%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV471^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 09:41:19 AM UTC 2026
% Result : Theorem 16.53s 3.66s
% Output : Refutation 16.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 46
% Syntax : Number of formulae : 720 ( 2 unt; 0 typ; 44 def)
% Number of atoms : 9070 (2778 equ; 0 cnn)
% Maximal formula atoms : 7 ( 12 avg)
% Number of connectives : 13591 ( 858 ~;2209 |; 475 &;9364 @)
% ( 44 <=>; 358 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 340 ( 340 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 62 usr; 51 con; 0-5 aty)
% ( 213 !!; 70 ??; 0 @@+; 0 @@-)
% Number of variables : 950 ( 322 ^; 612 !; 16 ?; 950 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
sK2: sK1 > sK0 ).
thf(func_def_17,type,
sK3: sK1 > $o ).
thf(func_def_18,type,
sK4: sK0 > $o ).
thf(func_def_20,type,
sK6: sK0 ).
thf(func_def_21,type,
sK7: ( sK0 > sK1 ) > sK1 ).
thf(func_def_22,type,
sK8: ( sK0 > sK1 ) > sK0 ).
thf(func_def_23,type,
sK9: sK1 ).
thf(func_def_24,type,
sK10: ( sK0 > sK1 ) > sK0 ).
thf(func_def_25,type,
sK11: sK1 ).
thf(func_def_26,type,
sK12: sK0 > sK1 ).
thf(func_def_27,type,
sK13: sK0 > sK1 ).
thf(func_def_28,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X0 > X1 ) ).
thf(func_def_29,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > $o ) > X1 ) ).
thf(func_def_30,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > $o ) > X1 ) ).
thf(func_def_31,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > ( X1 > $o ) > X1 ) ).
thf(func_def_33,type,
ph18:
!>[X0: $tType] : X0 ).
thf(f2587,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f67,f75,f87,f89,f102,f103,f111,f112,f124,f133,f135,f137,f149,f151,f153,f157,f175,f181,f187,f192,f204,f207,f210,f212,f227,f238,f243,f248,f265,f266,f269,f273,f296,f300,f302,f305,f309,f315,f316,f317,f327,f333,f334,f335,f341,f344,f346,f349,f365,f368,f370,f372,f378,f383,f385,f386,f397,f399,f406,f408,f411,f413,f418,f420,f445,f453,f468,f469,f483,f484,f505,f600,f724,f739,f900,f1055,f1083,f1095,f1113,f1194,f1197,f1201,f1236,f1237,f1282,f1366,f1371,f1483,f1561,f1568,f1569,f1575,f1581,f1593,f1706,f1790,f1808,f1820,f1826,f1868,f1896,f1972,f1990,f2098,f2214,f2331,f2344,f2400,f2430,f2439,f2534,f2547,f2572,f2575,f2583]) ).
thf(f2583,plain,
( ~ spl5_7
| ~ spl5_24 ),
inference(avatar_contradiction_clause,[status(thm)],[f2582]) ).
thf(f2582,plain,
( $false
| ~ spl5_7
| ~ spl5_24 ),
inference(trivial_inequality_removal,[status(thm)],[f2581]) ).
thf(f2581,plain,
( ( $false = $true )
| ~ spl5_7
| ~ spl5_24 ),
inference(backward_demodulation,[status(thm)],[f110,f640]) ).
thf(f640,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
| ~ spl5_24 ),
inference(avatar_component_clause,[status(thm)],[f638]) ).
thf(f638,definition,
( spl5_24
<=> ( $false
= ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_24])],[avatar_definition]) ).
thf(f110,plain,
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ~ spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl5_7
<=> ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f2575,plain,
( spl5_24
| spl5_23
| ~ spl5_6
| ~ spl5_20 ),
inference(avatar_split_clause,[status(thm)],[f2158,f503,f99,f635,f638]) ).
thf(f635,definition,
( spl5_23
<=> ! [X0: sK1] :
( ( ( sK2 @ X0 )
!= ( sK2 @ sK9 ) )
| ( sK11 = X0 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_23])],[avatar_definition]) ).
thf(f99,definition,
( spl5_6
<=> ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f503,definition,
( spl5_20
<=> ! [X2: sK1,X1: sK1] :
( ( ( sK2 @ X2 )
!= ( sK2 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( X1 = X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_20])],[avatar_definition]) ).
thf(f2158,plain,
( ! [X0: sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
| ( ( sK2 @ X0 )
!= ( sK2 @ sK9 ) )
| ( sK11 = X0 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) ) )
| ~ spl5_6
| ~ spl5_20 ),
inference(superposition,[status(thm)],[f504,f101]) ).
thf(f101,plain,
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f504,plain,
( ! [X2: sK1,X1: sK1] :
( ( ( sK2 @ X2 )
!= ( sK2 @ X1 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
| ( X1 = X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ~ spl5_20 ),
inference(avatar_component_clause,[status(thm)],[f503]) ).
thf(f2572,plain,
( spl5_2
| ~ spl5_5
| ~ spl5_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f2571]) ).
thf(f2571,plain,
( $false
| spl5_2
| ~ spl5_5
| ~ spl5_23 ),
inference(trivial_inequality_removal,[status(thm)],[f2570]) ).
thf(f2570,plain,
( ( $false = $true )
| spl5_2
| ~ spl5_5
| ~ spl5_23 ),
inference(forward_demodulation,[status(thm)],[f86,f2129]) ).
thf(f2129,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| spl5_2
| ~ spl5_23 ),
inference(subsumption_resolution,[status(thm)],[f2127,f63]) ).
thf(f63,plain,
( ( sK9 != sK11 )
| spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl5_2
<=> ( sK9 = sK11 ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f2127,plain,
( ( sK9 = sK11 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ~ spl5_23 ),
inference(equality_resolution,[status(thm)],[f636]) ).
thf(f636,plain,
( ! [X0: sK1] :
( ( ( sK2 @ X0 )
!= ( sK2 @ sK9 ) )
| ( sK11 = X0 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) ) )
| ~ spl5_23 ),
inference(avatar_component_clause,[status(thm)],[f635]) ).
thf(f86,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl5_5
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f2547,plain,
( spl5_62
| ~ spl5_4
| spl5_70
| ~ spl5_113 ),
inference(avatar_split_clause,[status(thm)],[f2546,f2328,f1363,f73,f1270]) ).
thf(f1270,definition,
( spl5_62
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_62])],[avatar_definition]) ).
thf(f73,definition,
( spl5_4
<=> ! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f1363,definition,
( spl5_70
<=> ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl5_70])],[avatar_definition]) ).
thf(f2328,definition,
( spl5_113
<=> ( ( sK7 @ sK13 )
= ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_113])],[avatar_definition]) ).
thf(f2546,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_4
| spl5_70
| ~ spl5_113 ),
inference(subsumption_resolution,[status(thm)],[f2364,f1364]) ).
thf(f1364,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
!= $false )
| spl5_70 ),
inference(avatar_component_clause,[status(thm)],[f1363]) ).
thf(f2364,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_4
| ~ spl5_113 ),
inference(trivial_inequality_removal,[status(thm)],[f2357]) ).
thf(f2357,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ( ( sK7 @ sK13 )
!= ( sK7 @ sK13 ) )
| ~ spl5_4
| ~ spl5_113 ),
inference(superposition,[status(thm)],[f74,f2330]) ).
thf(f2330,plain,
( ( ( sK7 @ sK13 )
= ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) )
| ~ spl5_113 ),
inference(avatar_component_clause,[status(thm)],[f2328]) ).
thf(f74,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f2534,plain,
( ~ spl5_17
| spl5_64
| ~ spl5_70 ),
inference(avatar_contradiction_clause,[status(thm)],[f2533]) ).
thf(f2533,plain,
( $false
| ~ spl5_17
| spl5_64
| ~ spl5_70 ),
inference(subsumption_resolution,[status(thm)],[f2529,f1279]) ).
thf(f1279,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
!= $false )
| spl5_64 ),
inference(avatar_component_clause,[status(thm)],[f1278]) ).
thf(f1278,definition,
( spl5_64
<=> ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl5_64])],[avatar_definition]) ).
thf(f2529,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false )
| ~ spl5_17
| ~ spl5_70 ),
inference(trivial_inequality_removal,[status(thm)],[f2526]) ).
thf(f2526,plain,
( ( $false = $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false )
| ~ spl5_17
| ~ spl5_70 ),
inference(superposition,[status(thm)],[f1365,f452]) ).
thf(f452,plain,
( ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) )
| ~ spl5_17 ),
inference(avatar_component_clause,[status(thm)],[f451]) ).
thf(f451,definition,
( spl5_17
<=> ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl5_17])],[avatar_definition]) ).
thf(f1365,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ~ spl5_70 ),
inference(avatar_component_clause,[status(thm)],[f1363]) ).
thf(f2439,plain,
( spl5_70
| ~ spl5_12
| ~ spl5_16
| ~ spl5_62
| ~ spl5_113 ),
inference(avatar_split_clause,[status(thm)],[f2436,f2328,f1270,f443,f225,f1363]) ).
thf(f225,definition,
( spl5_12
<=> ! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_12])],[avatar_definition]) ).
thf(f443,definition,
( spl5_16
<=> ! [X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_16])],[avatar_definition]) ).
thf(f2436,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ~ spl5_12
| ~ spl5_16
| ~ spl5_62
| ~ spl5_113 ),
inference(subsumption_resolution,[status(thm)],[f2362,f2425]) ).
thf(f2425,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ~ spl5_16
| ~ spl5_62 ),
inference(trivial_inequality_removal,[status(thm)],[f2424]) ).
thf(f2424,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ( $false = $true )
| ~ spl5_16
| ~ spl5_62 ),
inference(superposition,[status(thm)],[f444,f1272]) ).
thf(f1272,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_62 ),
inference(avatar_component_clause,[status(thm)],[f1270]) ).
thf(f444,plain,
( ! [X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 ) )
| ~ spl5_16 ),
inference(avatar_component_clause,[status(thm)],[f443]) ).
thf(f2362,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
!= ( sK10 @ sK13 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ~ spl5_12
| ~ spl5_113 ),
inference(trivial_inequality_removal,[status(thm)],[f2359]) ).
thf(f2359,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ( ( sK7 @ sK13 )
!= ( sK7 @ sK13 ) )
| ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
!= ( sK10 @ sK13 ) )
| ~ spl5_12
| ~ spl5_113 ),
inference(superposition,[status(thm)],[f226,f2330]) ).
thf(f226,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[status(thm)],[f225]) ).
thf(f2430,plain,
( ~ spl5_13
| ~ spl5_16
| ~ spl5_62
| spl5_71
| ~ spl5_113 ),
inference(avatar_contradiction_clause,[status(thm)],[f2429]) ).
thf(f2429,plain,
( $false
| ~ spl5_13
| ~ spl5_16
| ~ spl5_62
| spl5_71
| ~ spl5_113 ),
inference(subsumption_resolution,[status(thm)],[f2425,f2401]) ).
thf(f2401,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
!= ( sK10 @ sK13 ) )
| ~ spl5_13
| spl5_71
| ~ spl5_113 ),
inference(subsumption_resolution,[status(thm)],[f2361,f1369]) ).
thf(f1369,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
!= $true )
| spl5_71 ),
inference(avatar_component_clause,[status(thm)],[f1368]) ).
thf(f1368,definition,
( spl5_71
<=> ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_71])],[avatar_definition]) ).
thf(f2361,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
!= ( sK10 @ sK13 ) )
| ~ spl5_13
| ~ spl5_113 ),
inference(trivial_inequality_removal,[status(thm)],[f2360]) ).
thf(f2360,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
!= ( sK10 @ sK13 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ( ( sK7 @ sK13 )
!= ( sK7 @ sK13 ) )
| ~ spl5_13
| ~ spl5_113 ),
inference(superposition,[status(thm)],[f264,f2330]) ).
thf(f264,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) )
| ~ spl5_13 ),
inference(avatar_component_clause,[status(thm)],[f263]) ).
thf(f263,definition,
( spl5_13
<=> ! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_13])],[avatar_definition]) ).
thf(f2400,plain,
( ~ spl5_8
| spl5_71
| ~ spl5_73
| ~ spl5_113 ),
inference(avatar_contradiction_clause,[status(thm)],[f2399]) ).
thf(f2399,plain,
( $false
| ~ spl5_8
| spl5_71
| ~ spl5_73
| ~ spl5_113 ),
inference(trivial_inequality_removal,[status(thm)],[f2398]) ).
thf(f2398,plain,
( ( $false = $true )
| ~ spl5_8
| spl5_71
| ~ spl5_73
| ~ spl5_113 ),
inference(forward_demodulation,[status(thm)],[f2397,f1394]) ).
thf(f1394,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_73 ),
inference(avatar_component_clause,[status(thm)],[f1392]) ).
thf(f1392,definition,
( spl5_73
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_73])],[avatar_definition]) ).
thf(f2397,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_8
| spl5_71
| ~ spl5_113 ),
inference(subsumption_resolution,[status(thm)],[f2365,f1369]) ).
thf(f2365,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ~ spl5_8
| ~ spl5_113 ),
inference(trivial_inequality_removal,[status(thm)],[f2358]) ).
thf(f2358,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ( ( sK7 @ sK13 )
!= ( sK7 @ sK13 ) )
| ~ spl5_8
| ~ spl5_113 ),
inference(superposition,[status(thm)],[f123,f2330]) ).
thf(f123,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl5_8
<=> ! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f2344,plain,
( ~ spl5_63
| ~ spl5_112 ),
inference(avatar_contradiction_clause,[status(thm)],[f2343]) ).
thf(f2343,plain,
( $false
| ~ spl5_63
| ~ spl5_112 ),
inference(trivial_inequality_removal,[status(thm)],[f2342]) ).
thf(f2342,plain,
( ( $false = $true )
| ~ spl5_63
| ~ spl5_112 ),
inference(backward_demodulation,[status(thm)],[f1276,f2326]) ).
thf(f2326,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $false )
| ~ spl5_112 ),
inference(avatar_component_clause,[status(thm)],[f2324]) ).
thf(f2324,definition,
( spl5_112
<=> ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl5_112])],[avatar_definition]) ).
thf(f1276,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ~ spl5_63 ),
inference(avatar_component_clause,[status(thm)],[f1274]) ).
thf(f1274,definition,
( spl5_63
<=> ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_63])],[avatar_definition]) ).
thf(f2331,plain,
( spl5_112
| spl5_113
| ~ spl5_100 ),
inference(avatar_split_clause,[status(thm)],[f2322,f2084,f2328,f2324]) ).
thf(f2084,definition,
( spl5_100
<=> ! [X0: sK1] :
( ( ( sK2 @ X0 )
!= ( sK2 @ ( sK7 @ sK13 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) )
| ( ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) )
= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_100])],[avatar_definition]) ).
thf(f2322,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $false )
| ( ( sK7 @ sK13 )
= ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) )
| ~ spl5_100 ),
inference(equality_resolution,[status(thm)],[f2085]) ).
thf(f2085,plain,
( ! [X0: sK1] :
( ( ( sK2 @ X0 )
!= ( sK2 @ ( sK7 @ sK13 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) )
| ( ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) )
= X0 ) )
| ~ spl5_100 ),
inference(avatar_component_clause,[status(thm)],[f2084]) ).
thf(f2214,plain,
( ~ spl5_17
| ~ spl5_63
| ~ spl5_98 ),
inference(avatar_contradiction_clause,[status(thm)],[f2213]) ).
thf(f2213,plain,
( $false
| ~ spl5_17
| ~ spl5_63
| ~ spl5_98 ),
inference(trivial_inequality_removal,[status(thm)],[f2212]) ).
thf(f2212,plain,
( ( $false = $true )
| ~ spl5_17
| ~ spl5_63
| ~ spl5_98 ),
inference(backward_demodulation,[status(thm)],[f1738,f2211]) ).
thf(f2211,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK7 @ sK13 ) ) @ sK4 ) )
| ~ spl5_17
| ~ spl5_98 ),
inference(trivial_inequality_removal,[status(thm)],[f2208]) ).
thf(f2208,plain,
( ( $false = $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK7 @ sK13 ) ) @ sK4 ) )
| ~ spl5_17
| ~ spl5_98 ),
inference(superposition,[status(thm)],[f452,f2077]) ).
thf(f2077,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) @ sK3 ) )
| ~ spl5_98 ),
inference(avatar_component_clause,[status(thm)],[f2075]) ).
thf(f2075,definition,
( spl5_98
<=> ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_98])],[avatar_definition]) ).
thf(f1738,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK7 @ sK13 ) ) @ sK4 )
= $true )
| ~ spl5_63 ),
inference(trivial_inequality_removal,[status(thm)],[f1736]) ).
thf(f1736,plain,
( ( $true != $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK7 @ sK13 ) ) @ sK4 )
= $true )
| ~ spl5_63 ),
inference(superposition,[status(thm)],[f21,f1276]) ).
thf(f21,plain,
! [X5: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ X5 ) @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X5: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ X5 ) @ sK4 ) ) )
& ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
!= ( ?? @ ( sK0 > sK1 )
@ ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 )
= $true ) )
& ( ( ( !! @ X1
@ ^ [Y0: X1] :
( !! @ X1
@ ^ [Y1: X1] :
( ( ( ( X2 @ Y1 )
= ( X2 @ Y0 ) )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X4 )
=> ( ?? @ X1
@ ^ [Y1: X1] :
( ( ( X2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 ) ) ) ) ) )
!= ( ?? @ ( X0 > X1 )
@ ^ [Y0: X0 > X1] :
( ( !! @ X1
@ ^ [Y1: X1] :
( ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
=> ( ( Y0 @ ( X2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( Y0 @ Y1 ) @ X3 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( ( X2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) )
=> ( ! [X5: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X5 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ X5 ) @ sK4 ) ) )
& ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
!= ( ?? @ ( sK0 > sK1 )
@ ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 )
= $true ) )
& ( ( ( !! @ X1
@ ^ [Y0: X1] :
( !! @ X1
@ ^ [Y1: X1] :
( ( ( ( X2 @ Y1 )
= ( X2 @ Y0 ) )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X4 )
=> ( ?? @ X1
@ ^ [Y1: X1] :
( ( ( X2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 ) ) ) ) ) )
!= ( ?? @ ( X0 > X1 )
@ ^ [Y0: X0 > X1] :
( ( !! @ X1
@ ^ [Y1: X1] :
( ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
=> ( ( Y0 @ ( X2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( Y0 @ Y1 ) @ X3 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( ( X2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
= $true )
=> ( ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 )
= $true ) )
=> ( ( ( !! @ X1
@ ^ [Y0: X1] :
( !! @ X1
@ ^ [Y1: X1] :
( ( ( ( X2 @ Y1 )
= ( X2 @ Y0 ) )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X4 )
=> ( ?? @ X1
@ ^ [Y1: X1] :
( ( ( X2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ X1 @ Y1 @ X3 ) ) ) ) ) )
= ( ?? @ ( X0 > X1 )
@ ^ [Y0: X0 > X1] :
( ( !! @ X1
@ ^ [Y1: X1] :
( ( 'const/sets/IN' @ X1 @ Y1 @ X3 )
=> ( ( Y0 @ ( X2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( Y0 @ Y1 ) @ X3 ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X4 )
=> ( ( X2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
=> ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 ) )
=> ( ? [X6: X0 > X1] :
( ( ! [X7: X0] :
( ( 'const/sets/IN' @ X0 @ X7 @ X4 )
=> ( ( X2 @ ( X6 @ X7 ) )
= X7 ) )
& ! [X8: X0] :
( ( 'const/sets/IN' @ X0 @ X8 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( X6 @ X8 ) @ X3 ) )
& ! [X9: X1] :
( ( 'const/sets/IN' @ X1 @ X9 @ X3 )
=> ( ( X6 @ ( X2 @ X9 ) )
= X9 ) ) )
= ( ! [X10: X0] :
( ( 'const/sets/IN' @ X0 @ X10 @ X4 )
=> ? [X11: X1] :
( ( 'const/sets/IN' @ X1 @ X11 @ X3 )
& ( ( X2 @ X11 )
= X10 ) ) ) ) )
& ! [X12: X1,X13: X1] :
( ( ( 'const/sets/IN' @ X1 @ X13 @ X3 )
& ( 'const/sets/IN' @ X1 @ X12 @ X3 )
& ( ( X2 @ X12 )
= ( X2 @ X13 ) ) )
=> ( X12 = X13 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
=> ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 ) )
=> ( ? [X5: X0 > X1] :
( ( ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
=> ( ( X2 @ ( X5 @ X6 ) )
= X6 ) )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( X5 @ X6 ) @ X3 ) )
& ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
=> ( ( X5 @ ( X2 @ X6 ) )
= X6 ) ) )
= ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
=> ? [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
& ( ( X2 @ X6 )
= X5 ) ) ) ) )
& ! [X5: X1,X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
& ( 'const/sets/IN' @ X1 @ X5 @ X3 )
& ( ( X2 @ X5 )
= ( X2 @ X6 ) ) )
=> ( X5 = X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > $o,X4: X0 > $o] :
( ! [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
=> ( 'const/sets/IN' @ X0 @ ( X2 @ X5 ) @ X4 ) )
=> ( ? [X5: X0 > X1] :
( ( ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
=> ( ( X2 @ ( X5 @ X6 ) )
= X6 ) )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X4 )
=> ( 'const/sets/IN' @ X1 @ ( X5 @ X6 ) @ X3 ) )
& ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
=> ( ( X5 @ ( X2 @ X6 ) )
= X6 ) ) )
= ( ! [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
=> ? [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
& ( ( X2 @ X6 )
= X5 ) ) ) ) )
& ! [X5: X1,X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
& ( 'const/sets/IN' @ X1 @ X5 @ X3 )
& ( ( X2 @ X5 )
= ( X2 @ X6 ) ) )
=> ( X5 = X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OORBxcTjsE/DTF2THF_3780.p','thm/sets/BIJECTIVE_ON_LEFT_RIGHT_INVERSE_') ).
thf(f2098,plain,
( spl5_98
| spl5_100
| ~ spl5_16
| ~ spl5_20
| ~ spl5_63 ),
inference(avatar_split_clause,[status(thm)],[f2071,f1274,f503,f443,f2084,f2075]) ).
thf(f2071,plain,
( ! [X0: sK1] :
( ( ( sK2 @ X0 )
!= ( sK2 @ ( sK7 @ sK13 ) ) )
| ( ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) )
= X0 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) @ sK3 ) ) )
| ~ spl5_16
| ~ spl5_20
| ~ spl5_63 ),
inference(superposition,[status(thm)],[f504,f1900]) ).
thf(f1900,plain,
( ( ( sK2 @ ( sK7 @ sK13 ) )
= ( sK2 @ ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) ) )
| ~ spl5_16
| ~ spl5_63 ),
inference(trivial_inequality_removal,[status(thm)],[f1897]) ).
thf(f1897,plain,
( ( ( sK2 @ ( sK7 @ sK13 ) )
= ( sK2 @ ( sK13 @ ( sK2 @ ( sK7 @ sK13 ) ) ) ) )
| ( $false = $true )
| ~ spl5_16
| ~ spl5_63 ),
inference(superposition,[status(thm)],[f1738,f444]) ).
thf(f1990,plain,
( ~ spl5_3
| spl5_37
| spl5_38
| ~ spl5_78 ),
inference(avatar_contradiction_clause,[status(thm)],[f1989]) ).
thf(f1989,plain,
( $false
| ~ spl5_3
| spl5_37
| spl5_38
| ~ spl5_78 ),
inference(trivial_inequality_removal,[status(thm)],[f1988]) ).
thf(f1988,plain,
( ( $false = $true )
| ~ spl5_3
| spl5_37
| spl5_38
| ~ spl5_78 ),
inference(forward_demodulation,[status(thm)],[f1987,f1560]) ).
thf(f1560,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_78 ),
inference(avatar_component_clause,[status(thm)],[f1558]) ).
thf(f1558,definition,
( spl5_78
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_78])],[avatar_definition]) ).
thf(f1987,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_3
| spl5_37
| spl5_38 ),
inference(subsumption_resolution,[status(thm)],[f1985,f871]) ).
thf(f871,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
!= $true )
| spl5_37 ),
inference(avatar_component_clause,[status(thm)],[f870]) ).
thf(f870,definition,
( spl5_37
<=> ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_37])],[avatar_definition]) ).
thf(f1985,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_3
| spl5_38 ),
inference(trivial_inequality_removal,[status(thm)],[f1984]) ).
thf(f1984,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( $false != $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_3
| spl5_38 ),
inference(superposition,[status(thm)],[f889,f66]) ).
thf(f66,plain,
( ! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl5_3
<=> ! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f889,plain,
( ( $false
!= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| spl5_38 ),
inference(avatar_component_clause,[status(thm)],[f888]) ).
thf(f888,definition,
( spl5_38
<=> ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_38])],[avatar_definition]) ).
thf(f1972,plain,
( ~ spl5_16
| spl5_78
| spl5_95 ),
inference(avatar_contradiction_clause,[status(thm)],[f1971]) ).
thf(f1971,plain,
( $false
| ~ spl5_16
| spl5_78
| spl5_95 ),
inference(subsumption_resolution,[status(thm)],[f1970,f1834]) ).
thf(f1834,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
!= ( sK10 @ sK12 ) )
| spl5_95 ),
inference(avatar_component_clause,[status(thm)],[f1833]) ).
thf(f1833,definition,
( spl5_95
<=> ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_95])],[avatar_definition]) ).
thf(f1970,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_16
| spl5_78 ),
inference(trivial_inequality_removal,[status(thm)],[f1969]) ).
thf(f1969,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ( $false != $false )
| ~ spl5_16
| spl5_78 ),
inference(superposition,[status(thm)],[f1559,f444]) ).
thf(f1559,plain,
( ( $false
!= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| spl5_78 ),
inference(avatar_component_clause,[status(thm)],[f1558]) ).
thf(f1896,plain,
( ~ spl5_9
| spl5_35
| spl5_37
| spl5_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f1895]) ).
thf(f1895,plain,
( $false
| ~ spl5_9
| spl5_35
| spl5_37
| spl5_40 ),
inference(subsumption_resolution,[status(thm)],[f1879,f898]) ).
thf(f898,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| spl5_40 ),
inference(avatar_component_clause,[status(thm)],[f897]) ).
thf(f897,definition,
( spl5_40
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_40])],[avatar_definition]) ).
thf(f1879,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_9
| spl5_35
| spl5_37 ),
inference(subsumption_resolution,[status(thm)],[f1878,f871]) ).
thf(f1878,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_9
| spl5_35 ),
inference(trivial_inequality_removal,[status(thm)],[f1876]) ).
thf(f1876,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_9
| spl5_35 ),
inference(superposition,[status(thm)],[f863,f148]) ).
thf(f148,plain,
( ! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[status(thm)],[f147]) ).
thf(f147,definition,
( spl5_9
<=> ! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition]) ).
thf(f863,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| spl5_35 ),
inference(avatar_component_clause,[status(thm)],[f862]) ).
thf(f862,definition,
( spl5_35
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_35])],[avatar_definition]) ).
thf(f1868,plain,
( ~ spl5_17
| spl5_40
| spl5_78
| ~ spl5_95 ),
inference(avatar_contradiction_clause,[status(thm)],[f1867]) ).
thf(f1867,plain,
( $false
| ~ spl5_17
| spl5_40
| spl5_78
| ~ spl5_95 ),
inference(subsumption_resolution,[status(thm)],[f1866,f898]) ).
thf(f1866,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_17
| spl5_78
| ~ spl5_95 ),
inference(subsumption_resolution,[status(thm)],[f1853,f1559]) ).
thf(f1853,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_17
| ~ spl5_95 ),
inference(superposition,[status(thm)],[f1267,f1835]) ).
thf(f1835,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_95 ),
inference(avatar_component_clause,[status(thm)],[f1833]) ).
thf(f1267,plain,
( ! [X0: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK13 @ X0 ) ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK4 )
= $false ) )
| ~ spl5_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1262]) ).
thf(f1262,plain,
( ! [X0: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X0 @ sK4 )
= $false )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK2 @ ( sK13 @ X0 ) ) @ sK4 ) ) )
| ~ spl5_17 ),
inference(superposition,[status(thm)],[f21,f452]) ).
thf(f1826,plain,
( ~ spl5_10
| spl5_35
| spl5_37
| ~ spl5_39 ),
inference(avatar_contradiction_clause,[status(thm)],[f1825]) ).
thf(f1825,plain,
( $false
| ~ spl5_10
| spl5_35
| spl5_37
| ~ spl5_39 ),
inference(subsumption_resolution,[status(thm)],[f1824,f871]) ).
thf(f1824,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_10
| spl5_35
| ~ spl5_39 ),
inference(subsumption_resolution,[status(thm)],[f1693,f863]) ).
thf(f1693,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_10
| ~ spl5_39 ),
inference(trivial_inequality_removal,[status(thm)],[f1692]) ).
thf(f1692,plain,
( ( ( sK10 @ sK12 )
!= ( sK10 @ sK12 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_10
| ~ spl5_39 ),
inference(superposition,[status(thm)],[f174,f893]) ).
thf(f893,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_39 ),
inference(avatar_component_clause,[status(thm)],[f892]) ).
thf(f892,definition,
( spl5_39
<=> ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_39])],[avatar_definition]) ).
thf(f174,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[status(thm)],[f173]) ).
thf(f173,definition,
( spl5_10
<=> ! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition]) ).
thf(f1820,plain,
( ~ spl5_17
| ~ spl5_19
| ~ spl5_34
| spl5_51
| spl5_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f1819]) ).
thf(f1819,plain,
( $false
| ~ spl5_17
| ~ spl5_19
| ~ spl5_34
| spl5_51
| spl5_53 ),
inference(subsumption_resolution,[status(thm)],[f1818,f1028]) ).
thf(f1028,plain,
( ( ( sK13 @ ( sK8 @ sK12 ) )
!= ( sK12 @ ( sK8 @ sK12 ) ) )
| spl5_51 ),
inference(avatar_component_clause,[status(thm)],[f1027]) ).
thf(f1027,definition,
( spl5_51
<=> ( ( sK13 @ ( sK8 @ sK12 ) )
= ( sK12 @ ( sK8 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_51])],[avatar_definition]) ).
thf(f1818,plain,
( ( ( sK13 @ ( sK8 @ sK12 ) )
= ( sK12 @ ( sK8 @ sK12 ) ) )
| ~ spl5_17
| ~ spl5_19
| ~ spl5_34
| spl5_53 ),
inference(subsumption_resolution,[status(thm)],[f1812,f1038]) ).
thf(f1038,plain,
( ( $false
!= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| spl5_53 ),
inference(avatar_component_clause,[status(thm)],[f1037]) ).
thf(f1037,definition,
( spl5_53
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_53])],[avatar_definition]) ).
thf(f1812,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( sK13 @ ( sK8 @ sK12 ) )
= ( sK12 @ ( sK8 @ sK12 ) ) )
| ~ spl5_17
| ~ spl5_19
| ~ spl5_34 ),
inference(superposition,[status(thm)],[f1268,f860]) ).
thf(f860,plain,
( ( ( sK2 @ ( sK13 @ ( sK8 @ sK12 ) ) )
= ( sK8 @ sK12 ) )
| ~ spl5_34 ),
inference(avatar_component_clause,[status(thm)],[f858]) ).
thf(f858,definition,
( spl5_34
<=> ( ( sK2 @ ( sK13 @ ( sK8 @ sK12 ) ) )
= ( sK8 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_34])],[avatar_definition]) ).
thf(f1268,plain,
( ! [X0: sK0] :
( ( ( sK12 @ ( sK2 @ ( sK13 @ X0 ) ) )
= ( sK13 @ X0 ) )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK4 )
= $false ) )
| ~ spl5_17
| ~ spl5_19 ),
inference(trivial_inequality_removal,[status(thm)],[f1261]) ).
thf(f1261,plain,
( ! [X0: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X0 @ sK4 )
= $false )
| ( $false = $true )
| ( ( sK12 @ ( sK2 @ ( sK13 @ X0 ) ) )
= ( sK13 @ X0 ) ) )
| ~ spl5_17
| ~ spl5_19 ),
inference(superposition,[status(thm)],[f482,f452]) ).
thf(f482,plain,
( ! [X2: sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) )
| ~ spl5_19 ),
inference(avatar_component_clause,[status(thm)],[f481]) ).
thf(f481,definition,
( spl5_19
<=> ! [X2: sK1] :
( ( ( sK12 @ ( sK2 @ X2 ) )
= X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_19])],[avatar_definition]) ).
thf(f1808,plain,
( spl5_34
| ~ spl5_16
| ~ spl5_35 ),
inference(avatar_split_clause,[status(thm)],[f1801,f862,f443,f858]) ).
