%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV491^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 09:41:22 AM UTC 2026
% Result : Theorem 1.76s 1.51s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 125 ( 2 unt; 0 typ; 9 def)
% Number of atoms : 1487 ( 386 equ; 0 cnn)
% Maximal formula atoms : 18 ( 11 avg)
% Number of connectives : 2676 ( 191 ~; 299 |; 74 &;2078 @)
% ( 10 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 11 con; 0-6 aty)
% Number of variables : 275 ( 0 ^; 243 !; 32 ?; 275 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(type_def_8,type,
sK1: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/HAS_SIZE':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_8,type,
sK2: sK0 > $o ).
thf(func_def_9,type,
sK3: sK1 > $o ).
thf(func_def_10,type,
sK4: sK0 > sK1 ).
thf(func_def_11,type,
sK5: sK1 > sK0 ).
thf(func_def_12,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > ( X1 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > ( X1 > $o ) > ( X0 > $o ) > X1 ) ).
thf(func_def_15,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f280,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f106,f107,f135,f144,f145,f150,f151,f157,f166,f169,f218,f267,f279]) ).
thf(f279,plain,
( spl8_6
| spl8_6
| spl8_4
| ~ spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f278,f88,f84,f92,f92]) ).
thf(f92,definition,
( spl8_6
<=> ! [X0: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f84,definition,
( spl8_4
<=> ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f88,definition,
( spl8_5
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f278,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $false ) )
| spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f277,f85]) ).
thf(f85,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
!= $true )
| spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f277,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $false ) )
| ~ spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f171,f89]) ).
thf(f89,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f171,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $false )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $false )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) ) ),
inference(superposition,[status(thm)],[f76,f26]) ).
thf(f26,plain,
! [X7: sK1] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK5 @ X7 ) @ sK2 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ X7 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( 'const/sets/CARD' @ sK0 @ sK2 )
!= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
& ( ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK3 ) )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) )
& ! [X6: sK0] :
( ( ( ( sK5 @ ( sK4 @ X6 ) )
= X6 )
& ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK4 @ X6 ) @ sK3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ X6 @ sK2 ) ) )
& ! [X7: sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK5 @ X7 ) @ sK2 )
= $true )
& ( ( sK4 @ ( sK5 @ X7 ) )
= X7 ) )
| ( ( 'const/sets/IN' @ sK1 @ X7 @ sK3 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ( 'const/sets/CARD' @ X0 @ X2 )
!= ( 'const/sets/CARD' @ X1 @ X3 ) )
& ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
& ! [X6: X0] :
( ( ( ( X5 @ ( X4 @ X6 ) )
= X6 )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X6 ) @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ X2 ) ) )
& ! [X7: X1] :
( ( ( ( 'const/sets/IN' @ X0 @ ( X5 @ X7 ) @ X2 )
= $true )
& ( ( X4 @ ( X5 @ X7 ) )
= X7 ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X7 @ X3 ) ) ) )
=> ( ( ( 'const/sets/CARD' @ sK0 @ sK2 )
!= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
& ( ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK3 ) )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) )
& ! [X6: sK0] :
( ( ( ( sK5 @ ( sK4 @ X6 ) )
= X6 )
& ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK4 @ X6 ) @ sK3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ X6 @ sK2 ) ) )
& ! [X7: sK1] :
( ( ( ( 'const/sets/IN' @ sK0 @ ( sK5 @ X7 ) @ sK2 )
= $true )
& ( ( sK4 @ ( sK5 @ X7 ) )
= X7 ) )
| ( ( 'const/sets/IN' @ sK1 @ X7 @ sK3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ( 'const/sets/CARD' @ X0 @ X2 )
!= ( 'const/sets/CARD' @ X1 @ X3 ) )
& ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
& ! [X6: X0] :
( ( ( ( X5 @ ( X4 @ X6 ) )
= X6 )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X6 ) @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X6 @ X2 ) ) )
& ! [X7: X1] :
( ( ( ( 'const/sets/IN' @ X0 @ ( X5 @ X7 ) @ X2 )
= $true )
& ( ( X4 @ ( X5 @ X7 ) )
= X7 ) )
| ( $true
!= ( 'const/sets/IN' @ X1 @ X7 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ( 'const/sets/CARD' @ X0 @ X2 )
!= ( 'const/sets/CARD' @ X1 @ X3 ) )
& ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
& ! [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
= X7 )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) )
& ! [X6: X1] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) )
| ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ( 'const/sets/CARD' @ X0 @ X2 )
!= ( 'const/sets/CARD' @ X1 @ X3 ) )
& ! [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
= X7 )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) )
& ! [X6: X1] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) )
| ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
!= $true ) )
& ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ! [X7: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) )
=> ( ( ( X5 @ ( X4 @ X7 ) )
= X7 )
& ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) ) )
& ! [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
= $true )
=> ( ( $true
= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) ) )
& ( ( $true
= ( 'const/sets/FINITE' @ X1 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ) )
=> ( ( 'const/sets/CARD' @ X0 @ X2 )
= ( 'const/sets/CARD' @ X1 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
| ( 'const/sets/FINITE' @ X1 @ X3 ) )
& ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
=> ( ( ( X4 @ ( X5 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) ) )
& ! [X7: X0] :
( ( 'const/sets/IN' @ X0 @ X7 @ X2 )
=> ( ( ( X5 @ ( X4 @ X7 ) )
= X7 )
& ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) ) )
=> ( ( 'const/sets/CARD' @ X0 @ X2 )
= ( 'const/sets/CARD' @ X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X3: $tType,X1: X0 > $o,X2: X3 > $o,X4: X0 > X3,X5: X3 > X0] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
| ( 'const/sets/FINITE' @ X3 @ X2 ) )
& ! [X6: X3] :
( ( 'const/sets/IN' @ X3 @ X6 @ X2 )
=> ( ( ( X4 @ ( X5 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X1 ) ) )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X1 )
=> ( ( ( X5 @ ( X4 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X3 @ ( X4 @ X6 ) @ X2 ) ) ) )
=> ( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/CARD' @ X3 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X3: $tType,X1: X0 > $o,X2: X3 > $o,X4: X0 > X3,X5: X3 > X0] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
| ( 'const/sets/FINITE' @ X3 @ X2 ) )
& ! [X6: X3] :
( ( 'const/sets/IN' @ X3 @ X6 @ X2 )
=> ( ( ( X4 @ ( X5 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X1 ) ) )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X1 )
=> ( ( ( X5 @ ( X4 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X3 @ ( X4 @ X6 ) @ X2 ) ) ) )
=> ( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/CARD' @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/BIJECTIONS_CARD_EQ_') ).
thf(f76,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f34,f51]) ).
thf(f51,plain,
! [X0: $tType,X2: X0 > sK1,X3: X0 > $o,X1: sK1 > X0,X4: 'type/nums/num'] :
( ( ( sK4 @ ( sK5 @ ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) ) )
= ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) @ X3 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ X0 @ X3 @ X4 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $tType,X2: X0 > sK1,X3: X0 > $o,X1: sK1 > X0,X4: 'type/nums/num'] :
( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) @ X3 ) )
| ( ( sK4 @ ( sK5 @ ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) ) )
= ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X3 @ X4 )
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $tType,X2: X0 > sK1,X3: X0 > $o,X1: sK1 > X0,X4: 'type/nums/num'] :
( ( $true != $true )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X3 @ X4 )
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4 ) )
| ( ( sK4 @ ( sK5 @ ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) ) )
= ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) @ X3 ) ) ),
inference(superposition,[status(thm)],[f25,f35]) ).
thf(f35,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X6: 'type/nums/num',X4: X0 > X1,X5: X1 > X0] :
( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X3 ) )
| ( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ! [X6: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ( ( ( ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 )
!= ( X5 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) )
| ( ( 'const/sets/IN' @ X1 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X3 )
!= $true ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X2 ) ) )
| ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X3 ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X2 ) )
| ( ( X4 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) )
!= ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f21,f23,f22]) ).
