( ord_less_a_a_o @ X @ B2 )
% 0.29/0.48 => ( ord_less_a_a_o @ X @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI2
% 0.29/0.48 thf(fact_315_less__supI2,axiom,
% 0.29/0.48 ! [X: set_a,B2: set_a,A2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ B2 )
% 0.29/0.48 => ( ord_less_set_a @ X @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI2
% 0.29/0.48 thf(fact_316_less__supI2,axiom,
% 0.29/0.48 ! [X: a > $o,B2: a > $o,A2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ B2 )
% 0.29/0.48 => ( ord_less_a_o @ X @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI2
% 0.29/0.48 thf(fact_317_less__supI2,axiom,
% 0.29/0.48 ! [X: int,B2: int,A2: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ B2 )
% 0.29/0.48 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI2
% 0.29/0.48 thf(fact_318_less__supI1,axiom,
% 0.29/0.48 ! [X: a > a > $o,A2: a > a > $o,B2: a > a > $o] :
% 0.29/0.48 ( ( ord_less_a_a_o @ X @ A2 )
% 0.29/0.48 => ( ord_less_a_a_o @ X @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI1
% 0.29/0.48 thf(fact_319_less__supI1,axiom,
% 0.29/0.48 ! [X: set_a,A2: set_a,B2: set_a] :
% 0.29/0.48 ( ( ord_less_set_a @ X @ A2 )
% 0.29/0.48 => ( ord_less_set_a @ X @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI1
% 0.29/0.48 thf(fact_320_less__supI1,axiom,
% 0.29/0.48 ! [X: a > $o,A2: a > $o,B2: a > $o] :
% 0.29/0.48 ( ( ord_less_a_o @ X @ A2 )
% 0.29/0.48 => ( ord_less_a_o @ X @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI1
% 0.29/0.48 thf(fact_321_less__supI1,axiom,
% 0.29/0.48 ! [X: int,A2: int,B2: int] :
% 0.29/0.48 ( ( ord_less_int @ X @ A2 )
% 0.29/0.48 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_supI1
% 0.29/0.48 thf(fact_322_the__elem__def,axiom,
% 0.29/0.48 ( the_elem_a
% 0.29/0.48 = ( ^ [X7: set_a] :
% 0.29/0.48 ( the_a
% 0.29/0.48 @ ^ [X4: a] :
% 0.29/0.48 ( X7
% 0.29/0.48 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % the_elem_def
% 0.29/0.48 thf(fact_323_pred__on_Ochain__extend,axiom,
% 0.29/0.48 ! [A3: set_set_a,P: set_a > set_a > $o,C2: set_set_a,Z3: set_a] :
% 0.29/0.48 ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( ( member_set_a @ Z3 @ A3 )
% 0.29/0.48 => ( ! [X6: set_a] :
% 0.29/0.48 ( ( member_set_a @ X6 @ C2 )
% 0.29/0.48 => ( sup_su198629954et_a_o @ P
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ X6
% 0.29/0.48 @ Z3 ) )
% 0.29/0.48 => ( pred_chain_set_a @ A3 @ P @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain_extend
% 0.29/0.48 thf(fact_324_pred__on_Ochain__extend,axiom,
% 0.29/0.48 ! [A3: set_a,P: a > a > $o,C2: set_a,Z3: a] :
% 0.29/0.48 ( ( pred_chain_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( ( member_a @ Z3 @ A3 )
% 0.29/0.48 => ( ! [X6: a] :
% 0.29/0.48 ( ( member_a @ X6 @ C2 )
% 0.29/0.48 => ( sup_sup_a_a_o @ P
% 0.29/0.48 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 0.29/0.48 @ X6
% 0.29/0.48 @ Z3 ) )
% 0.29/0.48 => ( pred_chain_a @ A3 @ P @ ( sup_sup_set_a @ ( insert_a @ Z3 @ bot_bot_set_a ) @ C2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain_extend
% 0.29/0.48 thf(fact_325_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.48 semila1223476304_a_a_o @ sup_sup_a_a_o @ bot_bot_a_a_o ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.semilattice_neutr_axioms
% 0.29/0.48 thf(fact_326_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.48 semila1409648192_set_a @ sup_sup_set_a @ bot_bot_set_a ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.semilattice_neutr_axioms
% 0.29/0.48 thf(fact_327_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.48 semila980155549tr_a_o @ sup_sup_a_o @ bot_bot_a_o ).
% 0.29/0.48
% 0.29/0.48 % sup_bot.semilattice_neutr_axioms
% 0.29/0.48 thf(fact_328_subset_Ochain__extend,axiom,
% 0.29/0.48 ! [A3: set_set_a,C2: set_set_a,Z3: set_a] :
% 0.29/0.48 ( ( pred_chain_set_a @ A3 @ ord_less_set_a @ C2 )
% 0.29/0.48 => ( ( member_set_a @ Z3 @ A3 )
% 0.29/0.48 => ( ! [X6: set_a] :
% 0.29/0.48 ( ( member_set_a @ X6 @ C2 )
% 0.29/0.48 => ( sup_su198629954et_a_o @ ord_less_set_a
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ X6
% 0.29/0.48 @ Z3 ) )
% 0.29/0.48 => ( pred_chain_set_a @ A3 @ ord_less_set_a @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C2 ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % subset.chain_extend
% 0.29/0.48 thf(fact_329_subset_Ochain__total,axiom,
% 0.29/0.48 ! [A3: set_set_a,C2: set_set_a,X: set_a,Y: set_a] :
% 0.29/0.48 ( ( pred_chain_set_a @ A3 @ ord_less_set_a @ C2 )
% 0.29/0.48 => ( ( member_set_a @ X @ C2 )
% 0.29/0.48 => ( ( member_set_a @ Y @ C2 )
% 0.29/0.48 => ( ( sup_su198629954et_a_o @ ord_less_set_a
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ X
% 0.29/0.48 @ Y )
% 0.29/0.48 | ( sup_su198629954et_a_o @ ord_less_set_a
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ Y
% 0.29/0.48 @ X ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % subset.chain_total
% 0.29/0.48 thf(fact_330_pred__on_Ochain__total,axiom,
% 0.29/0.48 ! [A3: set_set_a,P: set_a > set_a > $o,C2: set_set_a,X: set_a,Y: set_a] :
% 0.29/0.48 ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( ( member_set_a @ X @ C2 )
% 0.29/0.48 => ( ( member_set_a @ Y @ C2 )
% 0.29/0.48 => ( ( sup_su198629954et_a_o @ P
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ X
% 0.29/0.48 @ Y )
% 0.29/0.48 | ( sup_su198629954et_a_o @ P
% 0.29/0.48 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 0.29/0.48 @ Y
% 0.29/0.48 @ X ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain_total
% 0.29/0.48 thf(fact_331_pred__on_Ochain__total,axiom,
% 0.29/0.48 ! [A3: set_a,P: a > a > $o,C2: set_a,X: a,Y: a] :
% 0.29/0.48 ( ( pred_chain_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( ( member_a @ X @ C2 )
% 0.29/0.48 => ( ( member_a @ Y @ C2 )
% 0.29/0.48 => ( ( sup_sup_a_a_o @ P
% 0.29/0.48 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 0.29/0.48 @ X
% 0.29/0.48 @ Y )
% 0.29/0.48 | ( sup_sup_a_a_o @ P
% 0.29/0.48 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 0.29/0.48 @ Y
% 0.29/0.48 @ X ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain_total
% 0.29/0.48 thf(fact_332_subset_Ochain__empty,axiom,
% 0.29/0.48 ! [A3: set_set_a] : ( pred_chain_set_a @ A3 @ ord_less_set_a @ bot_bot_set_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % subset.chain_empty
% 0.29/0.48 thf(fact_333_pred__on_Ochain__empty,axiom,
% 0.29/0.48 ! [A3: set_a,P: a > a > $o] : ( pred_chain_a @ A3 @ P @ bot_bot_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain_empty
% 0.29/0.48 thf(fact_334_chain__mono,axiom,
% 0.29/0.48 ! [A3: set_set_a,P: set_a > set_a > $o,Q: set_a > set_a > $o,C2: set_set_a] :
% 0.29/0.48 ( ! [X6: set_a,Y3: set_a] :
% 0.29/0.48 ( ( member_set_a @ X6 @ A3 )
% 0.29/0.48 => ( ( member_set_a @ Y3 @ A3 )
% 0.29/0.48 => ( ( P @ X6 @ Y3 )
% 0.29/0.48 => ( Q @ X6 @ Y3 ) ) ) )
% 0.29/0.48 => ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( pred_chain_set_a @ A3 @ Q @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % chain_mono
% 0.29/0.48 thf(fact_335_chain__mono,axiom,
% 0.29/0.48 ! [A3: set_a,P: a > a > $o,Q: a > a > $o,C2: set_a] :
% 0.29/0.48 ( ! [X6: a,Y3: a] :
% 0.29/0.48 ( ( member_a @ X6 @ A3 )
% 0.29/0.48 => ( ( member_a @ Y3 @ A3 )
% 0.29/0.48 => ( ( P @ X6 @ Y3 )
% 0.29/0.48 => ( Q @ X6 @ Y3 ) ) ) )
% 0.29/0.48 => ( ( pred_chain_a @ A3 @ P @ C2 )
% 0.29/0.48 => ( pred_chain_a @ A3 @ Q @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % chain_mono
% 0.29/0.48 thf(fact_336_pred__on_Ochain_Ocong,axiom,
% 0.29/0.48 pred_chain_a = pred_chain_a ).
% 0.29/0.48
% 0.29/0.48 % pred_on.chain.cong
% 0.29/0.48 thf(fact_337_chains__alt__def,axiom,
% 0.29/0.48 ( chains_a
% 0.29/0.48 = ( ^ [A5: set_set_a] : ( collect_set_set_a @ ( pred_chain_set_a @ A5 @ ord_less_set_a ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % chains_alt_def
% 0.29/0.48 thf(fact_338_Pow__empty,axiom,
% 0.29/0.48 ( ( pow_a @ bot_bot_set_a )
% 0.29/0.48 = ( insert_set_a @ bot_bot_set_a @ bot_bot_set_set_a ) ) ).
% 0.29/0.48
% 0.29/0.48 % Pow_empty
% 0.29/0.48 thf(fact_339_Pow__singleton__iff,axiom,
% 0.29/0.48 ! [X8: set_a,Y5: set_a] :
% 0.29/0.48 ( ( ( pow_a @ X8 )
% 0.29/0.48 = ( insert_set_a @ Y5 @ bot_bot_set_set_a ) )
% 0.29/0.48 = ( ( X8 = bot_bot_set_a )
% 0.29/0.48 & ( Y5 = bot_bot_set_a ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Pow_singleton_iff
% 0.29/0.48 thf(fact_340_Pow__not__empty,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( pow_a @ A3 )
% 0.29/0.48 != bot_bot_set_set_a ) ).
% 0.29/0.48
% 0.29/0.48 % Pow_not_empty
% 0.29/0.48 thf(fact_341_Pow__bottom,axiom,
% 0.29/0.48 ! [B4: set_a] : ( member_set_a @ bot_bot_set_a @ ( pow_a @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % Pow_bottom
% 0.29/0.48 thf(fact_342_Pow__top,axiom,
% 0.29/0.48 ! [A3: set_a] : ( member_set_a @ A3 @ ( pow_a @ A3 ) ) ).
% 0.29/0.48
% 0.29/0.48 % Pow_top
% 0.29/0.48 thf(fact_343_chains__extend,axiom,
% 0.29/0.48 ! [C: set_set_a,S: set_set_a,Z3: set_a] :
% 0.29/0.48 ( ( member_set_set_a @ C @ ( chains_a @ S ) )
% 0.29/0.48 => ( ( member_set_a @ Z3 @ S )
% 0.29/0.48 => ( ! [X6: set_a] :
% 0.29/0.48 ( ( member_set_a @ X6 @ C )
% 0.29/0.48 => ( ord_less_eq_set_a @ X6 @ Z3 ) )
% 0.29/0.48 => ( member_set_set_a @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C ) @ ( chains_a @ S ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % chains_extend
% 0.29/0.48 thf(fact_344_Powp__Pow__eq,axiom,
% 0.29/0.48 ! [A3: set_set_a] :
% 0.29/0.48 ( ( powp_set_a
% 0.29/0.48 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 0.29/0.48 = ( ^ [X4: set_set_a] : ( member_set_set_a @ X4 @ ( pow_set_a @ A3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Powp_Pow_eq
% 0.29/0.48 thf(fact_345_Powp__Pow__eq,axiom,
% 0.29/0.48 ! [A3: set_a] :
% 0.29/0.48 ( ( powp_a
% 0.29/0.48 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.29/0.48 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ ( pow_a @ A3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % Powp_Pow_eq
% 0.29/0.48 thf(fact_346_order__refl,axiom,
% 0.29/0.48 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 0.29/0.48
% 0.29/0.48 % order_refl
% 0.29/0.48 thf(fact_347_subset__antisym,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 0.29/0.48 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 0.29/0.48 => ( A3 = B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % subset_antisym
% 0.29/0.48 thf(fact_348_subsetI,axiom,
% 0.29/0.48 ! [A3: set_a,B4: set_a] :
% 0.29/0.48 ( ! [X6: a] :
% 0.29/0.48 ( ( member_a @ X6 @ A3 )
% 0.29/0.48 => ( member_a @ X6 @ B4 ) )
% 0.29/0.48 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 0.29/0.48
% 0.29/0.48 % subsetI
% 0.29/0.48 thf(fact_349_insert__subset,axiom,
% 0.29/0.48 ! [X: a,A3: set_a,B4: set_a] :
% 0.29/0.48 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A3 ) @ B4 )
% 0.29/0.48 = ( ( member_a @ X @ B4 )
% 0.29/0.48 & ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % insert_subset
% 0.29/0.48
% 0.29/0.48 % Conjectures (1)
% 0.29/0.48 thf(conj_0,conjecture,
% 0.29/0.48 a2 = b ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 2.64/1.54 ---- Embedded in THF ---
% 2.64/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.64/1.54 %%% Generated on Tue Feb 24 08:23:46 EST 2026
% 2.64/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.64/1.54 %%% Logic specification used:
% 2.64/1.54 %%% thf(spec, logic, $$dhol).