thf(f1801,plain,
( ( ( sK2 @ ( sK13 @ ( sK8 @ sK12 ) ) )
= ( sK8 @ sK12 ) )
| ~ spl5_16
| ~ spl5_35 ),
inference(trivial_inequality_removal,[status(thm)],[f1799]) ).
thf(f1799,plain,
( ( ( sK2 @ ( sK13 @ ( sK8 @ sK12 ) ) )
= ( sK8 @ sK12 ) )
| ( $false = $true )
| ~ spl5_16
| ~ spl5_35 ),
inference(superposition,[status(thm)],[f864,f444]) ).
thf(f864,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_35 ),
inference(avatar_component_clause,[status(thm)],[f862]) ).
thf(f1790,plain,
( ~ spl5_16
| ~ spl5_17
| spl5_62
| spl5_73 ),
inference(avatar_contradiction_clause,[status(thm)],[f1789]) ).
thf(f1789,plain,
( $false
| ~ spl5_16
| ~ spl5_17
| spl5_62
| spl5_73 ),
inference(subsumption_resolution,[status(thm)],[f1788,f1271]) ).
thf(f1271,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| spl5_62 ),
inference(avatar_component_clause,[status(thm)],[f1270]) ).
thf(f1788,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_16
| ~ spl5_17
| spl5_73 ),
inference(subsumption_resolution,[status(thm)],[f1771,f1393]) ).
thf(f1393,plain,
( ( $false
!= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| spl5_73 ),
inference(avatar_component_clause,[status(thm)],[f1392]) ).
thf(f1771,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_16
| ~ spl5_17
| spl5_73 ),
inference(superposition,[status(thm)],[f1267,f1766]) ).
thf(f1766,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ~ spl5_16
| spl5_73 ),
inference(trivial_inequality_removal,[status(thm)],[f1765]) ).
thf(f1765,plain,
( ( $false != $false )
| ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ~ spl5_16
| spl5_73 ),
inference(superposition,[status(thm)],[f1393,f444]) ).
thf(f1706,plain,
( spl5_62
| spl5_63
| ~ spl5_9
| ~ spl5_64 ),
inference(avatar_split_clause,[status(thm)],[f1698,f1278,f147,f1274,f1270]) ).
thf(f1698,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_9
| ~ spl5_64 ),
inference(trivial_inequality_removal,[status(thm)],[f1696]) ).
thf(f1696,plain,
( ( $false = $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_9
| ~ spl5_64 ),
inference(superposition,[status(thm)],[f148,f1280]) ).
thf(f1280,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false )
| ~ spl5_64 ),
inference(avatar_component_clause,[status(thm)],[f1278]) ).
thf(f1593,plain,
( ~ spl5_17
| ~ spl5_38
| ~ spl5_51
| spl5_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f1592]) ).
thf(f1592,plain,
( $false
| ~ spl5_17
| ~ spl5_38
| ~ spl5_51
| spl5_53 ),
inference(trivial_inequality_removal,[status(thm)],[f1591]) ).
thf(f1591,plain,
( ( $false = $true )
| ~ spl5_17
| ~ spl5_38
| ~ spl5_51
| spl5_53 ),
inference(forward_demodulation,[status(thm)],[f1590,f890]) ).
thf(f890,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_38 ),
inference(avatar_component_clause,[status(thm)],[f888]) ).
thf(f1590,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_17
| ~ spl5_51
| spl5_53 ),
inference(subsumption_resolution,[status(thm)],[f1258,f1038]) ).
thf(f1258,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_17
| ~ spl5_51 ),
inference(superposition,[status(thm)],[f452,f1029]) ).
thf(f1029,plain,
( ( ( sK13 @ ( sK8 @ sK12 ) )
= ( sK12 @ ( sK8 @ sK12 ) ) )
| ~ spl5_51 ),
inference(avatar_component_clause,[status(thm)],[f1027]) ).
thf(f1581,plain,
( spl5_39
| ~ spl5_16
| ~ spl5_40
| ~ spl5_77 ),
inference(avatar_split_clause,[status(thm)],[f1579,f1554,f897,f443,f892]) ).
thf(f1554,definition,
( spl5_77
<=> ( ( sK12 @ ( sK10 @ sK12 ) )
= ( sK13 @ ( sK10 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_77])],[avatar_definition]) ).
thf(f1579,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_16
| ~ spl5_40
| ~ spl5_77 ),
inference(backward_demodulation,[status(thm)],[f1544,f1556]) ).
thf(f1556,plain,
( ( ( sK12 @ ( sK10 @ sK12 ) )
= ( sK13 @ ( sK10 @ sK12 ) ) )
| ~ spl5_77 ),
inference(avatar_component_clause,[status(thm)],[f1554]) ).
thf(f1544,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_16
| ~ spl5_40 ),
inference(trivial_inequality_removal,[status(thm)],[f1542]) ).
thf(f1542,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ( $false = $true )
| ~ spl5_16
| ~ spl5_40 ),
inference(superposition,[status(thm)],[f444,f899]) ).
thf(f899,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_40 ),
inference(avatar_component_clause,[status(thm)],[f897]) ).
thf(f1575,plain,
( spl5_35
| ~ spl5_39
| ~ spl5_13
| ~ spl5_36 ),
inference(avatar_split_clause,[status(thm)],[f1326,f866,f263,f892,f862]) ).
thf(f866,definition,
( spl5_36
<=> ( ( sK7 @ sK12 )
= ( sK12 @ ( sK2 @ ( sK7 @ sK12 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_36])],[avatar_definition]) ).
thf(f1326,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
!= ( sK10 @ sK12 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_13
| ~ spl5_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1322]) ).
thf(f1322,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
!= ( sK10 @ sK12 ) )
| ( ( sK7 @ sK12 )
!= ( sK7 @ sK12 ) )
| ~ spl5_13
| ~ spl5_36 ),
inference(superposition,[status(thm)],[f264,f868]) ).
thf(f868,plain,
( ( ( sK7 @ sK12 )
= ( sK12 @ ( sK2 @ ( sK7 @ sK12 ) ) ) )
| ~ spl5_36 ),
inference(avatar_component_clause,[status(thm)],[f866]) ).
thf(f1569,plain,
( ~ spl5_39
| spl5_38
| ~ spl5_12
| ~ spl5_36 ),
inference(avatar_split_clause,[status(thm)],[f1325,f866,f225,f888,f892]) ).
thf(f1325,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
!= ( sK10 @ sK12 ) )
| ~ spl5_12
| ~ spl5_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
!= ( sK10 @ sK12 ) )
| ( ( sK7 @ sK12 )
!= ( sK7 @ sK12 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_12
| ~ spl5_36 ),
inference(superposition,[status(thm)],[f226,f868]) ).
thf(f1568,plain,
( ~ spl5_40
| ~ spl5_78 ),
inference(avatar_contradiction_clause,[status(thm)],[f1567]) ).
thf(f1567,plain,
( $false
| ~ spl5_40
| ~ spl5_78 ),
inference(trivial_inequality_removal,[status(thm)],[f1566]) ).
thf(f1566,plain,
( ( $false = $true )
| ~ spl5_40
| ~ spl5_78 ),
inference(backward_demodulation,[status(thm)],[f899,f1560]) ).
thf(f1561,plain,
( spl5_77
| spl5_78
| ~ spl5_16
| ~ spl5_17
| ~ spl5_19
| ~ spl5_40 ),
inference(avatar_split_clause,[status(thm)],[f1547,f897,f481,f451,f443,f1558,f1554]) ).
thf(f1547,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( ( sK12 @ ( sK10 @ sK12 ) )
= ( sK13 @ ( sK10 @ sK12 ) ) )
| ~ spl5_16
| ~ spl5_17
| ~ spl5_19
| ~ spl5_40 ),
inference(superposition,[status(thm)],[f1268,f1544]) ).
thf(f1483,plain,
( ~ spl5_64
| ~ spl5_71 ),
inference(avatar_contradiction_clause,[status(thm)],[f1482]) ).
thf(f1482,plain,
( $false
| ~ spl5_64
| ~ spl5_71 ),
inference(trivial_inequality_removal,[status(thm)],[f1481]) ).
thf(f1481,plain,
( ( $false = $true )
| ~ spl5_64
| ~ spl5_71 ),
inference(backward_demodulation,[status(thm)],[f1370,f1280]) ).
thf(f1370,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ~ spl5_71 ),
inference(avatar_component_clause,[status(thm)],[f1368]) ).
thf(f1371,plain,
( spl5_63
| spl5_71
| ~ spl5_10
| ~ spl5_16
| ~ spl5_62 ),
inference(avatar_split_clause,[status(thm)],[f1343,f1270,f443,f173,f1368,f1274]) ).
thf(f1343,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ~ spl5_10
| ~ spl5_16
| ~ spl5_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1342]) ).
thf(f1342,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $true )
| ( ( sK10 @ sK13 )
!= ( sK10 @ sK13 ) )
| ~ spl5_10
| ~ spl5_16
| ~ spl5_62 ),
inference(superposition,[status(thm)],[f174,f1335]) ).
thf(f1335,plain,
( ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ~ spl5_16
| ~ spl5_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1333]) ).
thf(f1333,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK13 @ ( sK10 @ sK13 ) ) )
= ( sK10 @ sK13 ) )
| ~ spl5_16
| ~ spl5_62 ),
inference(superposition,[status(thm)],[f444,f1272]) ).
thf(f1366,plain,
( spl5_63
| spl5_70
| ~ spl5_11
| ~ spl5_16
| ~ spl5_62 ),
inference(avatar_split_clause,[status(thm)],[f1344,f1270,f443,f202,f1363,f1274]) ).
thf(f202,definition,
( spl5_11
<=> ! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition]) ).
thf(f1344,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ~ spl5_11
| ~ spl5_16
| ~ spl5_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1341]) ).
thf(f1341,plain,
( ( ( sK10 @ sK13 )
!= ( sK10 @ sK13 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ ( sK8 @ sK13 ) ) @ sK3 )
= $false )
| ~ spl5_11
| ~ spl5_16
| ~ spl5_62 ),
inference(superposition,[status(thm)],[f203,f1335]) ).
thf(f203,plain,
( ! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ~ spl5_11 ),
inference(avatar_component_clause,[status(thm)],[f202]) ).
thf(f1282,plain,
( spl5_62
| spl5_64
| spl5_63
| ~ spl5_3
| ~ spl5_17 ),
inference(avatar_split_clause,[status(thm)],[f1264,f451,f65,f1274,f1278,f1270]) ).
thf(f1264,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ~ spl5_3
| ~ spl5_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1263]) ).
thf(f1263,plain,
( ( $false = $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK13 ) @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK13 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK13 ) @ sK4 ) )
| ~ spl5_3
| ~ spl5_17 ),
inference(superposition,[status(thm)],[f66,f452]) ).
thf(f1237,plain,
( spl5_37
| spl5_53
| spl5_40
| ~ spl5_3
| ~ spl5_18 ),
inference(avatar_split_clause,[status(thm)],[f1067,f466,f65,f897,f1037,f870]) ).
thf(f466,definition,
( spl5_18
<=> ! [X2: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_18])],[avatar_definition]) ).
thf(f1067,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_3
| ~ spl5_18 ),
inference(trivial_inequality_removal,[status(thm)],[f1065]) ).
thf(f1065,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( $false = $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_3
| ~ spl5_18 ),
inference(superposition,[status(thm)],[f467,f66]) ).
thf(f467,plain,
( ! [X2: sK0] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false ) )
| ~ spl5_18 ),
inference(avatar_component_clause,[status(thm)],[f466]) ).
thf(f1236,plain,
( ~ spl5_9
| spl5_37
| spl5_40
| ~ spl5_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f1235]) ).
thf(f1235,plain,
( $false
| ~ spl5_9
| spl5_37
| spl5_40
| ~ spl5_53 ),
inference(subsumption_resolution,[status(thm)],[f1234,f871]) ).
thf(f1234,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_9
| spl5_40
| ~ spl5_53 ),
inference(subsumption_resolution,[status(thm)],[f1229,f898]) ).
thf(f1229,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_9
| ~ spl5_53 ),
inference(trivial_inequality_removal,[status(thm)],[f1228]) ).
thf(f1228,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( $false = $true )
| ~ spl5_9
| ~ spl5_53 ),
inference(superposition,[status(thm)],[f148,f1039]) ).
thf(f1039,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_53 ),
inference(avatar_component_clause,[status(thm)],[f1037]) ).
thf(f1201,plain,
( ~ spl5_10
| spl5_37
| ~ spl5_39
| ~ spl5_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f1200]) ).
thf(f1200,plain,
( $false
| ~ spl5_10
| spl5_37
| ~ spl5_39
| ~ spl5_53 ),
inference(trivial_inequality_removal,[status(thm)],[f1199]) ).
thf(f1199,plain,
( ( $false = $true )
| ~ spl5_10
| spl5_37
| ~ spl5_39
| ~ spl5_53 ),
inference(forward_demodulation,[status(thm)],[f1198,f1039]) ).
thf(f1198,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_10
| spl5_37
| ~ spl5_39 ),
inference(subsumption_resolution,[status(thm)],[f1145,f871]) ).
thf(f1145,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_10
| ~ spl5_39 ),
inference(trivial_inequality_removal,[status(thm)],[f1144]) ).
thf(f1144,plain,
( ( ( sK10 @ sK12 )
!= ( sK10 @ sK12 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_10
| ~ spl5_39 ),
inference(superposition,[status(thm)],[f174,f893]) ).
thf(f1197,plain,
( ~ spl5_35
| ~ spl5_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f1196]) ).
thf(f1196,plain,
( $false
| ~ spl5_35
| ~ spl5_53 ),
inference(trivial_inequality_removal,[status(thm)],[f1195]) ).
thf(f1195,plain,
( ( $false = $true )
| ~ spl5_35
| ~ spl5_53 ),
inference(backward_demodulation,[status(thm)],[f864,f1039]) ).
thf(f1194,plain,
( spl5_38
| ~ spl5_11
| spl5_37
| ~ spl5_39 ),
inference(avatar_split_clause,[status(thm)],[f1193,f892,f870,f202,f888]) ).
thf(f1193,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_11
| spl5_37
| ~ spl5_39 ),
inference(subsumption_resolution,[status(thm)],[f1146,f871]) ).
thf(f1146,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_11
| ~ spl5_39 ),
inference(trivial_inequality_removal,[status(thm)],[f1143]) ).
thf(f1143,plain,
( ( ( sK10 @ sK12 )
!= ( sK10 @ sK12 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_11
| ~ spl5_39 ),
inference(superposition,[status(thm)],[f203,f893]) ).
thf(f1113,plain,
( ~ spl5_4
| ~ spl5_36
| spl5_38
| spl5_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f1112]) ).
thf(f1112,plain,
( $false
| ~ spl5_4
| ~ spl5_36
| spl5_38
| spl5_40 ),
inference(subsumption_resolution,[status(thm)],[f1111,f898]) ).
thf(f1111,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_4
| ~ spl5_36
| spl5_38 ),
inference(subsumption_resolution,[status(thm)],[f1109,f889]) ).
thf(f1109,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_4
| ~ spl5_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1103]) ).
thf(f1103,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( ( sK7 @ sK12 )
!= ( sK7 @ sK12 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ ( sK8 @ sK12 ) ) @ sK3 ) )
| ~ spl5_4
| ~ spl5_36 ),
inference(superposition,[status(thm)],[f74,f868]) ).
thf(f1095,plain,
( spl5_36
| ~ spl5_19
| ~ spl5_37 ),
inference(avatar_split_clause,[status(thm)],[f1087,f870,f481,f866]) ).
thf(f1087,plain,
( ( ( sK7 @ sK12 )
= ( sK12 @ ( sK2 @ ( sK7 @ sK12 ) ) ) )
| ~ spl5_19
| ~ spl5_37 ),
inference(trivial_inequality_removal,[status(thm)],[f1084]) ).
thf(f1084,plain,
( ( $false = $true )
| ( ( sK7 @ sK12 )
= ( sK12 @ ( sK2 @ ( sK7 @ sK12 ) ) ) )
| ~ spl5_19
| ~ spl5_37 ),
inference(superposition,[status(thm)],[f872,f482]) ).
thf(f872,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK12 ) @ sK3 )
= $true )
| ~ spl5_37 ),
inference(avatar_component_clause,[status(thm)],[f870]) ).
thf(f1083,plain,
( spl5_39
| ~ spl5_15
| ~ spl5_40 ),
inference(avatar_split_clause,[status(thm)],[f1080,f897,f440,f892]) ).
thf(f440,definition,
( spl5_15
<=> ! [X2: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_15])],[avatar_definition]) ).
thf(f1080,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ~ spl5_15
| ~ spl5_40 ),
inference(trivial_inequality_removal,[status(thm)],[f1074]) ).
thf(f1074,plain,
( ( ( sK2 @ ( sK12 @ ( sK10 @ sK12 ) ) )
= ( sK10 @ sK12 ) )
| ( $false = $true )
| ~ spl5_15
| ~ spl5_40 ),
inference(superposition,[status(thm)],[f899,f441]) ).
thf(f441,plain,
( ! [X2: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) )
| ~ spl5_15 ),
inference(avatar_component_clause,[status(thm)],[f440]) ).
thf(f1055,plain,
( spl5_53
| ~ spl5_18
| ~ spl5_38 ),
inference(avatar_split_clause,[status(thm)],[f1052,f888,f466,f1037]) ).
thf(f1052,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_18
| ~ spl5_38 ),
inference(trivial_inequality_removal,[status(thm)],[f1050]) ).
thf(f1050,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( $false = $true )
| ~ spl5_18
| ~ spl5_38 ),
inference(superposition,[status(thm)],[f467,f890]) ).
thf(f900,plain,
( spl5_35
| spl5_40
| ~ spl5_8
| ~ spl5_36 ),
inference(avatar_split_clause,[status(thm)],[f885,f866,f122,f897,f862]) ).
thf(f885,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ~ spl5_8
| ~ spl5_36 ),
inference(trivial_inequality_removal,[status(thm)],[f883]) ).
thf(f883,plain,
( ( ( sK7 @ sK12 )
!= ( sK7 @ sK12 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ sK12 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK10 @ sK12 ) @ sK4 ) )
| ~ spl5_8
| ~ spl5_36 ),
inference(superposition,[status(thm)],[f123,f868]) ).
thf(f739,plain,
( ~ spl5_1
| ~ spl5_14
| ~ spl5_16
| ~ spl5_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f738]) ).
thf(f738,plain,
( $false
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16
| ~ spl5_17 ),
inference(trivial_inequality_removal,[status(thm)],[f737]) ).
thf(f737,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16
| ~ spl5_17 ),
inference(backward_demodulation,[status(thm)],[f295,f735]) ).
thf(f735,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $false )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16
| ~ spl5_17 ),
inference(trivial_inequality_removal,[status(thm)],[f731]) ).
thf(f731,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16
| ~ spl5_17 ),
inference(superposition,[status(thm)],[f685,f452]) ).
thf(f685,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ sK6 ) @ sK3 )
= $false )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16 ),
inference(trivial_inequality_removal,[status(thm)],[f682]) ).
thf(f682,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK13 @ sK6 ) @ sK3 )
= $false )
| ( sK6 != sK6 )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_16 ),
inference(superposition,[status(thm)],[f59,f667]) ).
thf(f667,plain,
( ( ( sK2 @ ( sK13 @ sK6 ) )
= sK6 )
| ~ spl5_14
| ~ spl5_16 ),
inference(trivial_inequality_removal,[status(thm)],[f661]) ).
thf(f661,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK13 @ sK6 ) )
= sK6 )
| ~ spl5_14
| ~ spl5_16 ),
inference(superposition,[status(thm)],[f295,f444]) ).
thf(f59,plain,
( ! [X2: sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl5_1
<=> ! [X2: sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f295,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ~ spl5_14 ),
inference(avatar_component_clause,[status(thm)],[f293]) ).
thf(f293,definition,
( spl5_14
<=> ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_14])],[avatar_definition]) ).
thf(f724,plain,
( ~ spl5_1
| ~ spl5_14
| ~ spl5_15
| ~ spl5_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f723]) ).
thf(f723,plain,
( $false
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15
| ~ spl5_18 ),
inference(trivial_inequality_removal,[status(thm)],[f722]) ).
thf(f722,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15
| ~ spl5_18 ),
inference(backward_demodulation,[status(thm)],[f295,f721]) ).
thf(f721,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $false )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15
| ~ spl5_18 ),
inference(trivial_inequality_removal,[status(thm)],[f717]) ).
thf(f717,plain,
( ( $false = $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $false )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15
| ~ spl5_18 ),
inference(superposition,[status(thm)],[f684,f467]) ).
thf(f684,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ sK6 ) @ sK3 ) )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15 ),
inference(trivial_inequality_removal,[status(thm)],[f683]) ).
thf(f683,plain,
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( sK12 @ sK6 ) @ sK3 ) )
| ( sK6 != sK6 )
| ~ spl5_1
| ~ spl5_14
| ~ spl5_15 ),
inference(superposition,[status(thm)],[f59,f668]) ).
thf(f668,plain,
( ( ( sK2 @ ( sK12 @ sK6 ) )
= sK6 )
| ~ spl5_14
| ~ spl5_15 ),
inference(trivial_inequality_removal,[status(thm)],[f664]) ).
thf(f664,plain,
( ( $false = $true )
| ( ( sK2 @ ( sK12 @ sK6 ) )
= sK6 )
| ~ spl5_14
| ~ spl5_15 ),
inference(superposition,[status(thm)],[f441,f295]) ).
thf(f600,plain,
( spl5_2
| ~ spl5_5
| ~ spl5_6
| ~ spl5_7
| ~ spl5_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f599]) ).
thf(f599,plain,
( $false
| spl5_2
| ~ spl5_5
| ~ spl5_6
| ~ spl5_7
| ~ spl5_19 ),
inference(subsumption_resolution,[status(thm)],[f598,f63]) ).
thf(f598,plain,
( ( sK9 = sK11 )
| ~ spl5_5
| ~ spl5_6
| ~ spl5_7
| ~ spl5_19 ),
inference(forward_demodulation,[status(thm)],[f597,f590]) ).
thf(f590,plain,
( ( sK9
= ( sK12 @ ( sK2 @ sK9 ) ) )
| ~ spl5_5
| ~ spl5_19 ),
inference(trivial_inequality_removal,[status(thm)],[f583]) ).
thf(f583,plain,
( ( sK9
= ( sK12 @ ( sK2 @ sK9 ) ) )
| ( $false = $true )
| ~ spl5_5
| ~ spl5_19 ),
inference(superposition,[status(thm)],[f482,f86]) ).
thf(f597,plain,
( ( sK11
= ( sK12 @ ( sK2 @ sK9 ) ) )
| ~ spl5_6
| ~ spl5_7
| ~ spl5_19 ),
inference(forward_demodulation,[status(thm)],[f588,f101]) ).
thf(f588,plain,
( ( ( sK12 @ ( sK2 @ sK11 ) )
= sK11 )
| ~ spl5_7
| ~ spl5_19 ),
inference(trivial_inequality_removal,[status(thm)],[f587]) ).
thf(f587,plain,
( ( ( sK12 @ ( sK2 @ sK11 ) )
= sK11 )
| ( $false = $true )
| ~ spl5_7
| ~ spl5_19 ),
inference(superposition,[status(thm)],[f110,f482]) ).
thf(f505,plain,
( spl5_20
| spl5_19 ),
inference(avatar_split_clause,[status(thm)],[f501,f481,f503]) ).
thf(f501,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
= $false )
| ( ( sK2 @ X2 )
!= ( sK2 @ X1 ) )
| ( ( sK12 @ ( sK2 @ X3 ) )
= X3 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
| ( X1 = X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
= $false )
| ( ( sK12 @ ( sK2 @ X3 ) )
= X3 )
| ( X1 = X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( ( ( sK12 @ ( sK2 @ X3 ) )
= X3 )
= $true )
| ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
= $false )
| ( X1 = X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f498]) ).
thf(f498,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
| ( X1 = X2 )
| ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
= $false )
| ( ( ( sK12 @ ( sK2 @ X3 ) )
= X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( $true
= ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
=> ( ( sK12 @ ( sK2 @ X3 ) )
= X3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( X1 = X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( X1 = X2 )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) )
| ( $true
= ( ( 'const/sets/IN' @ sK1 @ X3 @ sK3 )
=> ( ( sK12 @ ( sK2 @ X3 ) )
= X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f495]) ).
thf(f495,plain,
! [X2: sK1,X3: sK1,X1: sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) )
| ( ( ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) )
@ X3 )
= $true )
| ( X1 = X2 ) ),
inference(pi_clausification,[status(thm)],[f494]) ).
thf(f494,plain,
! [X2: sK1,X1: sK1] :
( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
= $true )
| ( X1 = X2 )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f492]) ).
thf(f492,plain,
! [X2: sK1,X1: sK1] :
( ( $true
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) )
| ( X1 = X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
! [X2: sK1,X1: sK1] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true )
| ( X1 = X2 )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f489]) ).
thf(f489,plain,
! [X2: sK1,X1: sK1] :
( ( $true
= ( X2 = X1 ) )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f488]) ).
thf(f488,plain,
! [X2: sK1,X1: sK1] :
( ( ( ( ( ( sK2 @ X2 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
=> ( X2 = X1 ) )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f487]) ).
thf(f487,plain,
! [X2: sK1,X1: sK1] :
( ( ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f486]) ).
thf(f486,plain,
! [X1: sK1] :
( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ X1 @ sK3 ) )
=> ( Y0 = X1 ) ) )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,plain,
! [X1: sK1] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f424]) ).
thf(f424,plain,
( ( $true
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f422]) ).
thf(f422,plain,
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f421]) ).
thf(f421,plain,
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) )
@ sK12 ) ) ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( ?? @ ( sK0 > sK1 )
@ ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
!= ( ?? @ ( sK0 > sK1 )
@ ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f484,plain,
( spl5_17
| spl5_19 ),
inference(avatar_split_clause,[status(thm)],[f477,f481,f451]) ).
thf(f477,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( sK12 @ ( sK2 @ X2 ) )
= X2 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
! [X2: sK1,X1: sK0] :
( ( ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
& ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK12 @ ( sK2 @ X2 ) )
= X2 )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f475]) ).
thf(f475,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
& ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f474]) ).
thf(f474,plain,
! [X2: sK1,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) )
| ( $true
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f473]) ).
thf(f473,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
| ( $true
= ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f472]) ).
thf(f472,plain,
! [X2: sK1,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
=> ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) ) )
| ( $true
= ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f471]) ).
thf(f471,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) )
| ( $true
= ( ( 'const/sets/IN' @ sK1 @ X2 @ sK3 )
=> ( ( sK12 @ ( sK2 @ X2 ) )
= X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f470]) ).
thf(f470,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) )
| ( $true
= ( ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f455]) ).
thf(f455,plain,
! [X1: sK0] :
( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f428]) ).
thf(f428,plain,
! [X1: sK0] :
( ( $true
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) ) ) )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f426]) ).
thf(f426,plain,
! [X1: sK0] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f425]) ).
thf(f425,plain,
! [X1: sK0] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) )
= $true )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( sK12 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f422]) ).
thf(f483,plain,
( spl5_16
| spl5_19 ),
inference(avatar_split_clause,[status(thm)],[f479,f481,f443]) ).
thf(f479,plain,
! [X2: sK1,X1: sK0] :
( ( ( sK12 @ ( sK2 @ X2 ) )
= X2 )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f478]) ).
thf(f478,plain,
! [X2: sK1,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK12 @ ( sK2 @ X2 ) )
= X2 )
| ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f476]) ).
thf(f469,plain,
( spl5_18
| spl5_17 ),
inference(avatar_split_clause,[status(thm)],[f462,f451,f466]) ).
thf(f462,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f461]) ).
thf(f461,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
& ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f460]) ).
thf(f460,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true )
| ( $true
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ ( sK13 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f459]) ).
thf(f459,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f458]) ).
thf(f458,plain,
! [X2: sK0,X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f457]) ).
thf(f457,plain,
! [X2: sK0,X1: sK0] :
( ( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 ) )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f456]) ).
thf(f456,plain,
! [X2: sK0,X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) )
| ( $true
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
! [X1: sK0] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( sK12 @ Y0 ) @ sK3 ) ) )
= $true )
| ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f428]) ).
thf(f468,plain,
( spl5_16
| spl5_18 ),
inference(avatar_split_clause,[status(thm)],[f464,f466,f443]) ).
thf(f464,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f463]) ).
thf(f463,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK12 @ X2 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f461]) ).
thf(f453,plain,
( spl5_17
| spl5_15 ),
inference(avatar_split_clause,[status(thm)],[f449,f440,f451]) ).
thf(f449,plain,
! [X2: sK0,X1: sK0] :
( ( ( sK2 @ ( sK12 @ X2 ) )
= X2 )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f448]) ).
thf(f448,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f447]) ).
thf(f447,plain,
! [X2: sK0,X1: sK0] :
( ( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
=> ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f446]) ).
thf(f446,plain,
! [X2: sK0,X1: sK0] :
( ( ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) )
@ X2 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f432]) ).
thf(f432,plain,
! [X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f431]) ).
thf(f431,plain,
! [X1: sK0] :
( ( ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
& ( 'const/sets/IN' @ sK1 @ ( sK13 @ X1 ) @ sK3 ) )
= $true )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f430]) ).
thf(f430,plain,
! [X1: sK0] :
( ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
| ( $true
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ ( sK13 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f429]) ).
thf(f429,plain,
! [X1: sK0] :
( ( $true
= ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f427]) ).
thf(f427,plain,
! [X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= X1 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) ) )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f426]) ).
thf(f445,plain,
( spl5_15
| spl5_16 ),
inference(avatar_split_clause,[status(thm)],[f438,f443,f440]) ).
thf(f438,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f437]) ).
thf(f437,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
= $false )
| ( $true
= ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f436]) ).
thf(f436,plain,
! [X2: sK0,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( ( ( 'const/sets/IN' @ sK0 @ X2 @ sK4 )
=> ( ( sK2 @ ( sK12 @ X2 ) )
= X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f435]) ).
thf(f435,plain,
! [X2: sK0,X1: sK0] :
( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false )
| ( ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f434]) ).
thf(f434,plain,
! [X1: sK0] :
( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f433]) ).
thf(f433,plain,
! [X1: sK0] :
( ( ( ( sK2 @ ( sK13 @ X1 ) )
= X1 )
= $true )
| ( $true
= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( sK12 @ Y0 ) )
= Y0 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f431]) ).
thf(f420,plain,
( ~ spl5_2
| spl5_14
| spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f419,f147,f293,f61]) ).
thf(f419,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( sK9 != sK11 ) ),
inference(equality_proxy_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
! [X1: sK0 > sK1] :
( ( ( sK11 = sK9 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f391]) ).
thf(f391,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK11 = sK9 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f390]) ).
thf(f390,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f389]) ).
thf(f389,plain,
! [X1: sK0 > sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f388]) ).
thf(f388,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f387]) ).
thf(f387,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f353]) ).
thf(f353,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f351]) ).
thf(f351,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f350]) ).
thf(f350,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) )
@ sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f275]) ).
thf(f275,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: sK0 > sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) )
@ ( sK8 @ X1 ) )
= $false )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: sK0 > sK1] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
= $false )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: sK0 > sK1] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
= $false )
| ( $false
= ( ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: sK0 > sK1] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) )
@ sK6 ) ) ),
inference(sigma_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: sK0 > sK1] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: sK0 > sK1] :
( ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
=> ( ( X1 @ ( sK2 @ Y0 ) )
= Y0 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ Y0 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) )
@ X1 ) )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ?? @ ( sK0 > sK1 )
@ ^ [Y0: sK0 > sK1] :
( ( !! @ sK1
@ ^ [Y1: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
=> ( ( Y0 @ ( sK2 @ Y1 ) )
= Y1 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( Y0 @ Y1 ) @ sK3 ) ) )
& ( !! @ sK0
@ ^ [Y1: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y1 @ sK4 )
=> ( ( sK2 @ ( Y0 @ Y1 ) )
= Y1 ) ) ) ) )
= $false )
| ( ( ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ?? @ sK1
@ ^ [Y1: sK1] :
( ( ( sK2 @ Y1 )
= Y0 )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f418,plain,
( spl5_14
| ~ spl5_2
| spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f417,f173,f61,f293]) ).
thf(f417,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f416]) ).
thf(f416,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f414]) ).
thf(f414,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f391]) ).
thf(f413,plain,
( spl5_6
| spl5_14
| spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f412,f147,f293,f99]) ).
thf(f412,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f410]) ).
thf(f410,plain,
! [X1: sK0 > sK1] :
( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f401]) ).
thf(f401,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f394]) ).
thf(f394,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f392]) ).
thf(f392,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f390]) ).
thf(f411,plain,
( spl5_9
| spl5_14
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f409,f108,f293,f147]) ).
thf(f409,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f401]) ).