thf(f22,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ? [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
!= X7 )
| ( $true
!= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) )
=> ( ( ( ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 )
!= ( X5 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) )
| ( ( 'const/sets/IN' @ X1 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X3 )
!= $true ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ? [X8: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X8 @ X3 ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ X8 ) @ X2 ) )
| ( ( X4 @ ( X5 @ X8 ) )
!= X8 ) ) )
=> ( ( $true
= ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X3 ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X2 ) )
| ( ( X4 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) )
!= ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ! [X6: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ? [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
!= X7 )
| ( $true
!= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) )
| ? [X8: X1] :
( ( $true
= ( 'const/sets/IN' @ X1 @ X8 @ X3 ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ X8 ) @ X2 ) )
| ( ( X4 @ ( X5 @ X8 ) )
!= X8 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ! [X8: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X8 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X8 ) )
| ? [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
!= X7 )
| ( $true
!= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) )
| ? [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
= $true )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
| ( ( X4 @ ( X5 @ X6 ) )
!= X6 ) ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ! [X8: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X8 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X8 ) )
| ? [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
= $true )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
| ( ( X4 @ ( X5 @ X6 ) )
!= X6 ) ) )
| ? [X7: X0] :
( ( ( ( X5 @ ( X4 @ X7 ) )
!= X7 )
| ( $true
!= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ! [X6: X1] :
( ( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
= $true )
=> ( ( $true
= ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 ) )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) ) )
& ! [X7: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X7 @ X2 ) )
=> ( ( $true
= ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) )
& ( ( X5 @ ( X4 @ X7 ) )
= X7 ) ) ) )
=> ! [X8: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X8 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X8 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o,X4: X0 > X1,X5: X1 > X0] :
( ( ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X3 )
=> ( ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X2 )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) ) )
& ! [X7: X0] :
( ( 'const/sets/IN' @ X0 @ X7 @ X2 )
=> ( ( ( X5 @ ( X4 @ X7 ) )
= X7 )
& ( 'const/sets/IN' @ X1 @ ( X4 @ X7 ) @ X3 ) ) ) )
=> ! [X8: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X8 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X8 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X3: $tType,X1: X0 > $o,X2: X3 > $o,X4: X0 > X3,X5: X3 > X0] :
( ( ! [X6: X3] :
( ( 'const/sets/IN' @ X3 @ X6 @ X2 )
=> ( ( 'const/sets/IN' @ X0 @ ( X5 @ X6 ) @ X1 )
& ( ( X4 @ ( X5 @ X6 ) )
= X6 ) ) )
& ! [X6: X0] :
( ( 'const/sets/IN' @ X0 @ X6 @ X1 )
=> ( ( ( X5 @ ( X4 @ X6 ) )
= X6 )
& ( 'const/sets/IN' @ X3 @ ( X4 @ X6 ) @ X2 ) ) ) )
=> ! [X6: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X3 @ X2 @ X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/BIJECTIONS_HAS_SIZE_EQ_') ).
thf(f25,plain,
! [X7: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X7 @ sK3 )
!= $true )
| ( ( sK4 @ ( sK5 @ X7 ) )
= X7 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f34,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X6: 'type/nums/num',X4: X0 > X1,X5: X1 > X0] :
( ( ( X4 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) )
!= ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f267,plain,
( ~ spl8_1
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f266]) ).
thf(f266,plain,
( $false
| ~ spl8_1
| ~ spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f261,f30]) ).
thf(f30,plain,
( ( 'const/sets/CARD' @ sK0 @ sK2 )
!= ( 'const/sets/CARD' @ sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f261,plain,
( ( ( 'const/sets/CARD' @ sK0 @ sK2 )
= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
| ~ spl8_1
| ~ spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f258]) ).
thf(f258,plain,
( ( $true != $true )
| ( ( 'const/sets/CARD' @ sK0 @ sK2 )
= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
| ~ spl8_1
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f32,f255]) ).
thf(f255,plain,
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ ( 'const/sets/CARD' @ sK0 @ sK2 ) )
= $true )
| ~ spl8_1
| ~ spl8_6 ),
inference(subsumption_resolution,[status(thm)],[f242,f42]) ).
thf(f42,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl8_1
<=> ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f242,plain,
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ ( 'const/sets/CARD' @ sK0 @ sK2 ) )
= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[status(thm)],[f227]) ).
thf(f227,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ ( 'const/sets/CARD' @ sK0 @ sK2 ) )
= $true )
| ( $true = $false )
| ~ spl8_6 ),
inference(superposition,[status(thm)],[f93,f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ ( 'const/sets/CARD' @ X0 @ X1 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/CARD' @ X0 @ X1 )
!= X2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/CARD' @ X0 @ X1 )
!= X2 ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/CARD' @ X0 @ X1 )
!= X2 ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) )
<=> ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/HAS_SIZE_') ).
thf(f93,plain,
( ! [X0: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f32,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f218,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f217]) ).
thf(f217,plain,
( $false
| ~ spl8_2
| ~ spl8_3 ),
inference(subsumption_resolution,[status(thm)],[f216,f30]) ).
thf(f216,plain,
( ( ( 'const/sets/CARD' @ sK0 @ sK2 )
= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f214]) ).
thf(f214,plain,
( ( ( 'const/sets/CARD' @ sK0 @ sK2 )
= ( 'const/sets/CARD' @ sK1 @ sK3 ) )
| ( $true != $true )
| ~ spl8_2
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f32,f208]) ).
thf(f208,plain,
( ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ ( 'const/sets/CARD' @ sK1 @ sK3 ) ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(subsumption_resolution,[status(thm)],[f193,f46]) ).
thf(f46,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK3 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl8_2
<=> ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f193,plain,
( ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ ( 'const/sets/CARD' @ sK1 @ sK3 ) ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK1 @ sK3 ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f172]) ).
thf(f172,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK1 @ sK3 ) )
| ( $true = $false )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ ( 'const/sets/CARD' @ sK1 @ sK3 ) ) )
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f82,f38]) ).
thf(f82,plain,
( ! [X1: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl8_3
<=> ! [X1: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f169,plain,
( spl8_3
| spl8_3
| spl8_4
| ~ spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f168,f88,f84,f81,f81]) ).
thf(f168,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false ) )
| spl8_4
| ~ spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f167,f89]) ).
thf(f167,plain,
( ! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| spl8_4 ),
inference(subsumption_resolution,[status(thm)],[f162,f85]) ).
thf(f162,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( $true != $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f70,f26]) ).
thf(f70,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: 'type/nums/num',X0: sK0 > $o,X1: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) ) @ X0 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X2 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0 ) @ X0 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f34,f50]) ).
thf(f50,plain,
! [X0: $tType,X2: X0 > sK1,X3: X0 > $o,X1: sK1 > X0,X4: 'type/nums/num'] :
( ( ( sK4 @ ( sK5 @ ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) ) )
= ( sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3 ) @ X3 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ X0 @ X3 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f166,plain,
( ~ spl8_5
| spl8_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
| ~ spl8_5
| spl8_8 ),
inference(subsumption_resolution,[status(thm)],[f164,f89]) ).
thf(f164,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| spl8_8 ),
inference(trivial_inequality_removal,[status(thm)],[f163]) ).
thf(f163,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( $true != $true )
| spl8_8 ),
inference(superposition,[status(thm)],[f139,f26]) ).
thf(f139,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) )
| spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f137,definition,
( spl8_8
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f157,plain,
( spl8_9
| ~ spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f154,f88,f141]) ).
thf(f141,definition,
( spl8_9
<=> ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition]) ).
thf(f154,plain,
( ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true != $true )
| ~ spl8_5 ),
inference(superposition,[status(thm)],[f25,f89]) ).
thf(f151,plain,
( spl8_6
| spl8_5
| ~ spl8_7
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f126,f84,f130,f88,f92]) ).
thf(f130,definition,
( spl8_7
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition]) ).
thf(f126,plain,
( ! [X0: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) ) )
| ~ spl8_4 ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
( ! [X0: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 )
!= ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) ) )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f37,f116]) ).
thf(f116,plain,
( ( ( sK5 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
= ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true != $true )
| ( ( sK5 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
= ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f28,f86]) ).
