%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP163^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 08:56:03 AM UTC 2026
% Result : Theorem 3.40s 1.90s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 245 ( 55 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 275 ( 31 ~; 36 |; 12 &; 192 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 140 ( 137 usr; 8 con; 0-3 aty)
% Number of variables : 32 ( 12 ^; 20 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr384614482nres_a: $tType ).
thf(type_def_6,type,
refine424419629nres_a: $tType ).
thf(type_def_8,type,
set_a: $tType ).
thf(type_def_9,type,
produc1609974940nres_a: $tType ).
thf(type_def_10,type,
a: $tType ).
thf(type_def_11,type,
set_set_a: $tType ).
thf(func_def_0,type,
set_Pr384614482nres_a: $tType ).
thf(func_def_1,type,
produc1609974940nres_a: $tType ).
thf(func_def_2,type,
refine424419629nres_a: $tType ).
thf(func_def_3,type,
set_set_a: $tType ).
thf(func_def_4,type,
set_a: $tType ).
thf(func_def_5,type,
a: $tType ).
thf(func_def_6,type,
bNF_Ca459084161nres_a: set_Pr384614482nres_a > ( refine424419629nres_a > refine424419629nres_a ) > $o ).
thf(func_def_7,type,
bNF_Ca953716171_set_a: set_Pr384614482nres_a > ( refine424419629nres_a > set_a ) > $o ).
thf(func_def_8,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(func_def_9,type,
if_set_a: $o > set_a > set_a > set_a ).
thf(func_def_10,type,
ord_le1480771457nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_11,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_12,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(func_def_13,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_14,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(func_def_15,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(func_def_16,type,
produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
thf(func_def_17,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(func_def_18,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(func_def_19,type,
refine1048213316_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
thf(func_def_20,type,
refine260105272_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
thf(func_def_21,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(func_def_22,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(func_def_23,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(func_def_24,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(func_def_25,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(func_def_26,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_27,type,
accp_P624619091nres_a: ( produc1609974940nres_a > produc1609974940nres_a > $o ) > produc1609974940nres_a > $o ).
thf(func_def_28,type,
chain_subset_a: set_set_a > $o ).
thf(func_def_29,type,
member1468928819nres_a: produc1609974940nres_a > set_Pr384614482nres_a > $o ).
thf(func_def_30,type,
member_set_a: set_a > set_set_a > $o ).
thf(func_def_31,type,
member_a: a > set_a > $o ).
thf(func_def_32,type,
phi: a > $o ).
thf(func_def_33,type,
x: a ).
thf(func_def_49,type,
sK0: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_50,type,
sK1: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_51,type,
sK2: refine424419629nres_a > refine424419629nres_a > a ).
thf(func_def_52,type,
sK3: ( set_a > set_a ) > set_a ).
thf(func_def_53,type,
sK4: ( set_a > set_a ) > set_a ).
thf(func_def_54,type,
sK5: set_a > set_a > a ).
thf(func_def_55,type,
sK6: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_56,type,
sK7: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_57,type,
sK8: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_58,type,
sK9: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_59,type,
sK10: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_60,type,
sK11: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_61,type,
sK12: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_62,type,
sK13: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_63,type,
sK14: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_64,type,
sK15: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_65,type,
sK16: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_66,type,
sK17: ( set_a > set_a ) > set_a ).
thf(func_def_67,type,
sK18: ( set_a > set_a ) > set_a ).
thf(func_def_68,type,
sK19: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_69,type,
sK20: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_70,type,
sK21: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_71,type,
sK22: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_72,type,
sK23: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_73,type,
sK24: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_74,type,
sK25: ( set_a > set_a ) > set_a ).
thf(func_def_75,type,
sK26: ( set_a > set_a ) > set_a ).
thf(func_def_76,type,
sK27: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_77,type,
sK28: ( set_a > set_a ) > set_a ).
thf(func_def_78,type,
sK29: ( set_a > set_a ) > set_a ).
thf(func_def_79,type,
sK30: ( set_a > set_a ) > set_a ).
thf(func_def_80,type,
sK31: ( set_a > set_a ) > set_a ).
thf(func_def_81,type,
sK32: ( set_a > set_a ) > set_a ).
thf(func_def_82,type,
sK33: ( set_a > set_a ) > set_a ).
thf(func_def_83,type,
sK34: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_84,type,
sK35: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_85,type,
sK36: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_86,type,
sK37: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_87,type,
sK38: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_88,type,
sK39: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_89,type,
sK40: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_90,type,
sK41: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_91,type,
sK42: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_92,type,
sK43: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_93,type,
sK44: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_94,type,
sK45: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_95,type,
sK46: ( set_a > set_a ) > set_a ).
thf(func_def_96,type,
sK47: ( set_a > set_a ) > set_a ).
thf(func_def_97,type,
sK48: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_98,type,
sK49: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_99,type,
sK50: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_100,type,
sK51: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_101,type,
sK52: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_102,type,
sK53: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_103,type,
sK54: refine424419629nres_a > refine424419629nres_a > a ).
thf(func_def_104,type,
sK55: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_105,type,
sK56: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_106,type,
sK57: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_107,type,
sK58: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_108,type,
sK59: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_109,type,
sK60: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_110,type,
sK61: ( set_a > set_a ) > set_a ).
thf(func_def_111,type,
sK62: ( set_a > set_a ) > set_a ).
thf(func_def_112,type,
sK63: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_113,type,
sK64: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_114,type,
sK65: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_115,type,
sK66: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_116,type,
sK67: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_117,type,
sK68: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_118,type,
sK69: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_119,type,
sK70: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_120,type,
sK71: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_121,type,
sK72: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_122,type,
sK73: ( set_a > refine424419629nres_a ) > set_a ).
thf(func_def_123,type,
sK74: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_124,type,
sK75: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_125,type,
sK76: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_126,type,
sK77: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_127,type,
sK78: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_128,type,
sK79: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_129,type,
sK80: set_a > ( a > $o ) > a ).
thf(func_def_130,type,
sK81: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_131,type,
sK82: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_132,type,
sK83: ( set_a > set_a ) > set_a ).
thf(func_def_133,type,
sK84: ( set_a > set_a ) > set_a ).
thf(func_def_134,type,
sK85: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_135,type,
sK86: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_136,type,
sK87: ( set_a > set_a ) > set_a ).
thf(func_def_137,type,
sK88: ( set_a > set_a ) > set_a ).
thf(func_def_138,type,
sK89: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_139,type,
sK90: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_140,type,
sK91: ( set_a > set_a ) > set_a ).
thf(func_def_141,type,
sK92: ( set_a > set_a ) > set_a ).
thf(func_def_142,type,
sK93: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_143,type,
sK94: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_144,type,
sK95: ( set_a > set_a ) > set_a ).
thf(func_def_145,type,
sK96: ( set_a > set_a ) > set_a ).
thf(func_def_146,type,
sK97: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_147,type,
sK98: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_148,type,
sK99: refine424419629nres_a > refine424419629nres_a > a ).
thf(func_def_149,type,
sK100: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_150,type,
sK101: ( refine424419629nres_a > set_a ) > refine424419629nres_a ).
thf(func_def_151,type,
sK102: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_152,type,
sK103: ( refine424419629nres_a > refine424419629nres_a ) > refine424419629nres_a ).
thf(func_def_154,type,
ph105:
!>[X0: $tType] : X0 ).
thf(f1661,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1565,f1576,f1618,f1655,f1660]) ).
thf(f1660,plain,
( ~ spl104_1
| ~ spl104_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f1659]) ).
thf(f1659,plain,
( $false
| ~ spl104_1
| ~ spl104_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1658]) ).
thf(f1658,plain,
( ( $true = $false )
| ~ spl104_1
| ~ spl104_4 ),
inference(forward_demodulation,[status(thm)],[f1560,f1575]) ).
thf(f1575,plain,
( ( ( phi @ x )
= $false )
| ~ spl104_4 ),
inference(avatar_component_clause,[status(thm)],[f1573]) ).
thf(f1573,definition,
( spl104_4
<=> ( ( phi @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl104_4])],[avatar_definition]) ).
thf(f1560,plain,
( ( ( phi @ x )
= $true )
| ~ spl104_1 ),
inference(avatar_component_clause,[status(thm)],[f1558]) ).
thf(f1558,definition,
( spl104_1
<=> ( ( phi @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl104_1])],[avatar_definition]) ).
thf(f1655,plain,
( ~ spl104_2
| ~ spl104_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f1654]) ).
thf(f1654,plain,
( $false
| ~ spl104_2
| ~ spl104_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1653]) ).
thf(f1653,plain,
( ( $true = $false )
| ~ spl104_2
| ~ spl104_4 ),
inference(forward_demodulation,[status(thm)],[f1642,f1575]) ).
thf(f1642,plain,
( ( ( phi @ x )
= $true )
| ~ spl104_2 ),
inference(superposition,[status(thm)],[f1636,f1395]) ).
thf(f1395,plain,
! [X0: a > $o,X1: a] :
( ( member_a @ X1 @ ( collect_a @ X0 ) )
= ( X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
thf(f782,plain,
! [X0: a > $o,X1: a] :
( ( member_a @ X1 @ ( collect_a @ X0 ) )
= ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
! [X8: a > $o,X32: a] :
( ( member_a @ X32 @ ( collect_a @ X8 ) )
= ( X8 @ X32 ) ),
file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_41_mem__Collect__eq) ).
thf(f1636,plain,
( ( $true
= ( member_a @ x @ ( collect_a @ phi ) ) )
| ~ spl104_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1635]) ).
thf(f1635,plain,
( ( $true = $false )
| ( $true
= ( member_a @ x @ ( collect_a @ phi ) ) )
| ~ spl104_2 ),
inference(forward_demodulation,[status(thm)],[f1625,f1372]) ).
thf(f1372,plain,
! [X0: set_a] :
( ( refine412683989fail_a @ ( refine1198353288_RES_a @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f486]) ).
thf(f486,plain,
! [X0: set_a] :
( ( refine412683989fail_a @ ( refine1198353288_RES_a @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f485]) ).
thf(f485,plain,
! [X0: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_5_nofail__simps_I2_J) ).
thf(f1625,plain,
( ( $false
= ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
| ( $true
= ( member_a @ x @ ( collect_a @ phi ) ) )
| ~ spl104_2 ),
inference(binary_proxy_clausification,[status(thm)],[f1624]) ).
thf(f1624,plain,
( ( ( member_a @ x @ ( collect_a @ phi ) )
= ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
| ~ spl104_2 ),
inference(boolean_simplification,[status(thm)],[f1623]) ).
thf(f1623,plain,
( ( ( $true
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
= ( member_a @ x @ ( collect_a @ phi ) ) )
| ~ spl104_2 ),
inference(superposition,[status(thm)],[f1546,f1564]) ).
thf(f1564,plain,
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $true )
| ~ spl104_2 ),
inference(avatar_component_clause,[status(thm)],[f1562]) ).
thf(f1562,definition,
( spl104_2
<=> ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl104_2])],[avatar_definition]) ).
thf(f1546,plain,
! [X0: set_a,X1: a] :
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X0 ) @ X1 )
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ X0 ) ) )
= ( member_a @ X1 @ X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f1471]) ).
thf(f1471,plain,
! [X0: set_a,X1: a] :
( ( ^ [Y0: refine424419629nres_a,Y1: a] :
( ( refine1001002027nres_a @ Y0 @ Y1 )
& ( refine412683989fail_a @ Y0 ) )
@ ( refine1198353288_RES_a @ X0 )
@ X1 )
= ( member_a @ X1 @ X0 ) ),
inference(definition_unfolding,[status(thm)],[f1209,f1309]) ).
thf(f1309,plain,
( refine1312857699nres_a
= ( ^ [Y0: refine424419629nres_a,Y1: a] :
( ( refine1001002027nres_a @ Y0 @ Y1 )
& ( refine412683989fail_a @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f404]) ).
thf(f404,plain,
( refine1312857699nres_a
= ( ^ [Y0: refine424419629nres_a,Y1: a] :
( ( refine1001002027nres_a @ Y0 @ Y1 )
& ( refine412683989fail_a @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f403]) ).
thf(f403,plain,
( ( ^ [X0: refine424419629nres_a,X1: a] :
( ( refine412683989fail_a @ X0 )
& ( refine1001002027nres_a @ X0 @ X1 ) ) )
= refine1312857699nres_a ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
( ( ^ [X6: refine424419629nres_a,X5: a] :
( ( refine412683989fail_a @ X6 )
& ( refine1001002027nres_a @ X6 @ X5 ) ) )
= refine1312857699nres_a ),
file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_17_nf__inres__def) ).
thf(f1209,plain,
! [X0: set_a,X1: a] :
( ( member_a @ X1 @ X0 )
= ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f778]) ).
thf(f778,plain,
! [X0: set_a,X1: a] :
( ( member_a @ X1 @ X0 )
= ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: set_a,X4: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X0 ) @ X4 )
= ( member_a @ X4 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_2_nf__inres__RES) ).
thf(f1618,plain,
( spl104_4
| ~ spl104_3 ),
inference(avatar_split_clause,[status(thm)],[f1599,f1569,f1573]) ).
thf(f1569,definition,
( spl104_3
<=> ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl104_3])],[avatar_definition]) ).
thf(f1599,plain,
( ( ( phi @ x )
= $false )
| ~ spl104_3 ),
inference(superposition,[status(thm)],[f1395,f1590]) ).
thf(f1590,plain,
( ( ( member_a @ x @ ( collect_a @ phi ) )
= $false )
| ~ spl104_3 ),
inference(boolean_simplification,[status(thm)],[f1581]) ).
thf(f1581,plain,
( ( ( member_a @ x @ ( collect_a @ phi ) )
= ( $false
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) )
| ~ spl104_3 ),
inference(superposition,[status(thm)],[f1546,f1571]) ).
thf(f1571,plain,
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $false )
| ~ spl104_3 ),
inference(avatar_component_clause,[status(thm)],[f1569]) ).
thf(f1576,plain,
( spl104_3
| spl104_4 ),
inference(avatar_split_clause,[status(thm)],[f1567,f1573,f1569]) ).
thf(f1567,plain,
( ( ( phi @ x )
= $false )
| ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f1566]) ).
thf(f1566,plain,
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $false )
| ( ( phi @ x )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f1554,f1372]) ).
thf(f1554,plain,
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $false )
| ( $false
= ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) )
| ( ( phi @ x )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1553]) ).
thf(f1553,plain,
( ( ( phi @ x )
= $false )
| ( $false
= ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1551]) ).
thf(f1551,plain,
( ( phi @ x )
!= ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1472]) ).
thf(f1472,plain,
( ( phi @ x )
!= ( ^ [Y0: refine424419629nres_a,Y1: a] :
( ( refine1001002027nres_a @ Y0 @ Y1 )
& ( refine412683989fail_a @ Y0 ) )
@ ( refine1198353288_RES_a @ ( collect_a @ phi ) )
@ x ) ),
inference(definition_unfolding,[status(thm)],[f1297,f1309]) ).
thf(f1297,plain,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(cnf_transformation,[status(thm)],[f777]) ).
thf(f777,plain,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(flattening,[status(thm)],[f271]) ).
thf(f271,negated_conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
!= ( phi @ x ) ),
inference(negated_conjecture,[status(cth)],[f270]) ).
thf(f270,conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= ( phi @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',conj_0) ).
thf(f1565,plain,
( spl104_1
| spl104_2 ),
inference(avatar_split_clause,[status(thm)],[f1556,f1562,f1558]) ).
thf(f1556,plain,
( ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
= $true )
| ( ( phi @ x )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1552]) ).
thf(f1552,plain,
( ( ( phi @ x )
= $true )
| ( $true
= ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
& ( refine412683989fail_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP163^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:28:21 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : ITP163^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.45 % Domain : Interactive Theorem Proving
% 0.20/0.45 % Problem : Sledgehammer Refine_Basic problem prob_374__3586996_1
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Des21]
% 0.20/0.45 % Names : Refine_Basic/prob_374__3586996_1 [Des21]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.20/0.45 % Syntax : Number of formulae : 304 ( 78 unt; 34 typ; 0 def)
% 0.20/0.45 % Number of atoms : 936 ( 248 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 15 ( 3 avg)
% 0.20/0.45 % Number of connectives : 2423 ( 117 ~; 11 |; 24 &;1741 @)
% 0.20/0.45 % ( 0 <=>; 530 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 19 ( 8 avg)
% 0.20/0.45 % Number of types : 7 ( 6 usr)
% 0.20/0.45 % Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 31 ( 28 usr; 4 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 888 ( 86 ^; 794 !; 8 ?; 888 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:43.925
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % Could-be-implicit typings (6)
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_J,type,
% 0.20/0.45 set_Pr384614482nres_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.45 produc1609974940nres_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 refine424419629nres_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.20/0.45 set_set_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 set_a: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_tf__a,type,
% 0.20/0.45 a: $tType ).
% 0.20/0.45
% 0.20/0.45 % Explicit typings (28)
% 0.20/0.45 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 bNF_Ca459084161nres_a: set_Pr384614482nres_a > ( refine424419629nres_a > refine424419629nres_a ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 bNF_Ca953716171_set_a: set_Pr384614482nres_a > ( refine424419629nres_a > set_a ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 if_set_a: $o > set_a > set_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 ord_le1480771457nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 ord_less_set_a: set_a > set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 order_Greatest_set_a: ( set_a > $o ) > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Product__Type_OPair_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 0.20/0.45 produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 0.20/0.45 refine2063221604TURN_a: a > refine424419629nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 0.20/0.45 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oless__eq__nres__rel_001tf__a,type,
% 0.20/0.45 refine1048213316_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oless__nres__rel_001tf__a,type,
% 0.20/0.45 refine260105272_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 0.20/0.45 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 0.20/0.45 refine412683989fail_a: refine424419629nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 0.20/0.45 refine464223677AILi_a: refine424419629nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 0.20/0.45 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 0.20/0.45 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.20/0.45 collect_a: ( a > $o ) > set_a ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.45 accp_P624619091nres_a: ( produc1609974940nres_a > produc1609974940nres_a > $o ) > produc1609974940nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Zorn_Ochain__subset_001tf__a,type,
% 0.20/0.45 chain_subset_a: set_set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_member_001t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 0.20/0.45 member1468928819nres_a: produc1609974940nres_a > set_Pr384614482nres_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 0.20/0.45 member_set_a: set_a > set_set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_member_001tf__a,type,
% 0.20/0.45 member_a: a > set_a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v__092_060Phi_062,type,
% 0.20/0.45 phi: a > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_v_x,type,
% 0.20/0.45 x: a ).