thf(f408,plain,
( spl5_14
| spl5_10
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f407,f108,f173,f293]) ).
thf(f407,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f402]) ).
thf(f402,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f400]) ).
thf(f400,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f394]) ).
thf(f406,plain,
( spl5_6
| spl5_10
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f405,f293,f173,f99]) ).
thf(f405,plain,
! [X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f404]) ).
thf(f404,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f403]) ).
thf(f403,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f400]) ).
thf(f399,plain,
( spl5_10
| spl5_14
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f398,f84,f293,f173]) ).
thf(f398,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f395]) ).
thf(f395,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f393]) ).
thf(f393,plain,
! [X1: sK0 > sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f392]) ).
thf(f397,plain,
( spl5_5
| spl5_9
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f396,f293,f147,f84]) ).
thf(f396,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f393]) ).
thf(f386,plain,
( spl5_5
| spl5_3
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f379,f293,f65,f84]) ).
thf(f379,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f376]) ).
thf(f376,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f374]) ).
thf(f374,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f373]) ).
thf(f373,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f357]) ).
thf(f357,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f355]) ).
thf(f355,plain,
! [X1: sK0 > sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f354]) ).
thf(f354,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) )
@ ( sK10 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f352]) ).
thf(f352,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f351]) ).
thf(f385,plain,
( spl5_6
| spl5_14
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f384,f65,f293,f99]) ).
thf(f384,plain,
! [X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f382]) ).
thf(f382,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f380]) ).
thf(f380,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f376]) ).
thf(f383,plain,
( spl5_3
| spl5_7
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f381,f293,f108,f65]) ).
thf(f381,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f380]) ).
thf(f378,plain,
( spl5_3
| ~ spl5_2
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f377,f293,f61,f65]) ).
thf(f377,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f375]) ).
thf(f375,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f374]) ).
thf(f372,plain,
( spl5_14
| ~ spl5_2
| spl5_11 ),
inference(avatar_split_clause,[status(thm)],[f371,f202,f61,f293]) ).
thf(f371,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( sK9 != sK11 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f361]) ).
thf(f361,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK11 = sK9 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f360]) ).
thf(f360,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f359]) ).
thf(f359,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f358]) ).
thf(f358,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f356]) ).
thf(f356,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f355]) ).
thf(f370,plain,
( spl5_14
| spl5_11
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f369,f99,f202,f293]) ).
thf(f369,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f367]) ).
thf(f367,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f364]) ).
thf(f364,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f362]) ).
thf(f362,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f360]) ).
thf(f368,plain,
( spl5_7
| spl5_14
| spl5_11 ),
inference(avatar_split_clause,[status(thm)],[f366,f202,f293,f108]) ).
thf(f366,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f364]) ).
thf(f365,plain,
( spl5_5
| spl5_11
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f363,f293,f202,f84]) ).
thf(f363,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f362]) ).
thf(f349,plain,
( spl5_13
| ~ spl5_2
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f348,f293,f61,f263]) ).
thf(f348,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( sK9 != sK11 )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( sK9 != sK11 )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f322]) ).
thf(f322,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f321]) ).
thf(f321,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f320]) ).
thf(f320,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) ) ),
inference(sigma_clausification,[status(thm)],[f319]) ).
thf(f319,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f318]) ).
thf(f318,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) )
@ sK9 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(sigma_clausification,[status(thm)],[f280]) ).
thf(f280,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f278]) ).
thf(f278,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f277]) ).
thf(f277,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f276]) ).
thf(f276,plain,
! [X1: sK0 > sK1] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f274]) ).
thf(f274,plain,
! [X1: sK0 > sK1] :
( ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f346,plain,
( spl5_14
| spl5_13
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f345,f99,f263,f293]) ).
thf(f345,plain,
! [X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f340]) ).
thf(f340,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f338]) ).
thf(f338,plain,
! [X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f337]) ).
thf(f337,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f322]) ).
thf(f344,plain,
( spl5_14
| spl5_13
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f342,f108,f263,f293]) ).
thf(f342,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f340]) ).
thf(f341,plain,
( spl5_13
| spl5_5
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f339,f293,f84,f263]) ).
thf(f339,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f338]) ).
thf(f335,plain,
( spl5_14
| spl5_8
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f328,f84,f122,f293]) ).
thf(f328,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f325]) ).
thf(f325,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f323]) ).
thf(f323,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f321]) ).
thf(f334,plain,
( spl5_8
| spl5_7
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f330,f293,f108,f122]) ).
thf(f330,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f329]) ).
thf(f329,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f325]) ).
thf(f333,plain,
( spl5_14
| spl5_6
| spl5_8 ),
inference(avatar_split_clause,[status(thm)],[f332,f122,f99,f293]) ).
thf(f332,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f331]) ).
thf(f331,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f329]) ).
thf(f327,plain,
( spl5_14
| spl5_8
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f326,f61,f122,f293]) ).
thf(f326,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( sK9 != sK11 ) ),
inference(equality_proxy_clausification,[status(thm)],[f324]) ).
thf(f324,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f323]) ).
thf(f317,plain,
( spl5_5
| spl5_4
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f310,f293,f73,f84]) ).
thf(f310,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f307]) ).
thf(f307,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f286]) ).
thf(f286,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f284]) ).
thf(f284,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f283]) ).
thf(f283,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f281]) ).
thf(f281,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) )
@ sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f279]) ).
thf(f279,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f278]) ).
thf(f316,plain,
( spl5_7
| spl5_14
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f312,f73,f293,f108]) ).
thf(f312,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f311]) ).
thf(f311,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f307]) ).
thf(f315,plain,
( spl5_6
| spl5_4
| spl5_14 ),
inference(avatar_split_clause,[status(thm)],[f314,f293,f73,f99]) ).
thf(f314,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f313]) ).
thf(f313,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f311]) ).
thf(f309,plain,
( spl5_14
| spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f308,f61,f73,f293]) ).
thf(f308,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( sK9 != sK11 ) ),
inference(equality_proxy_clausification,[status(thm)],[f306]) ).
thf(f306,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f286]) ).
thf(f305,plain,
( spl5_14
| spl5_12
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f304,f61,f225,f293]) ).
thf(f304,plain,
! [X1: sK0 > sK1] :
( ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f303]) ).
thf(f303,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f287]) ).
thf(f287,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f285]) ).
thf(f285,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f284]) ).
thf(f302,plain,
( spl5_6
| spl5_14
| spl5_12 ),
inference(avatar_split_clause,[status(thm)],[f301,f225,f293,f99]) ).
thf(f301,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f299]) ).
thf(f299,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f297]) ).
thf(f297,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f290]) ).
thf(f290,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f288]) ).
thf(f288,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f285]) ).
thf(f300,plain,
( spl5_7
| spl5_14
| spl5_12 ),
inference(avatar_split_clause,[status(thm)],[f298,f225,f293,f108]) ).
thf(f298,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f297]) ).
thf(f296,plain,
( spl5_14
| spl5_12
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f291,f84,f225,f293]) ).
thf(f291,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f289]) ).
thf(f289,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f288]) ).
thf(f273,plain,
( ~ spl5_2
| spl5_13
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f272,f58,f263,f61]) ).
thf(f272,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( sK9 != sK11 )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( sK9 != sK11 )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f270]) ).
thf(f270,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( sK9 != sK11 )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f252]) ).
thf(f252,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f251]) ).
thf(f251,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f249]) ).
thf(f249,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
! [X1: sK0 > sK1] :
( ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f158]) ).
thf(f158,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: sK0 > sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
=> ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: sK0 > sK1] :
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( ( ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) )
@ sK9 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( !! @ sK1
@ ^ [Y1: sK1] :
( ( ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) )
& ( 'const/sets/IN' @ sK1 @ Y1 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK4 )
=> ( ( sK2 @ ( X1 @ Y0 ) )
= Y0 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f269,plain,
( spl5_1
| spl5_5
| spl5_13 ),
inference(avatar_split_clause,[status(thm)],[f268,f263,f84,f58]) ).
thf(f268,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f254]) ).
thf(f254,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f252]) ).
thf(f266,plain,
( spl5_7
| spl5_1
| spl5_13 ),
inference(avatar_split_clause,[status(thm)],[f259,f263,f58,f108]) ).
thf(f259,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f254]) ).
thf(f265,plain,
( spl5_13
| spl5_6
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f261,f58,f99,f263]) ).
thf(f261,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f260]) ).
thf(f260,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f248,plain,
( spl5_1
| spl5_12
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f247,f84,f225,f58]) ).
thf(f247,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f246]) ).
thf(f246,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f244]) ).
thf(f244,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(pi_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
! [X1: sK0 > sK1] :
( ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f160]) ).
thf(f243,plain,
( spl5_12
| spl5_7
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f242,f58,f108,f225]) ).
thf(f242,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f241]) ).
thf(f241,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f239]) ).
thf(f239,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(pi_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f230]) ).
thf(f230,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f228]) ).
thf(f238,plain,
( spl5_1
| spl5_6
| spl5_12 ),
inference(avatar_split_clause,[status(thm)],[f237,f225,f99,f58]) ).
thf(f237,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f234]) ).
thf(f234,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
! [X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f230]) ).
thf(f227,plain,
( ~ spl5_2
| spl5_1
| spl5_12 ),
inference(avatar_split_clause,[status(thm)],[f223,f225,f58,f61]) ).
thf(f223,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( sK9 != sK11 )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( sK9 != sK11 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f221]) ).
thf(f221,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( sK9 != sK11 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( sK9 != sK11 )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f219]) ).
thf(f219,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( sK9 != sK11 ) ),
inference(pi_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
! [X1: sK0 > sK1] :
( ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( sK9 != sK11 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
! [X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f215]) ).
thf(f212,plain,
( spl5_11
| spl5_1
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f211,f99,f58,f202]) ).
thf(f211,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f193]) ).
thf(f193,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
! [X1: sK0 > sK1] :
( ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
! [X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f159]) ).
thf(f210,plain,
( spl5_7
| spl5_11
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f208,f58,f202,f108]) ).
thf(f208,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f206]) ).
thf(f207,plain,
( spl5_1
| spl5_11
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f205,f84,f202,f58]) ).
thf(f205,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f199]) ).
thf(f204,plain,
( ~ spl5_2
| spl5_1
| spl5_11 ),
inference(avatar_split_clause,[status(thm)],[f200,f202,f58,f61]) ).
thf(f200,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f198]) ).
thf(f198,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f197]) ).
thf(f192,plain,
( spl5_10
| spl5_1
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f191,f99,f58,f173]) ).
thf(f191,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X1: sK0 > sK1] :
( ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f187,plain,
( spl5_10
| spl5_1
| spl5_7 ),
inference(avatar_split_clause,[status(thm)],[f186,f108,f58,f173]) ).
thf(f186,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f181,plain,
( spl5_5
| spl5_1
| spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f180,f173,f58,f84]) ).
thf(f180,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f175,plain,
( ~ spl5_2
| spl5_10
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f171,f58,f173,f61]) ).
thf(f171,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( sK9 != sK11 ) ),
inference(equality_proxy_clausification,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK10 @ X1 )
!= ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK11 = sK9 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( sK2 @ ( X1 @ ( sK10 @ X1 ) ) )
= ( sK10 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f165]) ).
thf(f157,plain,
( spl5_1
| ~ spl5_2
| spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f156,f147,f61,f58]) ).
thf(f156,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( sK9 != sK11 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( sK9 != sK11 )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) )
@ sK11 ) ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) )
@ X2 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ?? @ sK1
@ ^ [Y0: sK1] :
( ( ( sK2 @ Y0 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( ( ( sK2 @ Y0 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ Y0 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( Y0 = sK9 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 )
=> ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f153,plain,
( spl5_5
| spl5_1
| spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f152,f147,f58,f84]) ).
thf(f152,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f151,plain,
( spl5_9
| spl5_1
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f150,f99,f58,f147]) ).
thf(f150,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f149,plain,
( spl5_7
| spl5_9
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f144,f58,f147,f108]) ).
thf(f144,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f137,plain,
( spl5_8
| spl5_5
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f136,f58,f84,f122]) ).
thf(f136,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f135,plain,
( spl5_7
| spl5_8
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f134,f58,f122,f108]) ).
thf(f134,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f133,plain,
( spl5_8
| spl5_6
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f132,f58,f99,f122]) ).
thf(f132,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f124,plain,
( ~ spl5_2
| spl5_8
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f120,f58,f122,f61]) ).
thf(f120,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( sK9 != sK11 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( sK9 != sK11 )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK11 = sK9 )
= $false )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK8 @ X1 ) @ sK4 ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK11 = sK9 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f112,plain,
( spl5_7
| spl5_1
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f105,f65,f58,f108]) ).
thf(f105,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 ) )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
& ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
& ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
=> ( sK11 = sK9 ) )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f111,plain,
( spl5_1
| spl5_7
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f106,f73,f108,f58]) ).
thf(f106,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK11 @ sK3 )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f103,plain,
( spl5_3
| spl5_1
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f96,f99,f58,f65]) ).
thf(f96,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ sK11 )
= ( sK2 @ sK9 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f102,plain,
( spl5_1
| spl5_6
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f97,f73,f99,f58]) ).
thf(f97,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK2 @ sK9 )
= ( sK2 @ sK11 ) )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f89,plain,
( spl5_5
| spl5_1
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f88,f65,f58,f84]) ).
thf(f88,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f87,plain,
( spl5_4
| spl5_5
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f82,f58,f84,f73]) ).
thf(f82,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 ) ),
inference(equality_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK9 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f75,plain,
( ~ spl5_2
| spl5_4
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f71,f58,f73,f61]) ).
thf(f71,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( sK9 != sK11 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK2 @ X2 )
!= sK6 )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK7 @ X1 )
!= ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) )
= $false )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( sK11 = sK9 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
=> ( ( X1 @ ( sK2 @ ( sK7 @ X1 ) ) )
= ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( sK11 = sK9 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f67,plain,
( spl5_1
| ~ spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f56,f65,f61,f58]) ).
thf(f56,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK2 @ X2 )
!= sK6 )
| ( sK9 != sK11 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( sK9 != sK11 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( ( sK2 @ X2 )
= sK6 )
= $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( sK9 != sK11 ) ),
inference(equality_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: sK1,X1: sK0 > sK1] :
( ( ( 'const/sets/IN' @ sK1 @ ( sK7 @ X1 ) @ sK3 )
= $true )
| ( ( sK11 = sK9 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK10 @ X1 ) @ sK4 )
= $true )
| ( $false
= ( ( ( sK2 @ X2 )
= sK6 )
& ( 'const/sets/IN' @ sK1 @ X2 @ sK3 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ ( X1 @ ( sK8 @ X1 ) ) @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV471^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.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 12:47:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV471^1 : TPTP v9.2.1. Released v7.0.0.
% 0.29/0.46 % Domain : Analysis
% 0.29/0.46 % Problem : BIJECTIVE_ON_LEFT_RIGHT_INVERSE
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Kal16]
% 0.29/0.46 % Names : BIJECTIVE_ON_LEFT_RIGHT_INVERSE_.p [Kal16]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.67 v9.0.0, 1.00 v7.5.0, 0.67 v7.3.0, 1.00 v7.1.0
% 0.29/0.46 % Syntax : Number of formulae : 6 ( 3 unt; 2 typ; 0 def)
% 0.29/0.46 % Number of atoms : 31 ( 14 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 7 avg)
% 0.29/0.46 % Number of connectives : 91 ( 0 ~; 0 |; 10 &; 70 @)
% 0.29/0.46 % ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 12 ( 7 avg)
% 0.29/0.46 % Number of types : 1 ( 0 usr)
% 0.29/0.46 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 2-3 aty)
% 0.29/0.46 % Number of variables : 35 ( 0 ^; 28 !; 5 ?; 35 :)
% 0.29/0.46 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : Exported from core HOL Light.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf('thf_const_const/trivia/I',type,
% 0.29/0.46 'const/trivia/I':
% 0.29/0.46 !>[A: $tType] : ( A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf('thf_const_const/sets/IN',type,
% 0.29/0.46 'const/sets/IN':
% 0.29/0.46 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf('thm/trivia/I_THM_',axiom,
% 0.29/0.46 ! [A: $tType,A0: A] :
% 0.29/0.46 ( ( 'const/trivia/I' @ A @ A0 )
% 0.29/0.46 = A0 ) ).
% 0.29/0.46
% 0.29/0.46 thf('thm/sets/SURJECTIVE_ON_RIGHT_INVERSE_',axiom,
% 0.29/0.46 ! [A: $tType,A0: $tType,A1: A > $o,A2: A > A0,A3: A0 > $o] :
% 0.29/0.46 ( ( ! [A4: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A4 @ A3 )
% 0.29/0.46 => ? [A5: A] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 0.29/0.46 & ( ( A2 @ A5 )
% 0.29/0.46 = A4 ) ) ) )
% 0.29/0.46 = ( ? [A4: A0 > A] :
% 0.29/0.46 ! [A5: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A5 @ A3 )
% 0.29/0.46 => ( ( 'const/sets/IN' @ A @ ( A4 @ A5 ) @ A1 )
% 0.29/0.46 & ( ( A2 @ ( A4 @ A5 ) )
% 0.29/0.46 = A5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf('thm/sets/INJECTIVE_ON_LEFT_INVERSE_',axiom,
% 0.29/0.46 ! [A: $tType,A0: $tType,A1: A0 > A,A2: A0 > $o] :
% 0.29/0.46 ( ( ! [A3: A0,A4: A0] :
% 0.29/0.46 ( ( ( 'const/sets/IN' @ A0 @ A3 @ A2 )
% 0.29/0.46 & ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 0.29/0.46 & ( ( A1 @ A3 )
% 0.29/0.46 = ( A1 @ A4 ) ) )
% 0.29/0.46 => ( A3 = A4 ) ) )
% 0.29/0.46 = ( ? [A3: A > A0] :
% 0.29/0.46 ! [A4: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 0.29/0.46 => ( ( A3 @ ( A1 @ A4 ) )
% 0.29/0.46 = A4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf('thm/sets/BIJECTIVE_ON_LEFT_RIGHT_INVERSE_',conjecture,
% 0.29/0.46 ! [A: $tType,A0: $tType,A1: A0 > A,A2: A0 > $o,A3: A > $o] :
% 0.29/0.46 ( ! [A4: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 0.29/0.46 => ( 'const/sets/IN' @ A @ ( A1 @ A4 ) @ A3 ) )
% 0.29/0.46 => ( ( ! [A4: A0,A5: A0] :
% 0.29/0.46 ( ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 0.29/0.46 & ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 0.29/0.46 & ( ( A1 @ A4 )
% 0.29/0.46 = ( A1 @ A5 ) ) )
% 0.29/0.46 => ( A4 = A5 ) )
% 0.29/0.46 & ! [A4: A] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A @ A4 @ A3 )
% 0.29/0.46 => ? [A5: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 0.29/0.46 & ( ( A1 @ A5 )
% 0.29/0.46 = A4 ) ) ) )
% 0.29/0.46 = ( ? [A4: A > A0] :
% 0.29/0.46 ( ! [A5: A] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A @ A5 @ A3 )
% 0.29/0.46 => ( 'const/sets/IN' @ A0 @ ( A4 @ A5 ) @ A2 ) )
% 0.29/0.46 & ! [A5: A] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A @ A5 @ A3 )
% 0.29/0.46 => ( ( A1 @ ( A4 @ A5 ) )
% 0.29/0.46 = A5 ) )
% 0.29/0.46 & ! [A5: A0] :
% 0.29/0.46 ( ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 0.29/0.46 => ( ( A4 @ ( A1 @ A5 ) )
% 0.29/0.46 = A5 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.26 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 12:47:30 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OORBxcTjsE/DTF2DTF3780.p
% See solution above
% 1.49/1.26 ------------------------
% 1.49/1.27 ---- Cleaned THF ---
% 1.49/1.27 thf('thf_const_const/trivia/I',type,
% 1.49/1.27 'const/trivia/I':
% 1.49/1.27 !>[A: $tType] : ( A > A ) ).
% 1.49/1.27
% 1.49/1.27 thf('thf_const_const/sets/IN',type,
% 1.49/1.27 'const/sets/IN':
% 1.49/1.27 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/trivia/I_THM_',axiom,
% 1.49/1.27 ! [A: $tType,A0: A] :
% 1.49/1.27 ( ( 'const/trivia/I' @ A @ A0 )
% 1.49/1.27 = A0 ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/sets/SURJECTIVE_ON_RIGHT_INVERSE_',axiom,
% 1.49/1.27 ! [A: $tType,A0: $tType,A1: A > $o,A2: A > A0,A3: A0 > $o] :
% 1.49/1.27 ( ( ! [A4: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A4 @ A3 )
% 1.49/1.27 => ? [A5: A] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A @ A5 @ A1 )
% 1.49/1.27 & ( ( A2 @ A5 )
% 1.49/1.27 = A4 ) ) ) )
% 1.49/1.27 = ( ? [A4: A0 > A] :
% 1.49/1.27 ! [A5: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A5 @ A3 )
% 1.49/1.27 => ( ( 'const/sets/IN' @ A @ ( A4 @ A5 ) @ A1 )
% 1.49/1.27 & ( ( A2 @ ( A4 @ A5 ) )
% 1.49/1.27 = A5 ) ) ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/sets/INJECTIVE_ON_LEFT_INVERSE_',axiom,
% 1.49/1.27 ! [A: $tType,A0: $tType,A1: A0 > A,A2: A0 > $o] :
% 1.49/1.27 ( ( ! [A3: A0,A4: A0] :
% 1.49/1.27 ( ( ( 'const/sets/IN' @ A0 @ A3 @ A2 )
% 1.49/1.27 & ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 1.49/1.27 & ( ( A1 @ A3 )
% 1.49/1.27 = ( A1 @ A4 ) ) )
% 1.49/1.27 => ( A3 = A4 ) ) )
% 1.49/1.27 = ( ? [A3: A > A0] :
% 1.49/1.27 ! [A4: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 1.49/1.27 => ( ( A3 @ ( A1 @ A4 ) )
% 1.49/1.27 = A4 ) ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf('thm/sets/BIJECTIVE_ON_LEFT_RIGHT_INVERSE_',conjecture,
% 1.49/1.27 ! [A: $tType,A0: $tType,A1: A0 > A,A2: A0 > $o,A3: A > $o] :
% 1.49/1.27 ( ! [A4: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 1.49/1.27 => ( 'const/sets/IN' @ A @ ( A1 @ A4 ) @ A3 ) )
% 1.49/1.27 => ( ( ! [A4: A0,A5: A0] :
% 1.49/1.27 ( ( ( 'const/sets/IN' @ A0 @ A4 @ A2 )
% 1.49/1.27 & ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 1.49/1.27 & ( ( A1 @ A4 )
% 1.49/1.27 = ( A1 @ A5 ) ) )
% 1.49/1.27 => ( A4 = A5 ) )
% 1.49/1.27 & ! [A4: A] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A @ A4 @ A3 )
% 1.49/1.27 => ? [A5: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 1.49/1.27 & ( ( A1 @ A5 )
% 1.49/1.27 = A4 ) ) ) )
% 1.49/1.27 = ( ? [A4: A > A0] :
% 1.49/1.27 ( ! [A5: A] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A @ A5 @ A3 )
% 1.49/1.27 => ( 'const/sets/IN' @ A0 @ ( A4 @ A5 ) @ A2 ) )
% 1.49/1.27 & ! [A5: A] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A @ A5 @ A3 )
% 1.49/1.27 => ( ( A1 @ ( A4 @ A5 ) )
% 1.49/1.27 = A5 ) )
% 1.49/1.27 & ! [A5: A0] :
% 1.49/1.27 ( ( 'const/sets/IN' @ A0 @ A5 @ A2 )
% 1.49/1.27 => ( ( A4 @ ( A1 @ A5 ) )
% 1.49/1.27 = A5 ) ) ) ) ) ) ).
% 1.49/1.27 ------------------------
% 1.49/1.29 % (4000)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/2Mi)
% 1.49/1.29 % (4000)Instruction limit reached!
% 1.49/1.29 % (4000)------------------------------
% 1.49/1.29 % (4000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (4000)Termination reason: Unknown
% 1.49/1.29 % (4000)Termination phase: shuffling
% 1.49/1.29
% 1.49/1.29 % (4000)Memory used [KB]: 1023
% 1.49/1.29 % (4000)Time elapsed: 0.002 s
% 1.49/1.29 % (4000)Instructions burned: 2 (million)
% 1.49/1.29 % (4000)------------------------------
% 1.49/1.29 % (4000)------------------------------
% 1.49/1.29 % (3998)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_3780 for (2999ds/4Mi)
% 1.49/1.29 % (3998)Instruction limit reached!
% 1.49/1.29 % (3998)------------------------------
% 1.49/1.29 % (3998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (3998)Termination reason: Unknown
% 1.49/1.29 % (3998)Termination phase: Property scanning
% 1.49/1.29
% 1.49/1.29 % (3998)Memory used [KB]: 1023
% 1.49/1.29 % (3998)Time elapsed: 0.003 s
% 1.49/1.29 % (3998)Instructions burned: 5 (million)
% 1.49/1.29 % (3998)------------------------------
% 1.49/1.29 % (3998)------------------------------
% 1.49/1.30 % (3997)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/183Mi)
% 1.49/1.30 % (3999)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_3780 for (2999ds/27Mi)
% 1.62/1.30 % (4003)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/18Mi)
% 1.62/1.30 % (4002)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_3780 for (2999ds/275Mi)
% 1.62/1.30 % (4001)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_3780 for (2999ds/2Mi)
% 1.62/1.30 % Exception at run slice level
% 1.62/1.30 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.30 % (4004)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/3Mi)
% 1.62/1.30 % (4004)Instruction limit reached!
% 1.62/1.30 % (4004)------------------------------
% 1.62/1.30 % (4004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (4004)Termination reason: Unknown
% 1.62/1.30 % (4004)Termination phase: Preprocessing 3
% 1.62/1.30
% 1.62/1.30 % (4004)Memory used [KB]: 1023
% 1.62/1.30 % (4004)Time elapsed: 0.002 s
% 1.62/1.30 % (4004)Instructions burned: 4 (million)
% 1.62/1.30 % (4004)------------------------------
% 1.62/1.30 % (4004)------------------------------
% 1.62/1.30 % (4005)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_3780 for (2999ds/37Mi)
% 1.62/1.30 % Exception at run slice level
% 1.62/1.30 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.31 % (4003)Instruction limit reached!
% 1.62/1.31 % (4003)------------------------------
% 1.62/1.31 % (4003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (4003)Termination reason: Unknown
% 1.62/1.31 % (4003)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (4003)Memory used [KB]: 5628
% 1.62/1.31 % (4003)Time elapsed: 0.013 s
% 1.62/1.31 % (4003)Instructions burned: 18 (million)
% 1.62/1.31 % (4003)------------------------------
% 1.62/1.31 % (4003)------------------------------
% 1.62/1.31 % (4007)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_3780 for (2999ds/3Mi)
% 1.62/1.31 % (4007)Instruction limit reached!
% 1.62/1.31 % (4007)------------------------------
% 1.62/1.31 % (4007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (4007)Termination reason: Unknown
% 1.62/1.31 % (4007)Termination phase: Preprocessing 3
% 1.62/1.31
% 1.62/1.31 % (4007)Memory used [KB]: 1023
% 1.62/1.31 % (4007)Time elapsed: 0.002 s
% 1.62/1.31 % (4007)Instructions burned: 4 (million)
% 1.62/1.31 % (4007)------------------------------
% 1.62/1.31 % (4007)------------------------------
% 1.62/1.31 % (3999)Instruction limit reached!
% 1.62/1.31 % (3999)------------------------------
% 1.62/1.31 % (3999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (3999)Termination reason: Unknown
% 1.62/1.31 % (3999)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (3999)Memory used [KB]: 5628
% 1.62/1.31 % (3999)Time elapsed: 0.017 s
% 1.62/1.31 % (3999)Instructions burned: 27 (million)
% 1.62/1.31 % (3999)------------------------------
% 1.62/1.31 % (3999)------------------------------
% 1.62/1.31 % (4008)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_3780 for (2999ds/1041Mi)
% 1.62/1.31 % Exception at run slice level
% 1.62/1.31 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.32 % (4006)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_3780 for (2999ds/15Mi)
% 1.62/1.32 % (4010)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/16Mi)
% 1.62/1.32 % (4012)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_3780 for (2999ds/3Mi)
% 1.62/1.32 % (4012)Instruction limit reached!
% 1.62/1.32 % (4012)------------------------------
% 1.62/1.32 % (4012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4012)Termination reason: Unknown
% 1.62/1.32 % (4012)Termination phase: Preprocessing 3
% 1.62/1.32
% 1.62/1.32 % (4012)Memory used [KB]: 1023
% 1.62/1.32 % (4012)Time elapsed: 0.003 s
% 1.62/1.32 % (4012)Instructions burned: 4 (million)
% 1.62/1.32 % (4012)------------------------------
% 1.62/1.32 % (4012)------------------------------
% 1.62/1.32 % (4010)Instruction limit reached!
% 1.62/1.32 % (4010)------------------------------
% 1.62/1.32 % (4010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4010)Termination reason: Unknown
% 1.62/1.32 % (4010)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (4010)Memory used [KB]: 5628
% 1.62/1.32 % (4010)Time elapsed: 0.006 s
% 1.62/1.32 % (4010)Instructions burned: 17 (million)
% 1.62/1.32 % (4010)------------------------------
% 1.62/1.32 % (4010)------------------------------
% 1.62/1.32 % (4006)Instruction limit reached!
% 1.62/1.32 % (4006)------------------------------
% 1.62/1.32 % (4006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (4006)Termination reason: Unknown
% 1.62/1.32 % (4006)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (4006)Memory used [KB]: 5756
% 1.62/1.32 % (4006)Time elapsed: 0.011 s
% 1.62/1.32 % (4006)Instructions burned: 15 (million)
% 1.62/1.32 % (4006)------------------------------
% 1.62/1.32 % (4006)------------------------------
% 1.62/1.32 % (4009)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/7Mi)
% 1.62/1.33 % (4011)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_3780 for (2999ds/3Mi)
% 1.62/1.33 % (4009)Instruction limit reached!
% 1.62/1.33 % (4009)------------------------------
% 1.62/1.33 % (4009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (4009)Termination reason: Unknown
% 1.62/1.33 % (4009)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (4009)Memory used [KB]: 1023
% 1.62/1.33 % (4009)Time elapsed: 0.006 s
% 1.62/1.33 % (4009)Instructions burned: 7 (million)
% 1.62/1.33 % (4009)------------------------------
% 1.62/1.33 % (4009)------------------------------
% 1.62/1.33 % (4011)Instruction limit reached!
% 1.62/1.33 % (4011)------------------------------
% 1.62/1.33 % (4011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (4011)Termination reason: Unknown
% 1.62/1.33 % (4011)Termination phase: Preprocessing 3
% 1.62/1.33
% 1.62/1.33 % (4011)Memory used [KB]: 1023
% 1.62/1.33 % (4011)Time elapsed: 0.004 s
% 1.62/1.33 % (4011)Instructions burned: 4 (million)
% 1.62/1.33 % (4011)------------------------------
% 1.62/1.33 % (4011)------------------------------
% 1.62/1.33 % (4014)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/3Mi)
% 1.62/1.33 % (4013)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/7Mi)
% 1.62/1.33 % Exception at run slice level
% 1.62/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.34 % (4013)Instruction limit reached!
% 1.62/1.34 % (4013)------------------------------
% 1.62/1.34 % (4013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (4013)Termination reason: Unknown
% 1.62/1.34 % (4013)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (4013)Memory used [KB]: 5500
% 1.62/1.34 % (4013)Time elapsed: 0.004 s
% 1.62/1.34 % (4013)Instructions burned: 7 (million)
% 1.62/1.34 % (4013)------------------------------
% 1.62/1.34 % (4013)------------------------------
% 1.62/1.34 % (4015)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/4Mi)
% 1.62/1.34 % (4018)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/6Mi)
% 1.62/1.34 % (4015)Instruction limit reached!
% 1.62/1.34 % (4015)------------------------------
% 1.62/1.34 % (4015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (4015)Termination reason: Unknown
% 1.62/1.34 % (4015)Termination phase: Preprocessing 3
% 1.62/1.34
% 1.62/1.34 % (4015)Memory used [KB]: 1023
% 1.62/1.34 % (4015)Time elapsed: 0.004 s
% 1.62/1.34 % (4015)Instructions burned: 4 (million)
% 1.62/1.34 % (4015)------------------------------
% 1.62/1.34 % (4015)------------------------------
% 1.62/1.35 % (4018)Instruction limit reached!