thf(f86,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f28,plain,
! [X6: sK0] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ X6 @ sK2 ) )
| ( ( sK5 @ ( sK4 @ X6 ) )
= X6 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f37,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X6: 'type/nums/num',X4: X0 > X1,X5: X1 > X0] :
( ( ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 )
!= ( X5 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) )
| ( ( 'const/sets/IN' @ X1 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X3 )
!= $true )
| ( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ( $true
= ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f150,plain,
( ~ spl8_4
| spl8_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f149]) ).
thf(f149,plain,
( $false
| ~ spl8_4
| spl8_7 ),
inference(subsumption_resolution,[status(thm)],[f148,f86]) ).
thf(f148,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
!= $true )
| spl8_7 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
!= $true )
| ( $true != $true )
| spl8_7 ),
inference(superposition,[status(thm)],[f132,f27]) ).
thf(f27,plain,
! [X6: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK4 @ X6 ) @ sK3 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ X6 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f132,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| spl8_7 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f145,plain,
( ~ spl8_8
| ~ spl8_7
| spl8_3
| ~ spl8_9
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f124,f84,f141,f81,f130,f137]) ).
thf(f124,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| ~ spl8_4 ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
( ! [X0: 'type/nums/num'] :
( ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ! [X0: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) )
| ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 )
!= ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f36,f116]) ).
thf(f36,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X6: 'type/nums/num',X4: X0 > X1,X5: X1 > X0] :
( ( ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 )
!= ( X5 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) ) )
| ( ( 'const/sets/HAS_SIZE' @ X1 @ X3 @ X6 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X2 @ X6 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X2 ) )
| ( ( X4 @ ( X5 @ ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) )
!= ( sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) )
| ( ( 'const/sets/IN' @ X1 @ ( X4 @ ( sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2 ) ) @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f144,plain,
( ~ spl8_8
| ~ spl8_9
| spl8_6
| ~ spl8_7
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f123,f84,f130,f92,f141,f137]) ).
thf(f123,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( sK4 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) )
!= ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ ( sK5 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) ) )
| ~ spl8_4 ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f135,plain,
( spl8_3
| ~ spl8_7
| ~ spl8_4
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f134,f88,f84,f130,f81]) ).
thf(f134,plain,
( ! [X0: 'type/nums/num'] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false ) )
| ~ spl8_4
| spl8_5 ),
inference(subsumption_resolution,[status(thm)],[f127,f90]) ).
thf(f90,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f127,plain,
( ! [X0: 'type/nums/num'] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK3 ) )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK4 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) ) @ sK3 ) ) )
| ~ spl8_4 ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f107,plain,
( spl8_4
| spl8_3
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f105,f88,f81,f84]) ).
thf(f105,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $false )
| ( $true
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| spl8_5 ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| spl8_5 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X0: 'type/nums/num'] :
( ( $true != $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| spl8_5 ),
inference(superposition,[status(thm)],[f90,f35]) ).
thf(f106,plain,
( spl8_6
| spl8_4
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f104,f88,f84,f92]) ).
thf(f104,plain,
( ! [X0: 'type/nums/num'] :
( ( ( 'const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2 ) @ sK2 )
= $true )
| ( $false
= ( 'const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0 ) ) )
| spl8_5 ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f47,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f29,f44,f40]) ).
thf(f29,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( $true
= ( 'const/sets/FINITE' @ sK1 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV491^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.31 % Computer : n015.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Feb 24 12:48:16 EST 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : SEV491^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.41 % Domain : Analysis
% 0.17/0.41 % Problem : BIJECTIONS_CARD_EQ
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Kal16]
% 0.17/0.41 % Names : BIJECTIONS_CARD_EQ_.p [Kal16]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.17/0.41 % Syntax : Number of formulae : 8 ( 1 unt; 5 typ; 0 def)
% 0.17/0.41 % Number of atoms : 22 ( 8 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 9 ( 7 avg)
% 0.17/0.41 % Number of connectives : 72 ( 0 ~; 1 |; 8 &; 57 @)
% 0.17/0.41 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 16 ( 12 avg)
% 0.17/0.41 % Number of types : 2 ( 1 usr)
% 0.17/0.41 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% 0.17/0.41 % Number of variables : 24 ( 0 ^; 20 !; 0 ?; 24 :)
% 0.17/0.41 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.41 % SPC : TH1_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : Exported from core HOL Light.
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf('thf_type_type/nums/num',type,
% 0.17/0.41 'type/nums/num': $tType ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/sets/IN',type,
% 0.17/0.41 'const/sets/IN':
% 0.17/0.41 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/sets/HAS_SIZE',type,
% 0.17/0.41 'const/sets/HAS_SIZE':
% 0.17/0.41 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/sets/FINITE',type,
% 0.17/0.41 'const/sets/FINITE':
% 0.17/0.41 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.17/0.41
% 0.17/0.41 thf('thf_const_const/sets/CARD',type,
% 0.17/0.41 'const/sets/CARD':
% 0.17/0.41 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/sets/HAS_SIZE_',axiom,
% 0.17/0.41 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 0.17/0.41 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 0.17/0.41 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.17/0.41 & ( ( 'const/sets/CARD' @ A @ A0 )
% 0.17/0.41 = A1 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/sets/BIJECTIONS_HAS_SIZE_EQ_',axiom,
% 0.17/0.41 ! [A: $tType,B: $tType,A0: A > $o,A1: B > $o,A2: A > B,A3: B > A] :
% 0.17/0.41 ( ( ! [A4: A] :
% 0.17/0.41 ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 0.17/0.41 => ( ( 'const/sets/IN' @ B @ ( A2 @ A4 ) @ A1 )
% 0.17/0.41 & ( ( A3 @ ( A2 @ A4 ) )
% 0.17/0.41 = A4 ) ) )
% 0.17/0.41 & ! [A4: B] :
% 0.17/0.41 ( ( 'const/sets/IN' @ B @ A4 @ A1 )
% 0.17/0.41 => ( ( 'const/sets/IN' @ A @ ( A3 @ A4 ) @ A0 )
% 0.17/0.41 & ( ( A2 @ ( A3 @ A4 ) )
% 0.17/0.41 = A4 ) ) ) )
% 0.17/0.41 => ! [A4: 'type/nums/num'] :
% 0.17/0.41 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A4 )
% 0.17/0.41 = ( 'const/sets/HAS_SIZE' @ B @ A1 @ A4 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf('thm/sets/BIJECTIONS_CARD_EQ_',conjecture,
% 0.17/0.41 ! [A: $tType,B: $tType,A0: A > $o,A1: B > $o,A2: A > B,A3: B > A] :
% 0.17/0.41 ( ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.17/0.41 | ( 'const/sets/FINITE' @ B @ A1 ) )
% 0.17/0.41 & ! [A4: A] :
% 0.17/0.41 ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 0.17/0.41 => ( ( 'const/sets/IN' @ B @ ( A2 @ A4 ) @ A1 )
% 0.17/0.41 & ( ( A3 @ ( A2 @ A4 ) )
% 0.17/0.41 = A4 ) ) )
% 0.17/0.41 & ! [A4: B] :
% 0.17/0.41 ( ( 'const/sets/IN' @ B @ A4 @ A1 )
% 0.17/0.41 => ( ( 'const/sets/IN' @ A @ ( A3 @ A4 ) @ A0 )
% 0.17/0.41 & ( ( A2 @ ( A3 @ A4 ) )
% 0.17/0.41 = A4 ) ) ) )
% 0.17/0.41 => ( ( 'const/sets/CARD' @ A @ A0 )
% 0.17/0.41 = ( 'const/sets/CARD' @ B @ A1 ) ) ) ).
% 0.17/0.41
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 ------------------------
% 1.72/1.42 ---- Embedded in THF ---
% 1.72/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.42 %%% Generated on Tue Feb 24 12:48:17 EST 2026
% 1.72/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.42 %%% Logic specification used:
% 1.72/1.42 %%% thf(spec, logic, $$dhol).