% 0.20/0.45
% 0.20/0.45 % Relevant facts (264)
% 0.20/0.45 thf(fact_0_nres__more__simps_I4_J,axiom,
% 0.20/0.45 ! [X: set_a,Y: set_a] :
% 0.20/0.45 ( ( ( refine1198353288_RES_a @ X )
% 0.20/0.45 = ( refine1198353288_RES_a @ Y ) )
% 0.20/0.45 = ( X = Y ) ) ).
% 0.20/0.45
% 0.20/0.45 % nres_more_simps(4)
% 0.20/0.45 thf(fact_1_nres_Oinject,axiom,
% 0.20/0.45 ! [X2: set_a,Y2: set_a] :
% 0.20/0.45 ( ( ( refine1198353288_RES_a @ X2 )
% 0.20/0.45 = ( refine1198353288_RES_a @ Y2 ) )
% 0.20/0.45 = ( X2 = Y2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % nres.inject
% 0.20/0.45 thf(fact_2_nf__inres__RES,axiom,
% 0.20/0.45 ! [X: set_a,X3: a] :
% 0.20/0.45 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X3 )
% 0.20/0.45 = ( member_a @ X3 @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % nf_inres_RES
% 0.20/0.45 thf(fact_3_the__RES_Osimps,axiom,
% 0.20/0.45 ! [X: set_a] :
% 0.20/0.45 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 0.20/0.45 = X ) ).
% 0.20/0.45
% 0.20/0.45 % the_RES.simps
% 0.20/0.45 thf(fact_4_inres__simps_I2_J,axiom,
% 0.20/0.45 ! [X: set_a] :
% 0.20/0.45 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 0.20/0.45 = ( ^ [X4: a] : ( member_a @ X4 @ X ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % inres_simps(2)
% 0.20/0.45 thf(fact_5_nofail__simps_I2_J,axiom,
% 0.20/0.45 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 0.20/0.45
% 0.20/0.45 % nofail_simps(2)
% 0.20/0.45 thf(fact_6_nofail__RES__conv,axiom,
% 0.20/0.45 ( refine412683989fail_a
% 0.20/0.45 = ( ^ [M: refine424419629nres_a] :
% 0.20/0.45 ? [M2: set_a] :
% 0.20/0.45 ( M
% 0.20/0.45 = ( refine1198353288_RES_a @ M2 ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % nofail_RES_conv
% 0.20/0.45 thf(fact_7_nres_Odistinct_I1_J,axiom,
% 0.20/0.45 ! [X2: set_a] :
% 0.20/0.45 ( refine464223677AILi_a
% 0.20/0.45 != ( refine1198353288_RES_a @ X2 ) ) ).
% 0.20/0.45
% 0.20/0.45 % nres.distinct(1)
% 0.20/0.45 thf(fact_8_nres_Oinduct,axiom,
% 0.20/0.45 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 0.20/0.45 ( ( P @ refine464223677AILi_a )
% 0.20/0.45 => ( ! [X5: set_a] : ( P @ ( refine1198353288_RES_a @ X5 ) )
% 0.20/0.45 => ( P @ Nres ) ) ) ).
% 0.20/0.45
% 0.20/0.45 % nres.induct
% 0.20/0.45 thf(fact_9_nres_Oexhaust,axiom,
% 0.20/0.46 ! [Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( Y3 != refine464223677AILi_a )
% 0.20/0.46 => ~ ! [X22: set_a] :
% 0.20/0.46 ( Y3
% 0.20/0.46 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres.exhaust
% 0.20/0.46 thf(fact_10_sup__nres_Oinduct,axiom,
% 0.20/0.46 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.20/0.46 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.20/0.46 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 0.20/0.46 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_nres.induct
% 0.20/0.46 thf(fact_11_less__nres_Oinduct,axiom,
% 0.20/0.46 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.20/0.46 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 0.20/0.46 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 0.20/0.46 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.induct
% 0.20/0.46 thf(fact_12_less__eq__nres_Oinduct,axiom,
% 0.20/0.46 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.20/0.46 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.20/0.46 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.induct
% 0.20/0.46 thf(fact_13_the__RES__inv,axiom,
% 0.20/0.46 ! [M3: refine424419629nres_a] :
% 0.20/0.46 ( ( refine412683989fail_a @ M3 )
% 0.20/0.46 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M3 ) )
% 0.20/0.46 = M3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % the_RES_inv
% 0.20/0.46 thf(fact_14_pw__eqI,axiom,
% 0.20/0.46 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.20/0.46 ( ( ( refine412683989fail_a @ S )
% 0.20/0.46 = ( refine412683989fail_a @ S2 ) )
% 0.20/0.46 => ( ! [X5: a] :
% 0.20/0.46 ( ( refine1001002027nres_a @ S @ X5 )
% 0.20/0.46 = ( refine1001002027nres_a @ S2 @ X5 ) )
% 0.20/0.46 => ( S = S2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pw_eqI
% 0.20/0.46 thf(fact_15_pw__eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.20/0.46 ( ( ( refine412683989fail_a @ S3 )
% 0.20/0.46 = ( refine412683989fail_a @ S4 ) )
% 0.20/0.46 & ! [X4: a] :
% 0.20/0.46 ( ( refine1001002027nres_a @ S3 @ X4 )
% 0.20/0.46 = ( refine1001002027nres_a @ S4 @ X4 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pw_eq_iff
% 0.20/0.46 thf(fact_16_not__nofail__inres,axiom,
% 0.20/0.46 ! [S: refine424419629nres_a,X3: a] :
% 0.20/0.46 ( ~ ( refine412683989fail_a @ S )
% 0.20/0.46 => ( refine1001002027nres_a @ S @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_nofail_inres
% 0.20/0.46 thf(fact_17_nf__inres__def,axiom,
% 0.20/0.46 ( refine1312857699nres_a
% 0.20/0.46 = ( ^ [M: refine424419629nres_a,X4: a] :
% 0.20/0.46 ( ( refine412683989fail_a @ M )
% 0.20/0.46 & ( refine1001002027nres_a @ M @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % nf_inres_def
% 0.20/0.46 thf(fact_18_inres__simps_I3_J,axiom,
% 0.20/0.46 ! [X3: a] :
% 0.20/0.46 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X3 ) )
% 0.20/0.46 = ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 0.20/0.46 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % inres_simps(3)
% 0.20/0.46 thf(fact_19_nofail__simps_I3_J,axiom,
% 0.20/0.46 ! [X3: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nofail_simps(3)
% 0.20/0.46 thf(fact_20_pw__leI,axiom,
% 0.20/0.46 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.20/0.46 ( ( ( refine412683989fail_a @ S2 )
% 0.20/0.46 => ( ( refine412683989fail_a @ S )
% 0.20/0.46 & ! [X5: a] :
% 0.20/0.46 ( ( refine1001002027nres_a @ S @ X5 )
% 0.20/0.46 => ( refine1001002027nres_a @ S2 @ X5 ) ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % pw_leI
% 0.20/0.46 thf(fact_21_pw__leI_H,axiom,
% 0.20/0.46 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 0.20/0.46 ( ( ( refine412683989fail_a @ S2 )
% 0.20/0.46 => ( refine412683989fail_a @ S ) )
% 0.20/0.46 => ( ! [X5: a] :
% 0.20/0.46 ( ( refine412683989fail_a @ S2 )
% 0.20/0.46 => ( ( refine1001002027nres_a @ S @ X5 )
% 0.20/0.46 => ( refine1001002027nres_a @ S2 @ X5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pw_leI'
% 0.20/0.46 thf(fact_22_pw__le__iff,axiom,
% 0.20/0.46 ( ord_le519537037nres_a
% 0.20/0.46 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 0.20/0.46 ( ( refine412683989fail_a @ S4 )
% 0.20/0.46 => ( ( refine412683989fail_a @ S3 )
% 0.20/0.46 & ! [X4: a] :
% 0.20/0.46 ( ( refine1001002027nres_a @ S3 @ X4 )
% 0.20/0.46 => ( refine1001002027nres_a @ S4 @ X4 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pw_le_iff
% 0.20/0.46 thf(fact_23_less__eq__nres_Osimps_I3_J,axiom,
% 0.20/0.46 ! [Uv2: set_a] :
% 0.20/0.46 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.simps(3)
% 0.20/0.46 thf(fact_24_less__nres_Osimps_I2_J,axiom,
% 0.20/0.46 ! [Uv2: set_a] : ( ord_le1480771457nres_a @ ( refine1198353288_RES_a @ Uv2 ) @ refine464223677AILi_a ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.simps(2)
% 0.20/0.46 thf(fact_25_less__eq__nres_Ocases,axiom,
% 0.20/0.46 ! [X3: produc1609974940nres_a] :
% 0.20/0.46 ( ! [Uu: refine424419629nres_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.20/0.46 => ( ! [A: set_a,B: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 0.20/0.46 => ~ ! [Uv: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.cases
% 0.20/0.46 thf(fact_26_less__nres_Ocases,axiom,
% 0.20/0.46 ! [X3: produc1609974940nres_a] :
% 0.20/0.46 ( ! [Uu: refine424419629nres_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ refine464223677AILi_a @ Uu ) )
% 0.20/0.46 => ( ! [Uv: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) )
% 0.20/0.46 => ~ ! [A: set_a,B: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.cases
% 0.20/0.46 thf(fact_27_sup__nres_Ocases,axiom,
% 0.20/0.46 ! [X3: produc1609974940nres_a] :
% 0.20/0.46 ( ! [Uu: refine424419629nres_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.20/0.46 => ( ! [V: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) ) )
% 0.20/0.46 => ~ ! [A: set_a,B: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_nres.cases
% 0.20/0.46 thf(fact_28_nres__more__simps_I6_J,axiom,
% 0.20/0.46 ! [X3: a,Y3: a] :
% 0.20/0.46 ( ( ( refine2063221604TURN_a @ X3 )
% 0.20/0.46 = ( refine2063221604TURN_a @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_more_simps(6)
% 0.20/0.46 thf(fact_29_nres__order__simps_I20_J,axiom,
% 0.20/0.46 ! [X3: a,Y3: a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_order_simps(20)
% 0.20/0.46 thf(fact_30_nres__order__simps_I21_J,axiom,
% 0.20/0.46 ! [X3: a,Y: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ ( refine1198353288_RES_a @ Y ) )
% 0.20/0.46 = ( member_a @ X3 @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_order_simps(21)
% 0.20/0.46 thf(fact_31_inres__def,axiom,
% 0.20/0.46 ( refine1001002027nres_a
% 0.20/0.46 = ( ^ [S3: refine424419629nres_a,X4: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ S3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inres_def
% 0.20/0.46 thf(fact_32_less__nres_Osimps_I1_J,axiom,
% 0.20/0.46 ! [Uu2: refine424419629nres_a] :
% 0.20/0.46 ~ ( ord_le1480771457nres_a @ refine464223677AILi_a @ Uu2 ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.simps(1)
% 0.20/0.46 thf(fact_33_less__eq__nres_Osimps_I1_J,axiom,
% 0.20/0.46 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.simps(1)
% 0.20/0.46 thf(fact_34_le__nofailI,axiom,
% 0.20/0.46 ! [M4: refine424419629nres_a,M5: refine424419629nres_a] :
% 0.20/0.46 ( ( ( refine412683989fail_a @ M4 )
% 0.20/0.46 => ( ord_le519537037nres_a @ M5 @ M4 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ M5 @ M4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_nofailI
% 0.20/0.46 thf(fact_35_pwD1,axiom,
% 0.20/0.46 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.20/0.46 => ( ( refine412683989fail_a @ S2 )
% 0.20/0.46 => ( refine412683989fail_a @ S ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pwD1
% 0.20/0.46 thf(fact_36_pwD2,axiom,
% 0.20/0.46 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X3: a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ S @ S2 )
% 0.20/0.46 => ( ( refine1001002027nres_a @ S @ X3 )
% 0.20/0.46 => ( refine1001002027nres_a @ S2 @ X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % pwD2
% 0.20/0.46 thf(fact_37_old_Oprod_Oinject,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.20/0.46 ( ( ( produc1136923598nres_a @ A2 @ B2 )
% 0.20/0.46 = ( produc1136923598nres_a @ A3 @ B3 ) )
% 0.20/0.46 = ( ( A2 = A3 )
% 0.20/0.46 & ( B2 = B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.inject
% 0.20/0.46 thf(fact_38_prod_Oinject,axiom,
% 0.20/0.46 ! [X1: refine424419629nres_a,X2: refine424419629nres_a,Y1: refine424419629nres_a,Y2: refine424419629nres_a] :
% 0.20/0.46 ( ( ( produc1136923598nres_a @ X1 @ X2 )
% 0.20/0.46 = ( produc1136923598nres_a @ Y1 @ Y2 ) )
% 0.20/0.46 = ( ( X1 = Y1 )
% 0.20/0.46 & ( X2 = Y2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod.inject
% 0.20/0.46 thf(fact_39_order__mono__setup_Orefl,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a] : ( ord_le519537037nres_a @ X3 @ X3 ) ).
% 0.20/0.46
% 0.20/0.46 % order_mono_setup.refl
% 0.20/0.46 thf(fact_40_order__mono__setup_Orefl,axiom,
% 0.20/0.46 ! [X3: set_a] : ( ord_less_eq_set_a @ X3 @ X3 ) ).
% 0.20/0.46
% 0.20/0.46 % order_mono_setup.refl
% 0.20/0.46 thf(fact_41_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A2: a,P: a > $o] :
% 0.20/0.46 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.20/0.46 = ( P @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_42_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A4: set_a] :
% 0.20/0.46 ( ( collect_a
% 0.20/0.46 @ ^ [X4: a] : ( member_a @ X4 @ A4 ) )
% 0.20/0.46 = A4 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_43_Collect__cong,axiom,
% 0.20/0.46 ! [P: a > $o,Q: a > $o] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 = ( Q @ X5 ) )
% 0.20/0.46 => ( ( collect_a @ P )
% 0.20/0.46 = ( collect_a @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_cong
% 0.20/0.46 thf(fact_44_order_Onot__eq__order__implies__strict,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( A2 != B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.not_eq_order_implies_strict
% 0.20/0.46 thf(fact_45_order_Onot__eq__order__implies__strict,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( A2 != B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.not_eq_order_implies_strict
% 0.20/0.46 thf(fact_46_dual__order_Ostrict__implies__order,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ord_le519537037nres_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_implies_order
% 0.20/0.46 thf(fact_47_dual__order_Ostrict__implies__order,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_implies_order
% 0.20/0.46 thf(fact_48_dual__order_Ostrict__iff__order,axiom,
% 0.20/0.46 ( ord_le1480771457nres_a
% 0.20/0.46 = ( ^ [B4: refine424419629nres_a,A5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ B4 @ A5 )
% 0.20/0.46 & ( A5 != B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_iff_order
% 0.20/0.46 thf(fact_49_dual__order_Ostrict__iff__order,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [B4: set_a,A5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ B4 @ A5 )
% 0.20/0.46 & ( A5 != B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_iff_order
% 0.20/0.46 thf(fact_50_dual__order_Oorder__iff__strict,axiom,
% 0.20/0.46 ( ord_le519537037nres_a
% 0.20/0.46 = ( ^ [B4: refine424419629nres_a,A5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B4 @ A5 )
% 0.20/0.46 | ( A5 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.order_iff_strict
% 0.20/0.46 thf(fact_51_dual__order_Oorder__iff__strict,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [B4: set_a,A5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B4 @ A5 )
% 0.20/0.46 | ( A5 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.order_iff_strict
% 0.20/0.46 thf(fact_52_order_Ostrict__implies__order,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_implies_order
% 0.20/0.46 thf(fact_53_order_Ostrict__implies__order,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_implies_order
% 0.20/0.46 thf(fact_54_less__eq__nres_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 0.20/0.46 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.simps(2)
% 0.20/0.46 thf(fact_55_nres__order__simps_I5_J,axiom,
% 0.20/0.46 ! [X: set_a,Y: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 0.20/0.46 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % nres_order_simps(5)
% 0.20/0.46 thf(fact_56_less__nres_Osimps_I3_J,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 0.20/0.46 = ( ord_less_set_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.simps(3)
% 0.20/0.46 thf(fact_57_order__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_58_order__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_59_order__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_60_order__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst1
% 0.20/0.46 thf(fact_61_order__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_62_order__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_63_order__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_64_order__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_subst2
% 0.20/0.46 thf(fact_65_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_66_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_67_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_68_ord__eq__le__subst,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_subst
% 0.20/0.46 thf(fact_69_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_70_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_71_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_72_ord__le__eq__subst,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_subst
% 0.20/0.46 thf(fact_73_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 0.20/0.46 & ( ord_le519537037nres_a @ Y6 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_74_eq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [X4: set_a,Y6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 0.20/0.46 & ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_iff
% 0.20/0.46 thf(fact_75_antisym,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 0.20/0.46 => ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_76_antisym,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 0.20/0.46 => ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym
% 0.20/0.46 thf(fact_77_eq__refl,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( X3 = Y3 )
% 0.20/0.46 => ( ord_le519537037nres_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_78_eq__refl,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( X3 = Y3 )
% 0.20/0.46 => ( ord_less_eq_set_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % eq_refl
% 0.20/0.46 thf(fact_79_order_Otrans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_80_order_Otrans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.trans
% 0.20/0.46 thf(fact_81_antisym__conv,axiom,
% 0.20/0.46 ! [Y3: refine424419629nres_a,X3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_82_antisym__conv,axiom,
% 0.20/0.46 ! [Y3: set_a,X3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv
% 0.20/0.46 thf(fact_83_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A5 @ B4 )
% 0.20/0.46 & ( ord_le519537037nres_a @ B4 @ A5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_84_order__class_Oorder_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: set_a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A5 @ B4 )
% 0.20/0.46 & ( ord_less_eq_set_a @ B4 @ A5 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.eq_iff
% 0.20/0.46 thf(fact_85_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_86_ord__eq__le__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_trans
% 0.20/0.46 thf(fact_87_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( B2 = C )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_88_ord__le__eq__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( B2 = C )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_le_eq_trans
% 0.20/0.46 thf(fact_89_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_90_order__class_Oorder_Oantisym,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_class.order.antisym
% 0.20/0.46 thf(fact_91_order__trans,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_le519537037nres_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_92_order__trans,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_trans
% 0.20/0.46 thf(fact_93_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_94_dual__order_Orefl,axiom,
% 0.20/0.46 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.refl
% 0.20/0.46 thf(fact_95_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ C @ B2 )
% 0.20/0.46 => ( ord_le519537037nres_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_96_dual__order_Otrans,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ C @ B2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.trans
% 0.20/0.46 thf(fact_97_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ B4 @ A5 )
% 0.20/0.46 & ( ord_le519537037nres_a @ A5 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_98_dual__order_Oeq__iff,axiom,
% 0.20/0.46 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A5: set_a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ B4 @ A5 )
% 0.20/0.46 & ( ord_less_eq_set_a @ A5 @ B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.eq_iff
% 0.20/0.46 thf(fact_99_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_100_dual__order_Oantisym,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( A2 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.antisym
% 0.20/0.46 thf(fact_101_order__mono__setup_Omono__if,axiom,
% 0.20/0.46 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_mono_setup.mono_if
% 0.20/0.46 thf(fact_102_order__mono__setup_Omono__if,axiom,
% 0.20/0.46 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B2: $o] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ T @ T2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ E @ E2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ T @ E ) @ ( if_set_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_mono_setup.mono_if
% 0.20/0.46 thf(fact_103_surj__pair,axiom,
% 0.20/0.46 ! [P2: produc1609974940nres_a] :
% 0.20/0.46 ? [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( P2
% 0.20/0.46 = ( produc1136923598nres_a @ X5 @ Y5 ) ) ).