% 1.62/1.35 % (4018)------------------------------
% 1.62/1.35 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (4018)Termination reason: Unknown
% 1.62/1.35 % (4018)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (4018)Memory used [KB]: 5500
% 1.62/1.35 % (4018)Time elapsed: 0.003 s
% 1.62/1.35 % (4018)Instructions burned: 7 (million)
% 1.62/1.35 % (4018)------------------------------
% 1.62/1.35 % (4018)------------------------------
% 1.62/1.35 % (4019)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/902Mi)
% 1.62/1.35 % (4016)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/18Mi)
% 1.62/1.35 % (4017)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/710Mi)
% 1.62/1.35 % (4021)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/5Mi)
% 1.62/1.36 % Exception at run slice level
% 1.62/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.36 % (4016)Instruction limit reached!
% 1.62/1.36 % (4016)------------------------------
% 1.62/1.36 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (4016)Termination reason: Unknown
% 1.62/1.36 % (4016)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (4016)Memory used [KB]: 5500
% 1.62/1.36 % (4016)Time elapsed: 0.012 s
% 1.62/1.36 % (4016)Instructions burned: 19 (million)
% 1.62/1.36 % (4016)------------------------------
% 1.62/1.36 % (4016)------------------------------
% 1.62/1.36 % (4020)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/21Mi)
% 1.62/1.36 % (4022)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/6Mi)
% 1.62/1.37 % Exception at run slice level
% 1.62/1.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.37 % (4023)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/377Mi)
% 1.62/1.37 % (4020)Instruction limit reached!
% 1.62/1.37 % (4020)------------------------------
% 1.62/1.37 % (4020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (4020)Termination reason: Unknown
% 1.62/1.37 % (4020)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (4020)Memory used [KB]: 5628
% 1.62/1.37 % (4020)Time elapsed: 0.015 s
% 1.62/1.37 % (4020)Instructions burned: 21 (million)
% 1.62/1.37 % (4020)------------------------------
% 1.62/1.37 % (4020)------------------------------
% 1.62/1.37 % (3997)Instruction limit reached!
% 1.62/1.37 % (3997)------------------------------
% 1.62/1.37 % (3997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (3997)Termination reason: Unknown
% 1.62/1.37 % (3997)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (3997)Memory used [KB]: 6268
% 1.62/1.37 % (3997)Time elapsed: 0.081 s
% 1.62/1.37 % (3997)Instructions burned: 184 (million)
% 1.62/1.37 % (3997)------------------------------
% 1.62/1.37 % (3997)------------------------------
% 1.62/1.37 % (4024)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/779Mi)
% 1.62/1.38 % Exception at run slice level
% 1.62/1.38 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.38 % (4027)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/17Mi)
% 1.62/1.38 % (4026)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/879Mi)
% 1.62/1.39 % (4025)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/19Mi)
% 1.62/1.39 % Exception at run slice level
% 1.62/1.39 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.39 % (4027)Instruction limit reached!
% 1.62/1.39 % (4027)------------------------------
% 1.62/1.39 % (4027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (4027)Termination reason: Unknown
% 1.62/1.39 % (4027)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (4027)Memory used [KB]: 5500
% 1.62/1.39 % (4027)Time elapsed: 0.006 s
% 1.62/1.39 % (4027)Instructions burned: 17 (million)
% 1.62/1.39 % (4027)------------------------------
% 1.62/1.39 % (4027)------------------------------
% 1.62/1.40 % (4028)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/3Mi)
% 1.62/1.40 % (4029)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3780 for (2999ds/30Mi)
% 1.62/1.40 % (4028)Instruction limit reached!
% 1.62/1.40 % (4028)------------------------------
% 1.62/1.40 % (4028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (4028)Termination reason: Unknown
% 1.62/1.40 % (4028)Termination phase: Preprocessing 3
% 1.62/1.40
% 1.62/1.40 % (4028)Memory used [KB]: 1023
% 1.62/1.40 % (4028)Time elapsed: 0.002 s
% 1.62/1.40 % (4028)Instructions burned: 3 (million)
% 1.62/1.40 % (4028)------------------------------
% 1.62/1.40 % (4028)------------------------------
% 1.62/1.41 % (4029)Instruction limit reached!
% 1.62/1.41 % (4029)------------------------------
% 1.62/1.41 % (4029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (4029)Termination reason: Unknown
% 1.62/1.41 % (4029)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (4029)Memory used [KB]: 5628
% 1.62/1.41 % (4029)Time elapsed: 0.011 s
% 1.62/1.41 % (4029)Instructions burned: 30 (million)
% 1.62/1.41 % (4029)------------------------------
% 1.62/1.41 % (4029)------------------------------
% 1.62/1.41 % (4030)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/127Mi)
% 1.62/1.42 % (4031)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/100Mi)
% 1.62/1.43 % (4002)Instruction limit reached!
% 1.62/1.43 % (4002)------------------------------
% 1.62/1.43 % (4002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (4002)Termination reason: Unknown
% 1.62/1.43 % (4002)Termination phase: Saturation
% 1.62/1.43
% 1.62/1.43 % (4002)Memory used [KB]: 6396
% 1.62/1.43 % (4002)Time elapsed: 0.137 s
% 1.62/1.43 % (4002)Instructions burned: 277 (million)
% 1.62/1.43 % (4002)------------------------------
% 1.62/1.43 % (4002)------------------------------
% 1.62/1.44 % (4032)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/3Mi)
% 1.62/1.44 % Exception at run slice level
% 1.62/1.44 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.45 % (4031)Instruction limit reached!
% 1.62/1.45 % (4031)------------------------------
% 1.62/1.45 % (4031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (4031)Termination reason: Unknown
% 1.62/1.45 % (4031)Termination phase: Saturation
% 1.62/1.45
% 1.62/1.45 % (4031)Memory used [KB]: 5884
% 1.62/1.45 % (4031)Time elapsed: 0.031 s
% 1.62/1.45 % (4031)Instructions burned: 100 (million)
% 1.62/1.45 % (4031)------------------------------
% 1.62/1.45 % (4031)------------------------------
% 1.62/1.45 % (4033)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/20Mi)
% 1.62/1.45 % (4030)Instruction limit reached!
% 1.62/1.45 % (4030)------------------------------
% 1.62/1.45 % (4030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.45 % (4030)Termination reason: Unknown
% 1.62/1.45 % (4030)Termination phase: Saturation
% 1.62/1.45
% 1.62/1.45 % (4030)Memory used [KB]: 6140
% 1.62/1.45 % (4030)Time elapsed: 0.045 s
% 1.62/1.45 % (4030)Instructions burned: 128 (million)
% 1.62/1.45 % (4030)------------------------------
% 1.62/1.45 % (4030)------------------------------
% 1.62/1.46 % (4034)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/86Mi)
% 1.62/1.46 % (4033)Instruction limit reached!
% 1.62/1.46 % (4033)------------------------------
% 1.62/1.46 % (4033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (4033)Termination reason: Unknown
% 1.62/1.46 % (4033)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (4033)Memory used [KB]: 5628
% 1.62/1.46 % (4033)Time elapsed: 0.008 s
% 1.62/1.46 % (4033)Instructions burned: 20 (million)
% 1.62/1.46 % (4033)------------------------------
% 1.62/1.46 % (4033)------------------------------
% 1.62/1.46 % (4035)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/107Mi)
% 1.62/1.47 % (4036)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/39Mi)
% 1.62/1.47 % Exception at run slice level
% 1.62/1.47 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.48 % (4037)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/448Mi)
% 1.62/1.48 % Exception at run slice level
% 1.62/1.48 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.48 % (4034)Instruction limit reached!
% 1.62/1.48 % (4034)------------------------------
% 1.62/1.48 % (4034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.48 % (4034)Termination reason: Unknown
% 1.62/1.48 % (4034)Termination phase: Saturation
% 1.62/1.48
% 1.62/1.48 % (4034)Memory used [KB]: 6012
% 1.62/1.48 % (4034)Time elapsed: 0.049 s
% 1.62/1.48 % (4034)Instructions burned: 86 (million)
% 1.62/1.48 % (4034)------------------------------
% 1.62/1.48 % (4034)------------------------------
% 1.62/1.49 % (4038)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/46Mi)
% 1.62/1.49 % (4039)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/98Mi)
% 1.62/1.49 % Exception at run slice level
% 1.62/1.49 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.50 % (4035)Instruction limit reached!
% 1.62/1.50 % (4035)------------------------------
% 1.62/1.50 % (4035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.50 % (4035)Termination reason: Unknown
% 1.62/1.50 % (4035)Termination phase: Saturation
% 1.62/1.50
% 1.62/1.50 % (4035)Memory used [KB]: 6140
% 1.62/1.50 % (4035)Time elapsed: 0.059 s
% 1.62/1.50 % (4035)Instructions burned: 107 (million)
% 1.62/1.50 % (4035)------------------------------
% 1.62/1.50 % (4035)------------------------------
% 1.62/1.50 % (4040)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3780 for (2998ds/507Mi)
% 1.62/1.51 % (4038)Instruction limit reached!
% 1.62/1.51 % (4038)------------------------------
% 1.62/1.51 % (4038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (4038)Termination reason: Unknown
% 1.62/1.51 % (4038)Termination phase: Saturation
% 1.62/1.51
% 1.62/1.51 % (4038)Memory used [KB]: 5884
% 1.62/1.51 % (4038)Time elapsed: 0.042 s
% 1.62/1.51 % (4038)Instructions burned: 48 (million)
% 1.62/1.51 % (4038)------------------------------
% 1.62/1.51 % (4038)------------------------------
% 1.62/1.51 % (4040)Refutation not found, incomplete strategy
% 1.62/1.51 % (4040)------------------------------
% 1.62/1.51 % (4040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (4040)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.51
% 1.62/1.51
% 1.62/1.51 % (4040)Memory used [KB]: 5628
% 1.62/1.51 % (4040)Time elapsed: 0.031 s
% 1.62/1.51 % (4040)Instructions burned: 16 (million)
% 1.62/1.51 % (4040)------------------------------
% 1.62/1.51 % (4040)------------------------------
% 1.62/1.51 % (4041)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/149Mi)
% 1.62/1.51 % (4023)Instruction limit reached!
% 1.62/1.51 % (4023)------------------------------
% 1.62/1.51 % (4023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.51 % (4023)Termination reason: Unknown
% 1.62/1.51 % (4023)Termination phase: Saturation
% 1.62/1.51
% 1.62/1.51 % (4023)Memory used [KB]: 6652
% 1.62/1.51 % (4023)Time elapsed: 0.137 s
% 1.62/1.51 % (4023)Instructions burned: 378 (million)
% 1.62/1.51 % (4023)------------------------------
% 1.62/1.51 % (4023)------------------------------
% 1.62/1.52 % (4042)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/39Mi)
% 1.62/1.52 % (4043)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/6Mi)
% 1.62/1.52 % Exception at run slice level
% 1.62/1.52 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.52 % (4044)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/1087Mi)
% 1.62/1.53 % (4045)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/47Mi)
% 1.62/1.53 % (4042)Instruction limit reached!
% 1.62/1.53 % (4042)------------------------------
% 1.62/1.53 % (4042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.53 % (4042)Termination reason: Unknown
% 1.62/1.53 % (4042)Termination phase: Saturation
% 1.62/1.53
% 1.62/1.53 % (4042)Memory used [KB]: 5628
% 1.62/1.53 % (4042)Time elapsed: 0.014 s
% 1.62/1.53 % (4042)Instructions burned: 41 (million)
% 1.62/1.53 % (4042)------------------------------
% 1.62/1.53 % (4042)------------------------------
% 1.62/1.54 % (4046)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/44Mi)
% 1.62/1.54 % Exception at run slice level
% 1.62/1.54 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.54 % (4045)Instruction limit reached!
% 1.62/1.54 % (4045)------------------------------
% 1.62/1.54 % (4045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.54 % (4045)Termination reason: Unknown
% 1.62/1.54 % (4045)Termination phase: Saturation
% 1.62/1.54
% 1.62/1.54 % (4045)Memory used [KB]: 5628
% 1.62/1.54 % (4045)Time elapsed: 0.015 s
% 1.62/1.54 % (4045)Instructions burned: 49 (million)
% 1.62/1.54 % (4045)------------------------------
% 1.62/1.54 % (4045)------------------------------
% 1.62/1.55 % (4047)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/432Mi)
% 1.62/1.55 % Exception at run slice level
% 1.62/1.55 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.55 % (4048)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/62Mi)
% 1.62/1.55 % Exception at run slice level
% 1.62/1.55 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.56 % (4049)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/31Mi)
% 1.62/1.56 % (4041)Instruction limit reached!
% 1.62/1.56 % (4041)------------------------------
% 1.62/1.56 % (4041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.56 % (4041)Termination reason: Unknown
% 1.62/1.56 % (4041)Termination phase: Saturation
% 1.62/1.56
% 1.62/1.56 % (4041)Memory used [KB]: 6140
% 1.62/1.56 % (4041)Time elapsed: 0.054 s
% 1.62/1.56 % (4041)Instructions burned: 151 (million)
% 1.62/1.56 % (4041)------------------------------
% 1.62/1.56 % (4041)------------------------------
% 1.62/1.56 % (4050)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/96Mi)
% 1.62/1.57 % (4051)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/453Mi)
% 1.62/1.57 % (4049)Instruction limit reached!
% 1.62/1.57 % (4049)------------------------------
% 1.62/1.57 % (4049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.57 % (4049)Termination reason: Unknown
% 1.62/1.57 % (4049)Termination phase: Saturation
% 1.62/1.57
% 1.62/1.57 % (4049)Memory used [KB]: 5756
% 1.62/1.57 % (4049)Time elapsed: 0.013 s
% 1.62/1.57 % (4049)Instructions burned: 33 (million)
% 1.62/1.57 % (4049)------------------------------
% 1.62/1.57 % (4049)------------------------------
% 1.62/1.57 % Exception at run slice level
% 1.62/1.57 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.58 % (4052)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/71Mi)
% 1.62/1.58 % (4053)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3780 for (2997ds/83Mi)
% 1.62/1.59 % (4017)Instruction limit reached!
% 1.62/1.59 % (4017)------------------------------
% 1.62/1.59 % (4017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.59 % (4017)Termination reason: Unknown
% 1.62/1.59 % (4017)Termination phase: Saturation
% 1.62/1.59
% 1.62/1.59 % (4017)Memory used [KB]: 7419
% 1.62/1.59 % (4017)Time elapsed: 0.243 s
% 1.62/1.59 % (4017)Instructions burned: 711 (million)
% 1.62/1.59 % (4017)------------------------------
% 1.62/1.59 % (4017)------------------------------
% 1.62/1.59 % (4050)Instruction limit reached!
% 1.62/1.59 % (4050)------------------------------
% 1.62/1.59 % (4050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.59 % (4050)Termination reason: Unknown
% 1.62/1.59 % (4050)Termination phase: Saturation
% 1.62/1.59
% 1.62/1.59 % (4050)Memory used [KB]: 6012
% 1.62/1.59 % (4050)Time elapsed: 0.032 s
% 1.62/1.59 % (4050)Instructions burned: 98 (million)
% 1.62/1.59 % (4050)------------------------------
% 1.62/1.59 % (4050)------------------------------
% 1.62/1.60 % (4054)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/11Mi)
% 1.62/1.60 % Exception at run slice level
% 1.62/1.60 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.60 % (4055)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/41Mi)
% 1.62/1.60 % Exception at run slice level
% 1.62/1.60 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.61 % (4052)Instruction limit reached!
% 1.62/1.61 % (4052)------------------------------
% 1.62/1.61 % (4052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.61 % (4052)Termination reason: Unknown
% 1.62/1.61 % (4052)Termination phase: Saturation
% 1.62/1.61
% 1.62/1.61 % (4052)Memory used [KB]: 5884
% 1.62/1.61 % (4052)Time elapsed: 0.027 s
% 1.62/1.61 % (4052)Instructions burned: 73 (million)
% 1.62/1.61 % (4052)------------------------------
% 1.62/1.61 % (4052)------------------------------
% 1.62/1.61 % (4053)Instruction limit reached!
% 1.62/1.61 % (4053)------------------------------
% 1.62/1.61 % (4053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.61 % (4053)Termination reason: Unknown
% 1.62/1.61 % (4053)Termination phase: Saturation
% 1.62/1.61
% 1.62/1.61 % (4053)Memory used [KB]: 6012
% 1.62/1.61 % (4053)Time elapsed: 0.029 s
% 1.62/1.61 % (4053)Instructions burned: 85 (million)
% 1.62/1.61 % (4053)------------------------------
% 1.62/1.61 % (4053)------------------------------
% 1.62/1.61 % (4056)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/6Mi)
% 1.62/1.61 % (4057)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/150Mi)
% 1.62/1.61 % (4056)Instruction limit reached!
% 1.62/1.61 % (4056)------------------------------
% 1.62/1.61 % (4056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.61 % (4056)Termination reason: Unknown
% 1.62/1.61 % (4056)Termination phase: Saturation
% 1.62/1.61
% 1.62/1.61 % (4056)Memory used [KB]: 5500
% 1.62/1.61 % (4056)Time elapsed: 0.004 s
% 1.62/1.61 % (4056)Instructions burned: 8 (million)
% 1.62/1.61 % (4056)------------------------------
% 1.62/1.61 % (4056)------------------------------
% 1.62/1.62 % (4058)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/343Mi)
% 1.62/1.62 % (4059)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/109Mi)
% 1.62/1.62 % (4060)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/253Mi)
% 1.62/1.62 % (4019)Instruction limit reached!
% 1.62/1.62 % (4019)------------------------------
% 1.62/1.62 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.62 % (4019)Termination reason: Unknown
% 1.62/1.62 % (4019)Termination phase: Saturation
% 1.62/1.62
% 1.62/1.62 % (4019)Memory used [KB]: 8059
% 1.62/1.62 % (4019)Time elapsed: 0.278 s
% 1.62/1.62 % (4019)Instructions burned: 905 (million)
% 1.62/1.62 % (4019)------------------------------
% 1.62/1.62 % (4019)------------------------------
% 1.62/1.63 % (4061)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/140Mi)
% 1.62/1.65 % (4059)Instruction limit reached!
% 1.62/1.65 % (4059)------------------------------
% 1.62/1.65 % (4059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.65 % (4059)Termination reason: Unknown
% 1.62/1.65 % (4059)Termination phase: Saturation
% 1.62/1.65
% 1.62/1.65 % (4059)Memory used [KB]: 5884
% 1.62/1.65 % (4059)Time elapsed: 0.036 s
% 1.62/1.65 % (4059)Instructions burned: 109 (million)
% 1.62/1.65 % (4059)------------------------------
% 1.62/1.65 % (4059)------------------------------
% 1.62/1.66 % (4057)Instruction limit reached!
% 1.62/1.66 % (4057)------------------------------
% 1.62/1.66 % (4057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.66 % (4057)Termination reason: Unknown
% 1.62/1.66 % (4057)Termination phase: Saturation
% 1.62/1.66
% 1.62/1.66 % (4057)Memory used [KB]: 6140
% 1.62/1.66 % (4057)Time elapsed: 0.049 s
% 1.62/1.66 % (4057)Instructions burned: 153 (million)
% 1.62/1.66 % (4057)------------------------------
% 1.62/1.66 % (4057)------------------------------
% 1.62/1.66 % (4062)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/614Mi)
% 1.62/1.67 % (4063)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/202Mi)
% 1.62/1.67 % (4061)Instruction limit reached!
% 1.62/1.67 % (4061)------------------------------
% 1.62/1.67 % (4061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.67 % (4061)Termination reason: Unknown
% 1.62/1.67 % (4061)Termination phase: Saturation
% 1.62/1.67
% 1.62/1.67 % (4061)Memory used [KB]: 6012
% 1.62/1.67 % (4061)Time elapsed: 0.041 s
% 1.62/1.67 % (4061)Instructions burned: 141 (million)
% 1.62/1.67 % (4061)------------------------------
% 1.62/1.67 % (4061)------------------------------
% 1.62/1.68 % (4026)Instruction limit reached!
% 1.62/1.68 % (4026)------------------------------
% 1.62/1.68 % (4026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.68 % (4026)Termination reason: Unknown
% 1.62/1.68 % (4026)Termination phase: Saturation
% 1.62/1.68
% 1.62/1.68 % (4026)Memory used [KB]: 8187
% 1.62/1.68 % (4026)Time elapsed: 0.293 s
% 1.62/1.68 % (4026)Instructions burned: 879 (million)
% 1.62/1.68 % (4026)------------------------------
% 1.62/1.68 % (4026)------------------------------
% 1.62/1.68 % (4064)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/339Mi)
% 1.62/1.69 % (4065)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/283Mi)
% 1.62/1.69 % Exception at run slice level
% 1.62/1.69 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.70 % (4066)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3780 for (2996ds/134Mi)
% 1.62/1.70 % (4060)Instruction limit reached!
% 1.62/1.70 % (4060)------------------------------
% 1.62/1.70 % (4060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.70 % (4060)Termination reason: Unknown
% 1.62/1.70 % (4060)Termination phase: Saturation
% 1.62/1.70
% 1.62/1.70 % (4060)Memory used [KB]: 6268
% 1.62/1.70 % (4060)Time elapsed: 0.085 s
% 1.62/1.70 % (4060)Instructions burned: 255 (million)
% 1.62/1.70 % (4060)------------------------------
% 1.62/1.70 % (4060)------------------------------
% 1.62/1.71 % (4067)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/298Mi)
% 1.62/1.71 % Exception at run slice level
% 1.62/1.71 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.72 % (4068)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/192Mi)
% 1.62/1.73 % (4058)Instruction limit reached!
% 1.62/1.73 % (4058)------------------------------
% 1.62/1.73 % (4058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.73 % (4058)Termination reason: Unknown
% 1.62/1.73 % (4058)Termination phase: Saturation
% 1.62/1.73
% 1.62/1.73 % (4058)Memory used [KB]: 7164
% 1.62/1.73 % (4058)Time elapsed: 0.115 s
% 1.62/1.73 % (4058)Instructions burned: 344 (million)
% 1.62/1.73 % (4058)------------------------------
% 1.62/1.73 % (4058)------------------------------
% 1.62/1.73 % (4063)Instruction limit reached!
% 1.62/1.73 % (4063)------------------------------
% 1.62/1.73 % (4063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.73 % (4063)Termination reason: Unknown
% 1.62/1.73 % (4063)Termination phase: Saturation
% 1.62/1.73
% 1.62/1.73 % (4063)Memory used [KB]: 6652
% 1.62/1.73 % (4063)Time elapsed: 0.064 s
% 1.62/1.73 % (4063)Instructions burned: 202 (million)
% 1.62/1.73 % (4063)------------------------------
% 1.62/1.73 % (4063)------------------------------
% 1.62/1.74 % (4066)Instruction limit reached!
% 1.62/1.74 % (4066)------------------------------
% 1.62/1.74 % (4066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.74 % (4066)Termination reason: Unknown
% 1.62/1.74 % (4066)Termination phase: Saturation
% 1.62/1.74
% 1.62/1.74 % (4066)Memory used [KB]: 6140
% 1.62/1.74 % (4066)Time elapsed: 0.044 s
% 1.62/1.74 % (4066)Instructions burned: 135 (million)
% 1.62/1.74 % (4066)------------------------------
% 1.62/1.74 % (4066)------------------------------
% 1.62/1.74 % (4069)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/258Mi)
% 1.62/1.74 % (4070)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/90Mi)
% 1.62/1.75 % (4071)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/231Mi)
% 1.62/1.75 % Exception at run slice level
% 1.62/1.75 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.76 % (4072)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/458Mi)
% 1.62/1.77 % (4070)Instruction limit reached!
% 1.62/1.77 % (4070)------------------------------
% 1.62/1.77 % (4070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.77 % (4070)Termination reason: Unknown
% 1.62/1.77 % (4070)Termination phase: Saturation
% 1.62/1.77
% 1.62/1.77 % (4070)Memory used [KB]: 6140
% 1.62/1.77 % (4070)Time elapsed: 0.031 s
% 1.62/1.77 % (4070)Instructions burned: 92 (million)
% 1.62/1.77 % (4070)------------------------------
% 1.62/1.77 % (4070)------------------------------
% 1.62/1.78 % (4064)Instruction limit reached!
% 1.62/1.78 % (4064)------------------------------
% 1.62/1.78 % (4064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.78 % (4064)Termination reason: Unknown
% 1.62/1.78 % (4064)Termination phase: Saturation
% 1.62/1.78
% 1.62/1.78 % (4064)Memory used [KB]: 7419
% 1.62/1.78 % (4064)Time elapsed: 0.098 s
% 1.62/1.78 % (4064)Instructions burned: 340 (million)
% 1.62/1.78 % (4064)------------------------------
% 1.62/1.78 % (4064)------------------------------
% 1.62/1.78 % (4073)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/31Mi)
% 1.62/1.79 % (4074)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/297Mi)
% 1.62/1.79 % (4068)Instruction limit reached!
% 1.62/1.79 % (4068)------------------------------
% 1.62/1.79 % (4068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.79 % (4068)Termination reason: Unknown
% 1.62/1.79 % (4068)Termination phase: Saturation
% 1.62/1.79
% 1.62/1.79 % (4068)Memory used [KB]: 6268
% 1.62/1.79 % (4068)Time elapsed: 0.065 s
% 1.62/1.79 % (4068)Instructions burned: 194 (million)
% 1.62/1.79 % (4068)------------------------------
% 1.62/1.79 % (4068)------------------------------
% 1.62/1.79 % Exception at run slice level
% 1.62/1.79 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.79 % (4073)Instruction limit reached!
% 1.62/1.79 % (4073)------------------------------
% 1.62/1.79 % (4073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.79 % (4073)Termination reason: Unknown
% 1.62/1.79 % (4073)Termination phase: Saturation
% 1.62/1.79
% 1.62/1.79 % (4073)Memory used [KB]: 5756
% 1.62/1.79 % (4073)Time elapsed: 0.011 s
% 1.62/1.79 % (4073)Instructions burned: 31 (million)
% 1.62/1.79 % (4073)------------------------------
% 1.62/1.79 % (4073)------------------------------
% 1.62/1.80 % (4076)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/182Mi)
% 1.62/1.80 % (4077)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/182Mi)
% 1.62/1.81 % (4075)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_3780 for (2995ds/987Mi)
% 1.62/1.81 % Exception at run slice level
% 1.62/1.81 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.82 % (4069)Instruction limit reached!
% 1.62/1.82 % (4069)------------------------------
% 1.62/1.82 % (4069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.82 % (4069)Termination reason: Unknown
% 1.62/1.82 % (4069)Termination phase: Saturation
% 1.62/1.82
% 1.62/1.82 % (4069)Memory used [KB]: 6396
% 1.62/1.82 % (4069)Time elapsed: 0.085 s
% 1.62/1.82 % (4069)Instructions burned: 259 (million)
% 1.62/1.82 % (4069)------------------------------
% 1.62/1.82 % (4069)------------------------------
% 1.62/1.82 % (4078)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/154Mi)
% 1.62/1.82 % Exception at run slice level
% 1.62/1.82 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.83 % (4079)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/79Mi)
% 1.62/1.84 % (4080)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/216Mi)
% 1.62/1.84 % Exception at run slice level
% 1.62/1.84 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.85 % (4062)Instruction limit reached!
% 1.62/1.85 % (4062)------------------------------
% 1.62/1.85 % (4062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.85 % (4062)Termination reason: Unknown
% 1.62/1.85 % (4062)Termination phase: Saturation
% 1.62/1.85
% 1.62/1.85 % (4062)Memory used [KB]: 6908
% 1.62/1.85 % (4062)Time elapsed: 0.190 s
% 1.62/1.85 % (4062)Instructions burned: 614 (million)
% 1.62/1.85 % (4062)------------------------------
% 1.62/1.85 % (4062)------------------------------
% 1.62/1.85 % (4077)Instruction limit reached!
% 1.62/1.85 % (4077)------------------------------
% 1.62/1.85 % (4077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.85 % (4077)Termination reason: Unknown
% 1.62/1.85 % (4077)Termination phase: Saturation
% 1.62/1.85
% 1.62/1.85 % (4077)Memory used [KB]: 6012
% 1.62/1.85 % (4077)Time elapsed: 0.079 s
% 1.62/1.85 % (4077)Instructions burned: 183 (million)
% 1.62/1.85 % (4077)------------------------------
% 1.62/1.85 % (4077)------------------------------
% 1.62/1.85 % (4076)Instruction limit reached!
% 1.62/1.85 % (4076)------------------------------
% 1.62/1.85 % (4076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.85 % (4076)Termination reason: Unknown
% 1.62/1.85 % (4076)Termination phase: Saturation
% 1.62/1.85
% 1.62/1.85 % (4076)Memory used [KB]: 6140
% 1.62/1.85 % (4076)Time elapsed: 0.080 s
% 1.62/1.85 % (4076)Instructions burned: 182 (million)
% 1.62/1.85 % (4076)------------------------------
% 1.62/1.85 % (4076)------------------------------
% 1.62/1.86 % (4079)Instruction limit reached!
% 1.62/1.86 % (4079)------------------------------
% 1.62/1.86 % (4079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.86 % (4079)Termination reason: Unknown
% 1.62/1.86 % (4079)Termination phase: Saturation
% 1.62/1.86
% 1.62/1.86 % (4079)Memory used [KB]: 5884
% 1.62/1.86 % (4079)Time elapsed: 0.024 s
% 1.62/1.86 % (4079)Instructions burned: 80 (million)
% 1.62/1.86 % (4079)------------------------------
% 1.62/1.86 % (4079)------------------------------
% 1.62/1.86 % (4082)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/922Mi)
% 1.62/1.86 % (4081)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/114Mi)
% 1.62/1.86 % (4083)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/182Mi)
% 1.62/1.86 % Exception at run slice level
% 1.62/1.86 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.86 % (4084)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/164Mi)
% 1.62/1.86 % (4044)Instruction limit reached!
% 1.62/1.86 % (4044)------------------------------
% 1.62/1.86 % (4044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.86 % (4044)Termination reason: Unknown
% 1.62/1.86 % (4044)Termination phase: Saturation
% 1.62/1.86
% 1.62/1.86 % (4044)Memory used [KB]: 7547
% 1.62/1.86 % (4044)Time elapsed: 0.347 s
% 1.62/1.86 % (4044)Instructions burned: 1088 (million)
% 1.62/1.86 % (4044)------------------------------
% 1.62/1.86 % (4044)------------------------------
% 1.62/1.86 % (4085)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/50Mi)
% 1.62/1.87 % Exception at run slice level
% 1.62/1.87 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.87 % (4086)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/368Mi)
% 1.62/1.87 % (4087)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/1021Mi)
% 1.62/1.87 % (4088)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/267Mi)
% 1.62/1.88 % Exception at run slice level
% 1.62/1.88 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.88 % (4089)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3780 for (2994ds/204Mi)
% 1.62/1.89 % (4072)Instruction limit reached!
% 1.62/1.89 % (4072)------------------------------
% 1.62/1.89 % (4072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.89 % (4072)Termination reason: Unknown
% 1.62/1.89 % (4072)Termination phase: Saturation
% 1.62/1.89
% 1.62/1.89 % (4072)Memory used [KB]: 6908
% 1.62/1.89 % (4072)Time elapsed: 0.136 s
% 1.62/1.89 % (4072)Instructions burned: 458 (million)
% 1.62/1.89 % (4072)------------------------------
% 1.62/1.89 % (4072)------------------------------
% 1.62/1.90 % (4090)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/26Mi)
% 1.62/1.90 % Exception at run slice level
% 1.62/1.90 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.91 % (4084)Instruction limit reached!
% 1.62/1.91 % (4084)------------------------------
% 1.62/1.91 % (4084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.91 % (4084)Termination reason: Unknown
% 1.62/1.91 % (4084)Termination phase: Saturation
% 1.62/1.91
% 1.62/1.91 % (4084)Memory used [KB]: 1407
% 1.62/1.91 % (4084)Time elapsed: 0.049 s
% 1.62/1.91 % (4084)Instructions burned: 166 (million)
% 1.62/1.91 % (4084)------------------------------
% 1.62/1.91 % (4084)------------------------------
% 1.62/1.91 % (4091)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/53Mi)
% 1.62/1.91 % Exception at run slice level
% 1.62/1.91 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.91 % (4081)Instruction limit reached!
% 1.62/1.91 % (4081)------------------------------
% 1.62/1.91 % (4081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.91 % (4081)Termination reason: Unknown
% 1.62/1.91 % (4081)Termination phase: Saturation
% 1.62/1.91
% 1.62/1.91 % (4081)Memory used [KB]: 6652
% 1.62/1.91 % (4081)Time elapsed: 0.056 s
% 1.62/1.91 % (4081)Instructions burned: 114 (million)
% 1.62/1.91 % (4081)------------------------------
% 1.62/1.91 % (4081)------------------------------
% 1.62/1.92 % (4092)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/4436Mi)
% 1.62/1.92 % (4093)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/1539Mi)
% 1.62/1.92 % (4094)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/408Mi)
% 1.62/1.95 % (4089)Instruction limit reached!