% 1.72/1.42
% 1.72/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2DTF8193.p
% See solution above
% 1.72/1.42 ------------------------
% 1.72/1.43 ---- Cleaned THF ---
% 1.72/1.43 thf('thf_type_type/nums/num',type,
% 1.72/1.43 'type/nums/num': $tType ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/sets/IN',type,
% 1.72/1.43 'const/sets/IN':
% 1.72/1.43 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/sets/HAS_SIZE',type,
% 1.72/1.43 'const/sets/HAS_SIZE':
% 1.72/1.43 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/sets/FINITE',type,
% 1.72/1.43 'const/sets/FINITE':
% 1.72/1.43 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.72/1.43
% 1.72/1.43 thf('thf_const_const/sets/CARD',type,
% 1.72/1.43 'const/sets/CARD':
% 1.72/1.43 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/sets/HAS_SIZE_',axiom,
% 1.72/1.43 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 1.72/1.43 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 1.72/1.43 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.72/1.43 & ( ( 'const/sets/CARD' @ A @ A0 )
% 1.72/1.43 = A1 ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/sets/BIJECTIONS_HAS_SIZE_EQ_',axiom,
% 1.72/1.43 ! [A: $tType,B: $tType,A0: A > $o,A1: B > $o,A2: A > B,A3: B > A] :
% 1.72/1.43 ( ( ! [A4: A] :
% 1.72/1.43 ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 1.72/1.43 => ( ( 'const/sets/IN' @ B @ ( A2 @ A4 ) @ A1 )
% 1.72/1.43 & ( ( A3 @ ( A2 @ A4 ) )
% 1.72/1.43 = A4 ) ) )
% 1.72/1.43 & ! [A4: B] :
% 1.72/1.43 ( ( 'const/sets/IN' @ B @ A4 @ A1 )
% 1.72/1.43 => ( ( 'const/sets/IN' @ A @ ( A3 @ A4 ) @ A0 )
% 1.72/1.43 & ( ( A2 @ ( A3 @ A4 ) )
% 1.72/1.43 = A4 ) ) ) )
% 1.72/1.43 => ! [A4: 'type/nums/num'] :
% 1.72/1.43 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A4 )
% 1.72/1.43 = ( 'const/sets/HAS_SIZE' @ B @ A1 @ A4 ) ) ) ).
% 1.72/1.43
% 1.72/1.43 thf('thm/sets/BIJECTIONS_CARD_EQ_',conjecture,
% 1.72/1.43 ! [A: $tType,B: $tType,A0: A > $o,A1: B > $o,A2: A > B,A3: B > A] :
% 1.72/1.43 ( ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.72/1.43 | ( 'const/sets/FINITE' @ B @ A1 ) )
% 1.72/1.43 & ! [A4: A] :
% 1.72/1.43 ( ( 'const/sets/IN' @ A @ A4 @ A0 )
% 1.72/1.43 => ( ( 'const/sets/IN' @ B @ ( A2 @ A4 ) @ A1 )
% 1.72/1.43 & ( ( A3 @ ( A2 @ A4 ) )
% 1.72/1.43 = A4 ) ) )
% 1.72/1.43 & ! [A4: B] :
% 1.72/1.43 ( ( 'const/sets/IN' @ B @ A4 @ A1 )
% 1.72/1.43 => ( ( 'const/sets/IN' @ A @ ( A3 @ A4 ) @ A0 )
% 1.72/1.43 & ( ( A2 @ ( A3 @ A4 ) )
% 1.72/1.43 = A4 ) ) ) )
% 1.72/1.43 => ( ( 'const/sets/CARD' @ A @ A0 )
% 1.72/1.43 = ( 'const/sets/CARD' @ B @ A1 ) ) ) ).
% 1.72/1.43 ------------------------
% 1.72/1.45 % (8292)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_8193 for (2999ds/27Mi)
% 1.72/1.45 % (8295)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_8193 for (2999ds/275Mi)
% 1.72/1.45 % (8293)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/2Mi)
% 1.72/1.45 % (8291)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_8193 for (2999ds/4Mi)
% 1.72/1.45 % (8296)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/18Mi)
% 1.72/1.45 % (8294)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_8193 for (2999ds/2Mi)
% 1.72/1.45 % (8290)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/183Mi)
% 1.72/1.45 % Exception at run slice level
% 1.72/1.45 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
% 1.72/1.45 % (8293)Instruction limit reached!
% 1.72/1.45 % (8293)------------------------------
% 1.72/1.45 % (8293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (8293)Termination reason: Unknown
% 1.72/1.45 % (8293)Termination phase: Preprocessing 3
% 1.72/1.45
% 1.72/1.45 % (8293)Memory used [KB]: 1023
% 1.72/1.45 % (8293)Time elapsed: 0.003 s
% 1.72/1.45 % (8293)Instructions burned: 2 (million)
% 1.72/1.45 % (8293)------------------------------
% 1.72/1.45 % (8293)------------------------------
% 1.72/1.45 % (8291)Instruction limit reached!
% 1.72/1.45 % (8291)------------------------------
% 1.72/1.45 % (8291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (8291)Termination reason: Unknown
% 1.72/1.45 % (8291)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (8291)Memory used [KB]: 5500
% 1.72/1.45 % (8291)Time elapsed: 0.004 s
% 1.72/1.45 % (8291)Instructions burned: 4 (million)
% 1.72/1.45 % (8291)------------------------------
% 1.72/1.45 % (8291)------------------------------
% 1.72/1.46 % (8296)Instruction limit reached!
% 1.72/1.46 % (8296)------------------------------
% 1.72/1.46 % (8296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (8296)Termination reason: Unknown
% 1.72/1.46 % (8296)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (8296)Memory used [KB]: 5628
% 1.72/1.46 % (8296)Time elapsed: 0.013 s
% 1.72/1.46 % (8296)Instructions burned: 19 (million)
% 1.72/1.46 % (8296)------------------------------
% 1.72/1.46 % (8296)------------------------------
% 1.72/1.46 % (8292)Instruction limit reached!
% 1.72/1.46 % (8292)------------------------------
% 1.72/1.46 % (8292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (8292)Termination reason: Unknown
% 1.72/1.46 % (8292)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (8292)Memory used [KB]: 5628
% 1.72/1.46 % (8292)Time elapsed: 0.016 s
% 1.72/1.46 % (8292)Instructions burned: 27 (million)
% 1.72/1.46 % (8292)------------------------------
% 1.72/1.46 % (8292)------------------------------
% 1.72/1.47 % (8298)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_8193 for (2999ds/37Mi)
% 1.72/1.47 % (8299)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_8193 for (2999ds/15Mi)
% 1.72/1.47 % (8297)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/3Mi)
% 1.72/1.47 % Exception at run slice level
% 1.72/1.47 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
% 1.72/1.47 % (8297)Instruction limit reached!
% 1.72/1.47 % (8297)------------------------------
% 1.72/1.47 % (8297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (8297)Termination reason: Unknown
% 1.72/1.47 % (8297)Termination phase: Property scanning
% 1.72/1.47
% 1.72/1.47 % (8297)Memory used [KB]: 1023
% 1.72/1.47 % (8297)Time elapsed: 0.003 s
% 1.72/1.47 % (8297)Instructions burned: 3 (million)
% 1.72/1.47 % (8297)------------------------------
% 1.72/1.47 % (8297)------------------------------
% 1.72/1.47 % (8299)Instruction limit reached!
% 1.72/1.47 % (8299)------------------------------
% 1.72/1.47 % (8299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (8299)Termination reason: Unknown
% 1.72/1.48 % (8299)Termination phase: Saturation
% 1.72/1.48
% 1.72/1.48 % (8299)Memory used [KB]: 5756
% 1.72/1.48 % (8299)Time elapsed: 0.010 s
% 1.72/1.48 % (8299)Instructions burned: 16 (million)
% 1.72/1.48 % (8299)------------------------------
% 1.72/1.48 % (8299)------------------------------
% 1.72/1.48 % (8300)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_8193 for (2999ds/3Mi)
% 1.72/1.48 % (8301)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_8193 for (2999ds/1041Mi)
% 1.72/1.48 % Exception at run slice level
% 1.72/1.48 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
% 1.72/1.48 % (8300)Instruction limit reached!