% 0.20/0.46
% 0.20/0.46 % surj_pair
% 0.20/0.46 thf(fact_104_prod__cases,axiom,
% 0.20/0.46 ! [P: produc1609974940nres_a > $o,P2: produc1609974940nres_a] :
% 0.20/0.46 ( ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( P @ ( produc1136923598nres_a @ A @ B ) )
% 0.20/0.46 => ( P @ P2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % prod_cases
% 0.20/0.46 thf(fact_105_Pair__inject,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 0.20/0.46 ( ( ( produc1136923598nres_a @ A2 @ B2 )
% 0.20/0.46 = ( produc1136923598nres_a @ A3 @ B3 ) )
% 0.20/0.46 => ~ ( ( A2 = A3 )
% 0.20/0.46 => ( B2 != B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Pair_inject
% 0.20/0.46 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 0.20/0.46 ! [Y3: produc1609974940nres_a] :
% 0.20/0.46 ~ ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.20/0.46 ( Y3
% 0.20/0.46 != ( produc1136923598nres_a @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.exhaust
% 0.20/0.46 thf(fact_107_old_Oprod_Oinducts,axiom,
% 0.20/0.46 ! [P: produc1609974940nres_a > $o,Prod: produc1609974940nres_a] :
% 0.20/0.46 ( ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( P @ ( produc1136923598nres_a @ A @ B ) )
% 0.20/0.46 => ( P @ Prod ) ) ).
% 0.20/0.46
% 0.20/0.46 % old.prod.inducts
% 0.20/0.46 thf(fact_108_ord__eq__less__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_subst
% 0.20/0.46 thf(fact_109_ord__eq__less__subst,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_subst
% 0.20/0.46 thf(fact_110_ord__eq__less__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_subst
% 0.20/0.46 thf(fact_111_ord__eq__less__subst,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_subst
% 0.20/0.46 thf(fact_112_ord__less__eq__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_subst
% 0.20/0.46 thf(fact_113_ord__less__eq__subst,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_subst
% 0.20/0.46 thf(fact_114_ord__less__eq__subst,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_subst
% 0.20/0.46 thf(fact_115_ord__less__eq__subst,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ( F @ B2 )
% 0.20/0.46 = C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_subst
% 0.20/0.46 thf(fact_116_order__less__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst1
% 0.20/0.46 thf(fact_117_order__less__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst1
% 0.20/0.46 thf(fact_118_order__less__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst1
% 0.20/0.46 thf(fact_119_order__less__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst1
% 0.20/0.46 thf(fact_120_order__less__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst2
% 0.20/0.46 thf(fact_121_order__less__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst2
% 0.20/0.46 thf(fact_122_order__less__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst2
% 0.20/0.46 thf(fact_123_order__less__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_subst2
% 0.20/0.46 thf(fact_124_order_Oasym,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.asym
% 0.20/0.46 thf(fact_125_order_Oasym,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.asym
% 0.20/0.46 thf(fact_126_less__imp__neq,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( X3 != Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_neq
% 0.20/0.46 thf(fact_127_less__imp__neq,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( X3 != Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_neq
% 0.20/0.46 thf(fact_128_less__asym,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_asym
% 0.20/0.46 thf(fact_129_less__asym,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_asym
% 0.20/0.46 thf(fact_130_less__asym_H,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_asym'
% 0.20/0.46 thf(fact_131_less__asym_H,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_asym'
% 0.20/0.46 thf(fact_132_less__trans,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_trans
% 0.20/0.46 thf(fact_133_less__trans,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_set_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_trans
% 0.20/0.46 thf(fact_134_less__irrefl,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a] :
% 0.20/0.46 ~ ( ord_le1480771457nres_a @ X3 @ X3 ) ).
% 0.20/0.46
% 0.20/0.46 % less_irrefl
% 0.20/0.46 thf(fact_135_less__irrefl,axiom,
% 0.20/0.46 ! [X3: set_a] :
% 0.20/0.46 ~ ( ord_less_set_a @ X3 @ X3 ) ).
% 0.20/0.46
% 0.20/0.46 % less_irrefl
% 0.20/0.46 thf(fact_136_ord__eq__less__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_trans
% 0.20/0.46 thf(fact_137_ord__eq__less__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_less_trans
% 0.20/0.46 thf(fact_138_ord__less__eq__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( B2 = C )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_trans
% 0.20/0.46 thf(fact_139_ord__less__eq__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( B2 = C )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_less_eq_trans
% 0.20/0.46 thf(fact_140_dual__order_Oasym,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.asym
% 0.20/0.46 thf(fact_141_dual__order_Oasym,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B2 @ A2 )
% 0.20/0.46 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.asym
% 0.20/0.46 thf(fact_142_less__imp__not__eq,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( X3 != Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_eq
% 0.20/0.46 thf(fact_143_less__imp__not__eq,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( X3 != Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_eq
% 0.20/0.46 thf(fact_144_less__not__sym,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_not_sym
% 0.20/0.46 thf(fact_145_less__not__sym,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_not_sym
% 0.20/0.46 thf(fact_146_less__imp__not__eq2,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( Y3 != X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_eq2
% 0.20/0.46 thf(fact_147_less__imp__not__eq2,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( Y3 != X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_eq2
% 0.20/0.46 thf(fact_148_less__imp__triv,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,P: $o] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ Y3 @ X3 )
% 0.20/0.46 => P ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_triv
% 0.20/0.46 thf(fact_149_less__imp__triv,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a,P: $o] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_set_a @ Y3 @ X3 )
% 0.20/0.46 => P ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_triv
% 0.20/0.46 thf(fact_150_dual__order_Oirrefl,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a] :
% 0.20/0.46 ~ ( ord_le1480771457nres_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.irrefl
% 0.20/0.46 thf(fact_151_dual__order_Oirrefl,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.irrefl
% 0.20/0.46 thf(fact_152_order_Ostrict__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans
% 0.20/0.46 thf(fact_153_order_Ostrict__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans
% 0.20/0.46 thf(fact_154_less__imp__not__less,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_less
% 0.20/0.46 thf(fact_155_less__imp__not__less,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_not_less
% 0.20/0.46 thf(fact_156_dual__order_Ostrict__trans,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ C @ B2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans
% 0.20/0.46 thf(fact_157_dual__order_Ostrict__trans,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_less_set_a @ C @ B2 )
% 0.20/0.46 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans
% 0.20/0.46 thf(fact_158_order_Ostrict__implies__not__eq,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( A2 != B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_implies_not_eq
% 0.20/0.46 thf(fact_159_order_Ostrict__implies__not__eq,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( A2 != B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_implies_not_eq
% 0.20/0.46 thf(fact_160_dual__order_Ostrict__implies__not__eq,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 0.20/0.46 => ( A2 != B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_implies_not_eq
% 0.20/0.46 thf(fact_161_dual__order_Ostrict__implies__not__eq,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B2 @ A2 )
% 0.20/0.46 => ( A2 != B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_implies_not_eq
% 0.20/0.46 thf(fact_162_less__eq__nres_Oelims_I3_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ~ ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A @ B ) ) )
% 0.20/0.46 => ~ ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ! [Uv: set_a] :
% 0.20/0.46 ( Xa
% 0.20/0.46 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.elims(3)
% 0.20/0.46 thf(fact_163_less__eq__nres_Oelims_I2_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( Xa != refine464223677AILi_a )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.elims(2)
% 0.20/0.46 thf(fact_164_less__eq__nres_Oelims_I1_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.20/0.46 ( ( ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 = Y3 )
% 0.20/0.46 => ( ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ~ Y3 )
% 0.20/0.46 => ( ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( Y3
% 0.20/0.46 = ( ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) )
% 0.20/0.46 => ~ ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ( ? [Uv: set_a] :
% 0.20/0.46 ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => Y3 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.elims(1)
% 0.20/0.46 thf(fact_165_less__nres_Oelims_I3_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ~ ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( X3 != refine464223677AILi_a )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ord_less_set_a @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.elims(3)
% 0.20/0.46 thf(fact_166_less__nres_Oelims_I2_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( ? [Uv: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( Xa != refine464223677AILi_a ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.elims(2)
% 0.20/0.46 thf(fact_167_less__nres_Oelims_I1_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.20/0.46 ( ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 = Y3 )
% 0.20/0.46 => ( ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => Y3 )
% 0.20/0.46 => ( ( ? [Uv: set_a] :
% 0.20/0.46 ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ~ Y3 ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( Y3
% 0.20/0.46 = ( ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.elims(1)
% 0.20/0.46 thf(fact_168_leD,axiom,
% 0.20/0.46 ! [Y3: refine424419629nres_a,X3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 0.20/0.46 => ~ ( ord_le1480771457nres_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % leD
% 0.20/0.46 thf(fact_169_leD,axiom,
% 0.20/0.46 ! [Y3: set_a,X3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 0.20/0.46 => ~ ( ord_less_set_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % leD
% 0.20/0.46 thf(fact_170_le__less,axiom,
% 0.20/0.46 ( ord_le519537037nres_a
% 0.20/0.46 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X4 @ Y6 )
% 0.20/0.46 | ( X4 = Y6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_less
% 0.20/0.46 thf(fact_171_le__less,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [X4: set_a,Y6: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X4 @ Y6 )
% 0.20/0.46 | ( X4 = Y6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_less
% 0.20/0.46 thf(fact_172_less__le,axiom,
% 0.20/0.46 ( ord_le1480771457nres_a
% 0.20/0.46 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 0.20/0.46 & ( X4 != Y6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le
% 0.20/0.46 thf(fact_173_less__le,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [X4: set_a,Y6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 0.20/0.46 & ( X4 != Y6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le
% 0.20/0.46 thf(fact_174_order__le__less__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst1
% 0.20/0.46 thf(fact_175_order__le__less__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst1
% 0.20/0.46 thf(fact_176_order__le__less__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst1
% 0.20/0.46 thf(fact_177_order__le__less__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst1
% 0.20/0.46 thf(fact_178_order__le__less__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst2
% 0.20/0.46 thf(fact_179_order__le__less__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst2
% 0.20/0.46 thf(fact_180_order__le__less__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst2
% 0.20/0.46 thf(fact_181_order__le__less__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_le_less_subst2
% 0.20/0.46 thf(fact_182_order__less__le__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst1
% 0.20/0.46 thf(fact_183_order__less__le__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst1
% 0.20/0.46 thf(fact_184_order__less__le__subst1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst1
% 0.20/0.46 thf(fact_185_order__less__le__subst1,axiom,
% 0.20/0.46 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst1
% 0.20/0.46 thf(fact_186_order__less__le__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst2
% 0.20/0.46 thf(fact_187_order__less__le__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst2
% 0.20/0.46 thf(fact_188_order__less__le__subst2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst2
% 0.20/0.46 thf(fact_189_order__less__le__subst2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 0.20/0.46 => ( ! [X5: set_a,Y5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X5 @ Y5 )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.46 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_less_le_subst2
% 0.20/0.46 thf(fact_190_le__neq__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( A2 != B2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_neq_trans
% 0.20/0.46 thf(fact_191_le__neq__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( A2 != B2 )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_neq_trans
% 0.20/0.46 thf(fact_192_antisym__conv1,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ~ ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv1
% 0.20/0.46 thf(fact_193_antisym__conv1,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ~ ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv1
% 0.20/0.46 thf(fact_194_antisym__conv2,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ~ ( ord_le1480771457nres_a @ X3 @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv2
% 0.20/0.46 thf(fact_195_antisym__conv2,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ~ ( ord_less_set_a @ X3 @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % antisym_conv2
% 0.20/0.46 thf(fact_196_less__imp__le,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ord_le519537037nres_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_le
% 0.20/0.46 thf(fact_197_less__imp__le,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ord_less_eq_set_a @ X3 @ Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_imp_le
% 0.20/0.46 thf(fact_198_le__less__trans,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_less_trans
% 0.20/0.46 thf(fact_199_le__less__trans,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_set_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_less_trans
% 0.20/0.46 thf(fact_200_less__le__trans,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le_trans
% 0.20/0.46 thf(fact_201_less__le__trans,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 0.20/0.46 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le_trans
% 0.20/0.46 thf(fact_202_le__imp__less__or__eq,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 0.20/0.46 | ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_imp_less_or_eq
% 0.20/0.46 thf(fact_203_le__imp__less__or__eq,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 0.20/0.46 => ( ( ord_less_set_a @ X3 @ Y3 )
% 0.20/0.46 | ( X3 = Y3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_imp_less_or_eq
% 0.20/0.46 thf(fact_204_less__le__not__le,axiom,
% 0.20/0.46 ( ord_le1480771457nres_a
% 0.20/0.46 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 0.20/0.46 & ~ ( ord_le519537037nres_a @ Y6 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le_not_le
% 0.20/0.46 thf(fact_205_less__le__not__le,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [X4: set_a,Y6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 0.20/0.46 & ~ ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_le_not_le
% 0.20/0.46 thf(fact_206_order_Ostrict__trans1,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans1
% 0.20/0.46 thf(fact_207_order_Ostrict__trans1,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans1
% 0.20/0.46 thf(fact_208_order_Ostrict__trans2,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans2
% 0.20/0.46 thf(fact_209_order_Ostrict__trans2,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_trans2
% 0.20/0.46 thf(fact_210_order_Oorder__iff__strict,axiom,
% 0.20/0.46 ( ord_le519537037nres_a
% 0.20/0.46 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ A5 @ B4 )
% 0.20/0.46 | ( A5 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.order_iff_strict
% 0.20/0.46 thf(fact_211_order_Oorder__iff__strict,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A5: set_a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A5 @ B4 )
% 0.20/0.46 | ( A5 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.order_iff_strict
% 0.20/0.46 thf(fact_212_order_Ostrict__iff__order,axiom,
% 0.20/0.46 ( ord_le1480771457nres_a
% 0.20/0.46 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ A5 @ B4 )
% 0.20/0.46 & ( A5 != B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_iff_order
% 0.20/0.46 thf(fact_213_order_Ostrict__iff__order,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [A5: set_a,B4: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A5 @ B4 )
% 0.20/0.46 & ( A5 != B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % order.strict_iff_order
% 0.20/0.46 thf(fact_214_dual__order_Ostrict__trans1,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_le1480771457nres_a @ C @ B2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans1
% 0.20/0.46 thf(fact_215_dual__order_Ostrict__trans1,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_less_set_a @ C @ B2 )
% 0.20/0.46 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans1
% 0.20/0.46 thf(fact_216_dual__order_Ostrict__trans2,axiom,
% 0.20/0.46 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ C @ B2 )
% 0.20/0.46 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans2
% 0.20/0.46 thf(fact_217_dual__order_Ostrict__trans2,axiom,
% 0.20/0.46 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ B2 @ A2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ C @ B2 )
% 0.20/0.46 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dual_order.strict_trans2
% 0.20/0.46 thf(fact_218_relChain__def,axiom,
% 0.20/0.46 ( bNF_Ca459084161nres_a
% 0.20/0.46 = ( ^ [R: set_Pr384614482nres_a,As: refine424419629nres_a > refine424419629nres_a] :
% 0.20/0.46 ! [I: refine424419629nres_a,J: refine424419629nres_a] :
% 0.20/0.46 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ I @ J ) @ R )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % relChain_def
% 0.20/0.46 thf(fact_219_relChain__def,axiom,
% 0.20/0.46 ( bNF_Ca953716171_set_a
% 0.20/0.46 = ( ^ [R: set_Pr384614482nres_a,As: refine424419629nres_a > set_a] :
% 0.20/0.46 ! [I: refine424419629nres_a,J: refine424419629nres_a] :
% 0.20/0.46 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ I @ J ) @ R )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % relChain_def
% 0.20/0.46 thf(fact_220_verit__comp__simplify1_I1_J,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a] :
% 0.20/0.46 ~ ( ord_le1480771457nres_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % verit_comp_simplify1(1)
% 0.20/0.46 thf(fact_221_verit__comp__simplify1_I1_J,axiom,
% 0.20/0.46 ! [A2: set_a] :
% 0.20/0.46 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.20/0.46
% 0.20/0.46 % verit_comp_simplify1(1)
% 0.20/0.46 thf(fact_222_psubsetI,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( A4 != B5 )
% 0.20/0.46 => ( ord_less_set_a @ A4 @ B5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubsetI
% 0.20/0.46 thf(fact_223_subset__antisym,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B5 @ A4 )
% 0.20/0.46 => ( A4 = B5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_antisym
% 0.20/0.46 thf(fact_224_subsetI,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ( ( member_a @ X5 @ A4 )
% 0.20/0.46 => ( member_a @ X5 @ B5 ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetI
% 0.20/0.46 thf(fact_225_in__mono,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,X3: a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( member_a @ X3 @ A4 )
% 0.20/0.46 => ( member_a @ X3 @ B5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % in_mono
% 0.20/0.46 thf(fact_226_subsetD,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C: a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( member_a @ C @ A4 )
% 0.20/0.46 => ( member_a @ C @ B5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subsetD
% 0.20/0.46 thf(fact_227_equalityE,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( A4 = B5 )
% 0.20/0.46 => ~ ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ~ ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityE
% 0.20/0.46 thf(fact_228_subset__eq,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ! [X4: a] :
% 0.20/0.46 ( ( member_a @ X4 @ A6 )
% 0.20/0.46 => ( member_a @ X4 @ B6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_eq
% 0.20/0.46 thf(fact_229_equalityD1,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( A4 = B5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD1
% 0.20/0.46 thf(fact_230_equalityD2,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( A4 = B5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ B5 @ A4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equalityD2
% 0.20/0.46 thf(fact_231_subset__iff,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ! [T3: a] :
% 0.20/0.46 ( ( member_a @ T3 @ A6 )
% 0.20/0.46 => ( member_a @ T3 @ B6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff
% 0.20/0.46 thf(fact_232_subset__refl,axiom,
% 0.20/0.46 ! [A4: set_a] : ( ord_less_eq_set_a @ A4 @ A4 ) ).