% 2.64/1.54
% 2.64/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2DTF27328.p
% See solution above
% 2.64/1.54 ------------------------
% 2.64/1.58 ---- Cleaned THF ---
% 2.64/1.58 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 binary594033953_set_a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 2.64/1.58 binary1439146945Tree_a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 2.64/1.58 set_set_set_a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 set_set_a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 set_a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_t__Int__Oint,type,
% 2.64/1.58 int: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(ty_n_tf__a,type,
% 2.64/1.58 a: $tType ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 binary313540327_set_a: binary594033953_set_a > set_a > binary594033953_set_a > binary594033953_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 2.64/1.58 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 2.64/1.58 binary476621312_Tip_a: binary1439146945Tree_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 binary1613048283_set_a: binary594033953_set_a > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001tf__a,type,
% 2.64/1.58 binary256242811Tree_a: binary1439146945Tree_a > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001tf__a,type,
% 2.64/1.58 binary504661350_eqs_a: ( a > int ) > a > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 binary1001944660_set_a: binary594033953_set_a > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 2.64/1.58 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 binary512218034_set_a: ( set_a > int ) > binary594033953_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 2.64/1.58 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 binary1524747315_set_a: ( set_a > int ) > set_a > set_a > binary594033953_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 2.64/1.58 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_HOL_OThe_001tf__a,type,
% 2.64/1.58 the_a: ( a > $o ) > a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osemilattice__neutr_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 2.64/1.58 semila1223476304_a_a_o: ( ( a > a > $o ) > ( a > a > $o ) > a > a > $o ) > ( a > a > $o ) > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osemilattice__neutr_001_062_Itf__a_M_Eo_J,type,
% 2.64/1.58 semila980155549tr_a_o: ( ( a > $o ) > ( a > $o ) > a > $o ) > ( a > $o ) > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 semila1409648192_set_a: ( set_a > set_a > set_a ) > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_Itf__a_J_M_062_It__Set__Oset_Itf__a_J_M_Eo_J_J,type,
% 2.64/1.58 sup_su198629954et_a_o: ( set_a > set_a > $o ) > ( set_a > set_a > $o ) > set_a > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 2.64/1.58 sup_sup_set_a_o: ( set_a > $o ) > ( set_a > $o ) > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 2.64/1.58 sup_sup_a_a_o: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
% 2.64/1.58 sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 2.64/1.58 sup_sup_int: int > int > int ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 sup_sup_set_set_a: set_set_a > set_set_a > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 sup_sup_set_a: set_a > set_a > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 2.64/1.58 bot_bot_set_a_o: set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 2.64/1.58 bot_bot_a_a_o: a > a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 2.64/1.58 bot_bot_a_o: a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 2.64/1.58 bot_bot_o: $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 bot_bot_set_set_a: set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 bot_bot_set_a: set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Set__Oset_Itf__a_J_M_Eo_J,type,
% 2.64/1.58 ord_less_set_a_o: ( set_a > $o ) > ( set_a > $o ) > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J,type,
% 2.64/1.58 ord_less_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 2.64/1.58 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 2.64/1.58 ord_less_int: int > int > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 ord_less_set_set_a: set_set_a > set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 ord_less_set_a: set_a > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Relation_OPowp_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 powp_set_a: ( set_a > $o ) > set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Relation_OPowp_001tf__a,type,
% 2.64/1.58 powp_a: ( a > $o ) > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 collect_set_set_a: ( set_set_a > $o ) > set_set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 collect_set_a: ( set_a > $o ) > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.64/1.58 collect_a: ( a > $o ) > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_OPow_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 pow_set_a: set_set_a > set_set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_OPow_001tf__a,type,
% 2.64/1.58 pow_a: set_a > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Oinsert_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 insert_set_a: set_a > set_set_a > set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Oinsert_001tf__a,type,
% 2.64/1.58 insert_a: a > set_a > set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Ois__empty_001tf__a,type,
% 2.64/1.58 is_empty_a: set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Ois__singleton_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 is_singleton_set_a: set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 2.64/1.58 is_singleton_a: set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Set_Othe__elem_001tf__a,type,
% 2.64/1.58 the_elem_a: set_a > a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Zorn_Ochains_001tf__a,type,
% 2.64/1.58 chains_a: set_set_a > set_set_set_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Zorn_Opred__on_Ochain_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 pred_chain_set_a: set_set_a > ( set_a > set_a > $o ) > set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_Zorn_Opred__on_Ochain_001tf__a,type,
% 2.64/1.58 pred_chain_a: set_a > ( a > a > $o ) > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 2.64/1.58 member_set_set_a: set_set_a > set_set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 2.64/1.58 member_set_a: set_a > set_set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_c_member_001tf__a,type,
% 2.64/1.58 member_a: a > set_a > $o ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_a,type,
% 2.64/1.58 a2: a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_b,type,
% 2.64/1.58 b: a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_h,type,
% 2.64/1.58 h: a > int ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_t1____,type,
% 2.64/1.58 t1: binary1439146945Tree_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_t2____,type,
% 2.64/1.58 t2: binary1439146945Tree_a ).
% 2.64/1.58
% 2.64/1.58 thf(sy_v_x____,type,
% 2.64/1.58 x: a ).
% 2.64/1.58
% 2.64/1.58 thf(fact_0_hahb,axiom,
% 2.64/1.58 ( ( h @ a2 )
% 2.64/1.58 = ( h @ b ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062,axiom,
% 2.64/1.58 ord_less_int @ ( h @ b ) @ ( h @ a2 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_2__092_060open_062a_A_061_Ax_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 2.64/1.58 ( ( a2 = x )
% 2.64/1.58 => ( a2 = b ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_3_adef1,axiom,
% 2.64/1.58 member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_4_bdef1,axiom,
% 2.64/1.58 member_a @ b @ ( binary945792244etOf_a @ t1 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_5__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060Longrightarrow_062_Aa_A_061_Ab_092_060close_062,axiom,
% 2.64/1.58 ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
% 2.64/1.58 => ( a2 = b ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_6_o1,axiom,
% 2.64/1.58 ord_less_int @ ( h @ b ) @ ( h @ x ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_7_o2,axiom,
% 2.64/1.58 ord_less_int @ ( h @ x ) @ ( h @ a2 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_8_h2,axiom,
% 2.64/1.58 binary670562003pred_a @ h @ a2 @ b @ t2 ).
% 2.64/1.58
% 2.64/1.58 thf(fact_9_h1,axiom,
% 2.64/1.58 binary670562003pred_a @ h @ a2 @ b @ t1 ).
% 2.64/1.58
% 2.64/1.58 thf(fact_10__092_060open_062sorted__distinct__pred_Ah_Aa_Ab_ATip_092_060close_062,axiom,
% 2.64/1.58 binary670562003pred_a @ h @ a2 @ b @ binary476621312_Tip_a ).
% 2.64/1.58
% 2.64/1.58 thf(fact_11_calculation,axiom,
% 2.64/1.58 ( ( member_a @ b @ ( binary945792244etOf_a @ t1 ) )
% 2.64/1.58 | ( b = x )
% 2.64/1.58 | ( member_a @ b @ ( binary945792244etOf_a @ t2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_12__092_060open_062a_A_092_060in_062_AsetOf_At1_A_092_060or_062_Aa_A_061_Ax_A_092_060or_062_Aa_A_092_060in_062_AsetOf_At2_092_060close_062,axiom,
% 2.64/1.58 ( ( member_a @ a2 @ ( binary945792244etOf_a @ t1 ) )
% 2.64/1.58 | ( a2 = x )
% 2.64/1.58 | ( member_a @ a2 @ ( binary945792244etOf_a @ t2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_13_bdef,axiom,
% 2.64/1.58 member_a @ b @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_14_Tree_Oinject,axiom,
% 2.64/1.58 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 2.64/1.58 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 2.64/1.58 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 2.64/1.58 = ( ( X21 = Y21 )
% 2.64/1.58 & ( X22 = Y22 )
% 2.64/1.58 & ( X23 = Y23 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_15_adef,axiom,
% 2.64/1.58 member_a @ a2 @ ( binary945792244etOf_a @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_16_s,axiom,
% 2.64/1.58 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_17_Tree_Odistinct_I1_J,axiom,
% 2.64/1.58 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.64/1.58 ( binary476621312_Tip_a
% 2.64/1.58 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_18_Tree_Oinduct,axiom,
% 2.64/1.58 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 2.64/1.58 ( ( P @ binary476621312_Tip_a )
% 2.64/1.58 => ( ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
% 2.64/1.58 ( ( P @ X1 )
% 2.64/1.58 => ( ( P @ X3 )
% 2.64/1.58 => ( P @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) ) ) )
% 2.64/1.58 => ( P @ Tree ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_19_Tree_Oexhaust,axiom,
% 2.64/1.58 ! [Y: binary1439146945Tree_a] :
% 2.64/1.58 ( ( Y != binary476621312_Tip_a )
% 2.64/1.58 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 2.64/1.58 ( Y
% 2.64/1.58 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_20_s2,axiom,
% 2.64/1.58 binary1721989714Tree_a @ h @ t2 ).
% 2.64/1.58
% 2.64/1.58 thf(fact_21_s1,axiom,
% 2.64/1.58 binary1721989714Tree_a @ h @ t1 ).
% 2.64/1.58
% 2.64/1.58 thf(fact_22_sortedTree_Osimps_I2_J,axiom,
% 2.64/1.58 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.64/1.58 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.64/1.58 = ( ( binary1721989714Tree_a @ H @ T1 )
% 2.64/1.58 & ! [X4: a] :
% 2.64/1.58 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 2.64/1.58 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X ) ) )
% 2.64/1.58 & ! [X4: a] :
% 2.64/1.58 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 2.64/1.58 => ( ord_less_int @ ( H @ X ) @ ( H @ X4 ) ) )
% 2.64/1.58 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_23_sorted__distinct__pred__def,axiom,
% 2.64/1.58 ( binary1524747315_set_a
% 2.64/1.58 = ( ^ [H2: set_a > int,A: set_a,B: set_a,T: binary594033953_set_a] :
% 2.64/1.58 ( ( ( binary512218034_set_a @ H2 @ T )
% 2.64/1.58 & ( member_set_a @ A @ ( binary1001944660_set_a @ T ) )
% 2.64/1.58 & ( member_set_a @ B @ ( binary1001944660_set_a @ T ) )
% 2.64/1.58 & ( ( H2 @ A )
% 2.64/1.58 = ( H2 @ B ) ) )
% 2.64/1.58 => ( A = B ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_24_sorted__distinct__pred__def,axiom,
% 2.64/1.58 ( binary670562003pred_a
% 2.64/1.58 = ( ^ [H2: a > int,A: a,B: a,T: binary1439146945Tree_a] :
% 2.64/1.58 ( ( ( binary1721989714Tree_a @ H2 @ T )
% 2.64/1.58 & ( member_a @ A @ ( binary945792244etOf_a @ T ) )
% 2.64/1.58 & ( member_a @ B @ ( binary945792244etOf_a @ T ) )
% 2.64/1.58 & ( ( H2 @ A )
% 2.64/1.58 = ( H2 @ B ) ) )
% 2.64/1.58 => ( A = B ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_25_eqs__def,axiom,
% 2.64/1.58 ( binary504661350_eqs_a
% 2.64/1.58 = ( ^ [H2: a > int,X4: a] :
% 2.64/1.58 ( collect_a
% 2.64/1.58 @ ^ [Y2: a] :
% 2.64/1.58 ( ( H2 @ Y2 )
% 2.64/1.58 = ( H2 @ X4 ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_26_minf_I7_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ~ ( ord_less_int @ T3 @ X5 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_27_minf_I5_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ( ord_less_int @ X5 @ T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_28_minf_I4_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ( X5 != T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_29_minf_I3_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ( X5 != T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_30_minf_I2_J,axiom,
% 2.64/1.58 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.64/1.58 ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Z2 )
% 2.64/1.58 => ( ( P @ X6 )
% 2.64/1.58 = ( P2 @ X6 ) ) )
% 2.64/1.58 => ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Z2 )
% 2.64/1.58 => ( ( Q @ X6 )
% 2.64/1.58 = ( Q2 @ X6 ) ) )
% 2.64/1.58 => ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ( ( ( P @ X5 )
% 2.64/1.58 | ( Q @ X5 ) )
% 2.64/1.58 = ( ( P2 @ X5 )
% 2.64/1.58 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_31_sortLemmaR,axiom,
% 2.64/1.58 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.64/1.58 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.64/1.58 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_32_sortLemmaL,axiom,
% 2.64/1.58 ! [H: a > int,T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.64/1.58 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.64/1.58 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_33_sortedTree_Osimps_I1_J,axiom,
% 2.64/1.58 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_34_pinf_I1_J,axiom,
% 2.64/1.58 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.64/1.58 ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ Z2 @ X6 )
% 2.64/1.58 => ( ( P @ X6 )
% 2.64/1.58 = ( P2 @ X6 ) ) )
% 2.64/1.58 => ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ Z2 @ X6 )
% 2.64/1.58 => ( ( Q @ X6 )
% 2.64/1.58 = ( Q2 @ X6 ) ) )
% 2.64/1.58 => ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ( ( ( P @ X5 )
% 2.64/1.58 & ( Q @ X5 ) )
% 2.64/1.58 = ( ( P2 @ X5 )
% 2.64/1.58 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_35_pinf_I2_J,axiom,
% 2.64/1.58 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.64/1.58 ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ Z2 @ X6 )
% 2.64/1.58 => ( ( P @ X6 )
% 2.64/1.58 = ( P2 @ X6 ) ) )
% 2.64/1.58 => ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ Z2 @ X6 )
% 2.64/1.58 => ( ( Q @ X6 )
% 2.64/1.58 = ( Q2 @ X6 ) ) )
% 2.64/1.58 => ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ( ( ( P @ X5 )
% 2.64/1.58 | ( Q @ X5 ) )
% 2.64/1.58 = ( ( P2 @ X5 )
% 2.64/1.58 | ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_36_pinf_I3_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ( X5 != T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_37_pinf_I4_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ( X5 != T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_38_pinf_I5_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ~ ( ord_less_int @ X5 @ T3 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_39_pinf_I7_J,axiom,
% 2.64/1.58 ! [T3: int] :