% 1.62/1.95 % (4089)------------------------------
% 1.62/1.95 % (4089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.95 % (4089)Termination reason: Unknown
% 1.62/1.95 % (4089)Termination phase: Saturation
% 1.62/1.95
% 1.62/1.95 % (4089)Memory used [KB]: 6268
% 1.62/1.95 % (4089)Time elapsed: 0.065 s
% 1.62/1.95 % (4089)Instructions burned: 207 (million)
% 1.62/1.95 % (4089)------------------------------
% 1.62/1.95 % (4089)------------------------------
% 1.62/1.96 % (4095)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/5205Mi)
% 1.62/1.96 % Exception at run slice level
% 1.62/1.96 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.62/1.97 % (4096)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/1913Mi)
% 1.62/1.98 % (4086)Instruction limit reached!
% 1.62/1.98 % (4086)------------------------------
% 1.62/1.98 % (4086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.98 % (4086)Termination reason: Unknown
% 1.62/1.98 % (4086)Termination phase: Saturation
% 1.62/1.98
% 1.62/1.98 % (4086)Memory used [KB]: 6524
% 1.62/1.98 % (4086)Time elapsed: 0.111 s
% 1.62/1.98 % (4086)Instructions burned: 370 (million)
% 1.62/1.98 % (4086)------------------------------
% 1.62/1.98 % (4086)------------------------------
% 1.62/1.99 % (4097)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3780 for (2993ds/4350Mi)
% 6.68/2.06 % (4094)Instruction limit reached!
% 6.68/2.06 % (4094)------------------------------
% 6.68/2.06 % (4094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.06 % (4094)Termination reason: Unknown
% 6.68/2.06 % (4094)Termination phase: Saturation
% 6.68/2.06
% 6.68/2.06 % (4094)Memory used [KB]: 6652
% 6.68/2.06 % (4094)Time elapsed: 0.134 s
% 6.68/2.06 % (4094)Instructions burned: 408 (million)
% 6.68/2.06 % (4094)------------------------------
% 6.68/2.06 % (4094)------------------------------
% 6.68/2.07 % (4098)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3780 for (2992ds/68Mi)
% 6.68/2.09 % (4098)Instruction limit reached!
% 6.68/2.09 % (4098)------------------------------
% 6.68/2.09 % (4098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.09 % (4098)Termination reason: Unknown
% 6.68/2.09 % (4098)Termination phase: Saturation
% 6.68/2.09
% 6.68/2.09 % (4098)Memory used [KB]: 5884
% 6.68/2.09 % (4098)Time elapsed: 0.022 s
% 6.68/2.09 % (4098)Instructions burned: 68 (million)
% 6.68/2.09 % (4098)------------------------------
% 6.68/2.09 % (4098)------------------------------
% 6.68/2.10 % (4099)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3780 for (2991ds/358Mi)
% 7.38/2.14 % (4082)Instruction limit reached!
% 7.38/2.14 % (4082)------------------------------
% 7.38/2.14 % (4082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.14 % (4082)Termination reason: Unknown
% 7.38/2.14 % (4082)Termination phase: Saturation
% 7.38/2.14
% 7.38/2.14 % (4082)Memory used [KB]: 6908
% 7.38/2.14 % (4082)Time elapsed: 0.279 s
% 7.38/2.14 % (4082)Instructions burned: 923 (million)
% 7.38/2.14 % (4082)------------------------------
% 7.38/2.14 % (4082)------------------------------
% 7.38/2.15 % (4100)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3780 for (2991ds/31Mi)
% 7.38/2.16 % (4100)Instruction limit reached!
% 7.38/2.16 % (4100)------------------------------
% 7.38/2.16 % (4100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.16 % (4100)Termination reason: Unknown
% 7.38/2.16 % (4100)Termination phase: Saturation
% 7.38/2.16
% 7.38/2.16 % (4100)Memory used [KB]: 5756
% 7.38/2.16 % (4100)Time elapsed: 0.011 s
% 7.38/2.16 % (4100)Instructions burned: 32 (million)
% 7.38/2.16 % (4100)------------------------------
% 7.38/2.16 % (4100)------------------------------
% 7.38/2.17 % (4101)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3780 for (2991ds/279Mi)
% 7.38/2.17 % Exception at run slice level
% 7.38/2.17 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.38/2.18 % (4102)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3780 for (2991ds/258Mi)
% 7.38/2.18 % (4087)Instruction limit reached!
% 7.38/2.18 % (4087)------------------------------
% 7.38/2.18 % (4087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.18 % (4087)Termination reason: Unknown
% 7.38/2.18 % (4087)Termination phase: Saturation
% 7.38/2.18
% 7.38/2.18 % (4087)Memory used [KB]: 7036
% 7.38/2.18 % (4087)Time elapsed: 0.312 s
% 7.38/2.18 % (4087)Instructions burned: 1023 (million)
% 7.38/2.18 % (4087)------------------------------
% 7.38/2.18 % (4087)------------------------------
% 7.38/2.19 % (4103)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/26Mi)
% 7.38/2.19 % Exception at run slice level
% 7.38/2.19 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.88/2.20 % (4104)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/995Mi)
% 7.88/2.20 % Exception at run slice level
% 7.88/2.20 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.88/2.21 % (4105)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/373Mi)
% 7.88/2.21 % (4099)Instruction limit reached!
% 7.88/2.21 % (4099)------------------------------
% 7.88/2.21 % (4099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.21 % (4099)Termination reason: Unknown
% 7.88/2.21 % (4099)Termination phase: Saturation
% 7.88/2.21
% 7.88/2.21 % (4099)Memory used [KB]: 6524
% 7.88/2.21 % (4099)Time elapsed: 0.117 s
% 7.88/2.21 % (4099)Instructions burned: 359 (million)
% 7.88/2.21 % (4099)------------------------------
% 7.88/2.21 % (4099)------------------------------
% 7.88/2.22 % (4106)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/253Mi)
% 7.88/2.22 % Exception at run slice level
% 7.88/2.22 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.88/2.23 % (4107)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/832Mi)
% 7.88/2.26 % (4102)Instruction limit reached!
% 7.88/2.26 % (4102)------------------------------
% 7.88/2.26 % (4102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.88/2.26 % (4102)Termination reason: Unknown
% 7.88/2.26 % (4102)Termination phase: Saturation
% 7.88/2.26
% 7.88/2.26 % (4102)Memory used [KB]: 6396
% 7.88/2.26 % (4102)Time elapsed: 0.081 s
% 7.88/2.26 % (4102)Instructions burned: 259 (million)
% 7.88/2.26 % (4102)------------------------------
% 7.88/2.26 % (4102)------------------------------
% 7.88/2.27 % (4108)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/668Mi)
% 7.88/2.27 % Exception at run slice level
% 7.88/2.27 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.88/2.28 % (4109)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/40Mi)
% 7.88/2.28 % Exception at run slice level
% 7.88/2.28 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 7.88/2.29 % (4110)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3780 for (2990ds/294Mi)
% 7.88/2.29 % Exception at run slice level
% 7.88/2.29 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 8.55/2.30 % (4111)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3780 for (2989ds/187Mi)
% 8.55/2.33 % (4105)Instruction limit reached!
% 8.55/2.33 % (4105)------------------------------
% 8.55/2.33 % (4105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.33 % (4105)Termination reason: Unknown
% 8.55/2.33 % (4105)Termination phase: Saturation
% 8.55/2.33
% 8.55/2.33 % (4105)Memory used [KB]: 6268
% 8.55/2.33 % (4105)Time elapsed: 0.118 s
% 8.55/2.33 % (4105)Instructions burned: 375 (million)
% 8.55/2.33 % (4105)------------------------------
% 8.55/2.33 % (4105)------------------------------
% 8.55/2.34 % (4112)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3780 for (2989ds/371Mi)
% 8.55/2.35 % (4111)Instruction limit reached!
% 8.55/2.35 % (4111)------------------------------
% 8.55/2.35 % (4111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.35 % (4111)Termination reason: Unknown
% 8.55/2.35 % (4111)Termination phase: Saturation
% 8.55/2.35
% 8.55/2.35 % (4111)Memory used [KB]: 6780
% 8.55/2.35 % (4111)Time elapsed: 0.059 s
% 8.55/2.35 % (4111)Instructions burned: 190 (million)
% 8.55/2.35 % (4111)------------------------------
% 8.55/2.35 % (4111)------------------------------
% 8.55/2.36 % (4113)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3780 for (2989ds/1827Mi)
% 8.55/2.39 % (4093)Instruction limit reached!
% 8.55/2.39 % (4093)------------------------------
% 8.55/2.39 % (4093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.39 % (4093)Termination reason: Unknown
% 8.55/2.39 % (4093)Termination phase: Saturation
% 8.55/2.39
% 8.55/2.39 % (4093)Memory used [KB]: 8315
% 8.55/2.39 % (4093)Time elapsed: 0.467 s
% 8.55/2.39 % (4093)Instructions burned: 1539 (million)
% 8.55/2.39 % (4093)------------------------------
% 8.55/2.39 % (4093)------------------------------
% 9.14/2.40 % (4114)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/70Mi)
% 9.14/2.40 % Exception at run slice level
% 9.14/2.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 9.14/2.41 % (4115)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/316Mi)
% 9.14/2.41 % Exception at run slice level
% 9.14/2.41 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 9.14/2.42 % (4116)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/932Mi)
% 9.14/2.42 % Exception at run slice level
% 9.14/2.42 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 9.14/2.43 % (4117)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/4714Mi)
% 9.14/2.43 % Exception at run slice level
% 9.14/2.43 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 9.14/2.44 % (4118)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/8250Mi)
% 9.14/2.45 % (4112)Instruction limit reached!
% 9.14/2.45 % (4112)------------------------------
% 9.14/2.45 % (4112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.14/2.45 % (4112)Termination reason: Unknown
% 9.14/2.45 % (4112)Termination phase: Saturation
% 9.14/2.45
% 9.14/2.45 % (4112)Memory used [KB]: 7547
% 9.14/2.45 % (4112)Time elapsed: 0.115 s
% 9.14/2.45 % (4112)Instructions burned: 372 (million)
% 9.14/2.45 % (4112)------------------------------
% 9.14/2.45 % (4112)------------------------------
% 9.14/2.46 % (4119)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3780 for (2988ds/770Mi)
% 9.14/2.49 % (4107)Instruction limit reached!
% 9.14/2.49 % (4107)------------------------------
% 9.14/2.49 % (4107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.14/2.49 % (4107)Termination reason: Unknown
% 9.14/2.49 % (4107)Termination phase: Saturation
% 9.14/2.49
% 9.14/2.49 % (4107)Memory used [KB]: 6780
% 9.14/2.49 % (4107)Time elapsed: 0.259 s
% 9.14/2.49 % (4107)Instructions burned: 834 (million)
% 9.14/2.49 % (4107)------------------------------
% 9.14/2.49 % (4107)------------------------------
% 9.87/2.50 % (4120)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3780 for (2987ds/794Mi)
% 9.87/2.57 % (4096)Instruction limit reached!
% 9.87/2.57 % (4096)------------------------------
% 9.87/2.57 % (4096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.57 % (4096)Termination reason: Unknown
% 9.87/2.57 % (4096)Termination phase: Saturation
% 9.87/2.57
% 9.87/2.57 % (4096)Memory used [KB]: 3326
% 9.87/2.57 % (4096)Time elapsed: 0.603 s
% 9.87/2.57 % (4096)Instructions burned: 1915 (million)
% 9.87/2.57 % (4096)------------------------------
% 9.87/2.57 % (4096)------------------------------
% 9.87/2.58 % (4121)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3780 for (2987ds/464Mi)
% 10.36/2.70 % (4119)Refutation not found, non-redundant clauses discarded% (4119)------------------------------
% 10.36/2.70 % (4119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.36/2.70 % (4119)Termination reason: Refutation not found, non-redundant clauses discarded
% 10.36/2.70
% 10.36/2.70 % (4119)Memory used [KB]: 7164
% 10.36/2.70 % (4119)Time elapsed: 0.235 s
% 10.36/2.70 % (4119)Instructions burned: 765 (million)
% 10.36/2.70 % (4119)------------------------------
% 10.36/2.70 % (4119)------------------------------
% 10.36/2.71 % (4122)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3780 for (2985ds/1376Mi)
% 10.36/2.71 % Exception at run slice level
% 10.36/2.71 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 10.36/2.72 % (4123)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3780 for (2985ds/906Mi)
% 10.36/2.73 % (4121)Instruction limit reached!
% 10.36/2.73 % (4121)------------------------------
% 10.36/2.73 % (4121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.36/2.73 % (4121)Termination reason: Unknown
% 10.36/2.73 % (4121)Termination phase: Saturation
% 10.36/2.73
% 10.36/2.73 % (4121)Memory used [KB]: 6524
% 10.36/2.73 % (4121)Time elapsed: 0.149 s
% 10.36/2.73 % (4121)Instructions burned: 464 (million)
% 10.36/2.73 % (4121)------------------------------
% 10.36/2.73 % (4121)------------------------------
% 10.36/2.74 % (4124)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3780 for (2985ds/434Mi)
% 10.36/2.74 % (4120)Instruction limit reached!
% 10.36/2.74 % (4120)------------------------------
% 10.36/2.74 % (4120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.36/2.74 % (4120)Termination reason: Unknown
% 10.36/2.74 % (4120)Termination phase: Saturation
% 10.36/2.74
% 10.36/2.74 % (4120)Memory used [KB]: 3198
% 10.36/2.74 % (4120)Time elapsed: 0.243 s
% 10.36/2.74 % (4120)Instructions burned: 794 (million)
% 10.36/2.74 % (4120)------------------------------
% 10.36/2.74 % (4120)------------------------------
% 10.36/2.75 % (4125)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3780 for (2985ds/865Mi)
% 11.21/2.86 % (4124)Instruction limit reached!
% 11.21/2.86 % (4124)------------------------------
% 11.21/2.86 % (4124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.21/2.86 % (4124)Termination reason: Unknown
% 11.21/2.86 % (4124)Termination phase: Saturation
% 11.21/2.86
% 11.21/2.86 % (4124)Memory used [KB]: 6908
% 11.21/2.86 % (4124)Time elapsed: 0.128 s
% 11.21/2.86 % (4124)Instructions burned: 435 (million)
% 11.21/2.86 % (4124)------------------------------
% 11.21/2.86 % (4124)------------------------------
% 11.21/2.88 % (4126)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3780 for (2984ds/593Mi)
% 11.21/2.88 % Exception at run slice level
% 11.21/2.88 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 11.21/2.88 % (4127)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3780 for (2984ds/443Mi)
% 11.57/2.93 % (4113)Instruction limit reached!
% 11.57/2.93 % (4113)------------------------------
% 11.57/2.93 % (4113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/2.93 % (4113)Termination reason: Unknown
% 11.57/2.93 % (4113)Termination phase: Saturation
% 11.57/2.93
% 11.57/2.93 % (4113)Memory used [KB]: 7547
% 11.57/2.93 % (4113)Time elapsed: 0.564 s
% 11.57/2.93 % (4113)Instructions burned: 1829 (million)
% 11.57/2.93 % (4113)------------------------------
% 11.57/2.93 % (4113)------------------------------
% 11.57/2.94 % (4128)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3780 for (2983ds/594Mi)
% 11.57/3.01 % (4123)Instruction limit reached!
% 11.57/3.01 % (4123)------------------------------
% 11.57/3.01 % (4123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.01 % (4123)Termination reason: Unknown
% 11.57/3.01 % (4123)Termination phase: Saturation
% 11.57/3.01
% 11.57/3.01 % (4123)Memory used [KB]: 8955
% 11.57/3.01 % (4123)Time elapsed: 0.292 s
% 11.57/3.01 % (4123)Instructions burned: 907 (million)
% 11.57/3.01 % (4123)------------------------------
% 11.57/3.01 % (4123)------------------------------
% 11.57/3.02 % (4129)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3780 for (2982ds/327Mi)
% 11.57/3.02 % (4125)Instruction limit reached!
% 11.57/3.02 % (4125)------------------------------
% 11.57/3.02 % (4125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.02 % (4125)Termination reason: Unknown
% 11.57/3.02 % (4125)Termination phase: Saturation
% 11.57/3.02
% 11.57/3.02 % (4125)Memory used [KB]: 8699
% 11.57/3.02 % (4125)Time elapsed: 0.269 s
% 11.57/3.02 % (4125)Instructions burned: 867 (million)
% 11.57/3.02 % (4125)------------------------------
% 11.57/3.02 % (4125)------------------------------
% 13.73/3.02 % (4127)Instruction limit reached!
% 13.73/3.02 % (4127)------------------------------
% 13.73/3.02 % (4127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.02 % (4127)Termination reason: Unknown
% 13.73/3.02 % (4127)Termination phase: Saturation
% 13.73/3.02
% 13.73/3.02 % (4127)Memory used [KB]: 6652
% 13.73/3.02 % (4127)Time elapsed: 0.161 s
% 13.73/3.02 % (4127)Instructions burned: 444 (million)
% 13.73/3.02 % (4127)------------------------------
% 13.73/3.02 % (4127)------------------------------
% 13.73/3.03 % (4130)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3780 for (2982ds/5411Mi)
% 13.73/3.03 % (4131)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3780 for (2982ds/1762Mi)
% 13.73/3.03 % Exception at run slice level
% 13.73/3.03 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 13.73/3.04 % (4132)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3780 for (2982ds/96Mi)
% 13.73/3.04 % Exception at run slice level
% 13.73/3.04 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 13.73/3.05 % (4133)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3780 for (2982ds/503Mi)
% 13.73/3.11 % (4128)Instruction limit reached!
% 13.73/3.11 % (4128)------------------------------
% 13.73/3.11 % (4128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.11 % (4128)Termination reason: Unknown
% 13.73/3.11 % (4128)Termination phase: Saturation
% 13.73/3.11
% 13.73/3.11 % (4128)Memory used [KB]: 7291
% 13.73/3.11 % (4128)Time elapsed: 0.201 s
% 13.73/3.11 % (4128)Instructions burned: 596 (million)
% 13.73/3.11 % (4128)------------------------------
% 13.73/3.11 % (4128)------------------------------
% 13.73/3.12 % (4129)Instruction limit reached!
% 13.73/3.12 % (4129)------------------------------
% 13.73/3.12 % (4129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.12 % (4129)Termination reason: Unknown
% 13.73/3.12 % (4129)Termination phase: Saturation
% 13.73/3.12
% 13.73/3.12 % (4129)Memory used [KB]: 6268
% 13.73/3.12 % (4129)Time elapsed: 0.101 s
% 13.73/3.12 % (4129)Instructions burned: 327 (million)
% 13.73/3.12 % (4129)------------------------------
% 13.73/3.12 % (4129)------------------------------
% 14.34/3.12 % (4134)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3780 for (2981ds/90Mi)
% 14.34/3.13 % (4135)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3780 for (2981ds/593Mi)
% 14.34/3.15 % (4134)Instruction limit reached!
% 14.34/3.15 % (4134)------------------------------
% 14.34/3.15 % (4134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.15 % (4134)Termination reason: Unknown
% 14.34/3.15 % (4134)Termination phase: Saturation
% 14.34/3.15
% 14.34/3.15 % (4134)Memory used [KB]: 6140
% 14.34/3.15 % (4134)Time elapsed: 0.030 s
% 14.34/3.15 % (4134)Instructions burned: 91 (million)
% 14.34/3.15 % (4134)------------------------------
% 14.34/3.15 % (4134)------------------------------
% 14.34/3.16 % (4136)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3780 for (2981ds/1512Mi)
% 14.59/3.21 % (4133)Instruction limit reached!
% 14.59/3.21 % (4133)------------------------------
% 14.59/3.21 % (4133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.21 % (4133)Termination reason: Unknown
% 14.59/3.21 % (4133)Termination phase: Saturation
% 14.59/3.21
% 14.59/3.21 % (4133)Memory used [KB]: 7036
% 14.59/3.21 % (4133)Time elapsed: 0.157 s
% 14.59/3.21 % (4133)Instructions burned: 504 (million)
% 14.59/3.21 % (4133)------------------------------
% 14.59/3.21 % (4133)------------------------------
% 14.59/3.22 % (4137)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3780 for (2980ds/569Mi)
% 14.59/3.22 % Exception at run slice level
% 14.59/3.22 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 14.59/3.23 % (4138)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3780 for (2980ds/501Mi)
% 14.59/3.24 % (4092)Instruction limit reached!
% 14.59/3.24 % (4092)------------------------------
% 14.59/3.24 % (4092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.24 % (4092)Termination reason: Unknown
% 14.59/3.24 % (4092)Termination phase: Saturation
% 14.59/3.24
% 14.59/3.24 % (4092)Memory used [KB]: 12025
% 14.59/3.24 % (4092)Time elapsed: 1.324 s
% 14.59/3.24 % (4092)Instructions burned: 4436 (million)
% 14.59/3.24 % (4092)------------------------------
% 14.59/3.24 % (4092)------------------------------
% 14.59/3.25 % (4139)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3780 for (2980ds/562Mi)
% 15.03/3.31 % (4097)Refutation not found, non-redundant clauses discarded% (4097)------------------------------
% 15.03/3.31 % (4097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.03/3.31 % (4097)Termination reason: Refutation not found, non-redundant clauses discarded
% 15.03/3.31
% 15.03/3.31 % (4097)Memory used [KB]: 11385
% 15.03/3.31 % (4097)Time elapsed: 1.314 s
% 15.03/3.31 % (4097)Instructions burned: 4237 (million)
% 15.03/3.31 % (4097)------------------------------
% 15.03/3.31 % (4097)------------------------------
% 15.03/3.32 % (4140)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3780 for (2979ds/406Mi)
% 15.03/3.32 % (4135)Instruction limit reached!
% 15.03/3.32 % (4135)------------------------------
% 15.03/3.32 % (4135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.03/3.32 % (4135)Termination reason: Unknown
% 15.03/3.32 % (4135)Termination phase: Saturation
% 15.03/3.32
% 15.03/3.32 % (4135)Memory used [KB]: 6652
% 15.03/3.32 % (4135)Time elapsed: 0.191 s
% 15.03/3.32 % (4135)Instructions burned: 593 (million)
% 15.03/3.32 % (4135)------------------------------
% 15.03/3.32 % (4135)------------------------------
% 15.03/3.33 % (4141)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3780 for (2979ds/582Mi)
% 15.03/3.38 % (4138)Instruction limit reached!
% 15.03/3.38 % (4138)------------------------------
% 15.03/3.38 % (4138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.03/3.38 % (4138)Termination reason: Unknown
% 15.03/3.38 % (4138)Termination phase: Saturation
% 15.03/3.38
% 15.03/3.38 % (4138)Memory used [KB]: 7036
% 15.03/3.38 % (4138)Time elapsed: 0.156 s
% 15.03/3.38 % (4138)Instructions burned: 503 (million)
% 15.03/3.38 % (4138)------------------------------
% 15.03/3.38 % (4138)------------------------------
% 15.03/3.39 % (4142)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3780 for (2979ds/456Mi)
% 15.51/3.43 % (4140)Instruction limit reached!
% 15.51/3.43 % (4140)------------------------------
% 15.51/3.43 % (4140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.51/3.43 % (4140)Termination reason: Unknown
% 15.51/3.43 % (4140)Termination phase: Saturation
% 15.51/3.43
% 15.51/3.43 % (4140)Memory used [KB]: 6524
% 15.51/3.43 % (4140)Time elapsed: 0.117 s
% 15.51/3.43 % (4140)Instructions burned: 406 (million)
% 15.51/3.43 % (4140)------------------------------
% 15.51/3.43 % (4140)------------------------------
% 15.51/3.44 % (4139)Instruction limit reached!
% 15.51/3.44 % (4139)------------------------------
% 15.51/3.44 % (4139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.51/3.44 % (4139)Termination reason: Unknown
% 15.51/3.44 % (4139)Termination phase: Saturation
% 15.51/3.44
% 15.51/3.44 % (4139)Memory used [KB]: 6652
% 15.51/3.44 % (4139)Time elapsed: 0.184 s
% 15.51/3.44 % (4139)Instructions burned: 564 (million)
% 15.51/3.44 % (4139)------------------------------
% 15.51/3.44 % (4139)------------------------------
% 15.51/3.44 % (4143)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3780 for (2978ds/393Mi)
% 15.51/3.45 % (4145)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3780 for (2978ds/1335Mi)
% 15.94/3.50 % (4141)Instruction limit reached!
% 15.94/3.50 % (4141)------------------------------
% 15.94/3.50 % (4141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.94/3.50 % (4141)Termination reason: Unknown
% 15.94/3.50 % (4141)Termination phase: Saturation
% 15.94/3.50
% 15.94/3.50 % (4141)Memory used [KB]: 6524
% 15.94/3.50 % (4141)Time elapsed: 0.177 s
% 15.94/3.50 % (4141)Instructions burned: 582 (million)
% 15.94/3.50 % (4141)------------------------------
% 15.94/3.50 % (4141)------------------------------
% 15.94/3.51 % (4146)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3780 for (2977ds/3373Mi)
% 15.94/3.54 % (4142)Refutation not found, non-redundant clauses discarded% (4142)------------------------------
% 15.94/3.54 % (4142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.94/3.54 % (4142)Termination reason: Refutation not found, non-redundant clauses discarded
% 15.94/3.54
% 15.94/3.54 % (4142)Memory used [KB]: 6908
% 15.94/3.54 % (4142)Time elapsed: 0.145 s
% 15.94/3.54 % (4142)Instructions burned: 455 (million)
% 15.94/3.54 % (4142)------------------------------
% 15.94/3.54 % (4142)------------------------------
% 15.94/3.55 % (4147)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3780 for (2977ds/474Mi)
% 15.94/3.55 % Exception at run slice level
% 15.94/3.55 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 15.94/3.56 % (4148)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3780 for (2977ds/157Mi)
% 15.94/3.56 % Exception at run slice level
% 15.94/3.56 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 15.94/3.56 % (4143)Refutation not found, non-redundant clauses discarded% (4143)------------------------------
% 15.94/3.56 % (4143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.94/3.56 % (4143)Termination reason: Refutation not found, non-redundant clauses discarded
% 15.94/3.56
% 15.94/3.56 % (4143)Memory used [KB]: 6524
% 15.94/3.56 % (4143)Time elapsed: 0.121 s
% 15.94/3.56 % (4143)Instructions burned: 381 (million)
% 15.94/3.56 % (4143)------------------------------
% 15.94/3.56 % (4143)------------------------------
% 15.94/3.57 % (4149)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3780 for (2977ds/590Mi)
% 15.94/3.57 % (4150)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3780 for (2977ds/104Mi)
% 16.53/3.61 % (4150)Instruction limit reached!
% 16.53/3.61 % (4150)------------------------------
% 16.53/3.61 % (4150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.61 % (4150)Termination reason: Unknown
% 16.53/3.61 % (4150)Termination phase: Saturation
% 16.53/3.61
% 16.53/3.61 % (4150)Memory used [KB]: 6012
% 16.53/3.61 % (4150)Time elapsed: 0.035 s
% 16.53/3.61 % (4150)Instructions burned: 106 (million)
% 16.53/3.61 % (4150)------------------------------
% 16.53/3.61 % (4150)------------------------------
% 16.53/3.61 % (4151)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3780 for (2976ds/414Mi)
% 16.53/3.62 % Exception at run slice level
% 16.53/3.62 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 16.53/3.62 % (4136)Instruction limit reached!
% 16.53/3.62 % (4136)------------------------------
% 16.53/3.62 % (4136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.62 % (4136)Termination reason: Unknown
% 16.53/3.62 % (4136)Termination phase: Saturation
% 16.53/3.62
% 16.53/3.62 % (4136)Memory used [KB]: 7675
% 16.53/3.62 % (4136)Time elapsed: 0.462 s
% 16.53/3.62 % (4136)Instructions burned: 1513 (million)
% 16.53/3.62 % (4136)------------------------------
% 16.53/3.62 % (4136)------------------------------
% 16.53/3.62 % (4152)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3780 for (2976ds/715Mi)
% 16.53/3.63 % (4153)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3780 for (2976ds/961Mi)
% 16.53/3.64 % (4145)First to succeed.
% 16.53/3.66 % (4145)Refutation found. Thanks to Tanya!
% 16.53/3.66 % SZS status Theorem for DTF2THF_3780
% 16.53/3.66 % SZS output start Proof for DTF2THF_3780
% 16.53/3.66 thf(type_def_6, type, sK0: $tType).
% 16.53/3.66 thf(type_def_7, type, sK1: $tType).
% 16.53/3.66 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 16.53/3.66 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 16.53/3.66 thf(func_def_16, type, sK2: sK1 > sK0).
% 16.53/3.66 thf(func_def_17, type, sK3: sK1 > $o).
% 16.53/3.66 thf(func_def_18, type, sK4: sK0 > $o).
% 16.53/3.66 thf(func_def_20, type, sK6: sK0).
% 16.53/3.66 thf(func_def_21, type, sK7: (sK0 > sK1) > sK1).
% 16.53/3.66 thf(func_def_22, type, sK8: (sK0 > sK1) > sK0).
% 16.53/3.66 thf(func_def_23, type, sK9: sK1).
% 16.53/3.66 thf(func_def_24, type, sK10: (sK0 > sK1) > sK0).
% 16.53/3.66 thf(func_def_25, type, sK11: sK1).
% 16.53/3.66 thf(func_def_26, type, sK12: sK0 > sK1).
% 16.53/3.66 thf(func_def_27, type, sK13: sK0 > sK1).
% 16.53/3.66 thf(func_def_28, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X0 > X1)).
% 16.53/3.66 thf(func_def_29, type, sK15: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > $o) > X1)).
% 16.53/3.66 thf(func_def_30, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > $o) > X1)).
% 16.53/3.66 thf(func_def_31, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > (X1 > $o) > X1)).
% 16.53/3.66 thf(func_def_33, type, ph18: !>[X0: $tType]:(X0)).
% 16.53/3.66 thf(f2587,plain,(
% 16.53/3.66 $false),
% 16.53/3.66 inference(avatar_sat_refutation,[status(thm)],[f67,f75,f87,f89,f102,f103,f111,f112,f124,f133,f135,f137,f149,f151,f153,f157,f175,f181,f187,f192,f204,f207,f210,f212,f227,f238,f243,f248,f265,f266,f269,f273,f296,f300,f302,f305,f309,f315,f316,f317,f327,f333,f334,f335,f341,f344,f346,f349,f365,f368,f370,f372,f378,f383,f385,f386,f397,f399,f406,f408,f411,f413,f418,f420,f445,f453,f468,f469,f483,f484,f505,f600,f724,f739,f900,f1055,f1083,f1095,f1113,f1194,f1197,f1201,f1236,f1237,f1282,f1366,f1371,f1483,f1561,f1568,f1569,f1575,f1581,f1593,f1706,f1790,f1808,f1820,f1826,f1868,f1896,f1972,f1990,f2098,f2214,f2331,f2344,f2400,f2430,f2439,f2534,f2547,f2572,f2575,f2583])).
% 16.53/3.66 thf(f2583,plain,(
% 16.53/3.66 ~spl5_7 | ~spl5_24),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2582])).
% 16.53/3.66 thf(f2582,plain,(
% 16.53/3.66 $false | (~spl5_7 | ~spl5_24)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2581])).
% 16.53/3.66 thf(f2581,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_7 | ~spl5_24)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f110,f640])).
% 16.53/3.66 thf(f640,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ sK11 @ sK3)) | ~spl5_24),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f638])).
% 16.53/3.66 thf(f638,definition,(
% 16.53/3.66 spl5_24 <=> ($false = ('const/sets/IN' @ sK1 @ sK11 @ sK3))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_24])],[avatar_definition])).
% 16.53/3.66 thf(f110,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ~spl5_7),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f108])).
% 16.53/3.66 thf(f108,definition,(
% 16.53/3.66 spl5_7 <=> (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 16.53/3.66 thf(f2575,plain,(
% 16.53/3.66 spl5_24 | spl5_23 | ~spl5_6 | ~spl5_20),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f2158,f503,f99,f635,f638])).
% 16.53/3.66 thf(f635,definition,(
% 16.53/3.66 spl5_23 <=> ! [X0 : sK1] : (((sK2 @ X0) != (sK2 @ sK9)) | (sK11 = X0) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_23])],[avatar_definition])).
% 16.53/3.66 thf(f99,definition,(
% 16.53/3.66 spl5_6 <=> ((sK2 @ sK9) = (sK2 @ sK11))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 16.53/3.66 thf(f503,definition,(
% 16.53/3.66 spl5_20 <=> ! [X2 : sK1,X1 : sK1] : (((sK2 @ X2) != (sK2 @ X1)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (X1 = X2) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_20])],[avatar_definition])).