% 0.20/0.46
% 0.20/0.46 % subset_refl
% 0.20/0.46 thf(fact_233_Collect__mono,axiom,
% 0.20/0.46 ! [P: a > $o,Q: a > $o] :
% 0.20/0.46 ( ! [X5: a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( Q @ X5 ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono
% 0.20/0.46 thf(fact_234_subset__trans,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B5 @ C2 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A4 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_trans
% 0.20/0.46 thf(fact_235_set__eq__subset,axiom,
% 0.20/0.46 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 0.20/0.46 & ( ord_less_eq_set_a @ B6 @ A6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % set_eq_subset
% 0.20/0.46 thf(fact_236_Collect__mono__iff,axiom,
% 0.20/0.46 ! [P: a > $o,Q: a > $o] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.20/0.46 = ( ! [X4: a] :
% 0.20/0.46 ( ( P @ X4 )
% 0.20/0.46 => ( Q @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mono_iff
% 0.20/0.46 thf(fact_237_psubsetD,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C: a] :
% 0.20/0.46 ( ( ord_less_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( member_a @ C @ A4 )
% 0.20/0.46 => ( member_a @ C @ B5 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubsetD
% 0.20/0.46 thf(fact_238_psubset__trans,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( ord_less_set_a @ B5 @ C2 )
% 0.20/0.46 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubset_trans
% 0.20/0.46 thf(fact_239_psubsetE,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A4 @ B5 )
% 0.20/0.46 => ~ ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubsetE
% 0.20/0.46 thf(fact_240_psubset__eq,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 0.20/0.46 & ( A6 != B6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubset_eq
% 0.20/0.46 thf(fact_241_psubset__imp__subset,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubset_imp_subset
% 0.20/0.46 thf(fact_242_psubset__subset__trans,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C2: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B5 @ C2 )
% 0.20/0.46 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % psubset_subset_trans
% 0.20/0.46 thf(fact_243_subset__not__subset__eq,axiom,
% 0.20/0.46 ( ord_less_set_a
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 0.20/0.46 & ~ ( ord_less_eq_set_a @ B6 @ A6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_not_subset_eq
% 0.20/0.46 thf(fact_244_subset__psubset__trans,axiom,
% 0.20/0.46 ! [A4: set_a,B5: set_a,C2: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 0.20/0.46 => ( ( ord_less_set_a @ B5 @ C2 )
% 0.20/0.46 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_psubset_trans
% 0.20/0.46 thf(fact_245_subset__iff__psubset__eq,axiom,
% 0.20/0.46 ( ord_less_eq_set_a
% 0.20/0.46 = ( ^ [A6: set_a,B6: set_a] :
% 0.20/0.46 ( ( ord_less_set_a @ A6 @ B6 )
% 0.20/0.46 | ( A6 = B6 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_iff_psubset_eq
% 0.20/0.46 thf(fact_246_less__nres_Opelims_I1_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.20/0.46 ( ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 = Y3 )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ( ~ Y3
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ Xa ) ) ) )
% 0.20/0.46 => ( ! [Uv: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ( Y3
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) ) ) ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( Y3
% 0.20/0.46 = ( ord_less_set_a @ A @ B ) )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.pelims(1)
% 0.20/0.46 thf(fact_247_less__nres_Opelims_I2_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ! [Uv: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) ) ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 0.20/0.46 => ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.pelims(2)
% 0.20/0.46 thf(fact_248_less__nres_Opelims_I3_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ~ ( ord_le1480771457nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ Xa ) ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 0.20/0.46 => ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_nres.pelims(3)
% 0.20/0.46 thf(fact_249_less__eq__nres_Opelims_I3_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ~ ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ A @ B ) ) ) )
% 0.20/0.46 => ~ ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ! [Uv: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.pelims(3)
% 0.20/0.46 thf(fact_250_less__eq__nres_Opelims_I2_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.20/0.46 ( ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ refine464223677AILi_a ) ) )
% 0.20/0.46 => ~ ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 0.20/0.46 => ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.pelims(2)
% 0.20/0.46 thf(fact_251_less__eq__nres_Opelims_I1_J,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.20/0.46 ( ( ( ord_le519537037nres_a @ X3 @ Xa )
% 0.20/0.46 = Y3 )
% 0.20/0.46 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 0.20/0.46 => ( ( ( Xa = refine464223677AILi_a )
% 0.20/0.46 => ( Y3
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ refine464223677AILi_a ) ) ) )
% 0.20/0.46 => ( ! [A: set_a] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 = ( refine1198353288_RES_a @ A ) )
% 0.20/0.46 => ! [B: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ B ) )
% 0.20/0.46 => ( ( Y3
% 0.20/0.46 = ( ord_less_eq_set_a @ A @ B ) )
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) )
% 0.20/0.46 => ~ ( ( X3 = refine464223677AILi_a )
% 0.20/0.46 => ! [Uv: set_a] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( refine1198353288_RES_a @ Uv ) )
% 0.20/0.46 => ( ~ Y3
% 0.20/0.46 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % less_eq_nres.pelims(1)
% 0.20/0.46 thf(fact_252_GreatestI2__order,axiom,
% 0.20/0.46 ! [P: refine424419629nres_a > $o,X3: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( ! [Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ Y5 @ X3 ) )
% 0.20/0.46 => ( ! [X5: refine424419629nres_a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( ! [Y7: refine424419629nres_a] :
% 0.20/0.46 ( ( P @ Y7 )
% 0.20/0.46 => ( ord_le519537037nres_a @ Y7 @ X5 ) )
% 0.20/0.46 => ( Q @ X5 ) ) )
% 0.20/0.46 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % GreatestI2_order
% 0.20/0.46 thf(fact_253_GreatestI2__order,axiom,
% 0.20/0.46 ! [P: set_a > $o,X3: set_a,Q: set_a > $o] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( ! [Y5: set_a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ Y5 @ X3 ) )
% 0.20/0.46 => ( ! [X5: set_a] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( ! [Y7: set_a] :
% 0.20/0.46 ( ( P @ Y7 )
% 0.20/0.46 => ( ord_less_eq_set_a @ Y7 @ X5 ) )
% 0.20/0.46 => ( Q @ X5 ) ) )
% 0.20/0.46 => ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % GreatestI2_order
% 0.20/0.46 thf(fact_254_Greatest__equality,axiom,
% 0.20/0.46 ! [P: refine424419629nres_a > $o,X3: refine424419629nres_a] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( ! [Y5: refine424419629nres_a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_le519537037nres_a @ Y5 @ X3 ) )
% 0.20/0.46 => ( ( order_1714329108nres_a @ P )
% 0.20/0.46 = X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Greatest_equality
% 0.20/0.46 thf(fact_255_Greatest__equality,axiom,
% 0.20/0.46 ! [P: set_a > $o,X3: set_a] :
% 0.20/0.46 ( ( P @ X3 )
% 0.20/0.46 => ( ! [Y5: set_a] :
% 0.20/0.46 ( ( P @ Y5 )
% 0.20/0.46 => ( ord_less_eq_set_a @ Y5 @ X3 ) )
% 0.20/0.46 => ( ( order_Greatest_set_a @ P )
% 0.20/0.46 = X3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Greatest_equality
% 0.20/0.46 thf(fact_256_subset__Collect__conv,axiom,
% 0.20/0.46 ! [S: set_a,P: a > $o] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 0.20/0.46 = ( ! [X4: a] :
% 0.20/0.46 ( ( member_a @ X4 @ S )
% 0.20/0.46 => ( P @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subset_Collect_conv
% 0.20/0.46 thf(fact_257_relprop__triggers_I6_J,axiom,
% 0.20/0.46 ! [R2: set_a,R3: set_a] :
% 0.20/0.46 ( ( ord_less_eq_set_a @ R2 @ R3 )
% 0.20/0.46 => ( ord_less_eq_set_a @ R2 @ R3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % relprop_triggers(6)
% 0.20/0.46 thf(fact_258_ord__eq__le__eq__trans,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_le519537037nres_a @ B2 @ C )
% 0.20/0.46 => ( ( C = D )
% 0.20/0.46 => ( ord_le519537037nres_a @ A2 @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_eq_trans
% 0.20/0.46 thf(fact_259_ord__eq__le__eq__trans,axiom,
% 0.20/0.46 ! [A2: set_a,B2: set_a,C: set_a,D: set_a] :
% 0.20/0.46 ( ( A2 = B2 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ B2 @ C )
% 0.20/0.46 => ( ( C = D )
% 0.20/0.46 => ( ord_less_eq_set_a @ A2 @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord_eq_le_eq_trans
% 0.20/0.46 thf(fact_260_bex2I,axiom,
% 0.20/0.46 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,S: set_Pr384614482nres_a,P: refine424419629nres_a > refine424419629nres_a > $o] :
% 0.20/0.46 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A2 @ B2 ) @ S )
% 0.20/0.46 => ( ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A2 @ B2 ) @ S )
% 0.20/0.46 => ( P @ A2 @ B2 ) )
% 0.20/0.46 => ? [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.20/0.46 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A @ B ) @ S )
% 0.20/0.46 & ( P @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bex2I
% 0.20/0.46 thf(fact_261_Refine__Misc_Oif__mono,axiom,
% 0.20/0.46 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 0.20/0.46 ( ( B2
% 0.20/0.46 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.20/0.46 => ( ( ~ B2
% 0.20/0.46 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 0.20/0.46 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Refine_Misc.if_mono
% 0.20/0.46 thf(fact_262_Refine__Misc_Oif__mono,axiom,
% 0.20/0.46 ! [B2: $o,M1: set_a,M12: set_a,M22: set_a,M23: set_a] :
% 0.20/0.46 ( ( B2
% 0.20/0.46 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 0.20/0.46 => ( ( ~ B2
% 0.20/0.46 => ( ord_less_eq_set_a @ M22 @ M23 ) )
% 0.20/0.46 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ M1 @ M22 ) @ ( if_set_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Refine_Misc.if_mono
% 0.20/0.46 thf(fact_263_chain__subset__def,axiom,
% 0.20/0.46 ( chain_subset_a
% 0.20/0.46 = ( ^ [C3: set_set_a] :
% 0.20/0.46 ! [X4: set_a] :
% 0.20/0.46 ( ( member_set_a @ X4 @ C3 )
% 0.20/0.46 => ! [Y6: set_a] :
% 0.20/0.46 ( ( member_set_a @ Y6 @ C3 )
% 0.20/0.46 => ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 0.20/0.46 | ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % chain_subset_def
% 0.20/0.46
% 0.20/0.46 % Helper facts (5)
% 0.20/0.46 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( if_set_a @ $false @ X3 @ Y3 )
% 0.20/0.46 = Y3 ) ).
% 0.20/0.46
% 0.20/0.46 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.20/0.46 ! [X3: set_a,Y3: set_a] :
% 0.20/0.46 ( ( if_set_a @ $true @ X3 @ Y3 )
% 0.20/0.46 = X3 ) ).
% 0.20/0.46
% 0.20/0.46 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.20/0.46 ! [P: $o] :
% 0.20/0.46 ( ( P = $true )
% 0.20/0.46 | ( P = $false ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( if_Ref1724547303nres_a @ $false @ X3 @ Y3 )
% 0.20/0.46 = Y3 ) ).
% 0.20/0.46
% 0.20/0.46 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.20/0.46 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.20/0.46 ( ( if_Ref1724547303nres_a @ $true @ X3 @ Y3 )
% 0.20/0.46 = X3 ) ).
% 0.20/0.46
% 0.20/0.46 % Conjectures (1)
% 0.20/0.46 thf(conj_0,conjecture,
% 0.20/0.46 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
% 0.20/0.46 = ( phi @ x ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 3.26/1.76 ---- Embedded in THF ---
% 3.26/1.76 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.26/1.76 %%% Generated on Tue Feb 24 08:28:22 EST 2026
% 3.26/1.76 %%% using '$$dhol' embedding, version 1.3.0.
% 3.26/1.76 %%% Logic specification used:
% 3.26/1.76 %%% thf(spec, logic, $$dhol).
% 3.26/1.76
% 3.26/1.76 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2DTF30699.p
% See solution above
% 3.26/1.76 ------------------------
% 3.36/1.80 ---- Cleaned THF ---
% 3.36/1.80 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_J,type,
% 3.36/1.80 set_Pr384614482nres_a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(ty_n_t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.36/1.80 produc1609974940nres_a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(ty_n_t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 refine424419629nres_a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 3.36/1.80 set_set_a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 set_a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(ty_n_tf__a,type,
% 3.36/1.80 a: $tType ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 bNF_Ca459084161nres_a: set_Pr384614482nres_a > ( refine424419629nres_a > refine424419629nres_a ) > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 bNF_Ca953716171_set_a: set_Pr384614482nres_a > ( refine424419629nres_a > set_a ) > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_If_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 if_set_a: $o > set_a > set_a > set_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oord__class_Oless_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 ord_le1480771457nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 ord_less_set_a: set_a > set_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 ord_less_eq_set_a: set_a > set_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 order_Greatest_set_a: ( set_a > $o ) > set_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Product__Type_OPair_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J,type,
% 3.36/1.80 produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_ORETURN_001tf__a,type,
% 3.36/1.80 refine2063221604TURN_a: a > refine424419629nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oinres_001tf__a,type,
% 3.36/1.80 refine1001002027nres_a: refine424419629nres_a > a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oless__eq__nres__rel_001tf__a,type,
% 3.36/1.80 refine1048213316_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Oless__nres__rel_001tf__a,type,
% 3.36/1.80 refine260105272_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onf__inres_001tf__a,type,
% 3.36/1.80 refine1312857699nres_a: refine424419629nres_a > a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onofail_001tf__a,type,
% 3.36/1.80 refine412683989fail_a: refine424419629nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_OFAILi_001tf__a,type,
% 3.36/1.80 refine464223677AILi_a: refine424419629nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Onres_ORES_001tf__a,type,
% 3.36/1.80 refine1198353288_RES_a: set_a > refine424419629nres_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Refine__Basic__Mirabelle__kwjuvthmas_Othe__RES_001tf__a,type,
% 3.36/1.80 refine1822134885_RES_a: refine424419629nres_a > set_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.36/1.80 collect_a: ( a > $o ) > set_a ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.36/1.80 accp_P624619091nres_a: ( produc1609974940nres_a > produc1609974940nres_a > $o ) > produc1609974940nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_Zorn_Ochain__subset_001tf__a,type,
% 3.36/1.80 chain_subset_a: set_set_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_member_001t__Product____Type__Oprod_It__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J,type,
% 3.36/1.80 member1468928819nres_a: produc1609974940nres_a > set_Pr384614482nres_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 3.36/1.80 member_set_a: set_a > set_set_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_c_member_001tf__a,type,
% 3.36/1.80 member_a: a > set_a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_v__092_060Phi_062,type,
% 3.36/1.80 phi: a > $o ).
% 3.36/1.80
% 3.36/1.80 thf(sy_v_x,type,
% 3.36/1.80 x: a ).