% 2.64/1.58 ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ Z @ X5 )
% 2.64/1.58 => ( ord_less_int @ T3 @ X5 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_40_minf_I1_J,axiom,
% 2.64/1.58 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.64/1.58 ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Z2 )
% 2.64/1.58 => ( ( P @ X6 )
% 2.64/1.58 = ( P2 @ X6 ) ) )
% 2.64/1.58 => ( ? [Z2: int] :
% 2.64/1.58 ! [X6: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Z2 )
% 2.64/1.58 => ( ( Q @ X6 )
% 2.64/1.58 = ( Q2 @ X6 ) ) )
% 2.64/1.58 => ? [Z: int] :
% 2.64/1.58 ! [X5: int] :
% 2.64/1.58 ( ( ord_less_int @ X5 @ Z )
% 2.64/1.58 => ( ( ( P @ X5 )
% 2.64/1.58 & ( Q @ X5 ) )
% 2.64/1.58 = ( ( P2 @ X5 )
% 2.64/1.58 & ( Q2 @ X5 ) ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_41_linorder__neqE__linordered__idom,axiom,
% 2.64/1.58 ! [X: int,Y: int] :
% 2.64/1.58 ( ( X != Y )
% 2.64/1.58 => ( ~ ( ord_less_int @ X @ Y )
% 2.64/1.58 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_42_dual__order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [B2: set_a,A2: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ B2 @ A2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_43_dual__order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [B2: a > $o,A2: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ B2 @ A2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_44_dual__order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [B2: int,A2: int] :
% 2.64/1.58 ( ( ord_less_int @ B2 @ A2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_45_mem__Collect__eq,axiom,
% 2.64/1.58 ! [A2: set_a,P: set_a > $o] :
% 2.64/1.58 ( ( member_set_a @ A2 @ ( collect_set_a @ P ) )
% 2.64/1.58 = ( P @ A2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_46_mem__Collect__eq,axiom,
% 2.64/1.58 ! [A2: a,P: a > $o] :
% 2.64/1.58 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 2.64/1.58 = ( P @ A2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_47_Collect__mem__eq,axiom,
% 2.64/1.58 ! [A3: set_set_a] :
% 2.64/1.58 ( ( collect_set_a
% 2.64/1.58 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 2.64/1.58 = A3 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_48_Collect__mem__eq,axiom,
% 2.64/1.58 ! [A3: set_a] :
% 2.64/1.58 ( ( collect_a
% 2.64/1.58 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.64/1.58 = A3 ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_49_Collect__cong,axiom,
% 2.64/1.58 ! [P: a > $o,Q: a > $o] :
% 2.64/1.58 ( ! [X6: a] :
% 2.64/1.58 ( ( P @ X6 )
% 2.64/1.58 = ( Q @ X6 ) )
% 2.64/1.58 => ( ( collect_a @ P )
% 2.64/1.58 = ( collect_a @ Q ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_50_order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [A2: set_a,B2: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_51_order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [A2: a > $o,B2: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_52_order_Ostrict__implies__not__eq,axiom,
% 2.64/1.58 ! [A2: int,B2: int] :
% 2.64/1.58 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.58 => ( A2 != B2 ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_53_not__less__iff__gr__or__eq,axiom,
% 2.64/1.58 ! [X: int,Y: int] :
% 2.64/1.58 ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.64/1.58 = ( ( ord_less_int @ Y @ X )
% 2.64/1.58 | ( X = Y ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_54_dual__order_Ostrict__trans,axiom,
% 2.64/1.58 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ B2 @ A2 )
% 2.64/1.58 => ( ( ord_less_set_a @ C @ B2 )
% 2.64/1.58 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_55_dual__order_Ostrict__trans,axiom,
% 2.64/1.58 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ B2 @ A2 )
% 2.64/1.58 => ( ( ord_less_a_o @ C @ B2 )
% 2.64/1.58 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_56_dual__order_Ostrict__trans,axiom,
% 2.64/1.58 ! [B2: int,A2: int,C: int] :
% 2.64/1.58 ( ( ord_less_int @ B2 @ A2 )
% 2.64/1.58 => ( ( ord_less_int @ C @ B2 )
% 2.64/1.58 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_57_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_58_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_59_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_60_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_61_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_62_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_63_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_64_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_65_ord__eq__less__subst,axiom,
% 2.64/1.58 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.64/1.58 ( ( A2
% 2.64/1.58 = ( F @ B2 ) )
% 2.64/1.58 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_66_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.64/1.58 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_67_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.64/1.58 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_68_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.64/1.58 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_69_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_70_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.64/1.58 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.58 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_71_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.64/1.58 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_72_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.64/1.58 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_73_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.58 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.58
% 2.64/1.58 thf(fact_74_ord__less__eq__subst,axiom,
% 2.64/1.58 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.64/1.58 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.58 => ( ( ( F @ B2 )
% 2.64/1.58 = C )
% 2.64/1.58 => ( ! [X6: int,Y3: int] :
% 2.64/1.58 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.58 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.58 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_75_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_76_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_77_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_78_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_79_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_80_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_81_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_82_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_83_order__less__subst1,axiom,
% 2.64/1.59 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.64/1.59 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_84_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_85_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_86_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_87_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_88_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_89_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_90_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_91_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: a > $o,Y3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_92_order__less__subst2,axiom,
% 2.64/1.59 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.64/1.59 => ( ! [X6: int,Y3: int] :
% 2.64/1.59 ( ( ord_less_int @ X6 @ Y3 )
% 2.64/1.59 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y3 ) ) )
% 2.64/1.59 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_93_lt__ex,axiom,
% 2.64/1.59 ! [X: int] :
% 2.64/1.59 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_94_gt__ex,axiom,
% 2.64/1.59 ! [X: int] :
% 2.64/1.59 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_95_neqE,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( X != Y )
% 2.64/1.59 => ( ~ ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_96_neq__iff,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( X != Y )
% 2.64/1.59 = ( ( ord_less_int @ X @ Y )
% 2.64/1.59 | ( ord_less_int @ Y @ X ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_97_order_Oasym,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_98_order_Oasym,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_99_order_Oasym,axiom,
% 2.64/1.59 ! [A2: int,B2: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_100_less__imp__neq,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_101_less__imp__neq,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_102_less__imp__neq,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_103_less__asym,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_104_less__asym,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_105_less__asym,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_106_less__asym_H,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_107_less__asym_H,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_108_less__asym_H,axiom,
% 2.64/1.59 ! [A2: int,B2: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_109_less__trans,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a,Z3: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ( ( ord_less_set_a @ Y @ Z3 )
% 2.64/1.59 => ( ord_less_set_a @ X @ Z3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_110_less__trans,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o,Z3: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ( ( ord_less_a_o @ Y @ Z3 )
% 2.64/1.59 => ( ord_less_a_o @ X @ Z3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_111_less__trans,axiom,
% 2.64/1.59 ! [X: int,Y: int,Z3: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( ( ord_less_int @ Y @ Z3 )
% 2.64/1.59 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_112_less__linear,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 | ( X = Y )
% 2.64/1.59 | ( ord_less_int @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_113_less__irrefl,axiom,
% 2.64/1.59 ! [X: set_a] :
% 2.64/1.59 ~ ( ord_less_set_a @ X @ X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_114_less__irrefl,axiom,
% 2.64/1.59 ! [X: a > $o] :
% 2.64/1.59 ~ ( ord_less_a_o @ X @ X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_115_less__irrefl,axiom,
% 2.64/1.59 ! [X: int] :
% 2.64/1.59 ~ ( ord_less_int @ X @ X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_116_ord__eq__less__trans,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( A2 = B2 )
% 2.64/1.59 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_117_ord__eq__less__trans,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( A2 = B2 )
% 2.64/1.59 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_118_ord__eq__less__trans,axiom,
% 2.64/1.59 ! [A2: int,B2: int,C: int] :
% 2.64/1.59 ( ( A2 = B2 )
% 2.64/1.59 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.59 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_119_ord__less__eq__trans,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ( ( B2 = C )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_120_ord__less__eq__trans,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ( ( B2 = C )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_121_ord__less__eq__trans,axiom,
% 2.64/1.59 ! [A2: int,B2: int,C: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ( ( B2 = C )
% 2.64/1.59 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_122_dual__order_Oasym,axiom,
% 2.64/1.59 ! [B2: set_a,A2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_123_dual__order_Oasym,axiom,
% 2.64/1.59 ! [B2: a > $o,A2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_124_dual__order_Oasym,axiom,
% 2.64/1.59 ! [B2: int,A2: int] :
% 2.64/1.59 ( ( ord_less_int @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_125_less__imp__not__eq,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_126_less__imp__not__eq,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_127_less__imp__not__eq,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( X != Y ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_128_less__not__sym,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_129_less__not__sym,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_130_less__not__sym,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_131_antisym__conv3,axiom,
% 2.64/1.59 ! [Y: int,X: int] :
% 2.64/1.59 ( ~ ( ord_less_int @ Y @ X )
% 2.64/1.59 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 2.64/1.59 = ( X = Y ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_132_less__imp__not__eq2,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ( Y != X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_133_less__imp__not__eq2,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ( Y != X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_134_less__imp__not__eq2,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( Y != X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_135_less__imp__triv,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a,P: $o] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ( ( ord_less_set_a @ Y @ X )
% 2.64/1.59 => P ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_136_less__imp__triv,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o,P: $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ( ( ord_less_a_o @ Y @ X )
% 2.64/1.59 => P ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_137_less__imp__triv,axiom,
% 2.64/1.59 ! [X: int,Y: int,P: $o] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( ( ord_less_int @ Y @ X )
% 2.64/1.59 => P ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_138_linorder__cases,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ~ ( ord_less_int @ X @ Y )
% 2.64/1.59 => ( ( X != Y )
% 2.64/1.59 => ( ord_less_int @ Y @ X ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_139_dual__order_Oirrefl,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_140_dual__order_Oirrefl,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_141_dual__order_Oirrefl,axiom,
% 2.64/1.59 ! [A2: int] :
% 2.64/1.59 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_142_order_Ostrict__trans,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_set_a @ B2 @ C )
% 2.64/1.59 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_143_order_Ostrict__trans,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_a_o @ B2 @ C )
% 2.64/1.59 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_144_order_Ostrict__trans,axiom,
% 2.64/1.59 ! [A2: int,B2: int,C: int] :
% 2.64/1.59 ( ( ord_less_int @ A2 @ B2 )
% 2.64/1.59 => ( ( ord_less_int @ B2 @ C )
% 2.64/1.59 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_145_less__imp__not__less,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_set_a @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_146_less__imp__not__less,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_a_o @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_147_less__imp__not__less,axiom,
% 2.64/1.59 ! [X: int,Y: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ Y )
% 2.64/1.59 => ~ ( ord_less_int @ Y @ X ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_148_linorder__less__wlog,axiom,
% 2.64/1.59 ! [P: int > int > $o,A2: int,B2: int] :
% 2.64/1.59 ( ! [A4: int,B3: int] :
% 2.64/1.59 ( ( ord_less_int @ A4 @ B3 )
% 2.64/1.59 => ( P @ A4 @ B3 ) )
% 2.64/1.59 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 2.64/1.59 => ( ! [A4: int,B3: int] :
% 2.64/1.59 ( ( P @ B3 @ A4 )
% 2.64/1.59 => ( P @ A4 @ B3 ) )
% 2.64/1.59 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_149_verit__comp__simplify1_I1_J,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_150_verit__comp__simplify1_I1_J,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_151_verit__comp__simplify1_I1_J,axiom,
% 2.64/1.59 ! [A2: int] :
% 2.64/1.59 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_152_setOf_Osimps_I1_J,axiom,