% 1.72/1.48 % (8300)------------------------------
% 1.72/1.48 % (8300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (8300)Termination reason: Unknown
% 1.72/1.48 % (8300)Termination phase: Property scanning
% 1.72/1.48
% 1.72/1.48 % (8300)Memory used [KB]: 1023
% 1.72/1.48 % (8300)Time elapsed: 0.003 s
% 1.72/1.48 % (8300)Instructions burned: 3 (million)
% 1.72/1.48 % (8300)------------------------------
% 1.72/1.48 % (8300)------------------------------
% 1.72/1.48 % (8302)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/7Mi)
% 1.72/1.48 % (8303)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/16Mi)
% 1.72/1.49 % (8302)Instruction limit reached!
% 1.72/1.49 % (8302)------------------------------
% 1.72/1.49 % (8302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (8302)Termination reason: Unknown
% 1.72/1.49 % (8302)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (8302)Memory used [KB]: 1023
% 1.72/1.49 % (8302)Time elapsed: 0.005 s
% 1.72/1.49 % (8302)Instructions burned: 7 (million)
% 1.72/1.49 % (8302)------------------------------
% 1.72/1.49 % (8302)------------------------------
% 1.72/1.49 % (8303)Instruction limit reached!
% 1.72/1.49 % (8303)------------------------------
% 1.72/1.49 % (8303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (8303)Termination reason: Unknown
% 1.72/1.49 % (8303)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (8303)Memory used [KB]: 5628
% 1.72/1.49 % (8303)Time elapsed: 0.010 s
% 1.72/1.49 % (8303)Instructions burned: 16 (million)
% 1.72/1.49 % (8303)------------------------------
% 1.72/1.49 % (8303)------------------------------
% 1.72/1.49 % (8304)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_8193 for (2999ds/3Mi)
% 1.72/1.49 % (8304)Instruction limit reached!
% 1.72/1.49 % (8304)------------------------------
% 1.72/1.49 % (8304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (8304)Termination reason: Unknown
% 1.72/1.49 % (8304)Termination phase: Preprocessing 3
% 1.72/1.49
% 1.72/1.49 % (8304)Memory used [KB]: 1023
% 1.72/1.49 % (8304)Time elapsed: 0.003 s
% 1.72/1.49 % (8304)Instructions burned: 3 (million)
% 1.72/1.49 % (8304)------------------------------
% 1.72/1.49 % (8304)------------------------------
% 1.72/1.50 % (8305)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_8193 for (2999ds/3Mi)
% 1.76/1.50 % (8306)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/7Mi)
% 1.76/1.50 % (8305)Instruction limit reached!
% 1.76/1.50 % (8305)------------------------------
% 1.76/1.50 % (8305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.50 % (8305)Termination reason: Unknown
% 1.76/1.50 % (8305)Termination phase: Property scanning
% 1.76/1.50
% 1.76/1.50 % (8305)Memory used [KB]: 1023
% 1.76/1.50 % (8305)Time elapsed: 0.004 s
% 1.76/1.50 % (8305)Instructions burned: 5 (million)
% 1.76/1.50 % (8305)------------------------------
% 1.76/1.50 % (8305)------------------------------
% 1.76/1.50 % (8306)Instruction limit reached!
% 1.76/1.50 % (8306)------------------------------
% 1.76/1.50 % (8306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.50 % (8306)Termination reason: Unknown
% 1.76/1.50 % (8306)Termination phase: Saturation
% 1.76/1.50
% 1.76/1.50 % (8306)Memory used [KB]: 5500
% 1.76/1.50 % (8306)Time elapsed: 0.005 s
% 1.76/1.50 % (8306)Instructions burned: 7 (million)
% 1.76/1.50 % (8306)------------------------------
% 1.76/1.50 % (8306)------------------------------
% 1.76/1.50 % (8307)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/3Mi)
% 1.76/1.50 % (8295)First to succeed.
% 1.76/1.50 % Exception at run slice level
% 1.76/1.50 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
% 1.76/1.51 % (8308)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8193 for (2999ds/4Mi)
% 1.76/1.51 % (8295)Refutation found. Thanks to Tanya!
% 1.76/1.51 % SZS status Theorem for DTF2THF_8193
% 1.76/1.51 % SZS output start Proof for DTF2THF_8193
% 1.76/1.51 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.76/1.51 thf(type_def_7, type, sK0: $tType).
% 1.76/1.51 thf(type_def_8, type, sK1: $tType).
% 1.76/1.51 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.76/1.51 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.76/1.51 thf(func_def_2, type, 'const/sets/HAS_SIZE': !>[X0: $tType]:((X0 > $o) > 'type/nums/num' > $o)).
% 1.76/1.51 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.76/1.51 thf(func_def_4, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.76/1.51 thf(func_def_8, type, sK2: sK0 > $o).
% 1.76/1.51 thf(func_def_9, type, sK3: sK1 > $o).
% 1.76/1.51 thf(func_def_10, type, sK4: sK0 > sK1).
% 1.76/1.51 thf(func_def_11, type, sK5: sK1 > sK0).
% 1.76/1.51 thf(func_def_12, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > (X1 > $o) > (X0 > $o) > X0)).
% 1.76/1.51 thf(func_def_13, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > (X1 > $o) > (X0 > $o) > X1)).
% 1.76/1.51 thf(func_def_15, type, ph9: !>[X0: $tType]:(X0)).
% 1.76/1.51 thf(f280,plain,(
% 1.76/1.51 $false),
% 1.76/1.51 inference(avatar_sat_refutation,[status(thm)],[f47,f106,f107,f135,f144,f145,f150,f151,f157,f166,f169,f218,f267,f279])).
% 1.76/1.51 thf(f279,plain,(
% 1.76/1.51 spl8_6 | spl8_6 | spl8_4 | ~spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f278,f88,f84,f92,f92])).
% 1.76/1.51 thf(f92,definition,(
% 1.76/1.51 spl8_6 <=> ! [X0 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.76/1.51 thf(f84,definition,(
% 1.76/1.51 spl8_4 <=> (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true)),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.76/1.51 thf(f88,definition,(
% 1.76/1.51 spl8_5 <=> ($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.76/1.51 thf(f278,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $false)) ) | (spl8_4 | ~spl8_5)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f277,f85])).
% 1.76/1.51 thf(f85,plain,(
% 1.76/1.51 (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) != $true) | spl8_4),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.76/1.51 thf(f277,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $false)) ) | ~spl8_5),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f171,f89])).
% 1.76/1.51 thf(f89,plain,(
% 1.76/1.51 ($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | ~spl8_5),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.76/1.51 thf(f171,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $false) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true)) )),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.76/1.51 thf(f170,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $false) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($true != $true) | ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3))) )),
% 1.76/1.51 inference(superposition,[status(thm)],[f76,f26])).
% 1.76/1.51 thf(f26,plain,(
% 1.76/1.51 ( ! [X7 : sK1] : ((('const/sets/IN' @ sK0 @ (sK5 @ X7) @ sK2) = $true) | (('const/sets/IN' @ sK1 @ X7 @ sK3) != $true)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 thf(f18,plain,(
% 1.76/1.51 (('const/sets/CARD' @ sK0 @ sK2) != ('const/sets/CARD' @ sK1 @ sK3)) & (($true = ('const/sets/FINITE' @ sK1 @ sK3)) | ($true = ('const/sets/FINITE' @ sK0 @ sK2))) & ! [X6 : sK0] : ((((sK5 @ (sK4 @ X6)) = X6) & ($true = ('const/sets/IN' @ sK1 @ (sK4 @ X6) @ sK3))) | ($true != ('const/sets/IN' @ sK0 @ X6 @ sK2))) & ! [X7 : sK1] : (((('const/sets/IN' @ sK0 @ (sK5 @ X7) @ sK2) = $true) & ((sK4 @ (sK5 @ X7)) = X7)) | (('const/sets/IN' @ sK1 @ X7 @ sK3) != $true))),
% 1.76/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f16,f17])).