% 3.36/1.80
% 3.36/1.80 thf(fact_0_nres__more__simps_I4_J,axiom,
% 3.36/1.80 ! [X: set_a,Y: set_a] :
% 3.36/1.80 ( ( ( refine1198353288_RES_a @ X )
% 3.36/1.80 = ( refine1198353288_RES_a @ Y ) )
% 3.36/1.80 = ( X = Y ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_1_nres_Oinject,axiom,
% 3.36/1.80 ! [X2: set_a,Y2: set_a] :
% 3.36/1.80 ( ( ( refine1198353288_RES_a @ X2 )
% 3.36/1.80 = ( refine1198353288_RES_a @ Y2 ) )
% 3.36/1.80 = ( X2 = Y2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_2_nf__inres__RES,axiom,
% 3.36/1.80 ! [X: set_a,X3: a] :
% 3.36/1.80 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X3 )
% 3.36/1.80 = ( member_a @ X3 @ X ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_3_the__RES_Osimps,axiom,
% 3.36/1.80 ! [X: set_a] :
% 3.36/1.80 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 3.36/1.80 = X ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_4_inres__simps_I2_J,axiom,
% 3.36/1.80 ! [X: set_a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 3.36/1.80 = ( ^ [X4: a] : ( member_a @ X4 @ X ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_5_nofail__simps_I2_J,axiom,
% 3.36/1.80 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_6_nofail__RES__conv,axiom,
% 3.36/1.80 ( refine412683989fail_a
% 3.36/1.80 = ( ^ [M: refine424419629nres_a] :
% 3.36/1.80 ? [M2: set_a] :
% 3.36/1.80 ( M
% 3.36/1.80 = ( refine1198353288_RES_a @ M2 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_7_nres_Odistinct_I1_J,axiom,
% 3.36/1.80 ! [X2: set_a] :
% 3.36/1.80 ( refine464223677AILi_a
% 3.36/1.80 != ( refine1198353288_RES_a @ X2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_8_nres_Oinduct,axiom,
% 3.36/1.80 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 3.36/1.80 ( ( P @ refine464223677AILi_a )
% 3.36/1.80 => ( ! [X5: set_a] : ( P @ ( refine1198353288_RES_a @ X5 ) )
% 3.36/1.80 => ( P @ Nres ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_9_nres_Oexhaust,axiom,
% 3.36/1.80 ! [Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( Y3 != refine464223677AILi_a )
% 3.36/1.80 => ~ ! [X22: set_a] :
% 3.36/1.80 ( Y3
% 3.36/1.80 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_10_sup__nres_Oinduct,axiom,
% 3.36/1.80 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.36/1.80 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.36/1.80 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 3.36/1.80 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_11_less__nres_Oinduct,axiom,
% 3.36/1.80 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.36/1.80 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 3.36/1.80 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 3.36/1.80 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_12_less__eq__nres_Oinduct,axiom,
% 3.36/1.80 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 3.36/1.80 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 3.36/1.80 => ( ! [A: set_a,B: set_a] : ( P @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_13_the__RES__inv,axiom,
% 3.36/1.80 ! [M3: refine424419629nres_a] :
% 3.36/1.80 ( ( refine412683989fail_a @ M3 )
% 3.36/1.80 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M3 ) )
% 3.36/1.80 = M3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_14_pw__eqI,axiom,
% 3.36/1.80 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 3.36/1.80 ( ( ( refine412683989fail_a @ S )
% 3.36/1.80 = ( refine412683989fail_a @ S2 ) )
% 3.36/1.80 => ( ! [X5: a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ S @ X5 )
% 3.36/1.80 = ( refine1001002027nres_a @ S2 @ X5 ) )
% 3.36/1.80 => ( S = S2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_15_pw__eq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 3.36/1.80 ( ( ( refine412683989fail_a @ S3 )
% 3.36/1.80 = ( refine412683989fail_a @ S4 ) )
% 3.36/1.80 & ! [X4: a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ S3 @ X4 )
% 3.36/1.80 = ( refine1001002027nres_a @ S4 @ X4 ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_16_not__nofail__inres,axiom,
% 3.36/1.80 ! [S: refine424419629nres_a,X3: a] :
% 3.36/1.80 ( ~ ( refine412683989fail_a @ S )
% 3.36/1.80 => ( refine1001002027nres_a @ S @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_17_nf__inres__def,axiom,
% 3.36/1.80 ( refine1312857699nres_a
% 3.36/1.80 = ( ^ [M: refine424419629nres_a,X4: a] :
% 3.36/1.80 ( ( refine412683989fail_a @ M )
% 3.36/1.80 & ( refine1001002027nres_a @ M @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_18_inres__simps_I3_J,axiom,
% 3.36/1.80 ! [X3: a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ ( refine2063221604TURN_a @ X3 ) )
% 3.36/1.80 = ( ^ [Y4: a,Z: a] : ( Y4 = Z )
% 3.36/1.80 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_19_nofail__simps_I3_J,axiom,
% 3.36/1.80 ! [X3: a] : ( refine412683989fail_a @ ( refine2063221604TURN_a @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_20_pw__leI,axiom,
% 3.36/1.80 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 3.36/1.80 ( ( ( refine412683989fail_a @ S2 )
% 3.36/1.80 => ( ( refine412683989fail_a @ S )
% 3.36/1.80 & ! [X5: a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ S @ X5 )
% 3.36/1.80 => ( refine1001002027nres_a @ S2 @ X5 ) ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ S @ S2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_21_pw__leI_H,axiom,
% 3.36/1.80 ! [S2: refine424419629nres_a,S: refine424419629nres_a] :
% 3.36/1.80 ( ( ( refine412683989fail_a @ S2 )
% 3.36/1.80 => ( refine412683989fail_a @ S ) )
% 3.36/1.80 => ( ! [X5: a] :
% 3.36/1.80 ( ( refine412683989fail_a @ S2 )
% 3.36/1.80 => ( ( refine1001002027nres_a @ S @ X5 )
% 3.36/1.80 => ( refine1001002027nres_a @ S2 @ X5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ S @ S2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_22_pw__le__iff,axiom,
% 3.36/1.80 ( ord_le519537037nres_a
% 3.36/1.80 = ( ^ [S3: refine424419629nres_a,S4: refine424419629nres_a] :
% 3.36/1.80 ( ( refine412683989fail_a @ S4 )
% 3.36/1.80 => ( ( refine412683989fail_a @ S3 )
% 3.36/1.80 & ! [X4: a] :
% 3.36/1.80 ( ( refine1001002027nres_a @ S3 @ X4 )
% 3.36/1.80 => ( refine1001002027nres_a @ S4 @ X4 ) ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_23_less__eq__nres_Osimps_I3_J,axiom,
% 3.36/1.80 ! [Uv2: set_a] :
% 3.36/1.80 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_24_less__nres_Osimps_I2_J,axiom,
% 3.36/1.80 ! [Uv2: set_a] : ( ord_le1480771457nres_a @ ( refine1198353288_RES_a @ Uv2 ) @ refine464223677AILi_a ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_25_less__eq__nres_Ocases,axiom,
% 3.36/1.80 ! [X3: produc1609974940nres_a] :
% 3.36/1.80 ( ! [Uu: refine424419629nres_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 3.36/1.80 => ( ! [A: set_a,B: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 3.36/1.80 => ~ ! [Uv: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_26_less__nres_Ocases,axiom,
% 3.36/1.80 ! [X3: produc1609974940nres_a] :
% 3.36/1.80 ( ! [Uu: refine424419629nres_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ refine464223677AILi_a @ Uu ) )
% 3.36/1.80 => ( ! [Uv: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) )
% 3.36/1.80 => ~ ! [A: set_a,B: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_27_sup__nres_Ocases,axiom,
% 3.36/1.80 ! [X3: produc1609974940nres_a] :
% 3.36/1.80 ( ! [Uu: refine424419629nres_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 3.36/1.80 => ( ! [V: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) ) )
% 3.36/1.80 => ~ ! [A: set_a,B: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_28_nres__more__simps_I6_J,axiom,
% 3.36/1.80 ! [X3: a,Y3: a] :
% 3.36/1.80 ( ( ( refine2063221604TURN_a @ X3 )
% 3.36/1.80 = ( refine2063221604TURN_a @ Y3 ) )
% 3.36/1.80 = ( X3 = Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_29_nres__order__simps_I20_J,axiom,
% 3.36/1.80 ! [X3: a,Y3: a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 3.36/1.80 = ( X3 = Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_30_nres__order__simps_I21_J,axiom,
% 3.36/1.80 ! [X3: a,Y: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ ( refine1198353288_RES_a @ Y ) )
% 3.36/1.80 = ( member_a @ X3 @ Y ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_31_inres__def,axiom,
% 3.36/1.80 ( refine1001002027nres_a
% 3.36/1.80 = ( ^ [S3: refine424419629nres_a,X4: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ S3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_32_less__nres_Osimps_I1_J,axiom,
% 3.36/1.80 ! [Uu2: refine424419629nres_a] :
% 3.36/1.80 ~ ( ord_le1480771457nres_a @ refine464223677AILi_a @ Uu2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_33_less__eq__nres_Osimps_I1_J,axiom,
% 3.36/1.80 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_34_le__nofailI,axiom,
% 3.36/1.80 ! [M4: refine424419629nres_a,M5: refine424419629nres_a] :
% 3.36/1.80 ( ( ( refine412683989fail_a @ M4 )
% 3.36/1.80 => ( ord_le519537037nres_a @ M5 @ M4 ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ M5 @ M4 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_35_pwD1,axiom,
% 3.36/1.80 ! [S: refine424419629nres_a,S2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ S @ S2 )
% 3.36/1.80 => ( ( refine412683989fail_a @ S2 )
% 3.36/1.80 => ( refine412683989fail_a @ S ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_36_pwD2,axiom,
% 3.36/1.80 ! [S: refine424419629nres_a,S2: refine424419629nres_a,X3: a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ S @ S2 )
% 3.36/1.80 => ( ( refine1001002027nres_a @ S @ X3 )
% 3.36/1.80 => ( refine1001002027nres_a @ S2 @ X3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_37_old_Oprod_Oinject,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 3.36/1.80 ( ( ( produc1136923598nres_a @ A2 @ B2 )
% 3.36/1.80 = ( produc1136923598nres_a @ A3 @ B3 ) )
% 3.36/1.80 = ( ( A2 = A3 )
% 3.36/1.80 & ( B2 = B3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_38_prod_Oinject,axiom,
% 3.36/1.80 ! [X1: refine424419629nres_a,X2: refine424419629nres_a,Y1: refine424419629nres_a,Y2: refine424419629nres_a] :
% 3.36/1.80 ( ( ( produc1136923598nres_a @ X1 @ X2 )
% 3.36/1.80 = ( produc1136923598nres_a @ Y1 @ Y2 ) )
% 3.36/1.80 = ( ( X1 = Y1 )
% 3.36/1.80 & ( X2 = Y2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_39_order__mono__setup_Orefl,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a] : ( ord_le519537037nres_a @ X3 @ X3 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_40_order__mono__setup_Orefl,axiom,
% 3.36/1.80 ! [X3: set_a] : ( ord_less_eq_set_a @ X3 @ X3 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_41_mem__Collect__eq,axiom,
% 3.36/1.80 ! [A2: a,P: a > $o] :
% 3.36/1.80 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 3.36/1.80 = ( P @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_42_Collect__mem__eq,axiom,
% 3.36/1.80 ! [A4: set_a] :
% 3.36/1.80 ( ( collect_a
% 3.36/1.80 @ ^ [X4: a] : ( member_a @ X4 @ A4 ) )
% 3.36/1.80 = A4 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_43_Collect__cong,axiom,
% 3.36/1.80 ! [P: a > $o,Q: a > $o] :
% 3.36/1.80 ( ! [X5: a] :
% 3.36/1.80 ( ( P @ X5 )
% 3.36/1.80 = ( Q @ X5 ) )
% 3.36/1.80 => ( ( collect_a @ P )
% 3.36/1.80 = ( collect_a @ Q ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_44_order_Onot__eq__order__implies__strict,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( A2 != B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_45_order_Onot__eq__order__implies__strict,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( A2 != B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_46_dual__order_Ostrict__implies__order,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ord_le519537037nres_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_47_dual__order_Ostrict__implies__order,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_48_dual__order_Ostrict__iff__order,axiom,
% 3.36/1.80 ( ord_le1480771457nres_a
% 3.36/1.80 = ( ^ [B4: refine424419629nres_a,A5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ B4 @ A5 )
% 3.36/1.80 & ( A5 != B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_49_dual__order_Ostrict__iff__order,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [B4: set_a,A5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ B4 @ A5 )
% 3.36/1.80 & ( A5 != B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_50_dual__order_Oorder__iff__strict,axiom,
% 3.36/1.80 ( ord_le519537037nres_a
% 3.36/1.80 = ( ^ [B4: refine424419629nres_a,A5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B4 @ A5 )
% 3.36/1.80 | ( A5 = B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_51_dual__order_Oorder__iff__strict,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [B4: set_a,A5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B4 @ A5 )
% 3.36/1.80 | ( A5 = B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_52_order_Ostrict__implies__order,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_53_order_Ostrict__implies__order,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_54_less__eq__nres_Osimps_I2_J,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 3.36/1.80 = ( ord_less_eq_set_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_55_nres__order__simps_I5_J,axiom,
% 3.36/1.80 ! [X: set_a,Y: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 3.36/1.80 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_56_less__nres_Osimps_I3_J,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ ( refine1198353288_RES_a @ A2 ) @ ( refine1198353288_RES_a @ B2 ) )
% 3.36/1.80 = ( ord_less_set_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_57_order__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_58_order__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_59_order__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_60_order__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_61_order__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_62_order__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_63_order__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_64_order__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_65_ord__eq__le__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_66_ord__eq__le__subst,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_67_ord__eq__le__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_68_ord__eq__le__subst,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_69_ord__le__eq__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_70_ord__le__eq__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_71_ord__le__eq__subst,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_72_ord__le__eq__subst,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_73_eq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 3.36/1.80 & ( ord_le519537037nres_a @ Y6 @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_74_eq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [X4: set_a,Y6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 3.36/1.80 & ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_75_antisym,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 3.36/1.80 => ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_76_antisym,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 3.36/1.80 => ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_77_eq__refl,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( X3 = Y3 )
% 3.36/1.80 => ( ord_le519537037nres_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_78_eq__refl,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( X3 = Y3 )
% 3.36/1.80 => ( ord_less_eq_set_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_79_order_Otrans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_80_order_Otrans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_81_antisym__conv,axiom,
% 3.36/1.80 ! [Y3: refine424419629nres_a,X3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_82_antisym__conv,axiom,
% 3.36/1.80 ! [Y3: set_a,X3: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_83_order__class_Oorder_Oeq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A5 @ B4 )
% 3.36/1.80 & ( ord_le519537037nres_a @ B4 @ A5 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_84_order__class_Oorder_Oeq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [A5: set_a,B4: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A5 @ B4 )
% 3.36/1.80 & ( ord_less_eq_set_a @ B4 @ A5 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_85_ord__eq__le__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2 = B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_86_ord__eq__le__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2 = B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_87_ord__le__eq__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( B2 = C )
% 3.36/1.80 => ( ord_le519537037nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_88_ord__le__eq__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( B2 = C )
% 3.36/1.80 => ( ord_less_eq_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_89_order__class_Oorder_Oantisym,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.36/1.80 => ( A2 = B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_90_order__class_Oorder_Oantisym,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ A2 )
% 3.36/1.80 => ( A2 = B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_91_order__trans,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_le519537037nres_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_92_order__trans,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_93_dual__order_Orefl,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a] : ( ord_le519537037nres_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_94_dual__order_Orefl,axiom,
% 3.36/1.80 ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_95_dual__order_Otrans,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ C @ B2 )
% 3.36/1.80 => ( ord_le519537037nres_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_96_dual__order_Otrans,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ C @ B2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_97_dual__order_Oeq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: refine424419629nres_a,Z: refine424419629nres_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ B4 @ A5 )
% 3.36/1.80 & ( ord_le519537037nres_a @ A5 @ B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_98_dual__order_Oeq__iff,axiom,
% 3.36/1.80 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [A5: set_a,B4: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ B4 @ A5 )
% 3.36/1.80 & ( ord_less_eq_set_a @ A5 @ B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_99_dual__order_Oantisym,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( A2 = B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_100_dual__order_Oantisym,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( A2 = B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_101_order__mono__setup_Omono__if,axiom,
% 3.36/1.80 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B2: $o] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ T @ T2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ E @ E2 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ T @ E ) @ ( if_Ref1724547303nres_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_102_order__mono__setup_Omono__if,axiom,
% 3.36/1.80 ! [T: set_a,T2: set_a,E: set_a,E2: set_a,B2: $o] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ T @ T2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ E @ E2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ T @ E ) @ ( if_set_a @ B2 @ T2 @ E2 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_103_surj__pair,axiom,
% 3.36/1.80 ! [P2: produc1609974940nres_a] :
% 3.36/1.80 ? [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( P2
% 3.36/1.80 = ( produc1136923598nres_a @ X5 @ Y5 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_104_prod__cases,axiom,
% 3.36/1.80 ! [P: produc1609974940nres_a > $o,P2: produc1609974940nres_a] :
% 3.36/1.80 ( ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( P @ ( produc1136923598nres_a @ A @ B ) )
% 3.36/1.80 => ( P @ P2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_105_Pair__inject,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,A3: refine424419629nres_a,B3: refine424419629nres_a] :
% 3.36/1.80 ( ( ( produc1136923598nres_a @ A2 @ B2 )
% 3.36/1.80 = ( produc1136923598nres_a @ A3 @ B3 ) )
% 3.36/1.80 => ~ ( ( A2 = A3 )
% 3.36/1.80 => ( B2 != B3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 3.36/1.80 ! [Y3: produc1609974940nres_a] :
% 3.36/1.80 ~ ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.36/1.80 ( Y3
% 3.36/1.80 != ( produc1136923598nres_a @ A @ B ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_107_old_Oprod_Oinducts,axiom,
% 3.36/1.80 ! [P: produc1609974940nres_a > $o,Prod: produc1609974940nres_a] :
% 3.36/1.80 ( ! [A: refine424419629nres_a,B: refine424419629nres_a] : ( P @ ( produc1136923598nres_a @ A @ B ) )
% 3.36/1.80 => ( P @ Prod ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_108_ord__eq__less__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_109_ord__eq__less__subst,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_110_ord__eq__less__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_111_ord__eq__less__subst,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2
% 3.36/1.80 = ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_112_ord__less__eq__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_113_ord__less__eq__subst,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_114_ord__less__eq__subst,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_115_ord__less__eq__subst,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ( F @ B2 )
% 3.36/1.80 = C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_116_order__less__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_117_order__less__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_118_order__less__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_119_order__less__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_120_order__less__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_121_order__less__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_122_order__less__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_123_order__less__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_124_order_Oasym,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_125_order_Oasym,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_126_less__imp__neq,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( X3 != Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_127_less__imp__neq,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( X3 != Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_128_less__asym,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_129_less__asym,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_130_less__asym_H,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_131_less__asym_H,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_132_less__trans,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_133_less__trans,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_set_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_134_less__irrefl,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a] :
% 3.36/1.80 ~ ( ord_le1480771457nres_a @ X3 @ X3 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_135_less__irrefl,axiom,
% 3.36/1.80 ! [X3: set_a] :
% 3.36/1.80 ~ ( ord_less_set_a @ X3 @ X3 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_136_ord__eq__less__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( A2 = B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_137_ord__eq__less__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( A2 = B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_138_ord__less__eq__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( B2 = C )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_139_ord__less__eq__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( B2 = C )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_140_dual__order_Oasym,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_141_dual__order_Oasym,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B2 @ A2 )
% 3.36/1.80 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_142_less__imp__not__eq,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( X3 != Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_143_less__imp__not__eq,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( X3 != Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_144_less__not__sym,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_145_less__not__sym,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_146_less__imp__not__eq2,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( Y3 != X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_147_less__imp__not__eq2,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( Y3 != X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_148_less__imp__triv,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,P: $o] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ Y3 @ X3 )
% 3.36/1.80 => P ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_149_less__imp__triv,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a,P: $o] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_set_a @ Y3 @ X3 )
% 3.36/1.80 => P ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_150_dual__order_Oirrefl,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a] :
% 3.36/1.80 ~ ( ord_le1480771457nres_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_151_dual__order_Oirrefl,axiom,
% 3.36/1.80 ! [A2: set_a] :
% 3.36/1.80 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_152_order_Ostrict__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_153_order_Ostrict__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_154_less__imp__not__less,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_155_less__imp__not__less,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ~ ( ord_less_set_a @ Y3 @ X3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_156_dual__order_Ostrict__trans,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ C @ B2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_157_dual__order_Ostrict__trans,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_less_set_a @ C @ B2 )