% 2.64/1.59 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 2.64/1.59 = bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_153_bot__apply,axiom,
% 2.64/1.59 ( bot_bot_a_o
% 2.64/1.59 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_154_bot__fun__def,axiom,
% 2.64/1.59 ( bot_bot_a_o
% 2.64/1.59 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_155_bot_Oextremum__strict,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_156_bot_Oextremum__strict,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_157_bot_Onot__eq__extremum,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ( ( A2 != bot_bot_set_a )
% 2.64/1.59 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_158_bot_Onot__eq__extremum,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ( ( A2 != bot_bot_a_o )
% 2.64/1.59 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_159_empty__Collect__eq,axiom,
% 2.64/1.59 ! [P: a > $o] :
% 2.64/1.59 ( ( bot_bot_set_a
% 2.64/1.59 = ( collect_a @ P ) )
% 2.64/1.59 = ( ! [X4: a] :
% 2.64/1.59 ~ ( P @ X4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_160_Collect__empty__eq,axiom,
% 2.64/1.59 ! [P: a > $o] :
% 2.64/1.59 ( ( ( collect_a @ P )
% 2.64/1.59 = bot_bot_set_a )
% 2.64/1.59 = ( ! [X4: a] :
% 2.64/1.59 ~ ( P @ X4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_161_all__not__in__conv,axiom,
% 2.64/1.59 ! [A3: set_set_a] :
% 2.64/1.59 ( ( ! [X4: set_a] :
% 2.64/1.59 ~ ( member_set_a @ X4 @ A3 ) )
% 2.64/1.59 = ( A3 = bot_bot_set_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_162_all__not__in__conv,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( ! [X4: a] :
% 2.64/1.59 ~ ( member_a @ X4 @ A3 ) )
% 2.64/1.59 = ( A3 = bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_163_empty__iff,axiom,
% 2.64/1.59 ! [C: set_a] :
% 2.64/1.59 ~ ( member_set_a @ C @ bot_bot_set_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_164_empty__iff,axiom,
% 2.64/1.59 ! [C: a] :
% 2.64/1.59 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_165_empty__def,axiom,
% 2.64/1.59 ( bot_bot_set_a
% 2.64/1.59 = ( collect_a
% 2.64/1.59 @ ^ [X4: a] : $false ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_166_bot__set__def,axiom,
% 2.64/1.59 ( bot_bot_set_a
% 2.64/1.59 = ( collect_a @ bot_bot_a_o ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_167_not__psubset__empty,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_168_emptyE,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ~ ( member_set_a @ A2 @ bot_bot_set_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_169_emptyE,axiom,
% 2.64/1.59 ! [A2: a] :
% 2.64/1.59 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_170_equals0D,axiom,
% 2.64/1.59 ! [A3: set_set_a,A2: set_a] :
% 2.64/1.59 ( ( A3 = bot_bot_set_set_a )
% 2.64/1.59 => ~ ( member_set_a @ A2 @ A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_171_equals0D,axiom,
% 2.64/1.59 ! [A3: set_a,A2: a] :
% 2.64/1.59 ( ( A3 = bot_bot_set_a )
% 2.64/1.59 => ~ ( member_a @ A2 @ A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_172_equals0I,axiom,
% 2.64/1.59 ! [A3: set_set_a] :
% 2.64/1.59 ( ! [Y3: set_a] :
% 2.64/1.59 ~ ( member_set_a @ Y3 @ A3 )
% 2.64/1.59 => ( A3 = bot_bot_set_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_173_equals0I,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ! [Y3: a] :
% 2.64/1.59 ~ ( member_a @ Y3 @ A3 )
% 2.64/1.59 => ( A3 = bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_174_ex__in__conv,axiom,
% 2.64/1.59 ! [A3: set_set_a] :
% 2.64/1.59 ( ( ? [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 2.64/1.59 = ( A3 != bot_bot_set_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_175_ex__in__conv,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( ? [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.64/1.59 = ( A3 != bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_176_Set_Ois__empty__def,axiom,
% 2.64/1.59 ( is_empty_a
% 2.64/1.59 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_177_Collect__empty__eq__bot,axiom,
% 2.64/1.59 ! [P: a > $o] :
% 2.64/1.59 ( ( ( collect_a @ P )
% 2.64/1.59 = bot_bot_set_a )
% 2.64/1.59 = ( P = bot_bot_a_o ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_178_bot__empty__eq,axiom,
% 2.64/1.59 ( bot_bot_set_a_o
% 2.64/1.59 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ bot_bot_set_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_179_bot__empty__eq,axiom,
% 2.64/1.59 ( bot_bot_a_o
% 2.64/1.59 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_180_Tree_Osimps_I14_J,axiom,
% 2.64/1.59 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 2.64/1.59 = bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_181_is__singletonI_H,axiom,
% 2.64/1.59 ! [A3: set_set_a] :
% 2.64/1.59 ( ( A3 != bot_bot_set_set_a )
% 2.64/1.59 => ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( member_set_a @ X6 @ A3 )
% 2.64/1.59 => ( ( member_set_a @ Y3 @ A3 )
% 2.64/1.59 => ( X6 = Y3 ) ) )
% 2.64/1.59 => ( is_singleton_set_a @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_182_is__singletonI_H,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( A3 != bot_bot_set_a )
% 2.64/1.59 => ( ! [X6: a,Y3: a] :
% 2.64/1.59 ( ( member_a @ X6 @ A3 )
% 2.64/1.59 => ( ( member_a @ Y3 @ A3 )
% 2.64/1.59 => ( X6 = Y3 ) ) )
% 2.64/1.59 => ( is_singleton_a @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_183_psubsetD,axiom,
% 2.64/1.59 ! [A3: set_set_a,B4: set_set_a,C: set_a] :
% 2.64/1.59 ( ( ord_less_set_set_a @ A3 @ B4 )
% 2.64/1.59 => ( ( member_set_a @ C @ A3 )
% 2.64/1.59 => ( member_set_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_184_psubsetD,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,C: a] :
% 2.64/1.59 ( ( ord_less_set_a @ A3 @ B4 )
% 2.64/1.59 => ( ( member_a @ C @ A3 )
% 2.64/1.59 => ( member_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_185_less__set__def,axiom,
% 2.64/1.59 ( ord_less_set_set_a
% 2.64/1.59 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 2.64/1.59 ( ord_less_set_a_o
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A5 )
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ B5 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_186_less__set__def,axiom,
% 2.64/1.59 ( ord_less_set_a
% 2.64/1.59 = ( ^ [A5: set_a,B5: set_a] :
% 2.64/1.59 ( ord_less_a_o
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_187_psubset__trans,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ A3 @ B4 )
% 2.64/1.59 => ( ( ord_less_set_a @ B4 @ C2 )
% 2.64/1.59 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_188_Tree_Oset__cases,axiom,
% 2.64/1.59 ! [E: set_a,A2: binary594033953_set_a] :
% 2.64/1.59 ( ( member_set_a @ E @ ( binary1613048283_set_a @ A2 ) )
% 2.64/1.59 => ( ! [Z1: binary594033953_set_a] :
% 2.64/1.59 ( ? [Z22: set_a,Z32: binary594033953_set_a] :
% 2.64/1.59 ( A2
% 2.64/1.59 = ( binary313540327_set_a @ Z1 @ Z22 @ Z32 ) )
% 2.64/1.59 => ~ ( member_set_a @ E @ ( binary1613048283_set_a @ Z1 ) ) )
% 2.64/1.59 => ( ! [Z1: binary594033953_set_a,Z32: binary594033953_set_a] :
% 2.64/1.59 ( A2
% 2.64/1.59 != ( binary313540327_set_a @ Z1 @ E @ Z32 ) )
% 2.64/1.59 => ~ ! [Z1: binary594033953_set_a,Z22: set_a,Z32: binary594033953_set_a] :
% 2.64/1.59 ( ( A2
% 2.64/1.59 = ( binary313540327_set_a @ Z1 @ Z22 @ Z32 ) )
% 2.64/1.59 => ~ ( member_set_a @ E @ ( binary1613048283_set_a @ Z32 ) ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_189_Tree_Oset__cases,axiom,
% 2.64/1.59 ! [E: a,A2: binary1439146945Tree_a] :
% 2.64/1.59 ( ( member_a @ E @ ( binary256242811Tree_a @ A2 ) )
% 2.64/1.59 => ( ! [Z1: binary1439146945Tree_a] :
% 2.64/1.59 ( ? [Z22: a,Z32: binary1439146945Tree_a] :
% 2.64/1.59 ( A2
% 2.64/1.59 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 2.64/1.59 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 2.64/1.59 => ( ! [Z1: binary1439146945Tree_a,Z32: binary1439146945Tree_a] :
% 2.64/1.59 ( A2
% 2.64/1.59 != ( binary717961607le_T_a @ Z1 @ E @ Z32 ) )
% 2.64/1.59 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z32: binary1439146945Tree_a] :
% 2.64/1.59 ( ( A2
% 2.64/1.59 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 2.64/1.59 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z32 ) ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_190_Tree_Oset__intros_I1_J,axiom,
% 2.64/1.59 ! [Y: set_a,X21: binary594033953_set_a,X22: set_a,X23: binary594033953_set_a] :
% 2.64/1.59 ( ( member_set_a @ Y @ ( binary1613048283_set_a @ X21 ) )
% 2.64/1.59 => ( member_set_a @ Y @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_191_Tree_Oset__intros_I1_J,axiom,
% 2.64/1.59 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.64/1.59 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 2.64/1.59 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_192_Tree_Oset__intros_I2_J,axiom,
% 2.64/1.59 ! [X22: set_a,X21: binary594033953_set_a,X23: binary594033953_set_a] : ( member_set_a @ X22 @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_193_Tree_Oset__intros_I2_J,axiom,
% 2.64/1.59 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_194_Tree_Oset__intros_I3_J,axiom,
% 2.64/1.59 ! [Ya: set_a,X23: binary594033953_set_a,X21: binary594033953_set_a,X22: set_a] :
% 2.64/1.59 ( ( member_set_a @ Ya @ ( binary1613048283_set_a @ X23 ) )
% 2.64/1.59 => ( member_set_a @ Ya @ ( binary1613048283_set_a @ ( binary313540327_set_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_195_Tree_Oset__intros_I3_J,axiom,
% 2.64/1.59 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 2.64/1.59 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 2.64/1.59 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_196_is__singletonI,axiom,
% 2.64/1.59 ! [X: a] : ( is_singleton_a @ ( insert_a @ X @ bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_197_is__singleton__def,axiom,
% 2.64/1.59 ( is_singleton_a
% 2.64/1.59 = ( ^ [A5: set_a] :
% 2.64/1.59 ? [X4: a] :
% 2.64/1.59 ( A5
% 2.64/1.59 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_198_is__singletonE,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( is_singleton_a @ A3 )
% 2.64/1.59 => ~ ! [X6: a] :
% 2.64/1.59 ( A3
% 2.64/1.59 != ( insert_a @ X6 @ bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_199_insert__absorb2,axiom,
% 2.64/1.59 ! [X: a,A3: set_a] :
% 2.64/1.59 ( ( insert_a @ X @ ( insert_a @ X @ A3 ) )
% 2.64/1.59 = ( insert_a @ X @ A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_200_insert__iff,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ A2 @ ( insert_set_a @ B2 @ A3 ) )
% 2.64/1.59 = ( ( A2 = B2 )
% 2.64/1.59 | ( member_set_a @ A2 @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_201_insert__iff,axiom,
% 2.64/1.59 ! [A2: a,B2: a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 2.64/1.59 = ( ( A2 = B2 )
% 2.64/1.59 | ( member_a @ A2 @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_202_insertCI,axiom,
% 2.64/1.59 ! [A2: set_a,B4: set_set_a,B2: set_a] :
% 2.64/1.59 ( ( ~ ( member_set_a @ A2 @ B4 )
% 2.64/1.59 => ( A2 = B2 ) )
% 2.64/1.59 => ( member_set_a @ A2 @ ( insert_set_a @ B2 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_203_insertCI,axiom,
% 2.64/1.59 ! [A2: a,B4: set_a,B2: a] :
% 2.64/1.59 ( ( ~ ( member_a @ A2 @ B4 )
% 2.64/1.59 => ( A2 = B2 ) )
% 2.64/1.59 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_204_singletonI,axiom,
% 2.64/1.59 ! [A2: set_a] : ( member_set_a @ A2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_205_singletonI,axiom,
% 2.64/1.59 ! [A2: a] : ( member_a @ A2 @ ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_206_singleton__conv,axiom,
% 2.64/1.59 ! [A2: a] :
% 2.64/1.59 ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] : ( X4 = A2 ) )
% 2.64/1.59 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_207_singleton__conv2,axiom,
% 2.64/1.59 ! [A2: a] :
% 2.64/1.59 ( ( collect_a
% 2.64/1.59 @ ( ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 2.64/1.59 @ A2 ) )
% 2.64/1.59 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_208_singleton__inject,axiom,
% 2.64/1.59 ! [A2: a,B2: a] :
% 2.64/1.59 ( ( ( insert_a @ A2 @ bot_bot_set_a )
% 2.64/1.59 = ( insert_a @ B2 @ bot_bot_set_a ) )
% 2.64/1.59 => ( A2 = B2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_209_insert__not__empty,axiom,
% 2.64/1.59 ! [A2: a,A3: set_a] :
% 2.64/1.59 ( ( insert_a @ A2 @ A3 )
% 2.64/1.59 != bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_210_doubleton__eq__iff,axiom,
% 2.64/1.59 ! [A2: a,B2: a,C: a,D: a] :
% 2.64/1.59 ( ( ( insert_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) )
% 2.64/1.59 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 2.64/1.59 = ( ( ( A2 = C )
% 2.64/1.59 & ( B2 = D ) )
% 2.64/1.59 | ( ( A2 = D )
% 2.64/1.59 & ( B2 = C ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_211_singleton__iff,axiom,
% 2.64/1.59 ! [B2: set_a,A2: set_a] :
% 2.64/1.59 ( ( member_set_a @ B2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) )
% 2.64/1.59 = ( B2 = A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_212_singleton__iff,axiom,
% 2.64/1.59 ! [B2: a,A2: a] :
% 2.64/1.59 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 2.64/1.59 = ( B2 = A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_213_singletonD,axiom,
% 2.64/1.59 ! [B2: set_a,A2: set_a] :
% 2.64/1.59 ( ( member_set_a @ B2 @ ( insert_set_a @ A2 @ bot_bot_set_set_a ) )
% 2.64/1.59 => ( B2 = A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_214_singletonD,axiom,
% 2.64/1.59 ! [B2: a,A2: a] :
% 2.64/1.59 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 2.64/1.59 => ( B2 = A2 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_215_insert__compr,axiom,
% 2.64/1.59 ( insert_set_a
% 2.64/1.59 = ( ^ [A: set_a,B5: set_set_a] :
% 2.64/1.59 ( collect_set_a
% 2.64/1.59 @ ^ [X4: set_a] :
% 2.64/1.59 ( ( X4 = A )
% 2.64/1.59 | ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_216_insert__compr,axiom,
% 2.64/1.59 ( insert_a
% 2.64/1.59 = ( ^ [A: a,B5: set_a] :
% 2.64/1.59 ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( X4 = A )
% 2.64/1.59 | ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_217_insert__Collect,axiom,
% 2.64/1.59 ! [A2: a,P: a > $o] :
% 2.64/1.59 ( ( insert_a @ A2 @ ( collect_a @ P ) )
% 2.64/1.59 = ( collect_a
% 2.64/1.59 @ ^ [U: a] :
% 2.64/1.59 ( ( U != A2 )
% 2.64/1.59 => ( P @ U ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_218_mk__disjoint__insert,axiom,
% 2.64/1.59 ! [A2: set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ A2 @ A3 )
% 2.64/1.59 => ? [B6: set_set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_set_a @ A2 @ B6 ) )
% 2.64/1.59 & ~ ( member_set_a @ A2 @ B6 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_219_mk__disjoint__insert,axiom,
% 2.64/1.59 ! [A2: a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ A2 @ A3 )
% 2.64/1.59 => ? [B6: set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_a @ A2 @ B6 ) )
% 2.64/1.59 & ~ ( member_a @ A2 @ B6 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_220_insert__commute,axiom,
% 2.64/1.59 ! [X: a,Y: a,A3: set_a] :
% 2.64/1.59 ( ( insert_a @ X @ ( insert_a @ Y @ A3 ) )
% 2.64/1.59 = ( insert_a @ Y @ ( insert_a @ X @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_221_insert__eq__iff,axiom,
% 2.64/1.59 ! [A2: set_a,A3: set_set_a,B2: set_a,B4: set_set_a] :
% 2.64/1.59 ( ~ ( member_set_a @ A2 @ A3 )
% 2.64/1.59 => ( ~ ( member_set_a @ B2 @ B4 )
% 2.64/1.59 => ( ( ( insert_set_a @ A2 @ A3 )
% 2.64/1.59 = ( insert_set_a @ B2 @ B4 ) )
% 2.64/1.59 = ( ( ( A2 = B2 )
% 2.64/1.59 => ( A3 = B4 ) )
% 2.64/1.59 & ( ( A2 != B2 )
% 2.64/1.59 => ? [C3: set_set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_set_a @ B2 @ C3 ) )
% 2.64/1.59 & ~ ( member_set_a @ B2 @ C3 )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_set_a @ A2 @ C3 ) )
% 2.64/1.59 & ~ ( member_set_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_222_insert__eq__iff,axiom,
% 2.64/1.59 ! [A2: a,A3: set_a,B2: a,B4: set_a] :