% 1.76/1.51 thf(f17,plain,(
% 1.76/1.51 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((('const/sets/CARD' @ X0 @ X2) != ('const/sets/CARD' @ X1 @ X3)) & (($true = ('const/sets/FINITE' @ X1 @ X3)) | (('const/sets/FINITE' @ X0 @ X2) = $true)) & ! [X6 : X0] : ((((X5 @ (X4 @ X6)) = X6) & ($true = ('const/sets/IN' @ X1 @ (X4 @ X6) @ X3))) | ($true != ('const/sets/IN' @ X0 @ X6 @ X2))) & ! [X7 : X1] : (((('const/sets/IN' @ X0 @ (X5 @ X7) @ X2) = $true) & ((X4 @ (X5 @ X7)) = X7)) | ($true != ('const/sets/IN' @ X1 @ X7 @ X3)))) => ((('const/sets/CARD' @ sK0 @ sK2) != ('const/sets/CARD' @ sK1 @ sK3)) & (($true = ('const/sets/FINITE' @ sK1 @ sK3)) | ($true = ('const/sets/FINITE' @ sK0 @ sK2))) & ! [X6 : sK0] : ((((sK5 @ (sK4 @ X6)) = X6) & ($true = ('const/sets/IN' @ sK1 @ (sK4 @ X6) @ sK3))) | ($true != ('const/sets/IN' @ sK0 @ X6 @ sK2))) & ! [X7 : sK1] : (((('const/sets/IN' @ sK0 @ (sK5 @ X7) @ sK2) = $true) & ((sK4 @ (sK5 @ X7)) = X7)) | (('const/sets/IN' @ sK1 @ X7 @ sK3) != $true)))),
% 1.76/1.51 introduced(definition,[],[choice_axiom])).
% 1.76/1.51 thf(f16,plain,(
% 1.76/1.51 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((('const/sets/CARD' @ X0 @ X2) != ('const/sets/CARD' @ X1 @ X3)) & (($true = ('const/sets/FINITE' @ X1 @ X3)) | (('const/sets/FINITE' @ X0 @ X2) = $true)) & ! [X6 : X0] : ((((X5 @ (X4 @ X6)) = X6) & ($true = ('const/sets/IN' @ X1 @ (X4 @ X6) @ X3))) | ($true != ('const/sets/IN' @ X0 @ X6 @ X2))) & ! [X7 : X1] : (((('const/sets/IN' @ X0 @ (X5 @ X7) @ X2) = $true) & ((X4 @ (X5 @ X7)) = X7)) | ($true != ('const/sets/IN' @ X1 @ X7 @ X3))))),
% 1.76/1.51 inference(rectify,[status(thm)],[f13])).
% 1.76/1.51 thf(f13,plain,(
% 1.76/1.51 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((('const/sets/CARD' @ X0 @ X2) != ('const/sets/CARD' @ X1 @ X3)) & (($true = ('const/sets/FINITE' @ X1 @ X3)) | (('const/sets/FINITE' @ X0 @ X2) = $true)) & ! [X7 : X0] : ((((X5 @ (X4 @ X7)) = X7) & ($true = ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) | ($true != ('const/sets/IN' @ X0 @ X7 @ X2))) & ! [X6 : X1] : ((($true = ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) & ((X4 @ (X5 @ X6)) = X6)) | (('const/sets/IN' @ X1 @ X6 @ X3) != $true)))),
% 1.76/1.51 inference(flattening,[status(thm)],[f12])).
% 1.76/1.51 thf(f12,plain,(
% 1.76/1.51 ? [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((('const/sets/CARD' @ X0 @ X2) != ('const/sets/CARD' @ X1 @ X3)) & (! [X7 : X0] : ((((X5 @ (X4 @ X7)) = X7) & ($true = ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) | ($true != ('const/sets/IN' @ X0 @ X7 @ X2))) & ! [X6 : X1] : ((($true = ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) & ((X4 @ (X5 @ X6)) = X6)) | (('const/sets/IN' @ X1 @ X6 @ X3) != $true)) & (($true = ('const/sets/FINITE' @ X1 @ X3)) | (('const/sets/FINITE' @ X0 @ X2) = $true))))),
% 1.76/1.51 inference(ennf_transformation,[status(thm)],[f11])).
% 1.76/1.51 thf(f11,plain,(
% 1.76/1.51 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((! [X7 : X0] : (($true = ('const/sets/IN' @ X0 @ X7 @ X2)) => (((X5 @ (X4 @ X7)) = X7) & ($true = ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3)))) & ! [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) = $true) => (($true = ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) & ((X4 @ (X5 @ X6)) = X6))) & (($true = ('const/sets/FINITE' @ X1 @ X3)) | (('const/sets/FINITE' @ X0 @ X2) = $true))) => (('const/sets/CARD' @ X0 @ X2) = ('const/sets/CARD' @ X1 @ X3)))),
% 1.76/1.51 inference(fool_elimination,[status(thm)],[f10])).
% 1.76/1.51 thf(f10,plain,(
% 1.76/1.51 ~! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (((('const/sets/FINITE' @ X0 @ X2) | ('const/sets/FINITE' @ X1 @ X3)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => (((X4 @ (X5 @ X6)) = X6) & ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2))) & ! [X7 : X0] : (('const/sets/IN' @ X0 @ X7 @ X2) => (((X5 @ (X4 @ X7)) = X7) & ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3)))) => (('const/sets/CARD' @ X0 @ X2) = ('const/sets/CARD' @ X1 @ X3)))),
% 1.76/1.51 inference(rectify,[status(thm)],[f4])).
% 1.76/1.51 thf(f4,negated_conjecture,(
% 1.76/1.51 ~! [X0 : $tType,X3 : $tType,X1 : X0 > $o,X2 : X3 > $o,X4 : X0 > X3,X5 : X3 > X0] : (((('const/sets/FINITE' @ X0 @ X1) | ('const/sets/FINITE' @ X3 @ X2)) & ! [X6 : X3] : (('const/sets/IN' @ X3 @ X6 @ X2) => (((X4 @ (X5 @ X6)) = X6) & ('const/sets/IN' @ X0 @ (X5 @ X6) @ X1))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X1) => (((X5 @ (X4 @ X6)) = X6) & ('const/sets/IN' @ X3 @ (X4 @ X6) @ X2)))) => (('const/sets/CARD' @ X0 @ X1) = ('const/sets/CARD' @ X3 @ X2)))),
% 1.76/1.51 inference(negated_conjecture,[status(cth)],[f3])).
% 1.76/1.51 thf(f3,conjecture,(
% 1.76/1.51 ! [X0 : $tType,X3 : $tType,X1 : X0 > $o,X2 : X3 > $o,X4 : X0 > X3,X5 : X3 > X0] : (((('const/sets/FINITE' @ X0 @ X1) | ('const/sets/FINITE' @ X3 @ X2)) & ! [X6 : X3] : (('const/sets/IN' @ X3 @ X6 @ X2) => (((X4 @ (X5 @ X6)) = X6) & ('const/sets/IN' @ X0 @ (X5 @ X6) @ X1))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X1) => (((X5 @ (X4 @ X6)) = X6) & ('const/sets/IN' @ X3 @ (X4 @ X6) @ X2)))) => (('const/sets/CARD' @ X0 @ X1) = ('const/sets/CARD' @ X3 @ X2)))),
% 1.76/1.51 file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/BIJECTIONS_CARD_EQ_')).
% 1.76/1.51 thf(f76,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0)) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true)) )),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.76/1.51 thf(f75,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0))) )),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.76/1.51 thf(f74,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | ((sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0))) )),
% 1.76/1.51 inference(duplicate_literal_removal,[status(thm)],[f73])).
% 1.76/1.51 thf(f73,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (((sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1))) )),
% 1.76/1.51 inference(superposition,[status(thm)],[f34,f51])).
% 1.76/1.51 thf(f51,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : X0 > sK1,X3 : X0 > $o,X1 : sK1 > X0,X4 : 'type/nums/num'] : (((sK4 @ (sK5 @ (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3))) = (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3)) | ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3) @ X3)) | ($false = ('const/sets/HAS_SIZE' @ X0 @ X3 @ X4)) | ($true = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4))) )),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.76/1.51 thf(f49,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : X0 > sK1,X3 : X0 > $o,X1 : sK1 > X0,X4 : 'type/nums/num'] : (($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3) @ X3)) | ((sK4 @ (sK5 @ (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3))) = (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3)) | (('const/sets/HAS_SIZE' @ X0 @ X3 @ X4) = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4))) )),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.76/1.51 thf(f48,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : X0 > sK1,X3 : X0 > $o,X1 : sK1 > X0,X4 : 'type/nums/num'] : (($true != $true) | (('const/sets/HAS_SIZE' @ X0 @ X3 @ X4) = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4)) | ((sK4 @ (sK5 @ (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3))) = (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3)) | ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3) @ X3))) )),
% 1.76/1.51 inference(superposition,[status(thm)],[f25,f35])).