% 3.36/1.80 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_158_order_Ostrict__implies__not__eq,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( A2 != B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_159_order_Ostrict__implies__not__eq,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( A2 != B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_160_dual__order_Ostrict__implies__not__eq,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 3.36/1.80 => ( A2 != B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_161_dual__order_Ostrict__implies__not__eq,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B2 @ A2 )
% 3.36/1.80 => ( A2 != B2 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_162_less__eq__nres_Oelims_I3_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ~ ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A @ B ) ) )
% 3.36/1.80 => ~ ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => ! [Uv: set_a] :
% 3.36/1.80 ( Xa
% 3.36/1.80 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_163_less__eq__nres_Oelims_I2_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( Xa != refine464223677AILi_a )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_164_less__eq__nres_Oelims_I1_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.36/1.80 ( ( ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.80 = Y3 )
% 3.36/1.80 => ( ( ( Xa = refine464223677AILi_a )
% 3.36/1.80 => ~ Y3 )
% 3.36/1.80 => ( ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( Y3
% 3.36/1.80 = ( ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) )
% 3.36/1.80 => ~ ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => ( ? [Uv: set_a] :
% 3.36/1.80 ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => Y3 ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_165_less__nres_Oelims_I3_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ~ ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( X3 != refine464223677AILi_a )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ord_less_set_a @ A @ B ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_166_less__nres_Oelims_I2_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( ? [Uv: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => ( Xa != refine464223677AILi_a ) )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_167_less__nres_Oelims_I1_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.36/1.80 ( ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 = Y3 )
% 3.36/1.80 => ( ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => Y3 )
% 3.36/1.80 => ( ( ? [Uv: set_a] :
% 3.36/1.80 ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => ( ( Xa = refine464223677AILi_a )
% 3.36/1.80 => ~ Y3 ) )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( Y3
% 3.36/1.80 = ( ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_168_leD,axiom,
% 3.36/1.80 ! [Y3: refine424419629nres_a,X3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ Y3 @ X3 )
% 3.36/1.80 => ~ ( ord_le1480771457nres_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_169_leD,axiom,
% 3.36/1.80 ! [Y3: set_a,X3: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ Y3 @ X3 )
% 3.36/1.80 => ~ ( ord_less_set_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_170_le__less,axiom,
% 3.36/1.80 ( ord_le519537037nres_a
% 3.36/1.80 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X4 @ Y6 )
% 3.36/1.80 | ( X4 = Y6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_171_le__less,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [X4: set_a,Y6: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X4 @ Y6 )
% 3.36/1.80 | ( X4 = Y6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_172_less__le,axiom,
% 3.36/1.80 ( ord_le1480771457nres_a
% 3.36/1.80 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 3.36/1.80 & ( X4 != Y6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_173_less__le,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [X4: set_a,Y6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 3.36/1.80 & ( X4 != Y6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_174_order__le__less__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_175_order__le__less__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_176_order__le__less__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_177_order__le__less__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_178_order__le__less__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_179_order__le__less__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_180_order__le__less__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_181_order__le__less__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_182_order__less__le__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_183_order__less__le__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: refine424419629nres_a > set_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_184_order__less__le__subst1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,F: set_a > refine424419629nres_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_185_order__less__le__subst1,axiom,
% 3.36/1.80 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_186_order__less__le__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_187_order__less__le__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_le1480771457nres_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_188_order__less__le__subst2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,F: refine424419629nres_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: refine424419629nres_a,Y5: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_189_order__less__le__subst2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C )
% 3.36/1.80 => ( ! [X5: set_a,Y5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X5 @ Y5 )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 3.36/1.80 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_190_le__neq__trans,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( A2 != B2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_191_le__neq__trans,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( A2 != B2 )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ B2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_192_antisym__conv1,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ~ ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_193_antisym__conv1,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ~ ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_194_antisym__conv2,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ~ ( ord_le1480771457nres_a @ X3 @ Y3 ) )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_195_antisym__conv2,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ~ ( ord_less_set_a @ X3 @ Y3 ) )
% 3.36/1.80 = ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_196_less__imp__le,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ord_le519537037nres_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_197_less__imp__le,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ord_less_eq_set_a @ X3 @ Y3 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_198_le__less__trans,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_199_le__less__trans,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_set_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_200_less__le__trans,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_201_less__le__trans,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a,Z2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ Y3 @ Z2 )
% 3.36/1.80 => ( ord_less_set_a @ X3 @ Z2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_202_le__imp__less__or__eq,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ X3 @ Y3 )
% 3.36/1.80 | ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_203_le__imp__less__or__eq,axiom,
% 3.36/1.80 ! [X3: set_a,Y3: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X3 @ Y3 )
% 3.36/1.80 => ( ( ord_less_set_a @ X3 @ Y3 )
% 3.36/1.80 | ( X3 = Y3 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_204_less__le__not__le,axiom,
% 3.36/1.80 ( ord_le1480771457nres_a
% 3.36/1.80 = ( ^ [X4: refine424419629nres_a,Y6: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ X4 @ Y6 )
% 3.36/1.80 & ~ ( ord_le519537037nres_a @ Y6 @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_205_less__le__not__le,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [X4: set_a,Y6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 3.36/1.80 & ~ ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_206_order_Ostrict__trans1,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_207_order_Ostrict__trans1,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_208_order_Ostrict__trans2,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.80 => ( ord_le1480771457nres_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_209_order_Ostrict__trans2,axiom,
% 3.36/1.80 ! [A2: set_a,B2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A2 @ B2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.80 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_210_order_Oorder__iff__strict,axiom,
% 3.36/1.80 ( ord_le519537037nres_a
% 3.36/1.80 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ A5 @ B4 )
% 3.36/1.80 | ( A5 = B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_211_order_Oorder__iff__strict,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [A5: set_a,B4: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A5 @ B4 )
% 3.36/1.80 | ( A5 = B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_212_order_Ostrict__iff__order,axiom,
% 3.36/1.80 ( ord_le1480771457nres_a
% 3.36/1.80 = ( ^ [A5: refine424419629nres_a,B4: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ A5 @ B4 )
% 3.36/1.80 & ( A5 != B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_213_order_Ostrict__iff__order,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [A5: set_a,B4: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A5 @ B4 )
% 3.36/1.80 & ( A5 != B4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_214_dual__order_Ostrict__trans1,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_le1480771457nres_a @ C @ B2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_215_dual__order_Ostrict__trans1,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_less_set_a @ C @ B2 )
% 3.36/1.80 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_216_dual__order_Ostrict__trans2,axiom,
% 3.36/1.80 ! [B2: refine424419629nres_a,A2: refine424419629nres_a,C: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_le519537037nres_a @ C @ B2 )
% 3.36/1.80 => ( ord_le1480771457nres_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_217_dual__order_Ostrict__trans2,axiom,
% 3.36/1.80 ! [B2: set_a,A2: set_a,C: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ B2 @ A2 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ C @ B2 )
% 3.36/1.80 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_218_relChain__def,axiom,
% 3.36/1.80 ( bNF_Ca459084161nres_a
% 3.36/1.80 = ( ^ [R: set_Pr384614482nres_a,As: refine424419629nres_a > refine424419629nres_a] :
% 3.36/1.80 ! [I: refine424419629nres_a,J: refine424419629nres_a] :
% 3.36/1.80 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ I @ J ) @ R )
% 3.36/1.80 => ( ord_le519537037nres_a @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_219_relChain__def,axiom,
% 3.36/1.80 ( bNF_Ca953716171_set_a
% 3.36/1.80 = ( ^ [R: set_Pr384614482nres_a,As: refine424419629nres_a > set_a] :
% 3.36/1.80 ! [I: refine424419629nres_a,J: refine424419629nres_a] :
% 3.36/1.80 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ I @ J ) @ R )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_220_verit__comp__simplify1_I1_J,axiom,
% 3.36/1.80 ! [A2: refine424419629nres_a] :
% 3.36/1.80 ~ ( ord_le1480771457nres_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_221_verit__comp__simplify1_I1_J,axiom,
% 3.36/1.80 ! [A2: set_a] :
% 3.36/1.80 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_222_psubsetI,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( A4 != B5 )
% 3.36/1.80 => ( ord_less_set_a @ A4 @ B5 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_223_subset__antisym,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B5 @ A4 )
% 3.36/1.80 => ( A4 = B5 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_224_subsetI,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ! [X5: a] :
% 3.36/1.80 ( ( member_a @ X5 @ A4 )
% 3.36/1.80 => ( member_a @ X5 @ B5 ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_225_in__mono,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,X3: a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( member_a @ X3 @ A4 )
% 3.36/1.80 => ( member_a @ X3 @ B5 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_226_subsetD,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C: a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( member_a @ C @ A4 )
% 3.36/1.80 => ( member_a @ C @ B5 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_227_equalityE,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( A4 = B5 )
% 3.36/1.80 => ~ ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ~ ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_228_subset__eq,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ! [X4: a] :
% 3.36/1.80 ( ( member_a @ X4 @ A6 )
% 3.36/1.80 => ( member_a @ X4 @ B6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_229_equalityD1,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( A4 = B5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_230_equalityD2,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( A4 = B5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ B5 @ A4 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_231_subset__iff,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ! [T3: a] :
% 3.36/1.80 ( ( member_a @ T3 @ A6 )
% 3.36/1.80 => ( member_a @ T3 @ B6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_232_subset__refl,axiom,
% 3.36/1.80 ! [A4: set_a] : ( ord_less_eq_set_a @ A4 @ A4 ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_233_Collect__mono,axiom,
% 3.36/1.80 ! [P: a > $o,Q: a > $o] :
% 3.36/1.80 ( ! [X5: a] :
% 3.36/1.80 ( ( P @ X5 )
% 3.36/1.80 => ( Q @ X5 ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_234_subset__trans,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B5 @ C2 )
% 3.36/1.80 => ( ord_less_eq_set_a @ A4 @ C2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_235_set__eq__subset,axiom,
% 3.36/1.80 ( ( ^ [Y4: set_a,Z: set_a] : ( Y4 = Z ) )
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 3.36/1.80 & ( ord_less_eq_set_a @ B6 @ A6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_236_Collect__mono__iff,axiom,
% 3.36/1.80 ! [P: a > $o,Q: a > $o] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 3.36/1.80 = ( ! [X4: a] :
% 3.36/1.80 ( ( P @ X4 )
% 3.36/1.80 => ( Q @ X4 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_237_psubsetD,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C: a] :
% 3.36/1.80 ( ( ord_less_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( member_a @ C @ A4 )
% 3.36/1.80 => ( member_a @ C @ B5 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_238_psubset__trans,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( ord_less_set_a @ B5 @ C2 )
% 3.36/1.80 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_239_psubsetE,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A4 @ B5 )
% 3.36/1.80 => ~ ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ B5 @ A4 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_240_psubset__eq,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 3.36/1.80 & ( A6 != B6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_241_psubset__imp__subset,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ord_less_eq_set_a @ A4 @ B5 ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_242_psubset__subset__trans,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C2: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( ord_less_eq_set_a @ B5 @ C2 )
% 3.36/1.80 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_243_subset__not__subset__eq,axiom,
% 3.36/1.80 ( ord_less_set_a
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A6 @ B6 )
% 3.36/1.80 & ~ ( ord_less_eq_set_a @ B6 @ A6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_244_subset__psubset__trans,axiom,
% 3.36/1.80 ! [A4: set_a,B5: set_a,C2: set_a] :
% 3.36/1.80 ( ( ord_less_eq_set_a @ A4 @ B5 )
% 3.36/1.80 => ( ( ord_less_set_a @ B5 @ C2 )
% 3.36/1.80 => ( ord_less_set_a @ A4 @ C2 ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_245_subset__iff__psubset__eq,axiom,
% 3.36/1.80 ( ord_less_eq_set_a
% 3.36/1.80 = ( ^ [A6: set_a,B6: set_a] :
% 3.36/1.80 ( ( ord_less_set_a @ A6 @ B6 )
% 3.36/1.80 | ( A6 = B6 ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_246_less__nres_Opelims_I1_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.36/1.80 ( ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 = Y3 )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.80 => ( ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => ( ~ Y3
% 3.36/1.80 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ Xa ) ) ) )
% 3.36/1.80 => ( ! [Uv: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => ( ( Xa = refine464223677AILi_a )
% 3.36/1.80 => ( Y3
% 3.36/1.80 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) ) ) ) )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ( Y3
% 3.36/1.80 = ( ord_less_set_a @ A @ B ) )
% 3.36/1.80 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_247_less__nres_Opelims_I2_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.80 => ( ! [Uv: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.80 => ( ( Xa = refine464223677AILi_a )
% 3.36/1.80 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) ) ) )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 3.36/1.80 => ~ ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_248_less__nres_Opelims_I3_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ~ ( ord_le1480771457nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.80 => ( ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => ~ ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ Xa ) ) )
% 3.36/1.80 => ~ ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine260105272_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 3.36/1.80 => ( ord_less_set_a @ A @ B ) ) ) ) ) ) ) ).
% 3.36/1.80
% 3.36/1.80 thf(fact_249_less__eq__nres_Opelims_I3_J,axiom,
% 3.36/1.80 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.80 ( ~ ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.80 => ( ! [A: set_a] :
% 3.36/1.80 ( ( X3
% 3.36/1.80 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.80 => ! [B: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.80 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 3.36/1.80 => ( ord_less_eq_set_a @ A @ B ) ) ) )
% 3.36/1.80 => ~ ( ( X3 = refine464223677AILi_a )
% 3.36/1.80 => ! [Uv: set_a] :
% 3.36/1.80 ( ( Xa
% 3.36/1.80 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.81 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_250_less__eq__nres_Opelims_I2_J,axiom,
% 3.36/1.81 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a] :
% 3.36/1.81 ( ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.81 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.81 => ( ( ( Xa = refine464223677AILi_a )
% 3.36/1.81 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ refine464223677AILi_a ) ) )
% 3.36/1.81 => ~ ! [A: set_a] :
% 3.36/1.81 ( ( X3
% 3.36/1.81 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.81 => ! [B: set_a] :
% 3.36/1.81 ( ( Xa
% 3.36/1.81 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.81 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) )
% 3.36/1.81 => ~ ( ord_less_eq_set_a @ A @ B ) ) ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_251_less__eq__nres_Opelims_I1_J,axiom,
% 3.36/1.81 ! [X3: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 3.36/1.81 ( ( ( ord_le519537037nres_a @ X3 @ Xa )
% 3.36/1.81 = Y3 )
% 3.36/1.81 => ( ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ Xa ) )
% 3.36/1.81 => ( ( ( Xa = refine464223677AILi_a )
% 3.36/1.81 => ( Y3
% 3.36/1.81 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ X3 @ refine464223677AILi_a ) ) ) )
% 3.36/1.81 => ( ! [A: set_a] :
% 3.36/1.81 ( ( X3
% 3.36/1.81 = ( refine1198353288_RES_a @ A ) )
% 3.36/1.81 => ! [B: set_a] :
% 3.36/1.81 ( ( Xa
% 3.36/1.81 = ( refine1198353288_RES_a @ B ) )
% 3.36/1.81 => ( ( Y3
% 3.36/1.81 = ( ord_less_eq_set_a @ A @ B ) )
% 3.36/1.81 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) ) ) ) ) )
% 3.36/1.81 => ~ ( ( X3 = refine464223677AILi_a )
% 3.36/1.81 => ! [Uv: set_a] :
% 3.36/1.81 ( ( Xa
% 3.36/1.81 = ( refine1198353288_RES_a @ Uv ) )
% 3.36/1.81 => ( ~ Y3
% 3.36/1.81 => ~ ( accp_P624619091nres_a @ refine1048213316_rel_a @ ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_252_GreatestI2__order,axiom,
% 3.36/1.81 ! [P: refine424419629nres_a > $o,X3: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 3.36/1.81 ( ( P @ X3 )
% 3.36/1.81 => ( ! [Y5: refine424419629nres_a] :
% 3.36/1.81 ( ( P @ Y5 )
% 3.36/1.81 => ( ord_le519537037nres_a @ Y5 @ X3 ) )
% 3.36/1.81 => ( ! [X5: refine424419629nres_a] :
% 3.36/1.81 ( ( P @ X5 )
% 3.36/1.81 => ( ! [Y7: refine424419629nres_a] :
% 3.36/1.81 ( ( P @ Y7 )
% 3.36/1.81 => ( ord_le519537037nres_a @ Y7 @ X5 ) )
% 3.36/1.81 => ( Q @ X5 ) ) )
% 3.36/1.81 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_253_GreatestI2__order,axiom,
% 3.36/1.81 ! [P: set_a > $o,X3: set_a,Q: set_a > $o] :
% 3.36/1.81 ( ( P @ X3 )
% 3.36/1.81 => ( ! [Y5: set_a] :
% 3.36/1.81 ( ( P @ Y5 )
% 3.36/1.81 => ( ord_less_eq_set_a @ Y5 @ X3 ) )
% 3.36/1.81 => ( ! [X5: set_a] :
% 3.36/1.81 ( ( P @ X5 )
% 3.36/1.81 => ( ! [Y7: set_a] :
% 3.36/1.81 ( ( P @ Y7 )
% 3.36/1.81 => ( ord_less_eq_set_a @ Y7 @ X5 ) )
% 3.36/1.81 => ( Q @ X5 ) ) )
% 3.36/1.81 => ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_254_Greatest__equality,axiom,
% 3.36/1.81 ! [P: refine424419629nres_a > $o,X3: refine424419629nres_a] :
% 3.36/1.81 ( ( P @ X3 )
% 3.36/1.81 => ( ! [Y5: refine424419629nres_a] :
% 3.36/1.81 ( ( P @ Y5 )
% 3.36/1.81 => ( ord_le519537037nres_a @ Y5 @ X3 ) )
% 3.36/1.81 => ( ( order_1714329108nres_a @ P )
% 3.36/1.81 = X3 ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_255_Greatest__equality,axiom,
% 3.36/1.81 ! [P: set_a > $o,X3: set_a] :
% 3.36/1.81 ( ( P @ X3 )
% 3.36/1.81 => ( ! [Y5: set_a] :
% 3.36/1.81 ( ( P @ Y5 )
% 3.36/1.81 => ( ord_less_eq_set_a @ Y5 @ X3 ) )
% 3.36/1.81 => ( ( order_Greatest_set_a @ P )
% 3.36/1.81 = X3 ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_256_subset__Collect__conv,axiom,
% 3.36/1.81 ! [S: set_a,P: a > $o] :
% 3.36/1.81 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 3.36/1.81 = ( ! [X4: a] :
% 3.36/1.81 ( ( member_a @ X4 @ S )
% 3.36/1.81 => ( P @ X4 ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_257_relprop__triggers_I6_J,axiom,
% 3.36/1.81 ! [R2: set_a,R3: set_a] :
% 3.36/1.81 ( ( ord_less_eq_set_a @ R2 @ R3 )
% 3.36/1.81 => ( ord_less_eq_set_a @ R2 @ R3 ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_258_ord__eq__le__eq__trans,axiom,
% 3.36/1.81 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 3.36/1.81 ( ( A2 = B2 )
% 3.36/1.81 => ( ( ord_le519537037nres_a @ B2 @ C )
% 3.36/1.81 => ( ( C = D )
% 3.36/1.81 => ( ord_le519537037nres_a @ A2 @ D ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_259_ord__eq__le__eq__trans,axiom,
% 3.36/1.81 ! [A2: set_a,B2: set_a,C: set_a,D: set_a] :
% 3.36/1.81 ( ( A2 = B2 )
% 3.36/1.81 => ( ( ord_less_eq_set_a @ B2 @ C )
% 3.36/1.81 => ( ( C = D )
% 3.36/1.81 => ( ord_less_eq_set_a @ A2 @ D ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_260_bex2I,axiom,
% 3.36/1.81 ! [A2: refine424419629nres_a,B2: refine424419629nres_a,S: set_Pr384614482nres_a,P: refine424419629nres_a > refine424419629nres_a > $o] :
% 3.36/1.81 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A2 @ B2 ) @ S )
% 3.36/1.81 => ( ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A2 @ B2 ) @ S )
% 3.36/1.81 => ( P @ A2 @ B2 ) )
% 3.36/1.81 => ? [A: refine424419629nres_a,B: refine424419629nres_a] :
% 3.36/1.81 ( ( member1468928819nres_a @ ( produc1136923598nres_a @ A @ B ) @ S )
% 3.36/1.81 & ( P @ A @ B ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_261_Refine__Misc_Oif__mono,axiom,
% 3.36/1.81 ! [B2: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M22: refine424419629nres_a,M23: refine424419629nres_a] :
% 3.36/1.81 ( ( B2
% 3.36/1.81 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 3.36/1.81 => ( ( ~ B2
% 3.36/1.81 => ( ord_le519537037nres_a @ M22 @ M23 ) )
% 3.36/1.81 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B2 @ M1 @ M22 ) @ ( if_Ref1724547303nres_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_262_Refine__Misc_Oif__mono,axiom,
% 3.36/1.81 ! [B2: $o,M1: set_a,M12: set_a,M22: set_a,M23: set_a] :
% 3.36/1.81 ( ( B2
% 3.36/1.81 => ( ord_less_eq_set_a @ M1 @ M12 ) )
% 3.36/1.81 => ( ( ~ B2
% 3.36/1.81 => ( ord_less_eq_set_a @ M22 @ M23 ) )
% 3.36/1.81 => ( ord_less_eq_set_a @ ( if_set_a @ B2 @ M1 @ M22 ) @ ( if_set_a @ B2 @ M12 @ M23 ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(fact_263_chain__subset__def,axiom,
% 3.36/1.81 ( chain_subset_a
% 3.36/1.81 = ( ^ [C3: set_set_a] :
% 3.36/1.81 ! [X4: set_a] :
% 3.36/1.81 ( ( member_set_a @ X4 @ C3 )
% 3.36/1.81 => ! [Y6: set_a] :
% 3.36/1.81 ( ( member_set_a @ Y6 @ C3 )
% 3.36/1.81 => ( ( ord_less_eq_set_a @ X4 @ Y6 )
% 3.36/1.81 | ( ord_less_eq_set_a @ Y6 @ X4 ) ) ) ) ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.36/1.81 ! [X3: set_a,Y3: set_a] :
% 3.36/1.81 ( ( if_set_a @ $false @ X3 @ Y3 )
% 3.36/1.81 = Y3 ) ).