% 2.64/1.59 ( ~ ( member_a @ A2 @ A3 )
% 2.64/1.59 => ( ~ ( member_a @ B2 @ B4 )
% 2.64/1.59 => ( ( ( insert_a @ A2 @ A3 )
% 2.64/1.59 = ( insert_a @ B2 @ B4 ) )
% 2.64/1.59 = ( ( ( A2 = B2 )
% 2.64/1.59 => ( A3 = B4 ) )
% 2.64/1.59 & ( ( A2 != B2 )
% 2.64/1.59 => ? [C3: set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_a @ B2 @ C3 ) )
% 2.64/1.59 & ~ ( member_a @ B2 @ C3 )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_a @ A2 @ C3 ) )
% 2.64/1.59 & ~ ( member_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_223_insert__absorb,axiom,
% 2.64/1.59 ! [A2: set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ A2 @ A3 )
% 2.64/1.59 => ( ( insert_set_a @ A2 @ A3 )
% 2.64/1.59 = A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_224_insert__absorb,axiom,
% 2.64/1.59 ! [A2: a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ A2 @ A3 )
% 2.64/1.59 => ( ( insert_a @ A2 @ A3 )
% 2.64/1.59 = A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_225_insert__ident,axiom,
% 2.64/1.59 ! [X: set_a,A3: set_set_a,B4: set_set_a] :
% 2.64/1.59 ( ~ ( member_set_a @ X @ A3 )
% 2.64/1.59 => ( ~ ( member_set_a @ X @ B4 )
% 2.64/1.59 => ( ( ( insert_set_a @ X @ A3 )
% 2.64/1.59 = ( insert_set_a @ X @ B4 ) )
% 2.64/1.59 = ( A3 = B4 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_226_insert__ident,axiom,
% 2.64/1.59 ! [X: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ~ ( member_a @ X @ A3 )
% 2.64/1.59 => ( ~ ( member_a @ X @ B4 )
% 2.64/1.59 => ( ( ( insert_a @ X @ A3 )
% 2.64/1.59 = ( insert_a @ X @ B4 ) )
% 2.64/1.59 = ( A3 = B4 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_227_Set_Oset__insert,axiom,
% 2.64/1.59 ! [X: set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ X @ A3 )
% 2.64/1.59 => ~ ! [B6: set_set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_set_a @ X @ B6 ) )
% 2.64/1.59 => ( member_set_a @ X @ B6 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_228_Set_Oset__insert,axiom,
% 2.64/1.59 ! [X: a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ X @ A3 )
% 2.64/1.59 => ~ ! [B6: set_a] :
% 2.64/1.59 ( ( A3
% 2.64/1.59 = ( insert_a @ X @ B6 ) )
% 2.64/1.59 => ( member_a @ X @ B6 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_229_insertI2,axiom,
% 2.64/1.59 ! [A2: set_a,B4: set_set_a,B2: set_a] :
% 2.64/1.59 ( ( member_set_a @ A2 @ B4 )
% 2.64/1.59 => ( member_set_a @ A2 @ ( insert_set_a @ B2 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_230_insertI2,axiom,
% 2.64/1.59 ! [A2: a,B4: set_a,B2: a] :
% 2.64/1.59 ( ( member_a @ A2 @ B4 )
% 2.64/1.59 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_231_insertI1,axiom,
% 2.64/1.59 ! [A2: set_a,B4: set_set_a] : ( member_set_a @ A2 @ ( insert_set_a @ A2 @ B4 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_232_insertI1,axiom,
% 2.64/1.59 ! [A2: a,B4: set_a] : ( member_a @ A2 @ ( insert_a @ A2 @ B4 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_233_insertE,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ A2 @ ( insert_set_a @ B2 @ A3 ) )
% 2.64/1.59 => ( ( A2 != B2 )
% 2.64/1.59 => ( member_set_a @ A2 @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_234_insertE,axiom,
% 2.64/1.59 ! [A2: a,B2: a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 2.64/1.59 => ( ( A2 != B2 )
% 2.64/1.59 => ( member_a @ A2 @ A3 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_235_Collect__conv__if,axiom,
% 2.64/1.59 ! [P: a > $o,A2: a] :
% 2.64/1.59 ( ( ( P @ A2 )
% 2.64/1.59 => ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( X4 = A2 )
% 2.64/1.59 & ( P @ X4 ) ) )
% 2.64/1.59 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.64/1.59 & ( ~ ( P @ A2 )
% 2.64/1.59 => ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( X4 = A2 )
% 2.64/1.59 & ( P @ X4 ) ) )
% 2.64/1.59 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_236_Collect__conv__if2,axiom,
% 2.64/1.59 ! [P: a > $o,A2: a] :
% 2.64/1.59 ( ( ( P @ A2 )
% 2.64/1.59 => ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( A2 = X4 )
% 2.64/1.59 & ( P @ X4 ) ) )
% 2.64/1.59 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.64/1.59 & ( ~ ( P @ A2 )
% 2.64/1.59 => ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( A2 = X4 )
% 2.64/1.59 & ( P @ X4 ) ) )
% 2.64/1.59 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_237_is__singleton__the__elem,axiom,
% 2.64/1.59 ( is_singleton_a
% 2.64/1.59 = ( ^ [A5: set_a] :
% 2.64/1.59 ( A5
% 2.64/1.59 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_238_the__elem__eq,axiom,
% 2.64/1.59 ! [X: a] :
% 2.64/1.59 ( ( the_elem_a @ ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_239_setOf_Osimps_I2_J,axiom,
% 2.64/1.59 ! [T1: binary1439146945Tree_a,X: a,T2: binary1439146945Tree_a] :
% 2.64/1.59 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X @ T2 ) )
% 2.64/1.59 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T2 ) ) @ ( insert_a @ X @ bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_240_Tree_Osimps_I15_J,axiom,
% 2.64/1.59 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.64/1.59 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 2.64/1.59 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_241_UnCI,axiom,
% 2.64/1.59 ! [C: set_a,B4: set_set_a,A3: set_set_a] :
% 2.64/1.59 ( ( ~ ( member_set_a @ C @ B4 )
% 2.64/1.59 => ( member_set_a @ C @ A3 ) )
% 2.64/1.59 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_242_UnCI,axiom,
% 2.64/1.59 ! [C: a,B4: set_a,A3: set_a] :
% 2.64/1.59 ( ( ~ ( member_a @ C @ B4 )
% 2.64/1.59 => ( member_a @ C @ A3 ) )
% 2.64/1.59 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_243_Un__iff,axiom,
% 2.64/1.59 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) )
% 2.64/1.59 = ( ( member_set_a @ C @ A3 )
% 2.64/1.59 | ( member_set_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_244_Un__iff,axiom,
% 2.64/1.59 ! [C: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 = ( ( member_a @ C @ A3 )
% 2.64/1.59 | ( member_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_245_Un__empty,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 2.64/1.59 = bot_bot_set_a )
% 2.64/1.59 = ( ( A3 = bot_bot_set_a )
% 2.64/1.59 & ( B4 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_246_Un__insert__right,axiom,
% 2.64/1.59 ! [A3: set_a,A2: a,B4: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 2.64/1.59 = ( insert_a @ A2 @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_247_Un__insert__left,axiom,
% 2.64/1.59 ! [A2: a,B4: set_a,C2: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ ( insert_a @ A2 @ B4 ) @ C2 )
% 2.64/1.59 = ( insert_a @ A2 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_248_UnE,axiom,
% 2.64/1.59 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) )
% 2.64/1.59 => ( ~ ( member_set_a @ C @ A3 )
% 2.64/1.59 => ( member_set_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_249_UnE,axiom,
% 2.64/1.59 ! [C: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 => ( ~ ( member_a @ C @ A3 )
% 2.64/1.59 => ( member_a @ C @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_250_UnI1,axiom,
% 2.64/1.59 ! [C: set_a,A3: set_set_a,B4: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ C @ A3 )
% 2.64/1.59 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_251_UnI1,axiom,
% 2.64/1.59 ! [C: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( member_a @ C @ A3 )
% 2.64/1.59 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_252_UnI2,axiom,
% 2.64/1.59 ! [C: set_a,B4: set_set_a,A3: set_set_a] :
% 2.64/1.59 ( ( member_set_a @ C @ B4 )
% 2.64/1.59 => ( member_set_a @ C @ ( sup_sup_set_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_253_UnI2,axiom,
% 2.64/1.59 ! [C: a,B4: set_a,A3: set_a] :
% 2.64/1.59 ( ( member_a @ C @ B4 )
% 2.64/1.59 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_254_bex__Un,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,P: a > $o] :
% 2.64/1.59 ( ( ? [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 & ( P @ X4 ) ) )
% 2.64/1.59 = ( ? [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ A3 )
% 2.64/1.59 & ( P @ X4 ) )
% 2.64/1.59 | ? [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ B4 )
% 2.64/1.59 & ( P @ X4 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_255_ball__Un,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,P: a > $o] :
% 2.64/1.59 ( ( ! [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 => ( P @ X4 ) ) )
% 2.64/1.59 = ( ! [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ A3 )
% 2.64/1.59 => ( P @ X4 ) )
% 2.64/1.59 & ! [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ B4 )
% 2.64/1.59 => ( P @ X4 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_256_Un__assoc,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 2.64/1.59 = ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_257_Un__absorb,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A3 @ A3 )
% 2.64/1.59 = A3 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_258_Un__commute,axiom,
% 2.64/1.59 ( sup_sup_set_a
% 2.64/1.59 = ( ^ [A5: set_a,B5: set_a] : ( sup_sup_set_a @ B5 @ A5 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_259_Un__left__absorb,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_260_Un__left__commute,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 2.64/1.59 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_261_Collect__disj__eq,axiom,
% 2.64/1.59 ! [P: a > $o,Q: a > $o] :
% 2.64/1.59 ( ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( P @ X4 )
% 2.64/1.59 | ( Q @ X4 ) ) )
% 2.64/1.59 = ( sup_sup_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_262_Un__def,axiom,
% 2.64/1.59 ( sup_sup_set_set_a
% 2.64/1.59 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 2.64/1.59 ( collect_set_a
% 2.64/1.59 @ ^ [X4: set_a] :
% 2.64/1.59 ( ( member_set_a @ X4 @ A5 )
% 2.64/1.59 | ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_263_Un__def,axiom,
% 2.64/1.59 ( sup_sup_set_a
% 2.64/1.59 = ( ^ [A5: set_a,B5: set_a] :
% 2.64/1.59 ( collect_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( ( member_a @ X4 @ A5 )
% 2.64/1.59 | ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_264_Un__empty__left,axiom,
% 2.64/1.59 ! [B4: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ bot_bot_set_a @ B4 )
% 2.64/1.59 = B4 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_265_Un__empty__right,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A3 @ bot_bot_set_a )
% 2.64/1.59 = A3 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_266_insert__def,axiom,
% 2.64/1.59 ( insert_a
% 2.64/1.59 = ( ^ [A: a] :
% 2.64/1.59 ( sup_sup_set_a
% 2.64/1.59 @ ( collect_a
% 2.64/1.59 @ ^ [X4: a] : ( X4 = A ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_267_insert__is__Un,axiom,
% 2.64/1.59 ( insert_a
% 2.64/1.59 = ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_268_Un__singleton__iff,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a,X: a] :
% 2.64/1.59 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 = ( ( ( A3 = bot_bot_set_a )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) ) )
% 2.64/1.59 | ( ( A3
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 & ( B4 = bot_bot_set_a ) )
% 2.64/1.59 | ( ( A3
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_269_singleton__Un__iff,axiom,
% 2.64/1.59 ! [X: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( ( insert_a @ X @ bot_bot_set_a )
% 2.64/1.59 = ( sup_sup_set_a @ A3 @ B4 ) )
% 2.64/1.59 = ( ( ( A3 = bot_bot_set_a )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) ) )
% 2.64/1.59 | ( ( A3
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 & ( B4 = bot_bot_set_a ) )
% 2.64/1.59 | ( ( A3
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) )
% 2.64/1.59 & ( B4
% 2.64/1.59 = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_270_sup__bot__left,axiom,
% 2.64/1.59 ! [X: a > a > $o] :
% 2.64/1.59 ( ( sup_sup_a_a_o @ bot_bot_a_a_o @ X )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_271_sup__bot__left,axiom,
% 2.64/1.59 ! [X: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ bot_bot_set_a @ X )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_272_sup__bot__left,axiom,
% 2.64/1.59 ! [X: a > $o] :
% 2.64/1.59 ( ( sup_sup_a_o @ bot_bot_a_o @ X )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_273_sup__bot__right,axiom,
% 2.64/1.59 ! [X: a > a > $o] :
% 2.64/1.59 ( ( sup_sup_a_a_o @ X @ bot_bot_a_a_o )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_274_sup__bot__right,axiom,
% 2.64/1.59 ! [X: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ X @ bot_bot_set_a )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_275_sup__bot__right,axiom,
% 2.64/1.59 ! [X: a > $o] :
% 2.64/1.59 ( ( sup_sup_a_o @ X @ bot_bot_a_o )
% 2.64/1.59 = X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_276_bot__eq__sup__iff,axiom,
% 2.64/1.59 ! [X: a > a > $o,Y: a > a > $o] :
% 2.64/1.59 ( ( bot_bot_a_a_o
% 2.64/1.59 = ( sup_sup_a_a_o @ X @ Y ) )
% 2.64/1.59 = ( ( X = bot_bot_a_a_o )
% 2.64/1.59 & ( Y = bot_bot_a_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_277_bot__eq__sup__iff,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( bot_bot_set_a
% 2.64/1.59 = ( sup_sup_set_a @ X @ Y ) )
% 2.64/1.59 = ( ( X = bot_bot_set_a )
% 2.64/1.59 & ( Y = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_278_bot__eq__sup__iff,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( bot_bot_a_o
% 2.64/1.59 = ( sup_sup_a_o @ X @ Y ) )
% 2.64/1.59 = ( ( X = bot_bot_a_o )
% 2.64/1.59 & ( Y = bot_bot_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_279_sup__bot_Oright__neutral,axiom,
% 2.64/1.59 ! [A2: a > a > $o] :
% 2.64/1.59 ( ( sup_sup_a_a_o @ A2 @ bot_bot_a_a_o )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_280_sup__bot_Oright__neutral,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ A2 @ bot_bot_set_a )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_281_sup__bot_Oright__neutral,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ( ( sup_sup_a_o @ A2 @ bot_bot_a_o )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_282_sup__bot_Oneutr__eq__iff,axiom,
% 2.64/1.59 ! [A2: a > a > $o,B2: a > a > $o] :
% 2.64/1.59 ( ( bot_bot_a_a_o
% 2.64/1.59 = ( sup_sup_a_a_o @ A2 @ B2 ) )
% 2.64/1.59 = ( ( A2 = bot_bot_a_a_o )
% 2.64/1.59 & ( B2 = bot_bot_a_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_283_sup__bot_Oneutr__eq__iff,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( bot_bot_set_a
% 2.64/1.59 = ( sup_sup_set_a @ A2 @ B2 ) )
% 2.64/1.59 = ( ( A2 = bot_bot_set_a )
% 2.64/1.59 & ( B2 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_284_sup__bot_Oneutr__eq__iff,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( bot_bot_a_o
% 2.64/1.59 = ( sup_sup_a_o @ A2 @ B2 ) )
% 2.64/1.59 = ( ( A2 = bot_bot_a_o )
% 2.64/1.59 & ( B2 = bot_bot_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_285_sup__bot_Oleft__neutral,axiom,
% 2.64/1.59 ! [A2: a > a > $o] :
% 2.64/1.59 ( ( sup_sup_a_a_o @ bot_bot_a_a_o @ A2 )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_286_sup__bot_Oleft__neutral,axiom,
% 2.64/1.59 ! [A2: set_a] :
% 2.64/1.59 ( ( sup_sup_set_a @ bot_bot_set_a @ A2 )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_287_sup__bot_Oleft__neutral,axiom,
% 2.64/1.59 ! [A2: a > $o] :
% 2.64/1.59 ( ( sup_sup_a_o @ bot_bot_a_o @ A2 )
% 2.64/1.59 = A2 ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_288_sup__bot_Oeq__neutr__iff,axiom,
% 2.64/1.59 ! [A2: a > a > $o,B2: a > a > $o] :
% 2.64/1.59 ( ( ( sup_sup_a_a_o @ A2 @ B2 )
% 2.64/1.59 = bot_bot_a_a_o )
% 2.64/1.59 = ( ( A2 = bot_bot_a_a_o )
% 2.64/1.59 & ( B2 = bot_bot_a_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_289_sup__bot_Oeq__neutr__iff,axiom,
% 2.64/1.59 ! [A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( ( sup_sup_set_a @ A2 @ B2 )
% 2.64/1.59 = bot_bot_set_a )
% 2.64/1.59 = ( ( A2 = bot_bot_set_a )
% 2.64/1.59 & ( B2 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_290_sup__bot_Oeq__neutr__iff,axiom,