% 1.76/1.51 thf(f35,plain,(
% 1.76/1.51 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X6 : 'type/nums/num',X4 : X0 > X1,X5 : X1 > X0] : (($true = ('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X3)) | (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X2))) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.51 thf(f24,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (! [X6 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ((((sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) != (X5 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) | (('const/sets/IN' @ X1 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X3) != $true)) & ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X2))) | (($true = ('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X3)) & (($true != ('const/sets/IN' @ X0 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X2)) | ((X4 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))))),
% 1.76/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f21,f23,f22])).
% 1.76/1.51 thf(f22,plain,(
% 1.76/1.51 ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (? [X7 : X0] : ((((X5 @ (X4 @ X7)) != X7) | ($true != ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) & ($true = ('const/sets/IN' @ X0 @ X7 @ X2))) => ((((sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) != (X5 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) | (('const/sets/IN' @ X1 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X3) != $true)) & ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X2))))),
% 1.76/1.51 introduced(definition,[],[choice_axiom])).
% 1.76/1.51 thf(f23,plain,(
% 1.76/1.51 ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (? [X8 : X1] : (($true = ('const/sets/IN' @ X1 @ X8 @ X3)) & (($true != ('const/sets/IN' @ X0 @ (X5 @ X8) @ X2)) | ((X4 @ (X5 @ X8)) != X8))) => (($true = ('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X3)) & (($true != ('const/sets/IN' @ X0 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X2)) | ((X4 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))))),
% 1.76/1.51 introduced(definition,[],[choice_axiom])).
% 1.76/1.51 thf(f21,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (! [X6 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ? [X7 : X0] : ((((X5 @ (X4 @ X7)) != X7) | ($true != ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) & ($true = ('const/sets/IN' @ X0 @ X7 @ X2))) | ? [X8 : X1] : (($true = ('const/sets/IN' @ X1 @ X8 @ X3)) & (($true != ('const/sets/IN' @ X0 @ (X5 @ X8) @ X2)) | ((X4 @ (X5 @ X8)) != X8))))),
% 1.76/1.51 inference(rectify,[status(thm)],[f15])).
% 1.76/1.51 thf(f15,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (! [X8 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X8)) | ? [X7 : X0] : ((((X5 @ (X4 @ X7)) != X7) | ($true != ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) & ($true = ('const/sets/IN' @ X0 @ X7 @ X2))) | ? [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) = $true) & (($true != ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) | ((X4 @ (X5 @ X6)) != X6))))),
% 1.76/1.51 inference(flattening,[status(thm)],[f14])).
% 1.76/1.51 thf(f14,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : (! [X8 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X8)) | (? [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) = $true) & (($true != ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) | ((X4 @ (X5 @ X6)) != X6))) | ? [X7 : X0] : ((((X5 @ (X4 @ X7)) != X7) | ($true != ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3))) & ($true = ('const/sets/IN' @ X0 @ X7 @ X2)))))),
% 1.76/1.51 inference(ennf_transformation,[status(thm)],[f9])).
% 1.76/1.51 thf(f9,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((! [X6 : X1] : ((('const/sets/IN' @ X1 @ X6 @ X3) = $true) => (($true = ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) & ((X4 @ (X5 @ X6)) = X6))) & ! [X7 : X0] : (($true = ('const/sets/IN' @ X0 @ X7 @ X2)) => (($true = ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3)) & ((X5 @ (X4 @ X7)) = X7)))) => ! [X8 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X8)))),
% 1.76/1.51 inference(fool_elimination,[status(thm)],[f8])).
% 1.76/1.51 thf(f8,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : $tType,X2 : X0 > $o,X3 : X1 > $o,X4 : X0 > X1,X5 : X1 > X0] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => (('const/sets/IN' @ X0 @ (X5 @ X6) @ X2) & ((X4 @ (X5 @ X6)) = X6))) & ! [X7 : X0] : (('const/sets/IN' @ X0 @ X7 @ X2) => (((X5 @ (X4 @ X7)) = X7) & ('const/sets/IN' @ X1 @ (X4 @ X7) @ X3)))) => ! [X8 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X8)))),
% 1.76/1.51 inference(rectify,[status(thm)],[f2])).
% 1.76/1.51 thf(f2,axiom,(
% 1.76/1.51 ! [X0 : $tType,X3 : $tType,X1 : X0 > $o,X2 : X3 > $o,X4 : X0 > X3,X5 : X3 > X0] : ((! [X6 : X3] : (('const/sets/IN' @ X3 @ X6 @ X2) => (('const/sets/IN' @ X0 @ (X5 @ X6) @ X1) & ((X4 @ (X5 @ X6)) = X6))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X1) => (((X5 @ (X4 @ X6)) = X6) & ('const/sets/IN' @ X3 @ (X4 @ X6) @ X2)))) => ! [X6 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X0 @ X1 @ X6) = ('const/sets/HAS_SIZE' @ X3 @ X2 @ X6)))),
% 1.76/1.51 file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/BIJECTIONS_HAS_SIZE_EQ_')).
% 1.76/1.51 thf(f25,plain,(
% 1.76/1.51 ( ! [X7 : sK1] : ((('const/sets/IN' @ sK1 @ X7 @ sK3) != $true) | ((sK4 @ (sK5 @ X7)) = X7)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 thf(f34,plain,(
% 1.76/1.51 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X6 : 'type/nums/num',X4 : X0 > X1,X5 : X1 > X0] : (((X4 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) | ($true != ('const/sets/IN' @ X0 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X2)) | (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X2))) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.51 thf(f267,plain,(
% 1.76/1.51 ~spl8_1 | ~spl8_6),
% 1.76/1.51 inference(avatar_contradiction_clause,[status(thm)],[f266])).
% 1.76/1.51 thf(f266,plain,(
% 1.76/1.51 $false | (~spl8_1 | ~spl8_6)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f261,f30])).
% 1.76/1.51 thf(f30,plain,(
% 1.76/1.51 (('const/sets/CARD' @ sK0 @ sK2) != ('const/sets/CARD' @ sK1 @ sK3))),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 thf(f261,plain,(
% 1.76/1.51 (('const/sets/CARD' @ sK0 @ sK2) = ('const/sets/CARD' @ sK1 @ sK3)) | (~spl8_1 | ~spl8_6)),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f258])).
% 1.76/1.51 thf(f258,plain,(
% 1.76/1.51 ($true != $true) | (('const/sets/CARD' @ sK0 @ sK2) = ('const/sets/CARD' @ sK1 @ sK3)) | (~spl8_1 | ~spl8_6)),
% 1.76/1.51 inference(superposition,[status(thm)],[f32,f255])).
% 1.76/1.51 thf(f255,plain,(
% 1.76/1.51 (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ ('const/sets/CARD' @ sK0 @ sK2)) = $true) | (~spl8_1 | ~spl8_6)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f242,f42])).
% 1.76/1.51 thf(f42,plain,(
% 1.76/1.51 ($true = ('const/sets/FINITE' @ sK0 @ sK2)) | ~spl8_1),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.76/1.51 thf(f40,definition,(
% 1.76/1.51 spl8_1 <=> ($true = ('const/sets/FINITE' @ sK0 @ sK2))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.76/1.51 thf(f242,plain,(
% 1.76/1.51 (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ ('const/sets/CARD' @ sK0 @ sK2)) = $true) | ($true != ('const/sets/FINITE' @ sK0 @ sK2)) | ~spl8_6),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f227])).