% 3.36/1.81
% 3.36/1.81 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 3.36/1.81 ! [X3: set_a,Y3: set_a] :
% 3.36/1.81 ( ( if_set_a @ $true @ X3 @ Y3 )
% 3.36/1.81 = X3 ) ).
% 3.36/1.81
% 3.36/1.81 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.36/1.81 ! [P: $o] :
% 3.36/1.81 ( ( P = $true )
% 3.36/1.81 | ( P = $false ) ) ).
% 3.36/1.81
% 3.36/1.81 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.36/1.81 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.81 ( ( if_Ref1724547303nres_a @ $false @ X3 @ Y3 )
% 3.36/1.81 = Y3 ) ).
% 3.36/1.81
% 3.36/1.81 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 3.36/1.81 ! [X3: refine424419629nres_a,Y3: refine424419629nres_a] :
% 3.36/1.81 ( ( if_Ref1724547303nres_a @ $true @ X3 @ Y3 )
% 3.36/1.81 = X3 ) ).
% 3.36/1.81
% 3.36/1.81 thf(conj_0,conjecture,
% 3.36/1.81 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
% 3.36/1.81 = ( phi @ x ) ) ).
% 3.36/1.81 ------------------------
% 3.36/1.84 % (30814)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_30699 for (2999ds/2Mi)
% 3.36/1.84 % (30810)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/183Mi)
% 3.36/1.84 % (30811)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_30699 for (2999ds/4Mi)
% 3.36/1.84 % (30816)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/18Mi)
% 3.36/1.84 % (30815)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_30699 for (2999ds/275Mi)
% 3.36/1.84 % (30813)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/2Mi)
% 3.36/1.84 % (30812)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_30699 for (2999ds/27Mi)
% 3.36/1.84 % (30813)Instruction limit reached!
% 3.36/1.84 % (30813)------------------------------
% 3.36/1.84 % (30813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (30813)Termination reason: Unknown
% 3.36/1.84 % (30813)Termination phase: shuffling
% 3.36/1.84
% 3.36/1.84 % (30813)Memory used [KB]: 1279
% 3.36/1.84 % (30813)Time elapsed: 0.003 s
% 3.36/1.84 % (30813)Instructions burned: 2 (million)
% 3.36/1.84 % (30813)------------------------------
% 3.36/1.84 % (30813)------------------------------
% 3.36/1.84 % (30814)Instruction limit reached!
% 3.36/1.84 % (30814)------------------------------
% 3.36/1.84 % (30814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (30814)Termination reason: Unknown
% 3.36/1.84 % (30814)Termination phase: shuffling
% 3.36/1.84
% 3.36/1.84 % (30814)Memory used [KB]: 1279
% 3.36/1.84 % (30814)Time elapsed: 0.003 s
% 3.36/1.84 % (30814)Instructions burned: 3 (million)
% 3.36/1.84 % (30814)------------------------------
% 3.36/1.84 % (30814)------------------------------
% 3.36/1.84 % (30811)Instruction limit reached!
% 3.36/1.84 % (30811)------------------------------
% 3.36/1.84 % (30811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (30811)Termination reason: Unknown
% 3.36/1.84 % (30811)Termination phase: shuffling
% 3.36/1.84
% 3.36/1.84 % (30811)Memory used [KB]: 1407
% 3.36/1.84 % (30811)Time elapsed: 0.005 s
% 3.36/1.84 % (30811)Instructions burned: 5 (million)
% 3.36/1.84 % (30811)------------------------------
% 3.36/1.84 % (30811)------------------------------
% 3.36/1.85 % (30816)Instruction limit reached!
% 3.36/1.85 % (30816)------------------------------
% 3.36/1.85 % (30816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (30816)Termination reason: Unknown
% 3.36/1.85 % (30816)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (30816)Memory used [KB]: 1663
% 3.36/1.85 % (30816)Time elapsed: 0.012 s
% 3.36/1.85 % (30816)Instructions burned: 18 (million)
% 3.36/1.85 % (30816)------------------------------
% 3.36/1.85 % (30816)------------------------------
% 3.36/1.86 % (30812)Instruction limit reached!
% 3.36/1.86 % (30812)------------------------------
% 3.36/1.86 % (30812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (30812)Termination reason: Unknown
% 3.36/1.86 % (30812)Termination phase: Property scanning
% 3.36/1.86
% 3.36/1.86 % (30812)Memory used [KB]: 1663
% 3.36/1.86 % (30812)Time elapsed: 0.016 s
% 3.36/1.86 % (30812)Instructions burned: 27 (million)
% 3.36/1.86 % (30812)------------------------------
% 3.36/1.86 % (30812)------------------------------
% 3.36/1.86 % (30817)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/3Mi)
% 3.36/1.86 % (30818)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_30699 for (2999ds/37Mi)
% 3.36/1.86 % (30819)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_30699 for (2999ds/15Mi)
% 3.36/1.86 % (30817)Instruction limit reached!
% 3.36/1.86 % (30817)------------------------------
% 3.36/1.86 % (30817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (30817)Termination reason: Unknown
% 3.36/1.86 % (30817)Termination phase: shuffling
% 3.36/1.86
% 3.36/1.86 % (30817)Memory used [KB]: 1279
% 3.36/1.86 % (30817)Time elapsed: 0.004 s
% 3.36/1.86 % (30817)Instructions burned: 4 (million)
% 3.36/1.86 % (30817)------------------------------
% 3.36/1.86 % (30817)------------------------------
% 3.36/1.87 % (30820)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_30699 for (2999ds/3Mi)
% 3.36/1.87 % (30819)Instruction limit reached!
% 3.36/1.87 % (30819)------------------------------
% 3.36/1.87 % (30819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.87 % (30819)Termination reason: Unknown
% 3.36/1.87 % (30819)Termination phase: shuffling
% 3.36/1.87
% 3.36/1.87 % (30819)Memory used [KB]: 1535
% 3.36/1.87 % (30819)Time elapsed: 0.011 s
% 3.36/1.87 % (30819)Instructions burned: 16 (million)
% 3.36/1.87 % (30819)------------------------------
% 3.36/1.87 % (30819)------------------------------
% 3.36/1.87 % (30820)Instruction limit reached!
% 3.36/1.87 % (30820)------------------------------
% 3.36/1.87 % (30820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.87 % (30820)Termination reason: Unknown
% 3.36/1.87 % (30820)Termination phase: shuffling
% 3.36/1.87
% 3.36/1.87 % (30820)Memory used [KB]: 1279
% 3.36/1.87 % (30820)Time elapsed: 0.004 s
% 3.36/1.87 % (30820)Instructions burned: 4 (million)
% 3.36/1.87 % (30820)------------------------------
% 3.36/1.87 % (30820)------------------------------
% 3.36/1.87 % (30821)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_30699 for (2999ds/1041Mi)
% 3.36/1.88 % (30818)Instruction limit reached!
% 3.36/1.88 % (30818)------------------------------
% 3.36/1.88 % (30818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (30818)Termination reason: Unknown
% 3.36/1.88 % (30818)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (30818)Memory used [KB]: 2046
% 3.36/1.88 % (30818)Time elapsed: 0.021 s
% 3.36/1.88 % (30818)Instructions burned: 38 (million)
% 3.36/1.88 % (30818)------------------------------
% 3.36/1.88 % (30818)------------------------------
% 3.36/1.88 % (30822)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/7Mi)
% 3.36/1.89 % (30822)Instruction limit reached!
% 3.36/1.89 % (30822)------------------------------
% 3.36/1.89 % (30822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.89 % (30822)Termination reason: Unknown
% 3.36/1.89 % (30822)Termination phase: shuffling
% 3.36/1.89
% 3.36/1.89 % (30822)Memory used [KB]: 1407
% 3.36/1.89 % (30822)Time elapsed: 0.006 s
% 3.36/1.89 % (30822)Instructions burned: 7 (million)
% 3.36/1.89 % (30822)------------------------------
% 3.36/1.89 % (30822)------------------------------
% 3.36/1.89 % (30823)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30699 for (2999ds/16Mi)
% 3.36/1.89 % (30824)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_30699 for (2999ds/3Mi)
% 3.36/1.89 % (30824)Instruction limit reached!
% 3.36/1.89 % (30824)------------------------------
% 3.36/1.89 % (30824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.89 % (30824)Termination reason: Unknown
% 3.36/1.89 % (30824)Termination phase: shuffling
% 3.36/1.89
% 3.36/1.89 % (30824)Memory used [KB]: 1279
% 3.36/1.89 % (30824)Time elapsed: 0.003 s
% 3.36/1.89 % (30824)Instructions burned: 3 (million)
% 3.36/1.89 % (30824)------------------------------
% 3.36/1.89 % (30824)------------------------------
% 3.40/1.90 % (30823)Instruction limit reached!
% 3.40/1.90 % (30823)------------------------------
% 3.40/1.90 % (30823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.90 % (30823)Termination reason: Unknown
% 3.40/1.90 % (30823)Termination phase: shuffling
% 3.40/1.90
% 3.40/1.90 % (30823)Memory used [KB]: 1663
% 3.40/1.90 % (30823)Time elapsed: 0.011 s
% 3.40/1.90 % (30823)Instructions burned: 17 (million)
% 3.40/1.90 % (30823)------------------------------
% 3.40/1.90 % (30823)------------------------------
% 3.40/1.90 % (30815)First to succeed.
% 3.40/1.90 % (30825)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_30699 for (2999ds/3Mi)
% 3.40/1.90 % (30825)Instruction limit reached!
% 3.40/1.90 % (30825)------------------------------
% 3.40/1.90 % (30825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.90 % (30825)Termination reason: Unknown
% 3.40/1.90 % (30825)Termination phase: shuffling
% 3.40/1.90
% 3.40/1.90 % (30825)Memory used [KB]: 1279
% 3.40/1.90 % (30825)Time elapsed: 0.004 s
% 3.40/1.90 % (30825)Instructions burned: 4 (million)
% 3.40/1.90 % (30825)------------------------------
% 3.40/1.90 % (30825)------------------------------
% 3.40/1.90 % (30815)Refutation found. Thanks to Tanya!
% 3.40/1.90 % SZS status Theorem for DTF2THF_30699
% 3.40/1.90 % SZS output start Proof for DTF2THF_30699
% 3.40/1.90 thf(type_def_5, type, set_Pr384614482nres_a: $tType).
% 3.40/1.90 thf(type_def_6, type, refine424419629nres_a: $tType).
% 3.40/1.90 thf(type_def_8, type, set_a: $tType).
% 3.40/1.90 thf(type_def_9, type, produc1609974940nres_a: $tType).
% 3.40/1.90 thf(type_def_10, type, a: $tType).
% 3.40/1.90 thf(type_def_11, type, set_set_a: $tType).
% 3.40/1.90 thf(func_def_0, type, set_Pr384614482nres_a: $tType).
% 3.40/1.90 thf(func_def_1, type, produc1609974940nres_a: $tType).
% 3.40/1.90 thf(func_def_2, type, refine424419629nres_a: $tType).
% 3.40/1.90 thf(func_def_3, type, set_set_a: $tType).
% 3.40/1.90 thf(func_def_4, type, set_a: $tType).
% 3.40/1.90 thf(func_def_5, type, a: $tType).
% 3.40/1.90 thf(func_def_6, type, bNF_Ca459084161nres_a: set_Pr384614482nres_a > (refine424419629nres_a > refine424419629nres_a) > $o).
% 3.40/1.90 thf(func_def_7, type, bNF_Ca953716171_set_a: set_Pr384614482nres_a > (refine424419629nres_a > set_a) > $o).
% 3.40/1.90 thf(func_def_8, type, if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a).
% 3.40/1.90 thf(func_def_9, type, if_set_a: $o > set_a > set_a > set_a).
% 3.40/1.90 thf(func_def_10, type, ord_le1480771457nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 3.40/1.90 thf(func_def_11, type, ord_less_set_a: set_a > set_a > $o).
% 3.40/1.90 thf(func_def_12, type, ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o).
% 3.40/1.90 thf(func_def_13, type, ord_less_eq_set_a: set_a > set_a > $o).
% 3.40/1.90 thf(func_def_14, type, order_1714329108nres_a: (refine424419629nres_a > $o) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_15, type, order_Greatest_set_a: (set_a > $o) > set_a).
% 3.40/1.90 thf(func_def_16, type, produc1136923598nres_a: refine424419629nres_a > refine424419629nres_a > produc1609974940nres_a).
% 3.40/1.90 thf(func_def_17, type, refine2063221604TURN_a: a > refine424419629nres_a).
% 3.40/1.90 thf(func_def_18, type, refine1001002027nres_a: refine424419629nres_a > a > $o).
% 3.40/1.90 thf(func_def_19, type, refine1048213316_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o).
% 3.40/1.90 thf(func_def_20, type, refine260105272_rel_a: produc1609974940nres_a > produc1609974940nres_a > $o).
% 3.40/1.90 thf(func_def_21, type, refine1312857699nres_a: refine424419629nres_a > a > $o).
% 3.40/1.90 thf(func_def_22, type, refine412683989fail_a: refine424419629nres_a > $o).
% 3.40/1.90 thf(func_def_23, type, refine464223677AILi_a: refine424419629nres_a).
% 3.40/1.90 thf(func_def_24, type, refine1198353288_RES_a: set_a > refine424419629nres_a).
% 3.40/1.90 thf(func_def_25, type, refine1822134885_RES_a: refine424419629nres_a > set_a).
% 3.40/1.90 thf(func_def_26, type, collect_a: (a > $o) > set_a).
% 3.40/1.90 thf(func_def_27, type, accp_P624619091nres_a: (produc1609974940nres_a > produc1609974940nres_a > $o) > produc1609974940nres_a > $o).
% 3.40/1.90 thf(func_def_28, type, chain_subset_a: set_set_a > $o).
% 3.40/1.90 thf(func_def_29, type, member1468928819nres_a: produc1609974940nres_a > set_Pr384614482nres_a > $o).
% 3.40/1.90 thf(func_def_30, type, member_set_a: set_a > set_set_a > $o).
% 3.40/1.90 thf(func_def_31, type, member_a: a > set_a > $o).
% 3.40/1.90 thf(func_def_32, type, phi: a > $o).
% 3.40/1.90 thf(func_def_33, type, x: a).
% 3.40/1.90 thf(func_def_49, type, sK0: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_50, type, sK1: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_51, type, sK2: refine424419629nres_a > refine424419629nres_a > a).
% 3.40/1.90 thf(func_def_52, type, sK3: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_53, type, sK4: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_54, type, sK5: set_a > set_a > a).