% 2.64/1.59 ! [A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( ( sup_sup_a_o @ A2 @ B2 )
% 2.64/1.59 = bot_bot_a_o )
% 2.64/1.59 = ( ( A2 = bot_bot_a_o )
% 2.64/1.59 & ( B2 = bot_bot_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_291_sup__eq__bot__iff,axiom,
% 2.64/1.59 ! [X: a > a > $o,Y: a > a > $o] :
% 2.64/1.59 ( ( ( sup_sup_a_a_o @ X @ Y )
% 2.64/1.59 = bot_bot_a_a_o )
% 2.64/1.59 = ( ( X = bot_bot_a_a_o )
% 2.64/1.59 & ( Y = bot_bot_a_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_292_sup__eq__bot__iff,axiom,
% 2.64/1.59 ! [X: set_a,Y: set_a] :
% 2.64/1.59 ( ( ( sup_sup_set_a @ X @ Y )
% 2.64/1.59 = bot_bot_set_a )
% 2.64/1.59 = ( ( X = bot_bot_set_a )
% 2.64/1.59 & ( Y = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_293_sup__eq__bot__iff,axiom,
% 2.64/1.59 ! [X: a > $o,Y: a > $o] :
% 2.64/1.59 ( ( ( sup_sup_a_o @ X @ Y )
% 2.64/1.59 = bot_bot_a_o )
% 2.64/1.59 = ( ( X = bot_bot_a_o )
% 2.64/1.59 & ( Y = bot_bot_a_o ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_294_sup__set__def,axiom,
% 2.64/1.59 ( sup_sup_set_set_a
% 2.64/1.59 = ( ^ [A5: set_set_a,B5: set_set_a] :
% 2.64/1.59 ( collect_set_a
% 2.64/1.59 @ ( sup_sup_set_a_o
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A5 )
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_295_sup__set__def,axiom,
% 2.64/1.59 ( sup_sup_set_a
% 2.64/1.59 = ( ^ [A5: set_a,B5: set_a] :
% 2.64/1.59 ( collect_a
% 2.64/1.59 @ ( sup_sup_a_o
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ B5 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_296_sup__Un__eq,axiom,
% 2.64/1.59 ! [R: set_set_a,S: set_set_a] :
% 2.64/1.59 ( ( sup_sup_set_a_o
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ R )
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ S ) )
% 2.64/1.59 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ ( sup_sup_set_set_a @ R @ S ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_297_sup__Un__eq,axiom,
% 2.64/1.59 ! [R: set_a,S: set_a] :
% 2.64/1.59 ( ( sup_sup_a_o
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 2.64/1.59 = ( ^ [X4: a] : ( member_a @ X4 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_298_sup_Ostrict__coboundedI2,axiom,
% 2.64/1.59 ! [C: a > a > $o,B2: a > a > $o,A2: a > a > $o] :
% 2.64/1.59 ( ( ord_less_a_a_o @ C @ B2 )
% 2.64/1.59 => ( ord_less_a_a_o @ C @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_299_sup_Ostrict__coboundedI2,axiom,
% 2.64/1.59 ! [C: set_a,B2: set_a,A2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ C @ B2 )
% 2.64/1.59 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_300_sup_Ostrict__coboundedI2,axiom,
% 2.64/1.59 ! [C: a > $o,B2: a > $o,A2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ C @ B2 )
% 2.64/1.59 => ( ord_less_a_o @ C @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_301_sup_Ostrict__coboundedI2,axiom,
% 2.64/1.59 ! [C: int,B2: int,A2: int] :
% 2.64/1.59 ( ( ord_less_int @ C @ B2 )
% 2.64/1.59 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_302_sup_Ostrict__coboundedI1,axiom,
% 2.64/1.59 ! [C: a > a > $o,A2: a > a > $o,B2: a > a > $o] :
% 2.64/1.59 ( ( ord_less_a_a_o @ C @ A2 )
% 2.64/1.59 => ( ord_less_a_a_o @ C @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_303_sup_Ostrict__coboundedI1,axiom,
% 2.64/1.59 ! [C: set_a,A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ C @ A2 )
% 2.64/1.59 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_304_sup_Ostrict__coboundedI1,axiom,
% 2.64/1.59 ! [C: a > $o,A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ C @ A2 )
% 2.64/1.59 => ( ord_less_a_o @ C @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_305_sup_Ostrict__coboundedI1,axiom,
% 2.64/1.59 ! [C: int,A2: int,B2: int] :
% 2.64/1.59 ( ( ord_less_int @ C @ A2 )
% 2.64/1.59 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_306_sup_Ostrict__order__iff,axiom,
% 2.64/1.59 ( ord_less_a_a_o
% 2.64/1.59 = ( ^ [B: a > a > $o,A: a > a > $o] :
% 2.64/1.59 ( ( A
% 2.64/1.59 = ( sup_sup_a_a_o @ A @ B ) )
% 2.64/1.59 & ( A != B ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_307_sup_Ostrict__order__iff,axiom,
% 2.64/1.59 ( ord_less_set_a
% 2.64/1.59 = ( ^ [B: set_a,A: set_a] :
% 2.64/1.59 ( ( A
% 2.64/1.59 = ( sup_sup_set_a @ A @ B ) )
% 2.64/1.59 & ( A != B ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_308_sup_Ostrict__order__iff,axiom,
% 2.64/1.59 ( ord_less_a_o
% 2.64/1.59 = ( ^ [B: a > $o,A: a > $o] :
% 2.64/1.59 ( ( A
% 2.64/1.59 = ( sup_sup_a_o @ A @ B ) )
% 2.64/1.59 & ( A != B ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_309_sup_Ostrict__order__iff,axiom,
% 2.64/1.59 ( ord_less_int
% 2.64/1.59 = ( ^ [B: int,A: int] :
% 2.64/1.59 ( ( A
% 2.64/1.59 = ( sup_sup_int @ A @ B ) )
% 2.64/1.59 & ( A != B ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_310_sup_Ostrict__boundedE,axiom,
% 2.64/1.59 ! [B2: a > a > $o,C: a > a > $o,A2: a > a > $o] :
% 2.64/1.59 ( ( ord_less_a_a_o @ ( sup_sup_a_a_o @ B2 @ C ) @ A2 )
% 2.64/1.59 => ~ ( ( ord_less_a_a_o @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_a_a_o @ C @ A2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_311_sup_Ostrict__boundedE,axiom,
% 2.64/1.59 ! [B2: set_a,C: set_a,A2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ ( sup_sup_set_a @ B2 @ C ) @ A2 )
% 2.64/1.59 => ~ ( ( ord_less_set_a @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_312_sup_Ostrict__boundedE,axiom,
% 2.64/1.59 ! [B2: a > $o,C: a > $o,A2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ ( sup_sup_a_o @ B2 @ C ) @ A2 )
% 2.64/1.59 => ~ ( ( ord_less_a_o @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_313_sup_Ostrict__boundedE,axiom,
% 2.64/1.59 ! [B2: int,C: int,A2: int] :
% 2.64/1.59 ( ( ord_less_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 2.64/1.59 => ~ ( ( ord_less_int @ B2 @ A2 )
% 2.64/1.59 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_314_less__supI2,axiom,
% 2.64/1.59 ! [X: a > a > $o,B2: a > a > $o,A2: a > a > $o] :
% 2.64/1.59 ( ( ord_less_a_a_o @ X @ B2 )
% 2.64/1.59 => ( ord_less_a_a_o @ X @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_315_less__supI2,axiom,
% 2.64/1.59 ! [X: set_a,B2: set_a,A2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ B2 )
% 2.64/1.59 => ( ord_less_set_a @ X @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_316_less__supI2,axiom,
% 2.64/1.59 ! [X: a > $o,B2: a > $o,A2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ B2 )
% 2.64/1.59 => ( ord_less_a_o @ X @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_317_less__supI2,axiom,
% 2.64/1.59 ! [X: int,B2: int,A2: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ B2 )
% 2.64/1.59 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_318_less__supI1,axiom,
% 2.64/1.59 ! [X: a > a > $o,A2: a > a > $o,B2: a > a > $o] :
% 2.64/1.59 ( ( ord_less_a_a_o @ X @ A2 )
% 2.64/1.59 => ( ord_less_a_a_o @ X @ ( sup_sup_a_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_319_less__supI1,axiom,
% 2.64/1.59 ! [X: set_a,A2: set_a,B2: set_a] :
% 2.64/1.59 ( ( ord_less_set_a @ X @ A2 )
% 2.64/1.59 => ( ord_less_set_a @ X @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_320_less__supI1,axiom,
% 2.64/1.59 ! [X: a > $o,A2: a > $o,B2: a > $o] :
% 2.64/1.59 ( ( ord_less_a_o @ X @ A2 )
% 2.64/1.59 => ( ord_less_a_o @ X @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_321_less__supI1,axiom,
% 2.64/1.59 ! [X: int,A2: int,B2: int] :
% 2.64/1.59 ( ( ord_less_int @ X @ A2 )
% 2.64/1.59 => ( ord_less_int @ X @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_322_the__elem__def,axiom,
% 2.64/1.59 ( the_elem_a
% 2.64/1.59 = ( ^ [X7: set_a] :
% 2.64/1.59 ( the_a
% 2.64/1.59 @ ^ [X4: a] :
% 2.64/1.59 ( X7
% 2.64/1.59 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_323_pred__on_Ochain__extend,axiom,
% 2.64/1.59 ! [A3: set_set_a,P: set_a > set_a > $o,C2: set_set_a,Z3: set_a] :
% 2.64/1.59 ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( ( member_set_a @ Z3 @ A3 )
% 2.64/1.59 => ( ! [X6: set_a] :
% 2.64/1.59 ( ( member_set_a @ X6 @ C2 )
% 2.64/1.59 => ( sup_su198629954et_a_o @ P
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ X6
% 2.64/1.59 @ Z3 ) )
% 2.64/1.59 => ( pred_chain_set_a @ A3 @ P @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C2 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_324_pred__on_Ochain__extend,axiom,
% 2.64/1.59 ! [A3: set_a,P: a > a > $o,C2: set_a,Z3: a] :
% 2.64/1.59 ( ( pred_chain_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( ( member_a @ Z3 @ A3 )
% 2.64/1.59 => ( ! [X6: a] :
% 2.64/1.59 ( ( member_a @ X6 @ C2 )
% 2.64/1.59 => ( sup_sup_a_a_o @ P
% 2.64/1.59 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 2.64/1.59 @ X6
% 2.64/1.59 @ Z3 ) )
% 2.64/1.59 => ( pred_chain_a @ A3 @ P @ ( sup_sup_set_a @ ( insert_a @ Z3 @ bot_bot_set_a ) @ C2 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_325_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.64/1.59 semila1223476304_a_a_o @ sup_sup_a_a_o @ bot_bot_a_a_o ).
% 2.64/1.59
% 2.64/1.59 thf(fact_326_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.64/1.59 semila1409648192_set_a @ sup_sup_set_a @ bot_bot_set_a ).
% 2.64/1.59
% 2.64/1.59 thf(fact_327_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.64/1.59 semila980155549tr_a_o @ sup_sup_a_o @ bot_bot_a_o ).
% 2.64/1.59
% 2.64/1.59 thf(fact_328_subset_Ochain__extend,axiom,
% 2.64/1.59 ! [A3: set_set_a,C2: set_set_a,Z3: set_a] :
% 2.64/1.59 ( ( pred_chain_set_a @ A3 @ ord_less_set_a @ C2 )
% 2.64/1.59 => ( ( member_set_a @ Z3 @ A3 )
% 2.64/1.59 => ( ! [X6: set_a] :
% 2.64/1.59 ( ( member_set_a @ X6 @ C2 )
% 2.64/1.59 => ( sup_su198629954et_a_o @ ord_less_set_a
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ X6
% 2.64/1.59 @ Z3 ) )
% 2.64/1.59 => ( pred_chain_set_a @ A3 @ ord_less_set_a @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C2 ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_329_subset_Ochain__total,axiom,
% 2.64/1.59 ! [A3: set_set_a,C2: set_set_a,X: set_a,Y: set_a] :
% 2.64/1.59 ( ( pred_chain_set_a @ A3 @ ord_less_set_a @ C2 )
% 2.64/1.59 => ( ( member_set_a @ X @ C2 )
% 2.64/1.59 => ( ( member_set_a @ Y @ C2 )
% 2.64/1.59 => ( ( sup_su198629954et_a_o @ ord_less_set_a
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ X
% 2.64/1.59 @ Y )
% 2.64/1.59 | ( sup_su198629954et_a_o @ ord_less_set_a
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ Y
% 2.64/1.59 @ X ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_330_pred__on_Ochain__total,axiom,
% 2.64/1.59 ! [A3: set_set_a,P: set_a > set_a > $o,C2: set_set_a,X: set_a,Y: set_a] :
% 2.64/1.59 ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( ( member_set_a @ X @ C2 )
% 2.64/1.59 => ( ( member_set_a @ Y @ C2 )
% 2.64/1.59 => ( ( sup_su198629954et_a_o @ P
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ X
% 2.64/1.59 @ Y )
% 2.64/1.59 | ( sup_su198629954et_a_o @ P
% 2.64/1.59 @ ^ [Y4: set_a,Z4: set_a] : ( Y4 = Z4 )
% 2.64/1.59 @ Y
% 2.64/1.59 @ X ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_331_pred__on_Ochain__total,axiom,
% 2.64/1.59 ! [A3: set_a,P: a > a > $o,C2: set_a,X: a,Y: a] :
% 2.64/1.59 ( ( pred_chain_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( ( member_a @ X @ C2 )
% 2.64/1.59 => ( ( member_a @ Y @ C2 )
% 2.64/1.59 => ( ( sup_sup_a_a_o @ P
% 2.64/1.59 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 2.64/1.59 @ X
% 2.64/1.59 @ Y )
% 2.64/1.59 | ( sup_sup_a_a_o @ P
% 2.64/1.59 @ ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 2.64/1.59 @ Y
% 2.64/1.59 @ X ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_332_subset_Ochain__empty,axiom,
% 2.64/1.59 ! [A3: set_set_a] : ( pred_chain_set_a @ A3 @ ord_less_set_a @ bot_bot_set_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_333_pred__on_Ochain__empty,axiom,
% 2.64/1.59 ! [A3: set_a,P: a > a > $o] : ( pred_chain_a @ A3 @ P @ bot_bot_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_334_chain__mono,axiom,
% 2.64/1.59 ! [A3: set_set_a,P: set_a > set_a > $o,Q: set_a > set_a > $o,C2: set_set_a] :
% 2.64/1.59 ( ! [X6: set_a,Y3: set_a] :
% 2.64/1.59 ( ( member_set_a @ X6 @ A3 )
% 2.64/1.59 => ( ( member_set_a @ Y3 @ A3 )
% 2.64/1.59 => ( ( P @ X6 @ Y3 )
% 2.64/1.59 => ( Q @ X6 @ Y3 ) ) ) )
% 2.64/1.59 => ( ( pred_chain_set_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( pred_chain_set_a @ A3 @ Q @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_335_chain__mono,axiom,
% 2.64/1.59 ! [A3: set_a,P: a > a > $o,Q: a > a > $o,C2: set_a] :
% 2.64/1.59 ( ! [X6: a,Y3: a] :
% 2.64/1.59 ( ( member_a @ X6 @ A3 )
% 2.64/1.59 => ( ( member_a @ Y3 @ A3 )
% 2.64/1.59 => ( ( P @ X6 @ Y3 )
% 2.64/1.59 => ( Q @ X6 @ Y3 ) ) ) )
% 2.64/1.59 => ( ( pred_chain_a @ A3 @ P @ C2 )
% 2.64/1.59 => ( pred_chain_a @ A3 @ Q @ C2 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_336_pred__on_Ochain_Ocong,axiom,
% 2.64/1.59 pred_chain_a = pred_chain_a ).
% 2.64/1.59
% 2.64/1.59 thf(fact_337_chains__alt__def,axiom,
% 2.64/1.59 ( chains_a
% 2.64/1.59 = ( ^ [A5: set_set_a] : ( collect_set_set_a @ ( pred_chain_set_a @ A5 @ ord_less_set_a ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_338_Pow__empty,axiom,
% 2.64/1.59 ( ( pow_a @ bot_bot_set_a )
% 2.64/1.59 = ( insert_set_a @ bot_bot_set_a @ bot_bot_set_set_a ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_339_Pow__singleton__iff,axiom,
% 2.64/1.59 ! [X8: set_a,Y5: set_a] :
% 2.64/1.59 ( ( ( pow_a @ X8 )
% 2.64/1.59 = ( insert_set_a @ Y5 @ bot_bot_set_set_a ) )
% 2.64/1.59 = ( ( X8 = bot_bot_set_a )
% 2.64/1.59 & ( Y5 = bot_bot_set_a ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_340_Pow__not__empty,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( pow_a @ A3 )
% 2.64/1.59 != bot_bot_set_set_a ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_341_Pow__bottom,axiom,
% 2.64/1.59 ! [B4: set_a] : ( member_set_a @ bot_bot_set_a @ ( pow_a @ B4 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_342_Pow__top,axiom,
% 2.64/1.59 ! [A3: set_a] : ( member_set_a @ A3 @ ( pow_a @ A3 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_343_chains__extend,axiom,
% 2.64/1.59 ! [C: set_set_a,S: set_set_a,Z3: set_a] :
% 2.64/1.59 ( ( member_set_set_a @ C @ ( chains_a @ S ) )
% 2.64/1.59 => ( ( member_set_a @ Z3 @ S )
% 2.64/1.59 => ( ! [X6: set_a] :
% 2.64/1.59 ( ( member_set_a @ X6 @ C )
% 2.64/1.59 => ( ord_less_eq_set_a @ X6 @ Z3 ) )
% 2.64/1.59 => ( member_set_set_a @ ( sup_sup_set_set_a @ ( insert_set_a @ Z3 @ bot_bot_set_set_a ) @ C ) @ ( chains_a @ S ) ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_344_Powp__Pow__eq,axiom,
% 2.64/1.59 ! [A3: set_set_a] :
% 2.64/1.59 ( ( powp_set_a
% 2.64/1.59 @ ^ [X4: set_a] : ( member_set_a @ X4 @ A3 ) )
% 2.64/1.59 = ( ^ [X4: set_set_a] : ( member_set_set_a @ X4 @ ( pow_set_a @ A3 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_345_Powp__Pow__eq,axiom,
% 2.64/1.59 ! [A3: set_a] :
% 2.64/1.59 ( ( powp_a
% 2.64/1.59 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.64/1.59 = ( ^ [X4: set_a] : ( member_set_a @ X4 @ ( pow_a @ A3 ) ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_346_order__refl,axiom,
% 2.64/1.59 ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_347_subset__antisym,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( ord_less_eq_set_a @ A3 @ B4 )
% 2.64/1.59 => ( ( ord_less_eq_set_a @ B4 @ A3 )
% 2.64/1.59 => ( A3 = B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_348_subsetI,axiom,
% 2.64/1.59 ! [A3: set_a,B4: set_a] :
% 2.64/1.59 ( ! [X6: a] :
% 2.64/1.59 ( ( member_a @ X6 @ A3 )
% 2.64/1.59 => ( member_a @ X6 @ B4 ) )
% 2.64/1.59 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(fact_349_insert__subset,axiom,
% 2.64/1.59 ! [X: a,A3: set_a,B4: set_a] :
% 2.64/1.59 ( ( ord_less_eq_set_a @ ( insert_a @ X @ A3 ) @ B4 )
% 2.64/1.59 = ( ( member_a @ X @ B4 )
% 2.64/1.59 & ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ).