% 16.53/3.66 thf(f2158,plain,(
% 16.53/3.66 ( ! [X0 : sK1] : (($false = ('const/sets/IN' @ sK1 @ sK11 @ sK3)) | ((sK2 @ X0) != (sK2 @ sK9)) | (sK11 = X0) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3))) ) | (~spl5_6 | ~spl5_20)),
% 16.53/3.66 inference(superposition,[status(thm)],[f504,f101])).
% 16.53/3.66 thf(f101,plain,(
% 16.53/3.66 ((sK2 @ sK9) = (sK2 @ sK11)) | ~spl5_6),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f99])).
% 16.53/3.66 thf(f504,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (((sK2 @ X2) != (sK2 @ X1)) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)) | (X1 = X2) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) ) | ~spl5_20),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f503])).
% 16.53/3.66 thf(f2572,plain,(
% 16.53/3.66 spl5_2 | ~spl5_5 | ~spl5_23),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2571])).
% 16.53/3.66 thf(f2571,plain,(
% 16.53/3.66 $false | (spl5_2 | ~spl5_5 | ~spl5_23)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2570])).
% 16.53/3.66 thf(f2570,plain,(
% 16.53/3.66 ($false = $true) | (spl5_2 | ~spl5_5 | ~spl5_23)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f86,f2129])).
% 16.53/3.66 thf(f2129,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (spl5_2 | ~spl5_23)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2127,f63])).
% 16.53/3.66 thf(f63,plain,(
% 16.53/3.66 (sK9 != sK11) | spl5_2),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f61])).
% 16.53/3.66 thf(f61,definition,(
% 16.53/3.66 spl5_2 <=> (sK9 = sK11)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 16.53/3.66 thf(f2127,plain,(
% 16.53/3.66 (sK9 = sK11) | ($false = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ~spl5_23),
% 16.53/3.66 inference(equality_resolution,[status(thm)],[f636])).
% 16.53/3.66 thf(f636,plain,(
% 16.53/3.66 ( ! [X0 : sK1] : (((sK2 @ X0) != (sK2 @ sK9)) | (sK11 = X0) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3))) ) | ~spl5_23),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f635])).
% 16.53/3.66 thf(f86,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ~spl5_5),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f84])).
% 16.53/3.66 thf(f84,definition,(
% 16.53/3.66 spl5_5 <=> ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 16.53/3.66 thf(f2547,plain,(
% 16.53/3.66 spl5_62 | ~spl5_4 | spl5_70 | ~spl5_113),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f2546,f2328,f1363,f73,f1270])).
% 16.53/3.66 thf(f1270,definition,(
% 16.53/3.66 spl5_62 <=> ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_62])],[avatar_definition])).
% 16.53/3.66 thf(f73,definition,(
% 16.53/3.66 spl5_4 <=> ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 16.53/3.66 thf(f1363,definition,(
% 16.53/3.66 spl5_70 <=> (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_70])],[avatar_definition])).
% 16.53/3.66 thf(f2328,definition,(
% 16.53/3.66 spl5_113 <=> ((sK7 @ sK13) = (sK13 @ (sK2 @ (sK7 @ sK13))))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_113])],[avatar_definition])).
% 16.53/3.66 thf(f2546,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_4 | spl5_70 | ~spl5_113)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2364,f1364])).
% 16.53/3.66 thf(f1364,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) != $false) | spl5_70),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1363])).
% 16.53/3.66 thf(f2364,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_4 | ~spl5_113)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2357])).
% 16.53/3.66 thf(f2357,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | ((sK7 @ sK13) != (sK7 @ sK13)) | (~spl5_4 | ~spl5_113)),
% 16.53/3.66 inference(superposition,[status(thm)],[f74,f2330])).
% 16.53/3.66 thf(f2330,plain,(
% 16.53/3.66 ((sK7 @ sK13) = (sK13 @ (sK2 @ (sK7 @ sK13)))) | ~spl5_113),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f2328])).
% 16.53/3.66 thf(f74,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) ) | ~spl5_4),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f73])).
% 16.53/3.66 thf(f2534,plain,(
% 16.53/3.66 ~spl5_17 | spl5_64 | ~spl5_70),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2533])).
% 16.53/3.66 thf(f2533,plain,(
% 16.53/3.66 $false | (~spl5_17 | spl5_64 | ~spl5_70)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2529,f1279])).
% 16.53/3.66 thf(f1279,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) != $false) | spl5_64),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1278])).
% 16.53/3.66 thf(f1278,definition,(
% 16.53/3.66 spl5_64 <=> (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_64])],[avatar_definition])).
% 16.53/3.66 thf(f2529,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false) | (~spl5_17 | ~spl5_70)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2526])).
% 16.53/3.66 thf(f2526,plain,(
% 16.53/3.66 ($false = $true) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false) | (~spl5_17 | ~spl5_70)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1365,f452])).
% 16.53/3.66 thf(f452,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) ) | ~spl5_17),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f451])).
% 16.53/3.66 thf(f451,definition,(
% 16.53/3.66 spl5_17 <=> ! [X1 : sK0] : (($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_17])],[avatar_definition])).
% 16.53/3.66 thf(f1365,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | ~spl5_70),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1363])).
% 16.53/3.66 thf(f2439,plain,(
% 16.53/3.66 spl5_70 | ~spl5_12 | ~spl5_16 | ~spl5_62 | ~spl5_113),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f2436,f2328,f1270,f443,f225,f1363])).
% 16.53/3.66 thf(f225,definition,(
% 16.53/3.66 spl5_12 <=> ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_12])],[avatar_definition])).
% 16.53/3.66 thf(f443,definition,(
% 16.53/3.66 spl5_16 <=> ! [X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ((sK2 @ (sK13 @ X1)) = X1))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_16])],[avatar_definition])).
% 16.53/3.66 thf(f2436,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | (~spl5_12 | ~spl5_16 | ~spl5_62 | ~spl5_113)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2362,f2425])).
% 16.53/3.66 thf(f2425,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | (~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2424])).
% 16.53/3.66 thf(f2424,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | ($false = $true) | (~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(superposition,[status(thm)],[f444,f1272])).
% 16.53/3.66 thf(f1272,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | ~spl5_62),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1270])).
% 16.53/3.66 thf(f444,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ((sK2 @ (sK13 @ X1)) = X1)) ) | ~spl5_16),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f443])).
% 16.53/3.66 thf(f2362,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) != (sK10 @ sK13)) | (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | (~spl5_12 | ~spl5_113)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2359])).
% 16.53/3.66 thf(f2359,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | ((sK7 @ sK13) != (sK7 @ sK13)) | ((sK2 @ (sK13 @ (sK10 @ sK13))) != (sK10 @ sK13)) | (~spl5_12 | ~spl5_113)),
% 16.53/3.66 inference(superposition,[status(thm)],[f226,f2330])).
% 16.53/3.66 thf(f226,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) ) | ~spl5_12),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f225])).
% 16.53/3.66 thf(f2430,plain,(
% 16.53/3.66 ~spl5_13 | ~spl5_16 | ~spl5_62 | spl5_71 | ~spl5_113),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2429])).
% 16.53/3.66 thf(f2429,plain,(
% 16.53/3.66 $false | (~spl5_13 | ~spl5_16 | ~spl5_62 | spl5_71 | ~spl5_113)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2425,f2401])).
% 16.53/3.66 thf(f2401,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) != (sK10 @ sK13)) | (~spl5_13 | spl5_71 | ~spl5_113)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2361,f1369])).
% 16.53/3.66 thf(f1369,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) != $true) | spl5_71),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1368])).
% 16.53/3.66 thf(f1368,definition,(
% 16.53/3.66 spl5_71 <=> (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_71])],[avatar_definition])).
% 16.53/3.66 thf(f2361,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | ((sK2 @ (sK13 @ (sK10 @ sK13))) != (sK10 @ sK13)) | (~spl5_13 | ~spl5_113)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2360])).
% 16.53/3.66 thf(f2360,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) != (sK10 @ sK13)) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | ((sK7 @ sK13) != (sK7 @ sK13)) | (~spl5_13 | ~spl5_113)),
% 16.53/3.66 inference(superposition,[status(thm)],[f264,f2330])).
% 16.53/3.66 thf(f264,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) ) | ~spl5_13),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f263])).
% 16.53/3.66 thf(f263,definition,(
% 16.53/3.66 spl5_13 <=> ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_13])],[avatar_definition])).
% 16.53/3.66 thf(f2400,plain,(
% 16.53/3.66 ~spl5_8 | spl5_71 | ~spl5_73 | ~spl5_113),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2399])).
% 16.53/3.66 thf(f2399,plain,(
% 16.53/3.66 $false | (~spl5_8 | spl5_71 | ~spl5_73 | ~spl5_113)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2398])).
% 16.53/3.66 thf(f2398,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_8 | spl5_71 | ~spl5_73 | ~spl5_113)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f2397,f1394])).
% 16.53/3.66 thf(f1394,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | ~spl5_73),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1392])).
% 16.53/3.66 thf(f1392,definition,(
% 16.53/3.66 spl5_73 <=> ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_73])],[avatar_definition])).
% 16.53/3.66 thf(f2397,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_8 | spl5_71 | ~spl5_113)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f2365,f1369])).
% 16.53/3.66 thf(f2365,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | (~spl5_8 | ~spl5_113)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2358])).
% 16.53/3.66 thf(f2358,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | ((sK7 @ sK13) != (sK7 @ sK13)) | (~spl5_8 | ~spl5_113)),
% 16.53/3.66 inference(superposition,[status(thm)],[f123,f2330])).
% 16.53/3.66 thf(f123,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) ) | ~spl5_8),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f122])).
% 16.53/3.66 thf(f122,definition,(
% 16.53/3.66 spl5_8 <=> ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 16.53/3.66 thf(f2344,plain,(
% 16.53/3.66 ~spl5_63 | ~spl5_112),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2343])).
% 16.53/3.66 thf(f2343,plain,(
% 16.53/3.66 $false | (~spl5_63 | ~spl5_112)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2342])).
% 16.53/3.66 thf(f2342,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_63 | ~spl5_112)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f1276,f2326])).
% 16.53/3.66 thf(f2326,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $false) | ~spl5_112),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f2324])).
% 16.53/3.66 thf(f2324,definition,(
% 16.53/3.66 spl5_112 <=> (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $false)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_112])],[avatar_definition])).
% 16.53/3.66 thf(f1276,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | ~spl5_63),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1274])).
% 16.53/3.66 thf(f1274,definition,(
% 16.53/3.66 spl5_63 <=> (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_63])],[avatar_definition])).
% 16.53/3.66 thf(f2331,plain,(
% 16.53/3.66 spl5_112 | spl5_113 | ~spl5_100),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f2322,f2084,f2328,f2324])).
% 16.53/3.66 thf(f2084,definition,(
% 16.53/3.66 spl5_100 <=> ! [X0 : sK1] : (((sK2 @ X0) != (sK2 @ (sK7 @ sK13))) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3)) | ((sK13 @ (sK2 @ (sK7 @ sK13))) = X0))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_100])],[avatar_definition])).
% 16.53/3.66 thf(f2322,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $false) | ((sK7 @ sK13) = (sK13 @ (sK2 @ (sK7 @ sK13)))) | ~spl5_100),
% 16.53/3.66 inference(equality_resolution,[status(thm)],[f2085])).
% 16.53/3.66 thf(f2085,plain,(
% 16.53/3.66 ( ! [X0 : sK1] : (((sK2 @ X0) != (sK2 @ (sK7 @ sK13))) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3)) | ((sK13 @ (sK2 @ (sK7 @ sK13))) = X0)) ) | ~spl5_100),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f2084])).
% 16.53/3.66 thf(f2214,plain,(
% 16.53/3.66 ~spl5_17 | ~spl5_63 | ~spl5_98),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f2213])).
% 16.53/3.66 thf(f2213,plain,(
% 16.53/3.66 $false | (~spl5_17 | ~spl5_63 | ~spl5_98)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2212])).
% 16.53/3.66 thf(f2212,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_17 | ~spl5_63 | ~spl5_98)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f1738,f2211])).
% 16.53/3.66 thf(f2211,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK2 @ (sK7 @ sK13)) @ sK4)) | (~spl5_17 | ~spl5_98)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f2208])).
% 16.53/3.66 thf(f2208,plain,(
% 16.53/3.66 ($false = $true) | ($false = ('const/sets/IN' @ sK0 @ (sK2 @ (sK7 @ sK13)) @ sK4)) | (~spl5_17 | ~spl5_98)),
% 16.53/3.66 inference(superposition,[status(thm)],[f452,f2077])).
% 16.53/3.66 thf(f2077,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK13 @ (sK2 @ (sK7 @ sK13))) @ sK3)) | ~spl5_98),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f2075])).
% 16.53/3.66 thf(f2075,definition,(
% 16.53/3.66 spl5_98 <=> ($false = ('const/sets/IN' @ sK1 @ (sK13 @ (sK2 @ (sK7 @ sK13))) @ sK3))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_98])],[avatar_definition])).
% 16.53/3.66 thf(f1738,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK2 @ (sK7 @ sK13)) @ sK4) = $true) | ~spl5_63),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1736])).
% 16.53/3.66 thf(f1736,plain,(
% 16.53/3.66 ($true != $true) | (('const/sets/IN' @ sK0 @ (sK2 @ (sK7 @ sK13)) @ sK4) = $true) | ~spl5_63),
% 16.53/3.66 inference(superposition,[status(thm)],[f21,f1276])).
% 16.53/3.66 thf(f21,plain,(
% 16.53/3.66 ( ! [X5 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X5 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK2 @ X5) @ sK4))) )),
% 16.53/3.66 inference(cnf_transformation,[status(thm)],[f18])).
% 16.53/3.66 thf(f18,plain,(
% 16.53/3.66 ! [X5 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X5 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK2 @ X5) @ sK4))) & (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) != (?? @ (sK0 > sK1) @ (^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1))))))))),
% 16.53/3.66 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f16,f17])).
% 16.53/3.66 thf(f17,plain,(
% 16.53/3.66 ? [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : ((('const/sets/IN' @ X1 @ X5 @ X3) != $true) | (('const/sets/IN' @ X0 @ (X2 @ X5) @ X4) = $true)) & (((!! @ X1 @ (^[Y0 : X1]: (!! @ X1 @ (^[Y1 : X1]: (((((X2 @ Y1) = (X2 @ Y0)) & ('const/sets/IN' @ X1 @ Y1 @ X3)) & ('const/sets/IN' @ X1 @ Y0 @ X3)) => (Y1 = Y0)))))) & (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X4) => (?? @ X1 @ (^[Y1 : X1]: (((X2 @ Y1) = Y0) & ('const/sets/IN' @ X1 @ Y1 @ X3)))))))) != (?? @ (X0 > X1) @ (^[Y0 : X0 > X1]: (((!! @ X1 @ (^[Y1 : X1]: (('const/sets/IN' @ X1 @ Y1 @ X3) => ((Y0 @ (X2 @ Y1)) = Y1)))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ('const/sets/IN' @ X1 @ (Y0 @ Y1) @ X3))))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ((X2 @ (Y0 @ Y1)) = Y1))))))))) => (! [X5 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X5 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK2 @ X5) @ sK4))) & (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) != (?? @ (sK0 > sK1) @ (^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1)))))))))),
% 16.53/3.66 introduced(definition,[],[choice_axiom])).
% 16.53/3.66 thf(f16,plain,(
% 16.53/3.66 ? [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : ((('const/sets/IN' @ X1 @ X5 @ X3) != $true) | (('const/sets/IN' @ X0 @ (X2 @ X5) @ X4) = $true)) & (((!! @ X1 @ (^[Y0 : X1]: (!! @ X1 @ (^[Y1 : X1]: (((((X2 @ Y1) = (X2 @ Y0)) & ('const/sets/IN' @ X1 @ Y1 @ X3)) & ('const/sets/IN' @ X1 @ Y0 @ X3)) => (Y1 = Y0)))))) & (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X4) => (?? @ X1 @ (^[Y1 : X1]: (((X2 @ Y1) = Y0) & ('const/sets/IN' @ X1 @ Y1 @ X3)))))))) != (?? @ (X0 > X1) @ (^[Y0 : X0 > X1]: (((!! @ X1 @ (^[Y1 : X1]: (('const/sets/IN' @ X1 @ Y1 @ X3) => ((Y0 @ (X2 @ Y1)) = Y1)))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ('const/sets/IN' @ X1 @ (Y0 @ Y1) @ X3))))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ((X2 @ (Y0 @ Y1)) = Y1)))))))))),
% 16.53/3.66 inference(ennf_transformation,[status(thm)],[f12])).
% 16.53/3.66 thf(f12,plain,(
% 16.53/3.66 ~! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : ((('const/sets/IN' @ X1 @ X5 @ X3) = $true) => (('const/sets/IN' @ X0 @ (X2 @ X5) @ X4) = $true)) => (((!! @ X1 @ (^[Y0 : X1]: (!! @ X1 @ (^[Y1 : X1]: (((((X2 @ Y1) = (X2 @ Y0)) & ('const/sets/IN' @ X1 @ Y1 @ X3)) & ('const/sets/IN' @ X1 @ Y0 @ X3)) => (Y1 = Y0)))))) & (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X4) => (?? @ X1 @ (^[Y1 : X1]: (((X2 @ Y1) = Y0) & ('const/sets/IN' @ X1 @ Y1 @ X3)))))))) = (?? @ (X0 > X1) @ (^[Y0 : X0 > X1]: (((!! @ X1 @ (^[Y1 : X1]: (('const/sets/IN' @ X1 @ Y1 @ X3) => ((Y0 @ (X2 @ Y1)) = Y1)))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ('const/sets/IN' @ X1 @ (Y0 @ Y1) @ X3))))) & (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X4) => ((X2 @ (Y0 @ Y1)) = Y1)))))))))),
% 16.53/3.66 inference(fool_elimination,[status(thm)],[f11])).
% 16.53/3.66 thf(f11,plain,(
% 16.53/3.66 ~! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : (('const/sets/IN' @ X1 @ X5 @ X3) => ('const/sets/IN' @ X0 @ (X2 @ X5) @ X4)) => (? [X6 : X0 > X1] : (! [X7 : X0] : (('const/sets/IN' @ X0 @ X7 @ X4) => ((X2 @ (X6 @ X7)) = X7)) & ! [X8 : X0] : (('const/sets/IN' @ X0 @ X8 @ X4) => ('const/sets/IN' @ X1 @ (X6 @ X8) @ X3)) & ! [X9 : X1] : (('const/sets/IN' @ X1 @ X9 @ X3) => ((X6 @ (X2 @ X9)) = X9))) = ! [X10 : X0] : (('const/sets/IN' @ X0 @ X10 @ X4) => ? [X11 : X1] : (('const/sets/IN' @ X1 @ X11 @ X3) & ((X2 @ X11) = X10))) & ! [X12 : X1,X13 : X1] : ((('const/sets/IN' @ X1 @ X13 @ X3) & ('const/sets/IN' @ X1 @ X12 @ X3) & ((X2 @ X12) = (X2 @ X13))) => (X12 = X13))))),
% 16.53/3.66 inference(rectify,[status(thm)],[f5])).
% 16.53/3.66 thf(f5,negated_conjecture,(
% 16.53/3.66 ~! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : (('const/sets/IN' @ X1 @ X5 @ X3) => ('const/sets/IN' @ X0 @ (X2 @ X5) @ X4)) => (? [X5 : X0 > X1] : (! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ((X2 @ (X5 @ X6)) = X6)) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ('const/sets/IN' @ X1 @ (X5 @ X6) @ X3)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => ((X5 @ (X2 @ X6)) = X6))) = ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ X4) => ? [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) & ((X2 @ X6) = X5))) & ! [X5 : X1,X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X1 @ X5 @ X3) & ((X2 @ X5) = (X2 @ X6))) => (X5 = X6))))),
% 16.53/3.66 inference(negated_conjecture,[status(cth)],[f4])).
% 16.53/3.66 thf(f4,conjecture,(
% 16.53/3.66 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X0 > $o] : (! [X5 : X1] : (('const/sets/IN' @ X1 @ X5 @ X3) => ('const/sets/IN' @ X0 @ (X2 @ X5) @ X4)) => (? [X5 : X0 > X1] : (! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ((X2 @ (X5 @ X6)) = X6)) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ('const/sets/IN' @ X1 @ (X5 @ X6) @ X3)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => ((X5 @ (X2 @ X6)) = X6))) = ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ X4) => ? [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) & ((X2 @ X6) = X5))) & ! [X5 : X1,X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X1 @ X5 @ X3) & ((X2 @ X5) = (X2 @ X6))) => (X5 = X6))))),
% 16.53/3.66 file('/export/starexec/sandbox2/tmp/tmp.OORBxcTjsE/DTF2THF_3780.p','thm/sets/BIJECTIVE_ON_LEFT_RIGHT_INVERSE_')).
% 16.53/3.66 thf(f2098,plain,(
% 16.53/3.66 spl5_98 | spl5_100 | ~spl5_16 | ~spl5_20 | ~spl5_63),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f2071,f1274,f503,f443,f2084,f2075])).
% 16.53/3.66 thf(f2071,plain,(
% 16.53/3.66 ( ! [X0 : sK1] : (((sK2 @ X0) != (sK2 @ (sK7 @ sK13))) | ((sK13 @ (sK2 @ (sK7 @ sK13))) = X0) | ($false = ('const/sets/IN' @ sK1 @ X0 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (sK13 @ (sK2 @ (sK7 @ sK13))) @ sK3))) ) | (~spl5_16 | ~spl5_20 | ~spl5_63)),
% 16.53/3.66 inference(superposition,[status(thm)],[f504,f1900])).
% 16.53/3.66 thf(f1900,plain,(
% 16.53/3.66 ((sK2 @ (sK7 @ sK13)) = (sK2 @ (sK13 @ (sK2 @ (sK7 @ sK13))))) | (~spl5_16 | ~spl5_63)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1897])).
% 16.53/3.66 thf(f1897,plain,(
% 16.53/3.66 ((sK2 @ (sK7 @ sK13)) = (sK2 @ (sK13 @ (sK2 @ (sK7 @ sK13))))) | ($false = $true) | (~spl5_16 | ~spl5_63)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1738,f444])).
% 16.53/3.66 thf(f1990,plain,(
% 16.53/3.66 ~spl5_3 | spl5_37 | spl5_38 | ~spl5_78),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1989])).
% 16.53/3.66 thf(f1989,plain,(
% 16.53/3.66 $false | (~spl5_3 | spl5_37 | spl5_38 | ~spl5_78)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1988])).
% 16.53/3.66 thf(f1988,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_3 | spl5_37 | spl5_38 | ~spl5_78)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f1987,f1560])).
% 16.53/3.66 thf(f1560,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ~spl5_78),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1558])).
% 16.53/3.66 thf(f1558,definition,(
% 16.53/3.66 spl5_78 <=> ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_78])],[avatar_definition])).
% 16.53/3.66 thf(f1987,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_3 | spl5_37 | spl5_38)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1985,f871])).
% 16.53/3.66 thf(f871,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) != $true) | spl5_37),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f870])).
% 16.53/3.66 thf(f870,definition,(
% 16.53/3.66 spl5_37 <=> (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_37])],[avatar_definition])).
% 16.53/3.66 thf(f1985,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_3 | spl5_38)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1984])).
% 16.53/3.66 thf(f1984,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ($false != $false) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_3 | spl5_38)),
% 16.53/3.66 inference(superposition,[status(thm)],[f889,f66])).
% 16.53/3.66 thf(f66,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) ) | ~spl5_3),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f65])).
% 16.53/3.66 thf(f65,definition,(
% 16.53/3.66 spl5_3 <=> ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 16.53/3.66 thf(f889,plain,(
% 16.53/3.66 ($false != ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | spl5_38),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f888])).
% 16.53/3.66 thf(f888,definition,(
% 16.53/3.66 spl5_38 <=> ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_38])],[avatar_definition])).
% 16.53/3.66 thf(f1972,plain,(
% 16.53/3.66 ~spl5_16 | spl5_78 | spl5_95),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1971])).
% 16.53/3.66 thf(f1971,plain,(
% 16.53/3.66 $false | (~spl5_16 | spl5_78 | spl5_95)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1970,f1834])).
% 16.53/3.66 thf(f1834,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) != (sK10 @ sK12)) | spl5_95),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1833])).
% 16.53/3.66 thf(f1833,definition,(
% 16.53/3.66 spl5_95 <=> ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_95])],[avatar_definition])).
% 16.53/3.66 thf(f1970,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12)) | (~spl5_16 | spl5_78)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1969])).
% 16.53/3.66 thf(f1969,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12)) | ($false != $false) | (~spl5_16 | spl5_78)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1559,f444])).
% 16.53/3.66 thf(f1559,plain,(
% 16.53/3.66 ($false != ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | spl5_78),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1558])).
% 16.53/3.66 thf(f1896,plain,(
% 16.53/3.66 ~spl5_9 | spl5_35 | spl5_37 | spl5_40),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1895])).
% 16.53/3.66 thf(f1895,plain,(
% 16.53/3.66 $false | (~spl5_9 | spl5_35 | spl5_37 | spl5_40)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1879,f898])).
% 16.53/3.66 thf(f898,plain,(
% 16.53/3.66 ($true != ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | spl5_40),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f897])).
% 16.53/3.66 thf(f897,definition,(
% 16.53/3.66 spl5_40 <=> ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_40])],[avatar_definition])).
% 16.53/3.66 thf(f1879,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_9 | spl5_35 | spl5_37)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1878,f871])).
% 16.53/3.66 thf(f1878,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_9 | spl5_35)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1876])).
% 16.53/3.66 thf(f1876,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($true != $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_9 | spl5_35)),
% 16.53/3.66 inference(superposition,[status(thm)],[f863,f148])).
% 16.53/3.66 thf(f148,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) ) | ~spl5_9),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f147])).
% 16.53/3.66 thf(f147,definition,(
% 16.53/3.66 spl5_9 <=> ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition])).
% 16.53/3.66 thf(f863,plain,(
% 16.53/3.66 ($true != ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | spl5_35),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f862])).
% 16.53/3.66 thf(f862,definition,(
% 16.53/3.66 spl5_35 <=> ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_35])],[avatar_definition])).
% 16.53/3.66 thf(f1868,plain,(
% 16.53/3.66 ~spl5_17 | spl5_40 | spl5_78 | ~spl5_95),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1867])).
% 16.53/3.66 thf(f1867,plain,(
% 16.53/3.66 $false | (~spl5_17 | spl5_40 | spl5_78 | ~spl5_95)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1866,f898])).
% 16.53/3.66 thf(f1866,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_17 | spl5_78 | ~spl5_95)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1853,f1559])).
% 16.53/3.66 thf(f1853,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_17 | ~spl5_95)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1267,f1835])).
% 16.53/3.66 thf(f1835,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12)) | ~spl5_95),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1833])).
% 16.53/3.66 thf(f1267,plain,(
% 16.53/3.66 ( ! [X0 : sK0] : (($true = ('const/sets/IN' @ sK0 @ (sK2 @ (sK13 @ X0)) @ sK4)) | (('const/sets/IN' @ sK0 @ X0 @ sK4) = $false)) ) | ~spl5_17),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1262])).
% 16.53/3.66 thf(f1262,plain,(
% 16.53/3.66 ( ! [X0 : sK0] : ((('const/sets/IN' @ sK0 @ X0 @ sK4) = $false) | ($true != $true) | ($true = ('const/sets/IN' @ sK0 @ (sK2 @ (sK13 @ X0)) @ sK4))) ) | ~spl5_17),
% 16.53/3.66 inference(superposition,[status(thm)],[f21,f452])).
% 16.53/3.66 thf(f1826,plain,(
% 16.53/3.66 ~spl5_10 | spl5_35 | spl5_37 | ~spl5_39),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1825])).
% 16.53/3.66 thf(f1825,plain,(
% 16.53/3.66 $false | (~spl5_10 | spl5_35 | spl5_37 | ~spl5_39)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1824,f871])).
% 16.53/3.66 thf(f1824,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_10 | spl5_35 | ~spl5_39)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1693,f863])).
% 16.53/3.66 thf(f1693,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_10 | ~spl5_39)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1692])).
% 16.53/3.66 thf(f1692,plain,(
% 16.53/3.66 ((sK10 @ sK12) != (sK10 @ sK12)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_10 | ~spl5_39)),
% 16.53/3.66 inference(superposition,[status(thm)],[f174,f893])).
% 16.53/3.66 thf(f893,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) = (sK10 @ sK12)) | ~spl5_39),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f892])).
% 16.53/3.66 thf(f892,definition,(
% 16.53/3.66 spl5_39 <=> ((sK2 @ (sK12 @ (sK10 @ sK12))) = (sK10 @ sK12))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_39])],[avatar_definition])).
% 16.53/3.66 thf(f174,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) ) | ~spl5_10),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f173])).
% 16.53/3.66 thf(f173,definition,(
% 16.53/3.66 spl5_10 <=> ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition])).
% 16.53/3.66 thf(f1820,plain,(
% 16.53/3.66 ~spl5_17 | ~spl5_19 | ~spl5_34 | spl5_51 | spl5_53),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1819])).
% 16.53/3.66 thf(f1819,plain,(
% 16.53/3.66 $false | (~spl5_17 | ~spl5_19 | ~spl5_34 | spl5_51 | spl5_53)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1818,f1028])).
% 16.53/3.66 thf(f1028,plain,(
% 16.53/3.66 ((sK13 @ (sK8 @ sK12)) != (sK12 @ (sK8 @ sK12))) | spl5_51),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1027])).
% 16.53/3.66 thf(f1027,definition,(
% 16.53/3.66 spl5_51 <=> ((sK13 @ (sK8 @ sK12)) = (sK12 @ (sK8 @ sK12)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_51])],[avatar_definition])).
% 16.53/3.66 thf(f1818,plain,(
% 16.53/3.66 ((sK13 @ (sK8 @ sK12)) = (sK12 @ (sK8 @ sK12))) | (~spl5_17 | ~spl5_19 | ~spl5_34 | spl5_53)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1812,f1038])).
% 16.53/3.66 thf(f1038,plain,(
% 16.53/3.66 ($false != ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | spl5_53),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1037])).
% 16.53/3.66 thf(f1037,definition,(
% 16.53/3.66 spl5_53 <=> ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_53])],[avatar_definition])).
% 16.53/3.66 thf(f1812,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ((sK13 @ (sK8 @ sK12)) = (sK12 @ (sK8 @ sK12))) | (~spl5_17 | ~spl5_19 | ~spl5_34)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1268,f860])).
% 16.53/3.66 thf(f860,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK8 @ sK12))) = (sK8 @ sK12)) | ~spl5_34),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f858])).
% 16.53/3.66 thf(f858,definition,(
% 16.53/3.66 spl5_34 <=> ((sK2 @ (sK13 @ (sK8 @ sK12))) = (sK8 @ sK12))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_34])],[avatar_definition])).
% 16.53/3.66 thf(f1268,plain,(
% 16.53/3.66 ( ! [X0 : sK0] : (((sK12 @ (sK2 @ (sK13 @ X0))) = (sK13 @ X0)) | (('const/sets/IN' @ sK0 @ X0 @ sK4) = $false)) ) | (~spl5_17 | ~spl5_19)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1261])).
% 16.53/3.66 thf(f1261,plain,(
% 16.53/3.66 ( ! [X0 : sK0] : ((('const/sets/IN' @ sK0 @ X0 @ sK4) = $false) | ($false = $true) | ((sK12 @ (sK2 @ (sK13 @ X0))) = (sK13 @ X0))) ) | (~spl5_17 | ~spl5_19)),
% 16.53/3.66 inference(superposition,[status(thm)],[f482,f452])).
% 16.53/3.66 thf(f482,plain,(
% 16.53/3.66 ( ! [X2 : sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK12 @ (sK2 @ X2)) = X2)) ) | ~spl5_19),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f481])).
% 16.53/3.66 thf(f481,definition,(
% 16.53/3.66 spl5_19 <=> ! [X2 : sK1] : (((sK12 @ (sK2 @ X2)) = X2) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_19])],[avatar_definition])).
% 16.53/3.66 thf(f1808,plain,(
% 16.53/3.66 spl5_34 | ~spl5_16 | ~spl5_35),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1801,f862,f443,f858])).
% 16.53/3.66 thf(f1801,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK8 @ sK12))) = (sK8 @ sK12)) | (~spl5_16 | ~spl5_35)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1799])).
% 16.53/3.66 thf(f1799,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK8 @ sK12))) = (sK8 @ sK12)) | ($false = $true) | (~spl5_16 | ~spl5_35)),
% 16.53/3.66 inference(superposition,[status(thm)],[f864,f444])).
% 16.53/3.66 thf(f864,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ~spl5_35),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f862])).