% 3.40/1.90 thf(func_def_55, type, sK6: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_56, type, sK7: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_57, type, sK8: (a > $o) > (a > $o) > a).
% 3.40/1.90 thf(func_def_58, type, sK9: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_59, type, sK10: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_60, type, sK11: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_61, type, sK12: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_62, type, sK13: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_63, type, sK14: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_64, type, sK15: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_65, type, sK16: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_66, type, sK17: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_67, type, sK18: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_68, type, sK19: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_69, type, sK20: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_70, type, sK21: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_71, type, sK22: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_72, type, sK23: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_73, type, sK24: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_74, type, sK25: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_75, type, sK26: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_76, type, sK27: (a > $o) > (a > $o) > a).
% 3.40/1.90 thf(func_def_77, type, sK28: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_78, type, sK29: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_79, type, sK30: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_80, type, sK31: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_81, type, sK32: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_82, type, sK33: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_83, type, sK34: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_84, type, sK35: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_85, type, sK36: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_86, type, sK37: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_87, type, sK38: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_88, type, sK39: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_89, type, sK40: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_90, type, sK41: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_91, type, sK42: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_92, type, sK43: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_93, type, sK44: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_94, type, sK45: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_95, type, sK46: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_96, type, sK47: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_97, type, sK48: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_98, type, sK49: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_99, type, sK50: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_100, type, sK51: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_101, type, sK52: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_102, type, sK53: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_103, type, sK54: refine424419629nres_a > refine424419629nres_a > a).
% 3.40/1.90 thf(func_def_104, type, sK55: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_105, type, sK56: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_106, type, sK57: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_107, type, sK58: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_108, type, sK59: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_109, type, sK60: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_110, type, sK61: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_111, type, sK62: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_112, type, sK63: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_113, type, sK64: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_114, type, sK65: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_115, type, sK66: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_116, type, sK67: (a > $o) > (a > $o) > a).
% 3.40/1.90 thf(func_def_117, type, sK68: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_118, type, sK69: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_119, type, sK70: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_120, type, sK71: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_121, type, sK72: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_122, type, sK73: (set_a > refine424419629nres_a) > set_a).
% 3.40/1.90 thf(func_def_123, type, sK74: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_124, type, sK75: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_125, type, sK76: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_126, type, sK77: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_127, type, sK78: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_128, type, sK79: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_129, type, sK80: set_a > (a > $o) > a).
% 3.40/1.90 thf(func_def_130, type, sK81: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_131, type, sK82: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_132, type, sK83: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_133, type, sK84: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_134, type, sK85: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_135, type, sK86: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_136, type, sK87: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_137, type, sK88: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_138, type, sK89: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_139, type, sK90: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_140, type, sK91: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_141, type, sK92: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_142, type, sK93: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_143, type, sK94: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_144, type, sK95: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_145, type, sK96: (set_a > set_a) > set_a).
% 3.40/1.90 thf(func_def_146, type, sK97: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_147, type, sK98: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_148, type, sK99: refine424419629nres_a > refine424419629nres_a > a).
% 3.40/1.90 thf(func_def_149, type, sK100: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_150, type, sK101: (refine424419629nres_a > set_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_151, type, sK102: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_152, type, sK103: (refine424419629nres_a > refine424419629nres_a) > refine424419629nres_a).
% 3.40/1.90 thf(func_def_154, type, ph105: !>[X0: $tType]:(X0)).
% 3.40/1.90 thf(f1661,plain,(
% 3.40/1.90 $false),
% 3.40/1.90 inference(avatar_sat_refutation,[status(thm)],[f1565,f1576,f1618,f1655,f1660])).
% 3.40/1.90 thf(f1660,plain,(
% 3.40/1.90 ~spl104_1 | ~spl104_4),
% 3.40/1.90 inference(avatar_contradiction_clause,[status(thm)],[f1659])).
% 3.40/1.90 thf(f1659,plain,(
% 3.40/1.90 $false | (~spl104_1 | ~spl104_4)),
% 3.40/1.90 inference(trivial_inequality_removal,[status(thm)],[f1658])).
% 3.40/1.90 thf(f1658,plain,(
% 3.40/1.90 ($true = $false) | (~spl104_1 | ~spl104_4)),
% 3.40/1.90 inference(forward_demodulation,[status(thm)],[f1560,f1575])).
% 3.40/1.90 thf(f1575,plain,(
% 3.40/1.90 ((phi @ x) = $false) | ~spl104_4),
% 3.40/1.90 inference(avatar_component_clause,[status(thm)],[f1573])).
% 3.40/1.90 thf(f1573,definition,(
% 3.40/1.90 spl104_4 <=> ((phi @ x) = $false)),
% 3.40/1.90 introduced(definition,[new_symbols(naming,[spl104_4])],[avatar_definition])).
% 3.40/1.90 thf(f1560,plain,(
% 3.40/1.90 ((phi @ x) = $true) | ~spl104_1),
% 3.40/1.90 inference(avatar_component_clause,[status(thm)],[f1558])).
% 3.40/1.90 thf(f1558,definition,(
% 3.40/1.90 spl104_1 <=> ((phi @ x) = $true)),
% 3.40/1.90 introduced(definition,[new_symbols(naming,[spl104_1])],[avatar_definition])).
% 3.40/1.90 thf(f1655,plain,(
% 3.40/1.90 ~spl104_2 | ~spl104_4),
% 3.40/1.90 inference(avatar_contradiction_clause,[status(thm)],[f1654])).
% 3.40/1.90 thf(f1654,plain,(
% 3.40/1.90 $false | (~spl104_2 | ~spl104_4)),
% 3.40/1.90 inference(trivial_inequality_removal,[status(thm)],[f1653])).
% 3.40/1.90 thf(f1653,plain,(
% 3.40/1.90 ($true = $false) | (~spl104_2 | ~spl104_4)),
% 3.40/1.90 inference(forward_demodulation,[status(thm)],[f1642,f1575])).
% 3.40/1.90 thf(f1642,plain,(
% 3.40/1.90 ((phi @ x) = $true) | ~spl104_2),
% 3.40/1.90 inference(superposition,[status(thm)],[f1636,f1395])).
% 3.40/1.90 thf(f1395,plain,(
% 3.40/1.90 ( ! [X0 : a > $o,X1 : a] : (((member_a @ X1 @ (collect_a @ X0)) = (X0 @ X1))) )),
% 3.40/1.90 inference(cnf_transformation,[status(thm)],[f782])).
% 3.40/1.90 thf(f782,plain,(
% 3.40/1.90 ! [X0 : a > $o,X1 : a] : ((member_a @ X1 @ (collect_a @ X0)) = (X0 @ X1))),
% 3.40/1.90 inference(rectify,[status(thm)],[f42])).
% 3.40/1.90 thf(f42,axiom,(
% 3.40/1.90 ! [X8 : a > $o,X32 : a] : ((member_a @ X32 @ (collect_a @ X8)) = (X8 @ X32))),
% 3.40/1.90 file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_41_mem__Collect__eq)).
% 3.40/1.90 thf(f1636,plain,(
% 3.40/1.90 ($true = (member_a @ x @ (collect_a @ phi))) | ~spl104_2),
% 3.40/1.90 inference(trivial_inequality_removal,[status(thm)],[f1635])).
% 3.40/1.90 thf(f1635,plain,(
% 3.40/1.90 ($true = $false) | ($true = (member_a @ x @ (collect_a @ phi))) | ~spl104_2),
% 3.40/1.90 inference(forward_demodulation,[status(thm)],[f1625,f1372])).
% 3.40/1.90 thf(f1372,plain,(
% 3.40/1.90 ( ! [X0 : set_a] : (((refine412683989fail_a @ (refine1198353288_RES_a @ X0)) = $true)) )),
% 3.40/1.90 inference(cnf_transformation,[status(thm)],[f486])).
% 3.40/1.90 thf(f486,plain,(
% 3.40/1.90 ! [X0 : set_a] : ((refine412683989fail_a @ (refine1198353288_RES_a @ X0)) = $true)),
% 3.40/1.90 inference(fool_elimination,[status(thm)],[f485])).
% 3.40/1.90 thf(f485,plain,(
% 3.40/1.90 ! [X0 : set_a] : (refine412683989fail_a @ (refine1198353288_RES_a @ X0))),
% 3.40/1.90 inference(rectify,[status(thm)],[f6])).
% 3.40/1.90 thf(f6,axiom,(
% 3.40/1.90 ! [X0 : set_a] : (refine412683989fail_a @ (refine1198353288_RES_a @ X0))),
% 3.40/1.90 file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_5_nofail__simps_I2_J)).
% 3.40/1.90 thf(f1625,plain,(
% 3.40/1.90 ($false = (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))) | ($true = (member_a @ x @ (collect_a @ phi))) | ~spl104_2),
% 3.40/1.90 inference(binary_proxy_clausification,[status(thm)],[f1624])).
% 3.40/1.90 thf(f1624,plain,(
% 3.40/1.90 ((member_a @ x @ (collect_a @ phi)) = (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))) | ~spl104_2),
% 3.40/1.90 inference(boolean_simplification,[status(thm)],[f1623])).
% 3.40/1.90 thf(f1623,plain,(
% 3.40/1.90 (($true & (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))) = (member_a @ x @ (collect_a @ phi))) | ~spl104_2),
% 3.40/1.90 inference(superposition,[status(thm)],[f1546,f1564])).
% 3.40/1.90 thf(f1564,plain,(
% 3.40/1.90 ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $true) | ~spl104_2),
% 3.40/1.90 inference(avatar_component_clause,[status(thm)],[f1562])).
% 3.40/1.90 thf(f1562,definition,(
% 3.40/1.90 spl104_2 <=> ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $true)),
% 3.40/1.90 introduced(definition,[new_symbols(naming,[spl104_2])],[avatar_definition])).
% 3.40/1.90 thf(f1546,plain,(
% 3.40/1.90 ( ! [X0 : set_a,X1 : a] : ((((refine1001002027nres_a @ (refine1198353288_RES_a @ X0) @ X1) & (refine412683989fail_a @ (refine1198353288_RES_a @ X0))) = (member_a @ X1 @ X0))) )),
% 3.40/1.90 inference(beta_eta_normalization,[status(thm)],[f1471])).
% 3.40/1.90 thf(f1471,plain,(
% 3.40/1.90 ( ! [X0 : set_a,X1 : a] : ((((^[Y0 : refine424419629nres_a]: ((^[Y1 : a]: ((refine1001002027nres_a @ Y0 @ Y1) & (refine412683989fail_a @ Y0))))) @ (refine1198353288_RES_a @ X0) @ X1) = (member_a @ X1 @ X0))) )),
% 3.40/1.90 inference(definition_unfolding,[status(thm)],[f1209,f1309])).
% 3.40/1.90 thf(f1309,plain,(
% 3.40/1.90 (refine1312857699nres_a = (^[Y0 : refine424419629nres_a]: ((^[Y1 : a]: ((refine1001002027nres_a @ Y0 @ Y1) & (refine412683989fail_a @ Y0))))))),
% 3.40/1.90 inference(cnf_transformation,[status(thm)],[f404])).
% 3.40/1.90 thf(f404,plain,(
% 3.40/1.90 (refine1312857699nres_a = (^[Y0 : refine424419629nres_a]: ((^[Y1 : a]: ((refine1001002027nres_a @ Y0 @ Y1) & (refine412683989fail_a @ Y0))))))),
% 3.40/1.90 inference(fool_elimination,[status(thm)],[f403])).
% 3.40/1.90 thf(f403,plain,(
% 3.40/1.90 ((^[X0 : refine424419629nres_a, X1 : a] : ((refine412683989fail_a @ X0) & (refine1001002027nres_a @ X0 @ X1))) = refine1312857699nres_a)),
% 3.40/1.90 inference(rectify,[status(thm)],[f18])).
% 3.40/1.90 thf(f18,axiom,(
% 3.40/1.90 ((^[X6 : refine424419629nres_a, X5 : a] : ((refine412683989fail_a @ X6) & (refine1001002027nres_a @ X6 @ X5))) = refine1312857699nres_a)),
% 3.40/1.90 file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_17_nf__inres__def)).
% 3.40/1.90 thf(f1209,plain,(
% 3.40/1.90 ( ! [X0 : set_a,X1 : a] : (((member_a @ X1 @ X0) = (refine1312857699nres_a @ (refine1198353288_RES_a @ X0) @ X1))) )),
% 3.40/1.90 inference(cnf_transformation,[status(thm)],[f778])).
% 3.40/1.90 thf(f778,plain,(
% 3.40/1.90 ! [X0 : set_a,X1 : a] : ((member_a @ X1 @ X0) = (refine1312857699nres_a @ (refine1198353288_RES_a @ X0) @ X1))),
% 3.40/1.90 inference(rectify,[status(thm)],[f3])).
% 3.40/1.90 thf(f3,axiom,(
% 3.40/1.90 ! [X0 : set_a,X4 : a] : ((refine1312857699nres_a @ (refine1198353288_RES_a @ X0) @ X4) = (member_a @ X4 @ X0))),
% 3.40/1.90 file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',fact_2_nf__inres__RES)).
% 3.40/1.90 thf(f1618,plain,(
% 3.40/1.90 spl104_4 | ~spl104_3),
% 3.40/1.90 inference(avatar_split_clause,[status(thm)],[f1599,f1569,f1573])).
% 3.40/1.90 thf(f1569,definition,(
% 3.40/1.90 spl104_3 <=> ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $false)),
% 3.40/1.90 introduced(definition,[new_symbols(naming,[spl104_3])],[avatar_definition])).
% 3.40/1.90 thf(f1599,plain,(
% 3.40/1.90 ((phi @ x) = $false) | ~spl104_3),
% 3.40/1.90 inference(superposition,[status(thm)],[f1395,f1590])).
% 3.40/1.90 thf(f1590,plain,(
% 3.40/1.90 ((member_a @ x @ (collect_a @ phi)) = $false) | ~spl104_3),
% 3.40/1.90 inference(boolean_simplification,[status(thm)],[f1581])).
% 3.40/1.90 thf(f1581,plain,(
% 3.40/1.90 ((member_a @ x @ (collect_a @ phi)) = ($false & (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi))))) | ~spl104_3),
% 3.40/1.90 inference(superposition,[status(thm)],[f1546,f1571])).
% 3.40/1.90 thf(f1571,plain,(
% 3.40/1.90 ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $false) | ~spl104_3),
% 3.40/1.90 inference(avatar_component_clause,[status(thm)],[f1569])).
% 3.40/1.90 thf(f1576,plain,(
% 3.40/1.90 spl104_3 | spl104_4),
% 3.40/1.90 inference(avatar_split_clause,[status(thm)],[f1567,f1573,f1569])).
% 3.40/1.90 thf(f1567,plain,(
% 3.40/1.90 ((phi @ x) = $false) | ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $false)),
% 3.40/1.90 inference(trivial_inequality_removal,[status(thm)],[f1566])).
% 3.40/1.90 thf(f1566,plain,(
% 3.40/1.90 ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $false) | ((phi @ x) = $false) | ($true = $false)),
% 3.40/1.90 inference(forward_demodulation,[status(thm)],[f1554,f1372])).
% 3.40/1.90 thf(f1554,plain,(
% 3.40/1.90 ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $false) | ($false = (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))) | ((phi @ x) = $false)),
% 3.40/1.90 inference(binary_proxy_clausification,[status(thm)],[f1553])).
% 3.40/1.90 thf(f1553,plain,(
% 3.40/1.90 ((phi @ x) = $false) | ($false = ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) & (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))))),
% 3.40/1.90 inference(binary_proxy_clausification,[status(thm)],[f1551])).
% 3.40/1.90 thf(f1551,plain,(
% 3.40/1.90 ((phi @ x) != ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) & (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))))),
% 3.40/1.90 inference(beta_eta_normalization,[status(thm)],[f1472])).
% 3.40/1.90 thf(f1472,plain,(
% 3.40/1.90 ((phi @ x) != ((^[Y0 : refine424419629nres_a]: ((^[Y1 : a]: ((refine1001002027nres_a @ Y0 @ Y1) & (refine412683989fail_a @ Y0))))) @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x))),
% 3.40/1.90 inference(definition_unfolding,[status(thm)],[f1297,f1309])).
% 3.40/1.90 thf(f1297,plain,(
% 3.40/1.90 ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) != (phi @ x))),
% 3.40/1.90 inference(cnf_transformation,[status(thm)],[f777])).
% 3.40/1.90 thf(f777,plain,(
% 3.40/1.90 ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) != (phi @ x))),
% 3.40/1.90 inference(flattening,[status(thm)],[f271])).
% 3.40/1.90 thf(f271,negated_conjecture,(
% 3.40/1.90 ~((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = (phi @ x))),
% 3.40/1.90 inference(negated_conjecture,[status(cth)],[f270])).
% 3.40/1.90 thf(f270,conjecture,(
% 3.40/1.90 ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = (phi @ x))),
% 3.40/1.90 file('/export/starexec/sandbox/tmp/tmp.2YbwGdrYzw/DTF2THF_30699.p',conj_0)).
% 3.40/1.90 thf(f1565,plain,(
% 3.40/1.90 spl104_1 | spl104_2),
% 3.40/1.90 inference(avatar_split_clause,[status(thm)],[f1556,f1562,f1558])).
% 3.40/1.90 thf(f1556,plain,(
% 3.40/1.90 ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) = $true) | ((phi @ x) = $true)),
% 3.40/1.90 inference(binary_proxy_clausification,[status(thm)],[f1552])).
% 3.40/1.90 thf(f1552,plain,(
% 3.40/1.90 ((phi @ x) = $true) | ($true = ((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ phi)) @ x) & (refine412683989fail_a @ (refine1198353288_RES_a @ (collect_a @ phi)))))),
% 3.40/1.90 inference(binary_proxy_clausification,[status(thm)],[f1551])).
% 3.40/1.90 % SZS output end Proof for DTF2THF_30699
% 3.40/1.90 % (30815)------------------------------
% 3.40/1.90 % (30815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.40/1.90 % (30815)Termination reason: Refutation
% 3.40/1.90
% 3.40/1.90 % (30815)Memory used [KB]: 6908
% 3.40/1.90 % (30815)Time elapsed: 0.061 s
% 3.40/1.90 % (30815)Instructions burned: 105 (million)
% 3.40/1.90 % (30815)------------------------------
% 3.40/1.90 % (30815)------------------------------
% 3.40/1.90 % (30809)Success in time 0.089 s
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