% 2.64/1.59
% 2.64/1.59 thf(conj_0,conjecture,
% 2.64/1.59 a2 = b ).
% 2.64/1.59 ------------------------
% 2.78/1.62 % (27449)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_27328 for (2999ds/275Mi)
% 2.78/1.62 % (27447)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/2Mi)
% 2.78/1.62 % (27444)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/183Mi)
% 2.78/1.62 % (27447)Instruction limit reached!
% 2.78/1.62 % (27447)------------------------------
% 2.78/1.62 % (27447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.62 % (27447)Termination reason: Unknown
% 2.78/1.62 % (27447)Termination phase: shuffling
% 2.78/1.62
% 2.78/1.62 % (27447)Memory used [KB]: 1407
% 2.78/1.62 % (27447)Time elapsed: 0.002 s
% 2.78/1.62 % (27447)Instructions burned: 2 (million)
% 2.78/1.62 % (27447)------------------------------
% 2.78/1.62 % (27447)------------------------------
% 2.78/1.63 % (27445)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_27328 for (2999ds/4Mi)
% 2.78/1.63 % (27448)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_27328 for (2999ds/2Mi)
% 2.78/1.63 % (27450)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/18Mi)
% 2.78/1.63 % (27446)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_27328 for (2999ds/27Mi)
% 2.78/1.63 % (27448)Instruction limit reached!
% 2.78/1.63 % (27448)------------------------------
% 2.78/1.63 % (27448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (27448)Termination reason: Unknown
% 2.78/1.63 % (27448)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (27448)Memory used [KB]: 1407
% 2.78/1.63 % (27448)Time elapsed: 0.004 s
% 2.78/1.63 % (27448)Instructions burned: 3 (million)
% 2.78/1.63 % (27448)------------------------------
% 2.78/1.63 % (27448)------------------------------
% 2.78/1.63 % (27445)Instruction limit reached!
% 2.78/1.63 % (27445)------------------------------
% 2.78/1.63 % (27445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (27445)Termination reason: Unknown
% 2.78/1.63 % (27445)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (27445)Memory used [KB]: 1407
% 2.78/1.63 % (27445)Time elapsed: 0.005 s
% 2.78/1.63 % (27445)Instructions burned: 4 (million)
% 2.78/1.63 % (27445)------------------------------
% 2.78/1.63 % (27445)------------------------------
% 2.78/1.63 % (27451)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/3Mi)
% 2.78/1.63 % (27451)Instruction limit reached!
% 2.78/1.63 % (27451)------------------------------
% 2.78/1.63 % (27451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (27451)Termination reason: Unknown
% 2.78/1.63 % (27451)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (27451)Memory used [KB]: 1407
% 2.78/1.63 % (27451)Time elapsed: 0.003 s
% 2.78/1.63 % (27451)Instructions burned: 5 (million)
% 2.78/1.63 % (27451)------------------------------
% 2.78/1.63 % (27451)------------------------------
% 2.78/1.63 % (27449)Refutation not found, incomplete strategy
% 2.78/1.63 % (27449)------------------------------
% 2.78/1.63 % (27449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (27449)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.63
% 2.78/1.63
% 2.78/1.63 % (27449)Memory used [KB]: 6396
% 2.78/1.63 % (27449)Time elapsed: 0.015 s
% 2.78/1.63 % (27449)Instructions burned: 44 (million)
% 2.78/1.63 % (27449)------------------------------
% 2.78/1.63 % (27449)------------------------------
% 2.78/1.63 % (27450)Instruction limit reached!
% 2.78/1.63 % (27450)------------------------------
% 2.78/1.63 % (27450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (27450)Termination reason: Unknown
% 2.78/1.63 % (27450)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (27450)Memory used [KB]: 1663
% 2.78/1.63 % (27450)Time elapsed: 0.011 s
% 2.78/1.63 % (27450)Instructions burned: 19 (million)
% 2.78/1.63 % (27450)------------------------------
% 2.78/1.63 % (27450)------------------------------
% 2.78/1.64 % (27454)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_27328 for (2999ds/3Mi)
% 2.78/1.64 % (27446)Instruction limit reached!
% 2.78/1.64 % (27446)------------------------------
% 2.78/1.64 % (27446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (27454)Instruction limit reached!
% 2.78/1.64 % (27454)------------------------------
% 2.78/1.64 % (27454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (27454)Termination reason: Unknown
% 2.78/1.64 % (27446)Termination reason: Unknown
% 2.78/1.64 % (27454)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (27454)Memory used [KB]: 1407
% 2.78/1.64 % (27446)Termination phase: shuffling
% 2.78/1.64 % (27454)Time elapsed: 0.003 s
% 2.78/1.64
% 2.78/1.64 % (27454)Instructions burned: 5 (million)
% 2.78/1.64 % (27454)------------------------------
% 2.78/1.64 % (27454)------------------------------
% 2.78/1.64 % (27446)Memory used [KB]: 1918
% 2.78/1.64 % (27446)Time elapsed: 0.018 s
% 2.78/1.64 % (27446)Instructions burned: 27 (million)
% 2.78/1.64 % (27446)------------------------------
% 2.78/1.64 % (27446)------------------------------
% 2.78/1.64 % (27455)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_27328 for (2999ds/1041Mi)
% 2.78/1.64 % (27453)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_27328 for (2999ds/15Mi)
% 2.78/1.65 % (27452)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_27328 for (2999ds/37Mi)
% 2.78/1.65 % (27456)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/7Mi)
% 2.78/1.65 % (27456)Instruction limit reached!
% 2.78/1.65 % (27456)------------------------------
% 2.78/1.65 % (27456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.65 % (27456)Termination reason: Unknown
% 2.78/1.65 % (27456)Termination phase: shuffling
% 2.78/1.65
% 2.78/1.65 % (27456)Memory used [KB]: 1535
% 2.78/1.65 % (27456)Time elapsed: 0.005 s
% 2.78/1.65 % (27456)Instructions burned: 10 (million)
% 2.78/1.65 % (27456)------------------------------
% 2.78/1.65 % (27456)------------------------------
% 2.78/1.65 % (27453)Instruction limit reached!
% 2.78/1.65 % (27453)------------------------------
% 2.78/1.65 % (27453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.65 % (27453)Termination reason: Unknown
% 2.78/1.65 % (27453)Termination phase: shuffling
% 2.78/1.65 % (27457)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/16Mi)
% 2.78/1.65
% 2.78/1.65 % (27453)Memory used [KB]: 1663
% 2.78/1.65 % (27453)Time elapsed: 0.009 s
% 2.78/1.65 % (27453)Instructions burned: 15 (million)
% 2.78/1.65 % (27453)------------------------------
% 2.78/1.65 % (27453)------------------------------
% 2.78/1.66 % (27458)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_27328 for (2999ds/3Mi)
% 2.78/1.66 % (27457)Instruction limit reached!
% 2.78/1.66 % (27457)------------------------------
% 2.78/1.66 % (27457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (27457)Termination reason: Unknown
% 2.78/1.66 % (27457)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (27457)Memory used [KB]: 1791
% 2.78/1.66 % (27457)Time elapsed: 0.007 s
% 2.78/1.66 % (27457)Instructions burned: 18 (million)
% 2.78/1.66 % (27457)------------------------------
% 2.78/1.66 % (27457)------------------------------
% 2.78/1.66 % (27458)Instruction limit reached!
% 2.78/1.66 % (27458)------------------------------
% 2.78/1.66 % (27458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (27458)Termination reason: Unknown
% 2.78/1.66 % (27458)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (27458)Memory used [KB]: 1407
% 2.78/1.66 % (27458)Time elapsed: 0.004 s
% 2.78/1.66 % (27458)Instructions burned: 5 (million)
% 2.78/1.66 % (27458)------------------------------
% 2.78/1.66 % (27458)------------------------------
% 2.78/1.66 % (27459)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_27328 for (2999ds/3Mi)
% 2.78/1.66 % (27459)Instruction limit reached!
% 2.78/1.66 % (27459)------------------------------
% 2.78/1.66 % (27459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (27459)Termination reason: Unknown
% 2.78/1.66 % (27459)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (27459)Memory used [KB]: 1407
% 2.78/1.66 % (27459)Time elapsed: 0.002 s
% 2.78/1.66 % (27459)Instructions burned: 3 (million)
% 2.78/1.66 % (27459)------------------------------
% 2.78/1.66 % (27459)------------------------------
% 2.78/1.66 % (27452)Instruction limit reached!
% 2.78/1.66 % (27452)------------------------------
% 2.78/1.66 % (27452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (27452)Termination reason: Unknown
% 2.78/1.66 % (27452)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (27452)Memory used [KB]: 2174
% 2.78/1.66 % (27452)Time elapsed: 0.021 s
% 2.78/1.66 % (27452)Instructions burned: 37 (million)
% 2.78/1.66 % (27452)------------------------------
% 2.78/1.66 % (27452)------------------------------
% 2.78/1.67 % (27461)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/3Mi)
% 2.78/1.67 % (27462)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/4Mi)
% 2.78/1.67 % (27461)Instruction limit reached!
% 2.78/1.67 % (27461)------------------------------
% 2.78/1.67 % (27461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (27461)Termination reason: Unknown
% 2.78/1.67 % (27461)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (27461)Memory used [KB]: 1407
% 2.78/1.67 % (27461)Time elapsed: 0.002 s
% 2.78/1.67 % (27461)Instructions burned: 3 (million)
% 2.78/1.67 % (27461)------------------------------
% 2.78/1.67 % (27461)------------------------------
% 2.78/1.67 % (27463)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/18Mi)
% 2.78/1.67 % (27460)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/7Mi)
% 2.78/1.67 % (27462)Instruction limit reached!
% 2.78/1.67 % (27462)------------------------------
% 2.78/1.67 % (27462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (27462)Termination reason: Unknown
% 2.78/1.67 % (27462)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (27462)Memory used [KB]: 1407
% 2.78/1.67 % (27462)Time elapsed: 0.004 s
% 2.78/1.67 % (27462)Instructions burned: 6 (million)
% 2.78/1.67 % (27462)------------------------------
% 2.78/1.67 % (27462)------------------------------
% 2.78/1.67 % (27444)Instruction limit reached!
% 2.78/1.67 % (27444)------------------------------
% 2.78/1.67 % (27444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (27444)Termination reason: Unknown
% 2.78/1.67 % (27444)Termination phase: Saturation
% 2.78/1.67
% 2.78/1.67 % (27444)Memory used [KB]: 7164
% 2.78/1.67 % (27444)Time elapsed: 0.056 s
% 2.78/1.67 % (27444)Instructions burned: 184 (million)
% 2.78/1.67 % (27444)------------------------------
% 2.78/1.67 % (27444)------------------------------
% 2.78/1.67 % (27460)Instruction limit reached!
% 2.78/1.67 % (27460)------------------------------
% 2.78/1.67 % (27460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (27460)Termination reason: Unknown
% 2.78/1.67 % (27460)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (27460)Memory used [KB]: 1535
% 2.78/1.67 % (27460)Time elapsed: 0.007 s
% 2.78/1.67 % (27460)Instructions burned: 8 (million)
% 2.78/1.67 % (27460)------------------------------
% 2.78/1.67 % (27460)------------------------------
% 2.78/1.67 % (27463)Instruction limit reached!
% 2.78/1.67 % (27463)------------------------------
% 2.78/1.67 % (27463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (27463)Termination reason: Unknown
% 2.78/1.67 % (27463)Termination phase: shuffling
% 2.78/1.68
% 2.78/1.68 % (27463)Memory used [KB]: 1791
% 2.78/1.68 % (27463)Time elapsed: 0.007 s
% 2.78/1.68 % (27463)Instructions burned: 19 (million)
% 2.78/1.68 % (27463)------------------------------
% 2.78/1.68 % (27463)------------------------------
% 2.78/1.68 % (27465)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/6Mi)
% 2.78/1.68 % (27465)Instruction limit reached!
% 2.78/1.68 % (27465)------------------------------
% 2.78/1.68 % (27465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.68 % (27465)Termination reason: Unknown
% 2.78/1.68 % (27465)Termination phase: shuffling
% 2.78/1.68
% 2.78/1.68 % (27465)Memory used [KB]: 1535
% 2.78/1.68 % (27465)Time elapsed: 0.004 s
% 2.78/1.68 % (27465)Instructions burned: 9 (million)
% 2.78/1.68 % (27465)------------------------------
% 2.78/1.68 % (27465)------------------------------
% 2.78/1.68 % (27466)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_27328 for (2999ds/902Mi)
% 2.78/1.68 % (27464)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/710Mi)
% 2.78/1.68 % (27467)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_27328 for (2999ds/21Mi)
% 2.78/1.68 % (27469)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_27328 for (2999ds/6Mi)
% 2.78/1.69 % (27469)Instruction limit reached!
% 2.78/1.69 % (27469)------------------------------
% 2.78/1.69 % (27469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.69 % (27469)Termination reason: Unknown
% 2.78/1.69 % (27469)Termination phase: shuffling
% 2.78/1.69
% 2.78/1.69 % (27469)Memory used [KB]: 1535
% 2.78/1.69 % (27469)Time elapsed: 0.003 s
% 2.78/1.69 % (27469)Instructions burned: 7 (million)
% 2.78/1.69 % (27469)------------------------------
% 2.78/1.69 % (27469)------------------------------
% 2.78/1.69 % (27470)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/377Mi)
% 2.78/1.69 % (27467)Instruction limit reached!
% 2.78/1.69 % (27467)------------------------------
% 2.78/1.69 % (27467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.69 % (27467)Termination reason: Unknown
% 2.78/1.69 % (27467)Termination phase: shuffling
% 2.78/1.69
% 2.78/1.69 % (27467)Memory used [KB]: 1791
% 2.78/1.69 % (27467)Time elapsed: 0.010 s
% 2.78/1.69 % (27467)Instructions burned: 23 (million)
% 2.78/1.69 % (27467)------------------------------
% 2.78/1.69 % (27467)------------------------------
% 2.78/1.69 % (27468)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/5Mi)
% 2.78/1.70 % (27468)Instruction limit reached!
% 2.78/1.70 % (27468)------------------------------
% 2.78/1.70 % (27468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.70 % (27468)Termination reason: Unknown
% 2.78/1.70 % (27468)Termination phase: shuffling
% 2.78/1.70
% 2.78/1.70 % (27468)Memory used [KB]: 1407
% 2.78/1.70 % (27468)Time elapsed: 0.005 s
% 2.78/1.70 % (27468)Instructions burned: 5 (million)
% 2.78/1.70 % (27468)------------------------------
% 2.78/1.70 % (27468)------------------------------
% 2.78/1.70 % (27471)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/779Mi)
% 2.78/1.70 % (27472)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/19Mi)
% 2.78/1.71 % (27464)Refutation not found, incomplete strategy
% 2.78/1.71 % (27464)------------------------------
% 2.78/1.71 % (27464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.71 % (27464)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.71
% 2.78/1.71
% 2.78/1.71 % (27464)Memory used [KB]: 6396
% 2.78/1.71 % (27464)Time elapsed: 0.027 s
% 2.78/1.71 % (27464)Instructions burned: 45 (million)
% 2.78/1.71 % (27464)------------------------------
% 2.78/1.71 % (27464)------------------------------
% 2.78/1.71 % (27472)Instruction limit reached!