% 16.53/3.66 thf(f1790,plain,(
% 16.53/3.66 ~spl5_16 | ~spl5_17 | spl5_62 | spl5_73),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1789])).
% 16.53/3.66 thf(f1789,plain,(
% 16.53/3.66 $false | (~spl5_16 | ~spl5_17 | spl5_62 | spl5_73)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1788,f1271])).
% 16.53/3.66 thf(f1271,plain,(
% 16.53/3.66 ($true != ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | spl5_62),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1270])).
% 16.53/3.66 thf(f1788,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_16 | ~spl5_17 | spl5_73)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1771,f1393])).
% 16.53/3.66 thf(f1393,plain,(
% 16.53/3.66 ($false != ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | spl5_73),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1392])).
% 16.53/3.66 thf(f1771,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_16 | ~spl5_17 | spl5_73)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1267,f1766])).
% 16.53/3.66 thf(f1766,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | (~spl5_16 | spl5_73)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1765])).
% 16.53/3.66 thf(f1765,plain,(
% 16.53/3.66 ($false != $false) | ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | (~spl5_16 | spl5_73)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1393,f444])).
% 16.53/3.66 thf(f1706,plain,(
% 16.53/3.66 spl5_62 | spl5_63 | ~spl5_9 | ~spl5_64),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1698,f1278,f147,f1274,f1270])).
% 16.53/3.66 thf(f1698,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_9 | ~spl5_64)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1696])).
% 16.53/3.66 thf(f1696,plain,(
% 16.53/3.66 ($false = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_9 | ~spl5_64)),
% 16.53/3.66 inference(superposition,[status(thm)],[f148,f1280])).
% 16.53/3.66 thf(f1280,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false) | ~spl5_64),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1278])).
% 16.53/3.66 thf(f1593,plain,(
% 16.53/3.66 ~spl5_17 | ~spl5_38 | ~spl5_51 | spl5_53),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1592])).
% 16.53/3.66 thf(f1592,plain,(
% 16.53/3.66 $false | (~spl5_17 | ~spl5_38 | ~spl5_51 | spl5_53)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1591])).
% 16.53/3.66 thf(f1591,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_17 | ~spl5_38 | ~spl5_51 | spl5_53)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f1590,f890])).
% 16.53/3.66 thf(f890,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | ~spl5_38),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f888])).
% 16.53/3.66 thf(f1590,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_17 | ~spl5_51 | spl5_53)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1258,f1038])).
% 16.53/3.66 thf(f1258,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ($true = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_17 | ~spl5_51)),
% 16.53/3.66 inference(superposition,[status(thm)],[f452,f1029])).
% 16.53/3.66 thf(f1029,plain,(
% 16.53/3.66 ((sK13 @ (sK8 @ sK12)) = (sK12 @ (sK8 @ sK12))) | ~spl5_51),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1027])).
% 16.53/3.66 thf(f1581,plain,(
% 16.53/3.66 spl5_39 | ~spl5_16 | ~spl5_40 | ~spl5_77),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1579,f1554,f897,f443,f892])).
% 16.53/3.66 thf(f1554,definition,(
% 16.53/3.66 spl5_77 <=> ((sK12 @ (sK10 @ sK12)) = (sK13 @ (sK10 @ sK12)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_77])],[avatar_definition])).
% 16.53/3.66 thf(f1579,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) = (sK10 @ sK12)) | (~spl5_16 | ~spl5_40 | ~spl5_77)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f1544,f1556])).
% 16.53/3.66 thf(f1556,plain,(
% 16.53/3.66 ((sK12 @ (sK10 @ sK12)) = (sK13 @ (sK10 @ sK12))) | ~spl5_77),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1554])).
% 16.53/3.66 thf(f1544,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12)) | (~spl5_16 | ~spl5_40)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1542])).
% 16.53/3.66 thf(f1542,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK12))) = (sK10 @ sK12)) | ($false = $true) | (~spl5_16 | ~spl5_40)),
% 16.53/3.66 inference(superposition,[status(thm)],[f444,f899])).
% 16.53/3.66 thf(f899,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ~spl5_40),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f897])).
% 16.53/3.66 thf(f1575,plain,(
% 16.53/3.66 spl5_35 | ~spl5_39 | ~spl5_13 | ~spl5_36),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1326,f866,f263,f892,f862])).
% 16.53/3.66 thf(f866,definition,(
% 16.53/3.66 spl5_36 <=> ((sK7 @ sK12) = (sK12 @ (sK2 @ (sK7 @ sK12))))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_36])],[avatar_definition])).
% 16.53/3.66 thf(f1326,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) != (sK10 @ sK12)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (~spl5_13 | ~spl5_36)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1322])).
% 16.53/3.66 thf(f1322,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ((sK2 @ (sK12 @ (sK10 @ sK12))) != (sK10 @ sK12)) | ((sK7 @ sK12) != (sK7 @ sK12)) | (~spl5_13 | ~spl5_36)),
% 16.53/3.66 inference(superposition,[status(thm)],[f264,f868])).
% 16.53/3.66 thf(f868,plain,(
% 16.53/3.66 ((sK7 @ sK12) = (sK12 @ (sK2 @ (sK7 @ sK12)))) | ~spl5_36),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f866])).
% 16.53/3.66 thf(f1569,plain,(
% 16.53/3.66 ~spl5_39 | spl5_38 | ~spl5_12 | ~spl5_36),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1325,f866,f225,f888,f892])).
% 16.53/3.66 thf(f1325,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | ((sK2 @ (sK12 @ (sK10 @ sK12))) != (sK10 @ sK12)) | (~spl5_12 | ~spl5_36)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1321])).
% 16.53/3.66 thf(f1321,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) != (sK10 @ sK12)) | ((sK7 @ sK12) != (sK7 @ sK12)) | ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_12 | ~spl5_36)),
% 16.53/3.66 inference(superposition,[status(thm)],[f226,f868])).
% 16.53/3.66 thf(f1568,plain,(
% 16.53/3.66 ~spl5_40 | ~spl5_78),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1567])).
% 16.53/3.66 thf(f1567,plain,(
% 16.53/3.66 $false | (~spl5_40 | ~spl5_78)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1566])).
% 16.53/3.66 thf(f1566,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_40 | ~spl5_78)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f899,f1560])).
% 16.53/3.66 thf(f1561,plain,(
% 16.53/3.66 spl5_77 | spl5_78 | ~spl5_16 | ~spl5_17 | ~spl5_19 | ~spl5_40),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1547,f897,f481,f451,f443,f1558,f1554])).
% 16.53/3.66 thf(f1547,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ((sK12 @ (sK10 @ sK12)) = (sK13 @ (sK10 @ sK12))) | (~spl5_16 | ~spl5_17 | ~spl5_19 | ~spl5_40)),
% 16.53/3.66 inference(superposition,[status(thm)],[f1268,f1544])).
% 16.53/3.66 thf(f1483,plain,(
% 16.53/3.66 ~spl5_64 | ~spl5_71),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1482])).
% 16.53/3.66 thf(f1482,plain,(
% 16.53/3.66 $false | (~spl5_64 | ~spl5_71)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1481])).
% 16.53/3.66 thf(f1481,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_64 | ~spl5_71)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f1370,f1280])).
% 16.53/3.66 thf(f1370,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | ~spl5_71),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1368])).
% 16.53/3.66 thf(f1371,plain,(
% 16.53/3.66 spl5_63 | spl5_71 | ~spl5_10 | ~spl5_16 | ~spl5_62),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1343,f1270,f443,f173,f1368,f1274])).
% 16.53/3.66 thf(f1343,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | (~spl5_10 | ~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1342])).
% 16.53/3.66 thf(f1342,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $true) | ((sK10 @ sK13) != (sK10 @ sK13)) | (~spl5_10 | ~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(superposition,[status(thm)],[f174,f1335])).
% 16.53/3.66 thf(f1335,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | (~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1333])).
% 16.53/3.66 thf(f1333,plain,(
% 16.53/3.66 ($false = $true) | ((sK2 @ (sK13 @ (sK10 @ sK13))) = (sK10 @ sK13)) | (~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(superposition,[status(thm)],[f444,f1272])).
% 16.53/3.66 thf(f1366,plain,(
% 16.53/3.66 spl5_63 | spl5_70 | ~spl5_11 | ~spl5_16 | ~spl5_62),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1344,f1270,f443,f202,f1363,f1274])).
% 16.53/3.66 thf(f202,definition,(
% 16.53/3.66 spl5_11 <=> ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition])).
% 16.53/3.66 thf(f1344,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | (~spl5_11 | ~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1341])).
% 16.53/3.66 thf(f1341,plain,(
% 16.53/3.66 ((sK10 @ sK13) != (sK10 @ sK13)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | (('const/sets/IN' @ sK1 @ (sK13 @ (sK8 @ sK13)) @ sK3) = $false) | (~spl5_11 | ~spl5_16 | ~spl5_62)),
% 16.53/3.66 inference(superposition,[status(thm)],[f203,f1335])).
% 16.53/3.66 thf(f203,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) ) | ~spl5_11),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f202])).
% 16.53/3.66 thf(f1282,plain,(
% 16.53/3.66 spl5_62 | spl5_64 | spl5_63 | ~spl5_3 | ~spl5_17),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1264,f451,f65,f1274,f1278,f1270])).
% 16.53/3.66 thf(f1264,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | (~spl5_3 | ~spl5_17)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1263])).
% 16.53/3.66 thf(f1263,plain,(
% 16.53/3.66 ($false = $true) | (('const/sets/IN' @ sK0 @ (sK8 @ sK13) @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ sK13) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK13) @ sK4)) | (~spl5_3 | ~spl5_17)),
% 16.53/3.66 inference(superposition,[status(thm)],[f66,f452])).
% 16.53/3.66 thf(f1237,plain,(
% 16.53/3.66 spl5_37 | spl5_53 | spl5_40 | ~spl5_3 | ~spl5_18),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1067,f466,f65,f897,f1037,f870])).
% 16.53/3.66 thf(f466,definition,(
% 16.53/3.66 spl5_18 <=> ! [X2 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_18])],[avatar_definition])).
% 16.53/3.66 thf(f1067,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (~spl5_3 | ~spl5_18)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1065])).
% 16.53/3.66 thf(f1065,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ($false = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_3 | ~spl5_18)),
% 16.53/3.66 inference(superposition,[status(thm)],[f467,f66])).
% 16.53/3.66 thf(f467,plain,(
% 16.53/3.66 ( ! [X2 : sK0] : ((('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false)) ) | ~spl5_18),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f466])).
% 16.53/3.66 thf(f1236,plain,(
% 16.53/3.66 ~spl5_9 | spl5_37 | spl5_40 | ~spl5_53),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1235])).
% 16.53/3.66 thf(f1235,plain,(
% 16.53/3.66 $false | (~spl5_9 | spl5_37 | spl5_40 | ~spl5_53)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1234,f871])).
% 16.53/3.66 thf(f1234,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_9 | spl5_40 | ~spl5_53)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1229,f898])).
% 16.53/3.66 thf(f1229,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_9 | ~spl5_53)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1228])).
% 16.53/3.66 thf(f1228,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ($false = $true) | (~spl5_9 | ~spl5_53)),
% 16.53/3.66 inference(superposition,[status(thm)],[f148,f1039])).
% 16.53/3.66 thf(f1039,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ~spl5_53),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f1037])).
% 16.53/3.66 thf(f1201,plain,(
% 16.53/3.66 ~spl5_10 | spl5_37 | ~spl5_39 | ~spl5_53),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1200])).
% 16.53/3.66 thf(f1200,plain,(
% 16.53/3.66 $false | (~spl5_10 | spl5_37 | ~spl5_39 | ~spl5_53)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1199])).
% 16.53/3.66 thf(f1199,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_10 | spl5_37 | ~spl5_39 | ~spl5_53)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f1198,f1039])).
% 16.53/3.66 thf(f1198,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (~spl5_10 | spl5_37 | ~spl5_39)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1145,f871])).
% 16.53/3.66 thf(f1145,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_10 | ~spl5_39)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1144])).
% 16.53/3.66 thf(f1144,plain,(
% 16.53/3.66 ((sK10 @ sK12) != (sK10 @ sK12)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | (~spl5_10 | ~spl5_39)),
% 16.53/3.66 inference(superposition,[status(thm)],[f174,f893])).
% 16.53/3.66 thf(f1197,plain,(
% 16.53/3.66 ~spl5_35 | ~spl5_53),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1196])).
% 16.53/3.66 thf(f1196,plain,(
% 16.53/3.66 $false | (~spl5_35 | ~spl5_53)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1195])).
% 16.53/3.66 thf(f1195,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_35 | ~spl5_53)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f864,f1039])).
% 16.53/3.66 thf(f1194,plain,(
% 16.53/3.66 spl5_38 | ~spl5_11 | spl5_37 | ~spl5_39),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1193,f892,f870,f202,f888])).
% 16.53/3.66 thf(f1193,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_11 | spl5_37 | ~spl5_39)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1146,f871])).
% 16.53/3.66 thf(f1146,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_11 | ~spl5_39)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1143])).
% 16.53/3.66 thf(f1143,plain,(
% 16.53/3.66 ((sK10 @ sK12) != (sK10 @ sK12)) | (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_11 | ~spl5_39)),
% 16.53/3.66 inference(superposition,[status(thm)],[f203,f893])).
% 16.53/3.66 thf(f1113,plain,(
% 16.53/3.66 ~spl5_4 | ~spl5_36 | spl5_38 | spl5_40),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f1112])).
% 16.53/3.66 thf(f1112,plain,(
% 16.53/3.66 $false | (~spl5_4 | ~spl5_36 | spl5_38 | spl5_40)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1111,f898])).
% 16.53/3.66 thf(f1111,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_4 | ~spl5_36 | spl5_38)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f1109,f889])).
% 16.53/3.66 thf(f1109,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_4 | ~spl5_36)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1103])).
% 16.53/3.66 thf(f1103,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ((sK7 @ sK12) != (sK7 @ sK12)) | ($false = ('const/sets/IN' @ sK1 @ (sK12 @ (sK8 @ sK12)) @ sK3)) | (~spl5_4 | ~spl5_36)),
% 16.53/3.66 inference(superposition,[status(thm)],[f74,f868])).
% 16.53/3.66 thf(f1095,plain,(
% 16.53/3.66 spl5_36 | ~spl5_19 | ~spl5_37),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1087,f870,f481,f866])).
% 16.53/3.66 thf(f1087,plain,(
% 16.53/3.66 ((sK7 @ sK12) = (sK12 @ (sK2 @ (sK7 @ sK12)))) | (~spl5_19 | ~spl5_37)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1084])).
% 16.53/3.66 thf(f1084,plain,(
% 16.53/3.66 ($false = $true) | ((sK7 @ sK12) = (sK12 @ (sK2 @ (sK7 @ sK12)))) | (~spl5_19 | ~spl5_37)),
% 16.53/3.66 inference(superposition,[status(thm)],[f872,f482])).
% 16.53/3.66 thf(f872,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK7 @ sK12) @ sK3) = $true) | ~spl5_37),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f870])).
% 16.53/3.66 thf(f1083,plain,(
% 16.53/3.66 spl5_39 | ~spl5_15 | ~spl5_40),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1080,f897,f440,f892])).
% 16.53/3.66 thf(f440,definition,(
% 16.53/3.66 spl5_15 <=> ! [X2 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | ((sK2 @ (sK12 @ X2)) = X2))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_15])],[avatar_definition])).
% 16.53/3.66 thf(f1080,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) = (sK10 @ sK12)) | (~spl5_15 | ~spl5_40)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1074])).
% 16.53/3.66 thf(f1074,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ (sK10 @ sK12))) = (sK10 @ sK12)) | ($false = $true) | (~spl5_15 | ~spl5_40)),
% 16.53/3.66 inference(superposition,[status(thm)],[f899,f441])).
% 16.53/3.66 thf(f441,plain,(
% 16.53/3.66 ( ! [X2 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | ((sK2 @ (sK12 @ X2)) = X2)) ) | ~spl5_15),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f440])).
% 16.53/3.66 thf(f1055,plain,(
% 16.53/3.66 spl5_53 | ~spl5_18 | ~spl5_38),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f1052,f888,f466,f1037])).
% 16.53/3.66 thf(f1052,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (~spl5_18 | ~spl5_38)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f1050])).
% 16.53/3.66 thf(f1050,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ($false = $true) | (~spl5_18 | ~spl5_38)),
% 16.53/3.66 inference(superposition,[status(thm)],[f467,f890])).
% 16.53/3.66 thf(f900,plain,(
% 16.53/3.66 spl5_35 | spl5_40 | ~spl5_8 | ~spl5_36),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f885,f866,f122,f897,f862])).
% 16.53/3.66 thf(f885,plain,(
% 16.53/3.66 ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | (~spl5_8 | ~spl5_36)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f883])).
% 16.53/3.66 thf(f883,plain,(
% 16.53/3.66 ((sK7 @ sK12) != (sK7 @ sK12)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ sK12) @ sK4)) | ($true = ('const/sets/IN' @ sK0 @ (sK10 @ sK12) @ sK4)) | (~spl5_8 | ~spl5_36)),
% 16.53/3.66 inference(superposition,[status(thm)],[f123,f868])).
% 16.53/3.66 thf(f739,plain,(
% 16.53/3.66 ~spl5_1 | ~spl5_14 | ~spl5_16 | ~spl5_17),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f738])).
% 16.53/3.66 thf(f738,plain,(
% 16.53/3.66 $false | (~spl5_1 | ~spl5_14 | ~spl5_16 | ~spl5_17)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f737])).
% 16.53/3.66 thf(f737,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_1 | ~spl5_14 | ~spl5_16 | ~spl5_17)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f295,f735])).
% 16.53/3.66 thf(f735,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $false) | (~spl5_1 | ~spl5_14 | ~spl5_16 | ~spl5_17)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f731])).
% 16.53/3.66 thf(f731,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $false) | ($false = $true) | (~spl5_1 | ~spl5_14 | ~spl5_16 | ~spl5_17)),
% 16.53/3.66 inference(superposition,[status(thm)],[f685,f452])).
% 16.53/3.66 thf(f685,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ sK6) @ sK3) = $false) | (~spl5_1 | ~spl5_14 | ~spl5_16)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f682])).
% 16.53/3.66 thf(f682,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK1 @ (sK13 @ sK6) @ sK3) = $false) | (sK6 != sK6) | (~spl5_1 | ~spl5_14 | ~spl5_16)),
% 16.53/3.66 inference(superposition,[status(thm)],[f59,f667])).
% 16.53/3.66 thf(f667,plain,(
% 16.53/3.66 ((sK2 @ (sK13 @ sK6)) = sK6) | (~spl5_14 | ~spl5_16)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f661])).
% 16.53/3.66 thf(f661,plain,(
% 16.53/3.66 ($false = $true) | ((sK2 @ (sK13 @ sK6)) = sK6) | (~spl5_14 | ~spl5_16)),
% 16.53/3.66 inference(superposition,[status(thm)],[f295,f444])).
% 16.53/3.66 thf(f59,plain,(
% 16.53/3.66 ( ! [X2 : sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) ) | ~spl5_1),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f58])).
% 16.53/3.66 thf(f58,definition,(
% 16.53/3.66 spl5_1 <=> ! [X2 : sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)))),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 16.53/3.66 thf(f295,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ~spl5_14),
% 16.53/3.66 inference(avatar_component_clause,[status(thm)],[f293])).
% 16.53/3.66 thf(f293,definition,(
% 16.53/3.66 spl5_14 <=> (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)),
% 16.53/3.66 introduced(definition,[new_symbols(naming,[spl5_14])],[avatar_definition])).
% 16.53/3.66 thf(f724,plain,(
% 16.53/3.66 ~spl5_1 | ~spl5_14 | ~spl5_15 | ~spl5_18),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f723])).
% 16.53/3.66 thf(f723,plain,(
% 16.53/3.66 $false | (~spl5_1 | ~spl5_14 | ~spl5_15 | ~spl5_18)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f722])).
% 16.53/3.66 thf(f722,plain,(
% 16.53/3.66 ($false = $true) | (~spl5_1 | ~spl5_14 | ~spl5_15 | ~spl5_18)),
% 16.53/3.66 inference(backward_demodulation,[status(thm)],[f295,f721])).
% 16.53/3.66 thf(f721,plain,(
% 16.53/3.66 (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $false) | (~spl5_1 | ~spl5_14 | ~spl5_15 | ~spl5_18)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f717])).
% 16.53/3.66 thf(f717,plain,(
% 16.53/3.66 ($false = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $false) | (~spl5_1 | ~spl5_14 | ~spl5_15 | ~spl5_18)),
% 16.53/3.66 inference(superposition,[status(thm)],[f684,f467])).
% 16.53/3.66 thf(f684,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ sK6) @ sK3)) | (~spl5_1 | ~spl5_14 | ~spl5_15)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f683])).
% 16.53/3.66 thf(f683,plain,(
% 16.53/3.66 ($false = ('const/sets/IN' @ sK1 @ (sK12 @ sK6) @ sK3)) | (sK6 != sK6) | (~spl5_1 | ~spl5_14 | ~spl5_15)),
% 16.53/3.66 inference(superposition,[status(thm)],[f59,f668])).
% 16.53/3.66 thf(f668,plain,(
% 16.53/3.66 ((sK2 @ (sK12 @ sK6)) = sK6) | (~spl5_14 | ~spl5_15)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f664])).
% 16.53/3.66 thf(f664,plain,(
% 16.53/3.66 ($false = $true) | ((sK2 @ (sK12 @ sK6)) = sK6) | (~spl5_14 | ~spl5_15)),
% 16.53/3.66 inference(superposition,[status(thm)],[f441,f295])).
% 16.53/3.66 thf(f600,plain,(
% 16.53/3.66 spl5_2 | ~spl5_5 | ~spl5_6 | ~spl5_7 | ~spl5_19),
% 16.53/3.66 inference(avatar_contradiction_clause,[status(thm)],[f599])).
% 16.53/3.66 thf(f599,plain,(
% 16.53/3.66 $false | (spl5_2 | ~spl5_5 | ~spl5_6 | ~spl5_7 | ~spl5_19)),
% 16.53/3.66 inference(subsumption_resolution,[status(thm)],[f598,f63])).
% 16.53/3.66 thf(f598,plain,(
% 16.53/3.66 (sK9 = sK11) | (~spl5_5 | ~spl5_6 | ~spl5_7 | ~spl5_19)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f597,f590])).
% 16.53/3.66 thf(f590,plain,(
% 16.53/3.66 (sK9 = (sK12 @ (sK2 @ sK9))) | (~spl5_5 | ~spl5_19)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f583])).
% 16.53/3.66 thf(f583,plain,(
% 16.53/3.66 (sK9 = (sK12 @ (sK2 @ sK9))) | ($false = $true) | (~spl5_5 | ~spl5_19)),
% 16.53/3.66 inference(superposition,[status(thm)],[f482,f86])).
% 16.53/3.66 thf(f597,plain,(
% 16.53/3.66 (sK11 = (sK12 @ (sK2 @ sK9))) | (~spl5_6 | ~spl5_7 | ~spl5_19)),
% 16.53/3.66 inference(forward_demodulation,[status(thm)],[f588,f101])).
% 16.53/3.66 thf(f588,plain,(
% 16.53/3.66 ((sK12 @ (sK2 @ sK11)) = sK11) | (~spl5_7 | ~spl5_19)),
% 16.53/3.66 inference(trivial_inequality_removal,[status(thm)],[f587])).
% 16.53/3.66 thf(f587,plain,(
% 16.53/3.66 ((sK12 @ (sK2 @ sK11)) = sK11) | ($false = $true) | (~spl5_7 | ~spl5_19)),
% 16.53/3.66 inference(superposition,[status(thm)],[f110,f482])).
% 16.53/3.66 thf(f505,plain,(
% 16.53/3.66 spl5_20 | spl5_19),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f501,f481,f503])).
% 16.53/3.66 thf(f501,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : ((('const/sets/IN' @ sK1 @ X3 @ sK3) = $false) | ((sK2 @ X2) != (sK2 @ X1)) | ((sK12 @ (sK2 @ X3)) = X3) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)) | (X1 = X2) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f500])).
% 16.53/3.66 thf(f500,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : ((((sK2 @ X2) = (sK2 @ X1)) = $false) | ((sK12 @ (sK2 @ X3)) = X3) | (X1 = X2) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ X3 @ sK3) = $false) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f499])).
% 16.53/3.66 thf(f499,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : ((((sK12 @ (sK2 @ X3)) = X3) = $true) | (((sK2 @ X2) = (sK2 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)) | (('const/sets/IN' @ sK1 @ X3 @ sK3) = $false) | (X1 = X2)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f498])).
% 16.53/3.66 thf(f498,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : (($false = (((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)) | (X1 = X2) | (('const/sets/IN' @ sK1 @ X3 @ sK3) = $false) | (((sK12 @ (sK2 @ X3)) = X3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f497])).
% 16.53/3.66 thf(f497,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : (($true = (('const/sets/IN' @ sK1 @ X3 @ sK3) => ((sK12 @ (sK2 @ X3)) = X3))) | ($false = ('const/sets/IN' @ sK1 @ X1 @ sK3)) | ($false = (((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (X1 = X2)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f496])).
% 16.53/3.66 thf(f496,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : ((X1 = X2) | ($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3))) | ($true = (('const/sets/IN' @ sK1 @ X3 @ sK3) => ((sK12 @ (sK2 @ X3)) = X3)))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f495])).
% 16.53/3.66 thf(f495,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X3 : sK1,X1 : sK1] : (($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3))) | (((^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0))) @ X3) = $true) | (X1 = X2)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f494])).
% 16.53/3.66 thf(f494,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) = $true) | (X1 = X2) | ($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f492])).
% 16.53/3.66 thf(f492,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (($true = ((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3)))))) | ($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3))) | (X1 = X2)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f490])).
% 16.53/3.66 thf(f490,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true) | (X1 = X2) | ($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f489])).
% 16.53/3.66 thf(f489,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (($true = (X2 = X1)) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true) | ($false = ((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f488])).
% 16.53/3.66 thf(f488,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : (((((((sK2 @ X2) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ X2 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)) => (X2 = X1)) = $true) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f487])).
% 16.53/3.66 thf(f487,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK1] : ((((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)) => (Y0 = X1))) @ X2) = $true) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f486])).
% 16.53/3.66 thf(f486,plain,(
% 16.53/3.66 ( ! [X1 : sK1] : (((!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ X1)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ X1 @ sK3)) => (Y0 = X1)))) = $true) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f485])).
% 16.53/3.66 thf(f485,plain,(
% 16.53/3.66 ( ! [X1 : sK1] : (((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true) | ($true = ((^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))) @ X1))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f424])).
% 16.53/3.66 thf(f424,plain,(
% 16.53/3.66 ($true = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f422])).
% 16.53/3.66 thf(f422,plain,(
% 16.53/3.66 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $true) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f421])).
% 16.53/3.66 thf(f421,plain,(
% 16.53/3.66 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $true) | ($true = ((^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1)))))) @ sK12))),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f23])).
% 16.53/3.66 thf(f23,plain,(
% 16.53/3.66 ((?? @ (sK0 > sK1) @ (^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1))))))) = $true) | (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $true)),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 16.53/3.66 thf(f20,plain,(
% 16.53/3.66 (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) != (?? @ (sK0 > sK1) @ (^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1))))))))),
% 16.53/3.66 inference(cnf_transformation,[status(thm)],[f18])).
% 16.53/3.66 thf(f484,plain,(
% 16.53/3.66 spl5_17 | spl5_19),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f477,f481,f451])).
% 16.53/3.66 thf(f477,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | ((sK12 @ (sK2 @ X2)) = X2) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f476])).
% 16.53/3.66 thf(f476,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (((((sK2 @ (sK13 @ X1)) = X1) & ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK12 @ (sK2 @ X2)) = X2) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f475])).
% 16.53/3.66 thf(f475,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (($true = ((sK12 @ (sK2 @ X2)) = X2)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((((sK2 @ (sK13 @ X1)) = X1) & ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f474])).
% 16.53/3.66 thf(f474,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = ((sK12 @ (sK2 @ X2)) = X2)) | ($true = ((^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ (sK13 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f473])).
% 16.53/3.66 thf(f473,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (($true = (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) | ($true = ((sK12 @ (sK2 @ X2)) = X2)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f472])).
% 16.53/3.66 thf(f472,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = (('const/sets/IN' @ sK1 @ X2 @ sK3) => ((sK12 @ (sK2 @ X2)) = X2))) | ($true = (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f471])).
% 16.53/3.66 thf(f471,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) | ($true = (('const/sets/IN' @ sK1 @ X2 @ sK3) => ((sK12 @ (sK2 @ X2)) = X2)))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f470])).
% 16.53/3.66 thf(f470,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) | ($true = ((^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0))) @ X2))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f455])).
% 16.53/3.66 thf(f455,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) = $true) | ($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f428])).
% 16.53/3.66 thf(f428,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (($true = ((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3)))))) | ($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f426])).
% 16.53/3.66 thf(f426,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true) | ($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f425])).
% 16.53/3.66 thf(f425,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true) | ($true = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))) @ X1))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f423])).
% 16.53/3.66 thf(f423,plain,(
% 16.53/3.66 ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3))))))) = $true) | ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((sK12 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) = $true)),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f422])).
% 16.53/3.66 thf(f483,plain,(
% 16.53/3.66 spl5_16 | spl5_19),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f479,f481,f443])).
% 16.53/3.66 thf(f479,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : (((sK12 @ (sK2 @ X2)) = X2) | ((sK2 @ (sK13 @ X1)) = X1) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f478])).
% 16.53/3.66 thf(f478,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK12 @ (sK2 @ X2)) = X2) | (((sK2 @ (sK13 @ X1)) = X1) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f476])).
% 16.53/3.66 thf(f469,plain,(
% 16.53/3.66 spl5_18 | spl5_17),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f462,f451,f466])).
% 16.53/3.66 thf(f462,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f461])).
% 16.53/3.66 thf(f461,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true) | ((((sK2 @ (sK13 @ X1)) = X1) & ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f460])).
% 16.53/3.66 thf(f460,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true) | ($true = ((^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ (sK13 @ X1)))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f459])).
% 16.53/3.66 thf(f459,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f458])).
% 16.53/3.66 thf(f458,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f457])).
% 16.53/3.66 thf(f457,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (((('const/sets/IN' @ sK0 @ X2 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3)) = $true) | ($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f456])).
% 16.53/3.66 thf(f456,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) | ($true = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3))) @ X2))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f454])).
% 16.53/3.66 thf(f454,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (sK12 @ Y0) @ sK3)))) = $true) | ($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f428])).
% 16.53/3.66 thf(f468,plain,(
% 16.53/3.66 spl5_16 | spl5_18),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f464,f466,f443])).
% 16.53/3.66 thf(f464,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ((sK2 @ (sK13 @ X1)) = X1) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f463])).
% 16.53/3.66 thf(f463,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (('const/sets/IN' @ sK1 @ (sK12 @ X2) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (((sK2 @ (sK13 @ X1)) = X1) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f461])).
% 16.53/3.66 thf(f453,plain,(
% 16.53/3.66 spl5_17 | spl5_15),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f449,f440,f451])).
% 16.53/3.66 thf(f449,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (((sK2 @ (sK12 @ X2)) = X2) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f448])).
% 16.53/3.66 thf(f448,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = ((sK2 @ (sK12 @ X2)) = X2)) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 16.53/3.66 thf(f447,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (((('const/sets/IN' @ sK0 @ X2 @ sK4) => ((sK2 @ (sK12 @ X2)) = X2)) = $true) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f446])).
% 16.53/3.66 thf(f446,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))) @ X2) = $true) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f432])).
% 16.53/3.66 thf(f432,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) | ($true = ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f431])).
% 16.53/3.66 thf(f431,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((((sK2 @ (sK13 @ X1)) = X1) & ('const/sets/IN' @ sK1 @ (sK13 @ X1) @ sK3)) = $true) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f430])).
% 16.53/3.66 thf(f430,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) | ($true = ((^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ (sK13 @ X1))) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f429])).
% 16.53/3.66 thf(f429,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (($true = (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0)))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f427])).
% 16.53/3.66 thf(f427,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X1 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = X1) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))))) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0)))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f426])).
% 16.53/3.66 thf(f445,plain,(
% 16.53/3.66 spl5_15 | spl5_16),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f438,f443,f440])).
% 16.53/3.66 thf(f438,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ((sK2 @ (sK13 @ X1)) = X1) | ((sK2 @ (sK12 @ X2)) = X2)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f437])).
% 16.53/3.66 thf(f437,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (('const/sets/IN' @ sK0 @ X2 @ sK4) = $false) | ($true = ((sK2 @ (sK12 @ X2)) = X2)) | ((sK2 @ (sK13 @ X1)) = X1)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f436])).