% 2.78/1.71 % (27472)------------------------------
% 2.78/1.71 % (27472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.71 % (27472)Termination reason: Unknown
% 2.78/1.71 % (27472)Termination phase: shuffling
% 2.78/1.71
% 2.78/1.71 % (27472)Memory used [KB]: 1791
% 2.78/1.71 % (27472)Time elapsed: 0.007 s
% 2.78/1.71 % (27472)Instructions burned: 19 (million)
% 2.78/1.71 % (27472)------------------------------
% 2.78/1.71 % (27472)------------------------------
% 2.78/1.71 % (27473)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27328 for (2999ds/879Mi)
% 2.78/1.72 % (27474)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27328 for (2998ds/17Mi)
% 2.78/1.72 % (27475)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27328 for (2998ds/3Mi)
% 2.78/1.72 % (27475)Instruction limit reached!
% 2.78/1.72 % (27475)------------------------------
% 2.78/1.72 % (27475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.72 % (27475)Termination reason: Unknown
% 2.78/1.72 % (27475)Termination phase: shuffling
% 2.78/1.72
% 2.78/1.72 % (27475)Memory used [KB]: 1407
% 2.78/1.72 % (27475)Time elapsed: 0.003 s
% 2.78/1.72 % (27475)Instructions burned: 4 (million)
% 2.78/1.72 % (27475)------------------------------
% 2.78/1.72 % (27475)------------------------------
% 2.78/1.72 % (27474)Instruction limit reached!
% 2.78/1.72 % (27474)------------------------------
% 2.78/1.72 % (27474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.72 % (27474)Termination reason: Unknown
% 2.78/1.72 % (27474)Termination phase: shuffling
% 2.78/1.72
% 2.78/1.72 % (27474)Memory used [KB]: 1663
% 2.78/1.72 % (27474)Time elapsed: 0.008 s
% 2.78/1.72 % (27474)Instructions burned: 17 (million)
% 2.78/1.72 % (27474)------------------------------
% 2.78/1.72 % (27474)------------------------------
% 2.78/1.73 % (27466)Refutation not found, incomplete strategy
% 2.78/1.73 % (27466)------------------------------
% 2.78/1.73 % (27466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.73 % (27466)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.73
% 2.78/1.73
% 2.78/1.73 % (27466)Memory used [KB]: 7547
% 2.78/1.73 % (27466)Time elapsed: 0.047 s
% 2.78/1.73 % (27466)Instructions burned: 139 (million)
% 2.78/1.73 % (27466)------------------------------
% 2.78/1.73 % (27466)------------------------------
% 2.78/1.73 % (27476)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27328 for (2998ds/30Mi)
% 2.78/1.74 % (27477)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27328 for (2998ds/127Mi)
% 2.78/1.74 % (27478)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27328 for (2998ds/100Mi)
% 2.78/1.74 % (27455)First to succeed.
% 2.78/1.74 % (27455)Refutation found. Thanks to Tanya!
% 2.78/1.74 % SZS status ContradictoryAxioms for DTF2THF_27328
% 2.78/1.74 % SZS output start Proof for DTF2THF_27328
% 2.78/1.74 thf(type_def_5, type, binary594033953_set_a: $tType).
% 2.78/1.74 thf(type_def_6, type, set_a: $tType).
% 2.78/1.74 thf(type_def_8, type, binary1439146945Tree_a: $tType).
% 2.78/1.74 thf(type_def_9, type, a: $tType).
% 2.78/1.74 thf(type_def_10, type, set_set_a: $tType).
% 2.78/1.74 thf(type_def_11, type, int: $tType).
% 2.78/1.74 thf(type_def_12, type, set_set_set_a: $tType).
% 2.78/1.74 thf(func_def_0, type, binary594033953_set_a: $tType).
% 2.78/1.74 thf(func_def_1, type, binary1439146945Tree_a: $tType).
% 2.78/1.74 thf(func_def_2, type, set_set_set_a: $tType).
% 2.78/1.74 thf(func_def_3, type, set_set_a: $tType).
% 2.78/1.74 thf(func_def_4, type, set_a: $tType).
% 2.78/1.74 thf(func_def_5, type, int: $tType).
% 2.78/1.74 thf(func_def_6, type, a: $tType).
% 2.78/1.74 thf(func_def_7, type, binary313540327_set_a: binary594033953_set_a > set_a > binary594033953_set_a > binary594033953_set_a).
% 2.78/1.74 thf(func_def_8, type, binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 2.78/1.74 thf(func_def_9, type, binary476621312_Tip_a: binary1439146945Tree_a).
% 2.78/1.74 thf(func_def_10, type, binary1613048283_set_a: binary594033953_set_a > set_set_a).
% 2.78/1.74 thf(func_def_11, type, binary256242811Tree_a: binary1439146945Tree_a > set_a).
% 2.78/1.74 thf(func_def_12, type, binary504661350_eqs_a: (a > int) > a > set_a).
% 2.78/1.74 thf(func_def_13, type, binary1001944660_set_a: binary594033953_set_a > set_set_a).
% 2.78/1.74 thf(func_def_14, type, binary945792244etOf_a: binary1439146945Tree_a > set_a).
% 2.78/1.74 thf(func_def_15, type, binary512218034_set_a: (set_a > int) > binary594033953_set_a > $o).
% 2.78/1.74 thf(func_def_16, type, binary1721989714Tree_a: (a > int) > binary1439146945Tree_a > $o).
% 2.78/1.74 thf(func_def_17, type, binary1524747315_set_a: (set_a > int) > set_a > set_a > binary594033953_set_a > $o).
% 2.78/1.74 thf(func_def_18, type, binary670562003pred_a: (a > int) > a > a > binary1439146945Tree_a > $o).
% 2.78/1.74 thf(func_def_19, type, the_a: (a > $o) > a).
% 2.78/1.74 thf(func_def_20, type, semila1223476304_a_a_o: ((a > a > $o) > (a > a > $o) > a > a > $o) > (a > a > $o) > $o).
% 2.78/1.74 thf(func_def_21, type, semila980155549tr_a_o: ((a > $o) > (a > $o) > a > $o) > (a > $o) > $o).
% 2.78/1.74 thf(func_def_22, type, semila1409648192_set_a: (set_a > set_a > set_a) > set_a > $o).
% 2.78/1.74 thf(func_def_23, type, sup_su198629954et_a_o: (set_a > set_a > $o) > (set_a > set_a > $o) > set_a > set_a > $o).
% 2.78/1.74 thf(func_def_24, type, sup_sup_set_a_o: (set_a > $o) > (set_a > $o) > set_a > $o).
% 2.78/1.74 thf(func_def_25, type, sup_sup_a_a_o: (a > a > $o) > (a > a > $o) > a > a > $o).
% 2.78/1.74 thf(func_def_26, type, sup_sup_a_o: (a > $o) > (a > $o) > a > $o).
% 2.78/1.74 thf(func_def_27, type, sup_sup_int: int > int > int).
% 2.78/1.74 thf(func_def_28, type, sup_sup_set_set_a: set_set_a > set_set_a > set_set_a).
% 2.78/1.74 thf(func_def_29, type, sup_sup_set_a: set_a > set_a > set_a).
% 2.78/1.74 thf(func_def_30, type, bot_bot_set_a_o: set_a > $o).
% 2.78/1.74 thf(func_def_31, type, bot_bot_a_a_o: a > a > $o).
% 2.78/1.74 thf(func_def_32, type, bot_bot_a_o: a > $o).
% 2.78/1.74 thf(func_def_34, type, bot_bot_set_set_a: set_set_a).
% 2.78/1.74 thf(func_def_35, type, bot_bot_set_a: set_a).
% 2.78/1.74 thf(func_def_36, type, ord_less_set_a_o: (set_a > $o) > (set_a > $o) > $o).
% 2.78/1.74 thf(func_def_37, type, ord_less_a_a_o: (a > a > $o) > (a > a > $o) > $o).
% 2.78/1.74 thf(func_def_38, type, ord_less_a_o: (a > $o) > (a > $o) > $o).
% 2.78/1.74 thf(func_def_39, type, ord_less_int: int > int > $o).
% 2.78/1.74 thf(func_def_40, type, ord_less_set_set_a: set_set_a > set_set_a > $o).
% 2.78/1.74 thf(func_def_41, type, ord_less_set_a: set_a > set_a > $o).
% 2.78/1.74 thf(func_def_42, type, ord_less_eq_set_a: set_a > set_a > $o).
% 2.78/1.74 thf(func_def_43, type, powp_set_a: (set_a > $o) > set_set_a > $o).
% 2.78/1.74 thf(func_def_44, type, powp_a: (a > $o) > set_a > $o).
% 2.78/1.74 thf(func_def_45, type, collect_set_set_a: (set_set_a > $o) > set_set_set_a).
% 2.78/1.74 thf(func_def_46, type, collect_set_a: (set_a > $o) > set_set_a).
% 2.78/1.74 thf(func_def_47, type, collect_a: (a > $o) > set_a).
% 2.78/1.74 thf(func_def_48, type, pow_set_a: set_set_a > set_set_set_a).
% 2.78/1.74 thf(func_def_49, type, pow_a: set_a > set_set_a).
% 2.78/1.74 thf(func_def_50, type, insert_set_a: set_a > set_set_a > set_set_a).
% 2.78/1.74 thf(func_def_51, type, insert_a: a > set_a > set_a).
% 2.78/1.74 thf(func_def_52, type, is_empty_a: set_a > $o).
% 2.78/1.74 thf(func_def_53, type, is_singleton_set_a: set_set_a > $o).
% 2.78/1.74 thf(func_def_54, type, is_singleton_a: set_a > $o).
% 2.78/1.74 thf(func_def_55, type, the_elem_a: set_a > a).
% 2.78/1.74 thf(func_def_56, type, chains_a: set_set_a > set_set_set_a).
% 2.78/1.74 thf(func_def_57, type, pred_chain_set_a: set_set_a > (set_a > set_a > $o) > set_set_a > $o).
% 2.78/1.74 thf(func_def_58, type, pred_chain_a: set_a > (a > a > $o) > set_a > $o).
% 2.78/1.74 thf(func_def_59, type, member_set_set_a: set_set_a > set_set_set_a > $o).
% 2.78/1.74 thf(func_def_60, type, member_set_a: set_a > set_set_a > $o).
% 2.78/1.74 thf(func_def_61, type, member_a: a > set_a > $o).
% 2.78/1.74 thf(func_def_62, type, a2: a).
% 2.78/1.74 thf(func_def_63, type, b: a).
% 2.78/1.74 thf(func_def_64, type, h: a > int).
% 2.78/1.74 thf(func_def_65, type, t1: binary1439146945Tree_a).
% 2.78/1.74 thf(func_def_66, type, t2: binary1439146945Tree_a).
% 2.78/1.74 thf(func_def_67, type, x: a).
% 2.78/1.74 thf(f1987,plain,(
% 2.78/1.74 $false),
% 2.78/1.74 inference(trivial_inequality_removal,[status(thm)],[f1986])).
% 2.78/1.74 thf(f1986,plain,(
% 2.78/1.74 ($true = $false)),
% 2.78/1.74 inference(boolean_simplification,[status(thm)],[f1985])).
% 2.78/1.74 thf(f1985,plain,(
% 2.78/1.74 ($true = (((sup_sup_int @ (h @ a2) @ (h @ a2)) = (h @ a2)) & $false))),
% 2.78/1.74 inference(boolean_simplification,[status(thm)],[f1984])).
% 2.78/1.74 thf(f1984,plain,(
% 2.78/1.74 ($true = (((sup_sup_int @ (h @ a2) @ (h @ a2)) = (h @ a2)) & (~ $true)))),
% 2.78/1.74 inference(boolean_simplification,[status(thm)],[f1980])).
% 2.78/1.74 thf(f1980,plain,(
% 2.78/1.74 ($true = (((sup_sup_int @ (h @ a2) @ (h @ a2)) = (h @ a2)) & (~ ((h @ a2) = (h @ a2)))))),
% 2.78/1.74 inference(backward_demodulation,[status(thm)],[f1893,f1180])).
% 2.78/1.74 thf(f1180,plain,(
% 2.78/1.74 ((h @ a2) = (h @ b))),
% 2.78/1.74 inference(cnf_transformation,[status(thm)],[f485])).
% 2.78/1.74 thf(f485,plain,(
% 2.78/1.74 ((h @ a2) = (h @ b))),
% 2.78/1.74 inference(fool_elimination,[status(thm)],[f1])).
% 2.78/1.74 thf(f1,axiom,(
% 2.78/1.74 ((h @ a2) = (h @ b))),
% 2.78/1.74 file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_0_hahb)).
% 2.78/1.74 thf(f1893,plain,(
% 2.78/1.74 ($true = (((sup_sup_int @ (h @ a2) @ (h @ b)) = (h @ a2)) & (~ ((h @ b) = (h @ a2)))))),
% 2.78/1.74 inference(beta_eta_normalization,[status(thm)],[f1655])).
% 2.78/1.74 thf(f1655,plain,(
% 2.78/1.74 ($true = ((^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))) @ (h @ b) @ (h @ a2)))),
% 2.78/1.74 inference(definition_unfolding,[status(thm)],[f1374,f1096])).
% 2.78/1.74 thf(f1096,plain,(
% 2.78/1.74 (ord_less_int = (^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))))),
% 2.78/1.74 inference(cnf_transformation,[status(thm)],[f499])).
% 2.78/1.74 thf(f499,plain,(
% 2.78/1.74 (ord_less_int = (^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))))),
% 2.78/1.74 inference(fool_elimination,[status(thm)],[f498])).
% 2.78/1.74 thf(f498,plain,(
% 2.78/1.74 ((^[X0 : int, X1 : int] : ((X0 != X1) & ((sup_sup_int @ X1 @ X0) = X1))) = ord_less_int)),
% 2.78/1.74 inference(rectify,[status(thm)],[f310])).
% 2.78/1.74 thf(f310,axiom,(
% 2.78/1.74 ((^[X22 : int, X21 : int] : ((X21 != X22) & ((sup_sup_int @ X21 @ X22) = X21))) = ord_less_int)),
% 2.78/1.74 file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_309_sup_Ostrict__order__iff)).
% 2.78/1.74 thf(f1374,plain,(
% 2.78/1.74 ((ord_less_int @ (h @ b) @ (h @ a2)) = $true)),
% 2.78/1.74 inference(cnf_transformation,[status(thm)],[f685])).
% 2.78/1.74 thf(f685,plain,(
% 2.78/1.74 ((ord_less_int @ (h @ b) @ (h @ a2)) = $true)),
% 2.78/1.74 inference(fool_elimination,[status(thm)],[f684])).
% 2.78/1.74 thf(f684,plain,(
% 2.78/1.74 (ord_less_int @ (h @ b) @ (h @ a2))),
% 2.78/1.74 inference(rectify,[status(thm)],[f2])).
% 2.78/1.74 thf(f2,axiom,(
% 2.78/1.74 (ord_less_int @ (h @ b) @ (h @ a2))),
% 2.78/1.74 file('/export/starexec/sandbox2/tmp/tmp.wypFpf0p5t/DTF2THF_27328.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062)).
% 2.78/1.74 % SZS output end Proof for DTF2THF_27328
% 2.78/1.74 % (27455)------------------------------
% 2.78/1.74 % (27455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.74 % (27455)Termination reason: Refutation
% 2.78/1.74
% 2.78/1.74 % (27455)Memory used [KB]: 7931
% 2.78/1.74 % (27455)Time elapsed: 0.096 s
% 2.78/1.74 % (27455)Instructions burned: 361 (million)
% 2.78/1.74 % (27455)------------------------------
% 2.78/1.74 % (27455)------------------------------
% 2.78/1.74 % (27443)Success in time 0.134 s
%------------------------------------------------------------------------------