% 16.53/3.66 thf(f436,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | ((sK2 @ (sK13 @ X1)) = X1) | ((('const/sets/IN' @ sK0 @ X2 @ sK4) => ((sK2 @ (sK12 @ X2)) = X2)) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f435])).
% 16.53/3.66 thf(f435,plain,(
% 16.53/3.66 ( ! [X2 : sK0,X1 : sK0] : (((sK2 @ (sK13 @ X1)) = X1) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false) | (((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))) @ X2) = $true)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f434])).
% 16.53/3.66 thf(f434,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : (((sK2 @ (sK13 @ X1)) = X1) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f433])).
% 16.53/3.66 thf(f433,plain,(
% 16.53/3.66 ( ! [X1 : sK0] : ((((sK2 @ (sK13 @ X1)) = X1) = $true) | ($true = (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (sK12 @ Y0)) = Y0))))) | (('const/sets/IN' @ sK0 @ X1 @ sK4) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f431])).
% 16.53/3.66 thf(f420,plain,(
% 16.53/3.66 ~spl5_2 | spl5_14 | spl5_9),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f419,f147,f293,f61])).
% 16.53/3.66 thf(f419,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (sK9 != sK11)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f415])).
% 16.53/3.66 thf(f415,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK11 = sK9) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f391])).
% 16.53/3.66 thf(f391,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK11 = sK9) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f390])).
% 16.53/3.66 thf(f390,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f389])).
% 16.53/3.66 thf(f389,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f388])).
% 16.53/3.66 thf(f388,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f387])).
% 16.53/3.66 thf(f387,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0))) @ (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f353])).
% 16.53/3.66 thf(f353,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f351])).
% 16.53/3.66 thf(f351,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f350])).
% 16.53/3.66 thf(f350,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (((^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))) @ sK9) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f275])).
% 16.53/3.66 thf(f275,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 16.53/3.66 thf(f37,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 16.53/3.66 thf(f35,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f34])).
% 16.53/3.66 thf(f34,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | (((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))) @ (sK8 @ X1)) = $false) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1))))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f33])).
% 16.53/3.66 thf(f33,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3)))) = $false) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f32])).
% 16.53/3.66 thf(f32,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3)))) = $false) | ($false = ((^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0))) @ (sK7 @ X1))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f31])).
% 16.53/3.66 thf(f31,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0))))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3)))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 16.53/3.66 thf(f30,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 16.53/3.66 thf(f29,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))))) | ((('const/sets/IN' @ sK0 @ sK6 @ sK4) => (?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f28])).
% 16.53/3.66 thf(f28,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))) @ sK6))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f27])).
% 16.53/3.66 thf(f27,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3))))))) = $false) | ($false = (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 16.53/3.66 thf(f26,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $false) | ($false = (((!! @ sK1 @ (^[Y0 : sK1]: (('const/sets/IN' @ sK1 @ Y0 @ sK3) => ((X1 @ (sK2 @ Y0)) = Y0)))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ Y0) @ sK3))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0))))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f25])).
% 16.53/3.66 thf(f25,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ((^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1)))))) @ X1)) | (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $false)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f24])).
% 16.53/3.66 thf(f24,plain,(
% 16.53/3.66 ((?? @ (sK0 > sK1) @ (^[Y0 : sK0 > sK1]: (((!! @ sK1 @ (^[Y1 : sK1]: (('const/sets/IN' @ sK1 @ Y1 @ sK3) => ((Y0 @ (sK2 @ Y1)) = Y1)))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ('const/sets/IN' @ sK1 @ (Y0 @ Y1) @ sK3))))) & (!! @ sK0 @ (^[Y1 : sK0]: (('const/sets/IN' @ sK0 @ Y1 @ sK4) => ((sK2 @ (Y0 @ Y1)) = Y1))))))) = $false) | (((!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))) & (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => (?? @ sK1 @ (^[Y1 : sK1]: (((sK2 @ Y1) = Y0) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)))))))) = $false)),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 16.53/3.66 thf(f418,plain,(
% 16.53/3.66 spl5_14 | ~spl5_2 | spl5_10),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f417,f173,f61,f293])).
% 16.53/3.66 thf(f417,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (sK9 != sK11) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f416])).
% 16.53/3.66 thf(f416,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f414])).
% 16.53/3.66 thf(f414,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f391])).
% 16.53/3.66 thf(f413,plain,(
% 16.53/3.66 spl5_6 | spl5_14 | spl5_9),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f412,f147,f293,f99])).
% 16.53/3.66 thf(f412,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f410])).
% 16.53/3.66 thf(f410,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((sK2 @ sK11) = (sK2 @ sK9)) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f401])).
% 16.53/3.66 thf(f401,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f394])).
% 16.53/3.66 thf(f394,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f392])).
% 16.53/3.66 thf(f392,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f390])).
% 16.53/3.66 thf(f411,plain,(
% 16.53/3.66 spl5_9 | spl5_14 | spl5_7),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f409,f108,f293,f147])).
% 16.53/3.66 thf(f409,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f401])).
% 16.53/3.66 thf(f408,plain,(
% 16.53/3.66 spl5_14 | spl5_10 | spl5_7),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f407,f108,f173,f293])).
% 16.53/3.66 thf(f407,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f402])).
% 16.53/3.66 thf(f402,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f400])).
% 16.53/3.66 thf(f400,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f394])).
% 16.53/3.66 thf(f406,plain,(
% 16.53/3.66 spl5_6 | spl5_10 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f405,f293,f173,f99])).
% 16.53/3.66 thf(f405,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f404])).
% 16.53/3.66 thf(f404,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f403])).
% 16.53/3.66 thf(f403,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f400])).
% 16.53/3.66 thf(f399,plain,(
% 16.53/3.66 spl5_10 | spl5_14 | spl5_5),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f398,f84,f293,f173])).
% 16.53/3.66 thf(f398,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f395])).
% 16.53/3.66 thf(f395,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f393])).
% 16.53/3.66 thf(f393,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f392])).
% 16.53/3.66 thf(f397,plain,(
% 16.53/3.66 spl5_5 | spl5_9 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f396,f293,f147,f84])).
% 16.53/3.66 thf(f396,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f393])).
% 16.53/3.66 thf(f386,plain,(
% 16.53/3.66 spl5_5 | spl5_3 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f379,f293,f65,f84])).
% 16.53/3.66 thf(f379,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f376])).
% 16.53/3.66 thf(f376,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f374])).
% 16.53/3.66 thf(f374,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f373])).
% 16.53/3.66 thf(f373,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f357])).
% 16.53/3.66 thf(f357,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f355])).
% 16.53/3.66 thf(f355,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9)))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f354])).
% 16.53/3.66 thf(f354,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0))) @ (sK10 @ X1)))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f352])).
% 16.53/3.66 thf(f352,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f351])).
% 16.53/3.66 thf(f385,plain,(
% 16.53/3.66 spl5_6 | spl5_14 | spl5_3),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f384,f65,f293,f99])).
% 16.53/3.66 thf(f384,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f382])).
% 16.53/3.66 thf(f382,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f380])).
% 16.53/3.66 thf(f380,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f376])).
% 16.53/3.66 thf(f383,plain,(
% 16.53/3.66 spl5_3 | spl5_7 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f381,f293,f108,f65])).
% 16.53/3.66 thf(f381,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f380])).
% 16.53/3.66 thf(f378,plain,(
% 16.53/3.66 spl5_3 | ~spl5_2 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f377,f293,f61,f65])).
% 16.53/3.66 thf(f377,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (sK9 != sK11) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f375])).
% 16.53/3.66 thf(f375,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f374])).
% 16.53/3.66 thf(f372,plain,(
% 16.53/3.66 spl5_14 | ~spl5_2 | spl5_11),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f371,f202,f61,f293])).
% 16.53/3.66 thf(f371,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (sK9 != sK11) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f361])).
% 16.53/3.66 thf(f361,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK11 = sK9) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f360])).
% 16.53/3.66 thf(f360,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f359])).
% 16.53/3.66 thf(f359,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f358])).
% 16.53/3.66 thf(f358,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f356])).
% 16.53/3.66 thf(f356,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f355])).
% 16.53/3.66 thf(f370,plain,(
% 16.53/3.66 spl5_14 | spl5_11 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f369,f99,f202,f293])).
% 16.53/3.66 thf(f369,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f367])).
% 16.53/3.66 thf(f367,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f364])).
% 16.53/3.66 thf(f364,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f362])).
% 16.53/3.66 thf(f362,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f360])).
% 16.53/3.66 thf(f368,plain,(
% 16.53/3.66 spl5_7 | spl5_14 | spl5_11),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f366,f202,f293,f108])).
% 16.53/3.66 thf(f366,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f364])).
% 16.53/3.66 thf(f365,plain,(
% 16.53/3.66 spl5_5 | spl5_11 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f363,f293,f202,f84])).
% 16.53/3.66 thf(f363,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f362])).
% 16.53/3.66 thf(f349,plain,(
% 16.53/3.66 spl5_13 | ~spl5_2 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f348,f293,f61,f263])).
% 16.53/3.66 thf(f348,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (sK9 != sK11) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f347])).
% 16.53/3.66 thf(f347,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (sK9 != sK11) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f336])).
% 16.53/3.66 thf(f336,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK11 = sK9) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f322])).
% 16.53/3.66 thf(f322,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f321])).
% 16.53/3.66 thf(f321,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f320])).
% 16.53/3.66 thf(f320,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f319])).
% 16.53/3.66 thf(f319,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f318])).
% 16.53/3.66 thf(f318,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | (((^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))) @ sK9) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f280])).
% 16.53/3.66 thf(f280,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f278])).
% 16.53/3.66 thf(f278,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f277])).
% 16.53/3.66 thf(f277,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0))) @ (sK10 @ X1))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f276])).
% 16.53/3.66 thf(f276,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f274])).
% 16.53/3.66 thf(f274,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0)))))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 16.53/3.66 thf(f346,plain,(
% 16.53/3.66 spl5_14 | spl5_13 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f345,f99,f263,f293])).
% 16.53/3.66 thf(f345,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f343])).
% 16.53/3.66 thf(f343,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f340])).
% 16.53/3.66 thf(f340,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f338])).
% 16.53/3.66 thf(f338,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f337])).
% 16.53/3.66 thf(f337,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f322])).
% 16.53/3.66 thf(f344,plain,(
% 16.53/3.66 spl5_14 | spl5_13 | spl5_7),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f342,f108,f263,f293])).
% 16.53/3.66 thf(f342,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f340])).
% 16.53/3.66 thf(f341,plain,(
% 16.53/3.66 spl5_13 | spl5_5 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f339,f293,f84,f263])).
% 16.53/3.66 thf(f339,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f338])).
% 16.53/3.66 thf(f335,plain,(
% 16.53/3.66 spl5_14 | spl5_8 | spl5_5),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f328,f84,f122,f293])).
% 16.53/3.66 thf(f328,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f325])).
% 16.53/3.66 thf(f325,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f323])).
% 16.53/3.66 thf(f323,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f321])).
% 16.53/3.66 thf(f334,plain,(
% 16.53/3.66 spl5_8 | spl5_7 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f330,f293,f108,f122])).
% 16.53/3.66 thf(f330,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f329])).
% 16.53/3.66 thf(f329,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f325])).
% 16.53/3.66 thf(f333,plain,(
% 16.53/3.66 spl5_14 | spl5_6 | spl5_8),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f332,f122,f99,f293])).
% 16.53/3.66 thf(f332,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f331])).
% 16.53/3.66 thf(f331,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f329])).
% 16.53/3.66 thf(f327,plain,(
% 16.53/3.66 spl5_14 | spl5_8 | ~spl5_2),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f326,f61,f122,f293])).
% 16.53/3.66 thf(f326,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (sK9 != sK11)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f324])).
% 16.53/3.66 thf(f324,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f323])).
% 16.53/3.66 thf(f317,plain,(
% 16.53/3.66 spl5_5 | spl5_4 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f310,f293,f73,f84])).
% 16.53/3.66 thf(f310,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f307])).
% 16.53/3.66 thf(f307,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f286])).
% 16.53/3.66 thf(f286,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f284])).
% 16.53/3.66 thf(f284,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f283])).
% 16.53/3.66 thf(f283,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f282])).
% 16.53/3.66 thf(f282,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f281])).
% 16.53/3.66 thf(f281,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))) @ sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f279])).
% 16.53/3.66 thf(f279,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f278])).
% 16.53/3.66 thf(f316,plain,(
% 16.53/3.66 spl5_7 | spl5_14 | spl5_4),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f312,f73,f293,f108])).
% 16.53/3.66 thf(f312,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f311])).
% 16.53/3.66 thf(f311,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f307])).
% 16.53/3.66 thf(f315,plain,(
% 16.53/3.66 spl5_6 | spl5_4 | spl5_14),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f314,f293,f73,f99])).
% 16.53/3.66 thf(f314,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f313])).
% 16.53/3.66 thf(f313,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f311])).
% 16.53/3.66 thf(f309,plain,(
% 16.53/3.66 spl5_14 | spl5_4 | ~spl5_2),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f308,f61,f73,f293])).
% 16.53/3.66 thf(f308,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (sK9 != sK11)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f306])).
% 16.53/3.66 thf(f306,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f286])).
% 16.53/3.66 thf(f305,plain,(
% 16.53/3.66 spl5_14 | spl5_12 | ~spl5_2),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f304,f61,f225,f293])).
% 16.53/3.66 thf(f304,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((sK9 != sK11) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f303])).
% 16.53/3.66 thf(f303,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f287])).
% 16.53/3.66 thf(f287,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f285])).
% 16.53/3.66 thf(f285,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f284])).
% 16.53/3.66 thf(f302,plain,(
% 16.53/3.66 spl5_6 | spl5_14 | spl5_12),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f301,f225,f293,f99])).
% 16.53/3.66 thf(f301,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f299])).
% 16.53/3.66 thf(f299,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f297])).
% 16.53/3.66 thf(f297,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f290])).
% 16.53/3.66 thf(f290,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f288])).
% 16.53/3.66 thf(f288,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f285])).
% 16.53/3.66 thf(f300,plain,(
% 16.53/3.66 spl5_7 | spl5_14 | spl5_12),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f298,f225,f293,f108])).
% 16.53/3.66 thf(f298,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f297])).
% 16.53/3.66 thf(f296,plain,(
% 16.53/3.66 spl5_14 | spl5_12 | spl5_5),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f291,f84,f225,f293])).
% 16.53/3.66 thf(f291,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f289])).
% 16.53/3.66 thf(f289,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK0 @ sK6 @ sK4) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f288])).
% 16.53/3.66 thf(f273,plain,(
% 16.53/3.66 ~spl5_2 | spl5_13 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f272,f58,f263,f61])).
% 16.53/3.66 thf(f272,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (sK9 != sK11) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f271])).
% 16.53/3.66 thf(f271,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (sK9 != sK11) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f270])).
% 16.53/3.66 thf(f270,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (sK9 != sK11) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f253])).
% 16.53/3.66 thf(f253,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK11 = sK9) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f252])).
% 16.53/3.66 thf(f252,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f251])).
% 16.53/3.66 thf(f251,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f250])).
% 16.53/3.66 thf(f250,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f249])).
% 16.53/3.66 thf(f249,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f214])).
% 16.53/3.66 thf(f214,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 16.53/3.66 thf(f160,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 16.53/3.66 thf(f159,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f158])).
% 16.53/3.66 thf(f158,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f42])).
% 16.53/3.66 thf(f42,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 16.53/3.66 thf(f41,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) => ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f40])).
% 16.53/3.66 thf(f40,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0))) @ (sK10 @ X1))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f39])).
% 16.53/3.66 thf(f39,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9)))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f38])).
% 16.53/3.66 thf(f38,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | (((^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))) @ sK9) = $false)) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f36])).
% 16.53/3.66 thf(f36,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (!! @ sK1 @ (^[Y0 : sK1]: (!! @ sK1 @ (^[Y1 : sK1]: (((((sK2 @ Y1) = (sK2 @ Y0)) & ('const/sets/IN' @ sK1 @ Y1 @ sK3)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) => (Y1 = Y0))))))) | ((!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ sK4) => ((sK2 @ (X1 @ Y0)) = Y0)))) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 16.53/3.66 thf(f269,plain,(
% 16.53/3.66 spl5_1 | spl5_5 | spl5_13),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f268,f263,f84,f58])).
% 16.53/3.66 thf(f268,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f267])).
% 16.53/3.66 thf(f267,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ X2) = sK6) = $false) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f255])).
% 16.53/3.66 thf(f255,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f254])).
% 16.53/3.66 thf(f254,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f252])).
% 16.53/3.66 thf(f266,plain,(
% 16.53/3.66 spl5_7 | spl5_1 | spl5_13),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f259,f263,f58,f108])).
% 16.53/3.66 thf(f259,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 16.53/3.66 thf(f258,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f257])).
% 16.53/3.66 thf(f257,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ X2) = sK6) = $false) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 16.53/3.66 thf(f256,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f254])).
% 16.53/3.66 thf(f265,plain,(
% 16.53/3.66 spl5_13 | spl5_6 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f261,f58,f99,f263])).
% 16.53/3.66 thf(f261,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f260])).
% 16.53/3.66 thf(f260,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK2 @ X2) != sK6) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 16.53/3.66 thf(f248,plain,(
% 16.53/3.66 spl5_1 | spl5_12 | spl5_5),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f247,f84,f225,f58])).
% 16.53/3.66 thf(f247,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f246])).
% 16.53/3.66 thf(f246,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f245])).
% 16.53/3.66 thf(f245,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f244])).
% 16.53/3.66 thf(f244,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f229])).
% 16.53/3.66 thf(f229,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f228])).
% 16.53/3.66 thf(f228,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f217])).
% 16.53/3.66 thf(f217,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f215])).
% 16.53/3.66 thf(f215,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f213])).
% 16.53/3.66 thf(f213,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f160])).
% 16.53/3.66 thf(f243,plain,(
% 16.53/3.66 spl5_12 | spl5_7 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f242,f58,f108,f225])).
% 16.53/3.66 thf(f242,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f241])).
% 16.53/3.66 thf(f241,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f240])).
% 16.53/3.66 thf(f240,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f239])).
% 16.53/3.66 thf(f239,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f231])).
% 16.53/3.66 thf(f231,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f230])).
% 16.53/3.66 thf(f230,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f228])).
% 16.53/3.66 thf(f238,plain,(
% 16.53/3.66 spl5_1 | spl5_6 | spl5_12),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f237,f225,f99,f58])).
% 16.53/3.66 thf(f237,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ X2) != sK6) | ((sK2 @ sK9) = (sK2 @ sK11)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f236])).
% 16.53/3.66 thf(f236,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f235])).
% 16.53/3.66 thf(f235,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f234])).
% 16.53/3.66 thf(f234,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2))) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f233])).
% 16.53/3.66 thf(f233,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f232])).
% 16.53/3.66 thf(f232,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f230])).
% 16.53/3.66 thf(f227,plain,(
% 16.53/3.66 ~spl5_2 | spl5_1 | spl5_12),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f223,f225,f58,f61])).
% 16.53/3.66 thf(f223,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | (sK9 != sK11) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f222])).
% 16.53/3.66 thf(f222,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (sK9 != sK11) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f221])).
% 16.53/3.66 thf(f221,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (((sK2 @ X2) = sK6) = $false) | (sK9 != sK11) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f220])).
% 16.53/3.66 thf(f220,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((sK9 != sK11) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f219])).
% 16.53/3.66 thf(f219,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (sK9 != sK11)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f218])).
% 16.53/3.66 thf(f218,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | (sK9 != sK11) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f216])).
% 16.53/3.66 thf(f216,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK11 = sK9) = $false) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f215])).
% 16.53/3.66 thf(f212,plain,(
% 16.53/3.66 spl5_11 | spl5_1 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f211,f99,f58,f202])).
% 16.53/3.66 thf(f211,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f209])).
% 16.53/3.66 thf(f209,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f206])).
% 16.53/3.66 thf(f206,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f199])).
% 16.53/3.66 thf(f199,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f197])).
% 16.53/3.66 thf(f197,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f196])).
% 16.53/3.66 thf(f196,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f195])).
% 16.53/3.66 thf(f195,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f194])).
% 16.53/3.66 thf(f194,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f193])).
% 16.53/3.66 thf(f193,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f162])).
% 16.53/3.66 thf(f162,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 16.53/3.66 thf(f161,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f159])).
% 16.53/3.66 thf(f210,plain,(
% 16.53/3.66 spl5_7 | spl5_11 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f208,f58,f202,f108])).
% 16.53/3.66 thf(f208,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f206])).
% 16.53/3.66 thf(f207,plain,(
% 16.53/3.66 spl5_1 | spl5_11 | spl5_5),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f205,f84,f202,f58])).
% 16.53/3.66 thf(f205,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f199])).
% 16.53/3.66 thf(f204,plain,(
% 16.53/3.66 ~spl5_2 | spl5_1 | spl5_11),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f200,f202,f58,f61])).
% 16.53/3.66 thf(f200,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (sK9 != sK11) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f198])).
% 16.53/3.66 thf(f198,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK11 = sK9) = $false) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f197])).
% 16.53/3.66 thf(f192,plain,(
% 16.53/3.66 spl5_10 | spl5_1 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f191,f99,f58,f173])).
% 16.53/3.66 thf(f191,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f190])).
% 16.53/3.66 thf(f190,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f189])).
% 16.53/3.66 thf(f189,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((sK2 @ X2) = sK6) = $false) | ((sK2 @ sK9) = (sK2 @ sK11)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 16.53/3.66 thf(f188,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f183])).
% 16.53/3.66 thf(f183,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 16.53/3.66 thf(f177,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 16.53/3.66 thf(f167,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 16.53/3.66 thf(f165,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f164])).
% 16.53/3.66 thf(f164,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f163])).
% 16.53/3.66 thf(f163,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : (((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 16.53/3.66 thf(f187,plain,(
% 16.53/3.66 spl5_10 | spl5_1 | spl5_7),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f186,f108,f58,f173])).
% 16.53/3.66 thf(f186,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f185])).
% 16.53/3.66 thf(f185,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f184])).
% 16.53/3.66 thf(f184,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((sK2 @ X2) = sK6) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f182])).
% 16.53/3.66 thf(f182,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 16.53/3.66 thf(f181,plain,(
% 16.53/3.66 spl5_5 | spl5_1 | spl5_10),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f180,f173,f58,f84])).
% 16.53/3.66 thf(f180,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f179])).
% 16.53/3.66 thf(f179,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f178])).
% 16.53/3.66 thf(f178,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ X2) = sK6) = $false) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f176])).
% 16.53/3.66 thf(f176,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 16.53/3.66 thf(f175,plain,(
% 16.53/3.66 ~spl5_2 | spl5_10 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f171,f58,f173,f61])).
% 16.53/3.66 thf(f171,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | (sK9 != sK11)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f170])).
% 16.53/3.66 thf(f170,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f169])).
% 16.53/3.66 thf(f169,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK10 @ X1) != (sK2 @ (X1 @ (sK10 @ X1)))) | (((sK2 @ X2) = sK6) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK11 = sK9) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f168])).
% 16.53/3.66 thf(f168,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1))) | (((sK2 @ X2) = sK6) = $false) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 16.53/3.66 thf(f166,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ((sK2 @ (X1 @ (sK10 @ X1))) = (sK10 @ X1)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f165])).
% 16.53/3.66 thf(f157,plain,(
% 16.53/3.66 spl5_1 | ~spl5_2 | spl5_9),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f156,f147,f61,f58])).
% 16.53/3.66 thf(f156,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (sK9 != sK11) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f155])).
% 16.53/3.66 thf(f155,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ X2) = sK6) = $false) | (sK9 != sK11) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 16.53/3.66 thf(f154,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((sK9 != sK11) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f138])).
% 16.53/3.66 thf(f138,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 16.53/3.66 thf(f114,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 16.53/3.66 thf(f49,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 16.53/3.66 thf(f47,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false)) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f46])).
% 16.53/3.66 thf(f46,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ((^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))) @ sK11))) )),
% 16.53/3.66 inference(sigma_clausification,[status(thm)],[f45])).
% 16.53/3.66 thf(f45,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)))) )),
% 16.53/3.66 inference(beta_eta_normalization,[status(thm)],[f44])).
% 16.53/3.66 thf(f44,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ((^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3))) @ X2)) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(pi_clausification,[status(thm)],[f43])).
% 16.53/3.66 thf(f43,plain,(
% 16.53/3.66 ( ! [X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((?? @ sK1 @ (^[Y0 : sK1]: (((sK2 @ Y0) = sK6) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)))) = $false) | ($false = (!! @ sK1 @ (^[Y0 : sK1]: (((((sK2 @ Y0) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ Y0 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (Y0 = sK9))))) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4) => ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 16.53/3.66 thf(f153,plain,(
% 16.53/3.66 spl5_5 | spl5_1 | spl5_9),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f152,f147,f58,f84])).
% 16.53/3.66 thf(f152,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f141])).
% 16.53/3.66 thf(f141,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((sK2 @ X2) = sK6) = $false) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 16.53/3.66 thf(f140,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 16.53/3.66 thf(f139,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 16.53/3.66 thf(f151,plain,(
% 16.53/3.66 spl5_9 | spl5_1 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f150,f99,f58,f147])).
% 16.53/3.66 thf(f150,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f145])).
% 16.53/3.66 thf(f145,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 16.53/3.66 thf(f143,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f142])).
% 16.53/3.66 thf(f142,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ X2) = sK6) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 16.53/3.66 thf(f149,plain,(
% 16.53/3.66 spl5_7 | spl5_9 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f144,f58,f147,f108])).
% 16.53/3.66 thf(f144,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 16.53/3.66 thf(f137,plain,(
% 16.53/3.66 spl5_8 | spl5_5 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f136,f58,f84,f122])).
% 16.53/3.66 thf(f136,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK2 @ X2) != sK6) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f127])).
% 16.53/3.66 thf(f127,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 16.53/3.66 thf(f126,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f125])).
% 16.53/3.66 thf(f125,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (((sK2 @ X2) = sK6) = $false) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 16.53/3.66 thf(f116,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 16.53/3.66 thf(f113,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 16.53/3.66 thf(f135,plain,(
% 16.53/3.66 spl5_7 | spl5_8 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f134,f58,f122,f108])).
% 16.53/3.66 thf(f134,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f129])).
% 16.53/3.66 thf(f129,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 16.53/3.66 thf(f128,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 16.53/3.66 thf(f133,plain,(
% 16.53/3.66 spl5_8 | spl5_6 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f132,f58,f99,f122])).
% 16.53/3.66 thf(f132,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK2 @ X2) != sK6) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f131])).
% 16.53/3.66 thf(f131,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ X2) = sK6) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f130])).
% 16.53/3.66 thf(f130,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 16.53/3.66 thf(f124,plain,(
% 16.53/3.66 ~spl5_2 | spl5_8 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f120,f58,f122,f61])).
% 16.53/3.66 thf(f120,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (sK9 != sK11) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f119])).
% 16.53/3.66 thf(f119,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | (sK9 != sK11) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f118])).
% 16.53/3.66 thf(f118,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((sK2 @ X2) = sK6) = $false) | (sK9 != sK11) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f117])).
% 16.53/3.66 thf(f117,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK11 = sK9) = $false) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (((sK2 @ X2) = sK6) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 16.53/3.66 thf(f115,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK0 @ (sK8 @ X1) @ sK4)) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK11 = sK9) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 16.53/3.66 thf(f112,plain,(
% 16.53/3.66 spl5_7 | spl5_1 | spl5_3),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f105,f65,f58,f108])).
% 16.53/3.66 thf(f105,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 16.53/3.66 thf(f92,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 16.53/3.66 thf(f91,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f90])).
% 16.53/3.66 thf(f90,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ X2) = sK6) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 16.53/3.66 thf(f77,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) = $true) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 16.53/3.66 thf(f51,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3)))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 16.53/3.66 thf(f48,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((((((sK2 @ sK11) = (sK2 @ sK9)) & ('const/sets/IN' @ sK1 @ sK11 @ sK3)) & ('const/sets/IN' @ sK1 @ sK9 @ sK3)) => (sK11 = sK9)) = $false) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 16.53/3.66 thf(f111,plain,(
% 16.53/3.66 spl5_1 | spl5_7 | spl5_4),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f106,f73,f108,f58])).
% 16.53/3.66 thf(f106,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1))))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f104])).
% 16.53/3.66 thf(f104,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK1 @ sK11 @ sK3) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 16.53/3.66 thf(f103,plain,(
% 16.53/3.66 spl5_3 | spl5_1 | spl5_6),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f96,f99,f58,f65])).
% 16.53/3.66 thf(f96,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ sK9) = (sK2 @ sK11)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 16.53/3.66 thf(f94,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ sK9) = (sK2 @ sK11)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f93])).
% 16.53/3.66 thf(f93,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ sK11) = (sK2 @ sK9)) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1))))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 16.53/3.66 thf(f102,plain,(
% 16.53/3.66 spl5_1 | spl5_6 | spl5_4),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f97,f73,f99,f58])).
% 16.53/3.66 thf(f97,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ X2) != sK6) | ((sK2 @ sK9) = (sK2 @ sK11))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f95])).
% 16.53/3.66 thf(f95,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK2 @ sK9) = (sK2 @ sK11)) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 16.53/3.66 thf(f89,plain,(
% 16.53/3.66 spl5_5 | spl5_1 | spl5_3),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f88,f65,f58,f84])).
% 16.53/3.66 thf(f88,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f80])).
% 16.53/3.66 thf(f80,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 16.53/3.66 thf(f78,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 16.53/3.66 thf(f76,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 16.53/3.66 thf(f87,plain,(
% 16.53/3.66 spl5_4 | spl5_5 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f82,f58,f84,f73])).
% 16.53/3.66 thf(f82,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK2 @ X2) != sK6)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f81])).
% 16.53/3.66 thf(f81,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f79])).
% 16.53/3.66 thf(f79,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($true = ('const/sets/IN' @ sK1 @ sK9 @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | (((sK2 @ X2) = sK6) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 16.53/3.66 thf(f75,plain,(
% 16.53/3.66 ~spl5_2 | spl5_4 | spl5_1),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f71,f58,f73,f61])).
% 16.53/3.66 thf(f71,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((sK9 != sK11) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ((sK2 @ X2) != sK6) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f70])).
% 16.53/3.66 thf(f70,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK2 @ X2) != sK6) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f69])).
% 16.53/3.66 thf(f69,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 16.53/3.66 thf(f68,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK7 @ X1) != (X1 @ (sK2 @ (sK7 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 16.53/3.66 thf(f52,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)) = $false) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | ((sK11 = sK9) = $false)) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 16.53/3.66 thf(f50,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) => ((X1 @ (sK2 @ (sK7 @ X1))) = (sK7 @ X1)))) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ((sK11 = sK9) = $false) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 16.53/3.66 thf(f67,plain,(
% 16.53/3.66 spl5_1 | ~spl5_2 | spl5_3),
% 16.53/3.66 inference(avatar_split_clause,[status(thm)],[f56,f65,f61,f58])).
% 16.53/3.66 thf(f56,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK2 @ X2) != sK6) | (sK9 != sK11) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3)) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 16.53/3.66 thf(f55,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (sK9 != sK11) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (((sK2 @ X2) = sK6) = $false) | ($false = ('const/sets/IN' @ sK1 @ X2 @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 16.53/3.66 thf(f54,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : (($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3)) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | (('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | (sK9 != sK11)) )),
% 16.53/3.66 inference(equality_proxy_clausification,[status(thm)],[f53])).
% 16.53/3.66 thf(f53,plain,(
% 16.53/3.66 ( ! [X2 : sK1,X1 : sK0 > sK1] : ((('const/sets/IN' @ sK1 @ (sK7 @ X1) @ sK3) = $true) | ((sK11 = sK9) = $false) | (('const/sets/IN' @ sK0 @ (sK10 @ X1) @ sK4) = $true) | ($false = (((sK2 @ X2) = sK6) & ('const/sets/IN' @ sK1 @ X2 @ sK3))) | ($false = ('const/sets/IN' @ sK1 @ (X1 @ (sK8 @ X1)) @ sK3))) )),
% 16.53/3.66 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 16.53/3.66 % SZS output end Proof for DTF2THF_3780
% 16.53/3.66 % (4145)------------------------------
% 16.53/3.66 % (4145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.53/3.66 % (4145)Termination reason: Refutation
% 16.53/3.66
% 16.53/3.66 % (4145)Memory used [KB]: 7164
% 16.53/3.66 % (4145)Time elapsed: 0.209 s
% 16.53/3.66 % (4145)Instructions burned: 595 (million)
% 16.53/3.66 % (4145)------------------------------
% 16.53/3.66 % (4145)------------------------------
% 16.53/3.66 % (3996)Success in time 2.365 s
%------------------------------------------------------------------------------