% 1.76/1.51 thf(f227,plain,(
% 1.76/1.51 ($true != ('const/sets/FINITE' @ sK0 @ sK2)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ ('const/sets/CARD' @ sK0 @ sK2)) = $true) | ($true = $false) | ~spl8_6),
% 1.76/1.51 inference(superposition,[status(thm)],[f93,f38])).
% 1.76/1.51 thf(f38,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = ('const/sets/HAS_SIZE' @ X0 @ X1 @ ('const/sets/CARD' @ X0 @ X1))) | (('const/sets/FINITE' @ X0 @ X1) != $true)) )),
% 1.76/1.51 inference(equality_resolution,[status(thm)],[f31])).
% 1.76/1.51 thf(f31,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true) | (('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/CARD' @ X0 @ X1) != X2)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f20])).
% 1.76/1.51 thf(f20,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : ((((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/CARD' @ X0 @ X1) = X2)) | (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true) | (('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/CARD' @ X0 @ X1) != X2)))),
% 1.76/1.51 inference(flattening,[status(thm)],[f19])).
% 1.76/1.51 thf(f19,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : ((((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/CARD' @ X0 @ X1) = X2)) | (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true) | ((('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/CARD' @ X0 @ X1) != X2))))),
% 1.76/1.51 inference(nnf_transformation,[status(thm)],[f7])).
% 1.76/1.51 thf(f7,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (((('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/CARD' @ X0 @ X1) = X2)) <=> (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true))),
% 1.76/1.51 inference(fool_elimination,[status(thm)],[f6])).
% 1.76/1.51 thf(f6,plain,(
% 1.76/1.51 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2))),
% 1.76/1.51 inference(rectify,[status(thm)],[f1])).
% 1.76/1.51 thf(f1,axiom,(
% 1.76/1.51 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2))),
% 1.76/1.51 file('/export/starexec/sandbox/tmp/tmp.CyT0n2PKmZ/DTF2THF_8193.p','thm/sets/HAS_SIZE_')).
% 1.76/1.51 thf(f93,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true)) ) | ~spl8_6),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.76/1.51 thf(f32,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) != $true) | (('const/sets/CARD' @ X0 @ X1) = X2)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f20])).
% 1.76/1.51 thf(f218,plain,(
% 1.76/1.51 ~spl8_2 | ~spl8_3),
% 1.76/1.51 inference(avatar_contradiction_clause,[status(thm)],[f217])).
% 1.76/1.51 thf(f217,plain,(
% 1.76/1.51 $false | (~spl8_2 | ~spl8_3)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f216,f30])).
% 1.76/1.51 thf(f216,plain,(
% 1.76/1.51 (('const/sets/CARD' @ sK0 @ sK2) = ('const/sets/CARD' @ sK1 @ sK3)) | (~spl8_2 | ~spl8_3)),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f214])).
% 1.76/1.51 thf(f214,plain,(
% 1.76/1.51 (('const/sets/CARD' @ sK0 @ sK2) = ('const/sets/CARD' @ sK1 @ sK3)) | ($true != $true) | (~spl8_2 | ~spl8_3)),
% 1.76/1.51 inference(superposition,[status(thm)],[f32,f208])).
% 1.76/1.51 thf(f208,plain,(
% 1.76/1.51 ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ ('const/sets/CARD' @ sK1 @ sK3))) | (~spl8_2 | ~spl8_3)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f193,f46])).
% 1.76/1.51 thf(f46,plain,(
% 1.76/1.51 ($true = ('const/sets/FINITE' @ sK1 @ sK3)) | ~spl8_2),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.76/1.51 thf(f44,definition,(
% 1.76/1.51 spl8_2 <=> ($true = ('const/sets/FINITE' @ sK1 @ sK3))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.76/1.51 thf(f193,plain,(
% 1.76/1.51 ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ ('const/sets/CARD' @ sK1 @ sK3))) | ($true != ('const/sets/FINITE' @ sK1 @ sK3)) | ~spl8_3),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f172])).
% 1.76/1.51 thf(f172,plain,(
% 1.76/1.51 ($true != ('const/sets/FINITE' @ sK1 @ sK3)) | ($true = $false) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ ('const/sets/CARD' @ sK1 @ sK3))) | ~spl8_3),
% 1.76/1.51 inference(superposition,[status(thm)],[f82,f38])).
% 1.76/1.51 thf(f82,plain,(
% 1.76/1.51 ( ! [X1 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true)) ) | ~spl8_3),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.76/1.51 thf(f81,definition,(
% 1.76/1.51 spl8_3 <=> ! [X1 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.76/1.51 thf(f169,plain,(
% 1.76/1.51 spl8_3 | spl8_3 | spl8_4 | ~spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f168,f88,f84,f81,f81])).
% 1.76/1.51 thf(f168,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false)) ) | (spl8_4 | ~spl8_5)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f167,f89])).
% 1.76/1.51 thf(f167,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true) | ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | spl8_4),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f162,f85])).
% 1.76/1.51 thf(f162,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true)) )),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.76/1.51 thf(f161,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X1) = $true) | ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false)) )),
% 1.76/1.51 inference(superposition,[status(thm)],[f70,f26])).
% 1.76/1.51 thf(f70,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2))) )),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.76/1.51 thf(f68,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2))) )),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.76/1.51 thf(f67,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (((sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0))) )),
% 1.76/1.51 inference(duplicate_literal_removal,[status(thm)],[f66])).
% 1.76/1.51 thf(f66,plain,(
% 1.76/1.51 ( ! [X2 : 'type/nums/num',X0 : sK0 > $o,X1 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) @ X0)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X2)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | ((sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X2)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ X0) @ X0) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X1) = ('const/sets/HAS_SIZE' @ sK0 @ X0 @ X1))) )),
% 1.76/1.51 inference(superposition,[status(thm)],[f34,f50])).
% 1.76/1.51 thf(f50,plain,(
% 1.76/1.51 ( ! [X0 : $tType,X2 : X0 > sK1,X3 : X0 > $o,X1 : sK1 > X0,X4 : 'type/nums/num'] : (((sK4 @ (sK5 @ (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3))) = (sK7 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3)) | ($true = ('const/sets/IN' @ X0 @ (sK6 @ X0 @ sK1 @ X1 @ X2 @ sK3 @ X3) @ X3)) | ($false = ('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X4)) | ($true = ('const/sets/HAS_SIZE' @ X0 @ X3 @ X4))) )),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.76/1.51 thf(f166,plain,(
% 1.76/1.51 ~spl8_5 | spl8_8),
% 1.76/1.51 inference(avatar_contradiction_clause,[status(thm)],[f165])).
% 1.76/1.51 thf(f165,plain,(
% 1.76/1.51 $false | (~spl8_5 | spl8_8)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f164,f89])).
% 1.76/1.51 thf(f164,plain,(
% 1.76/1.51 ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | spl8_8),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f163])).
% 1.76/1.51 thf(f163,plain,(
% 1.76/1.51 ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | ($true != $true) | spl8_8),
% 1.76/1.51 inference(superposition,[status(thm)],[f139,f26])).
% 1.76/1.51 thf(f139,plain,(
% 1.76/1.51 ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2)) | spl8_8),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f137])).
% 1.76/1.51 thf(f137,definition,(
% 1.76/1.51 spl8_8 <=> ($true = ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 1.76/1.51 thf(f157,plain,(
% 1.76/1.51 spl8_9 | ~spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f154,f88,f141])).
% 1.76/1.51 thf(f141,definition,(
% 1.76/1.51 spl8_9 <=> ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) = (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition])).
% 1.76/1.51 thf(f154,plain,(
% 1.76/1.51 ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) = (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ~spl8_5),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.76/1.51 thf(f153,plain,(
% 1.76/1.51 ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) = (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true != $true) | ~spl8_5),
% 1.76/1.51 inference(superposition,[status(thm)],[f25,f89])).
% 1.76/1.51 thf(f151,plain,(
% 1.76/1.51 spl8_6 | spl8_5 | ~spl8_7 | ~spl8_4),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f126,f84,f130,f88,f92])).
% 1.76/1.51 thf(f130,definition,(
% 1.76/1.51 spl8_7 <=> ($true = ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3))),
% 1.76/1.51 introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition])).
% 1.76/1.51 thf(f126,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3))) ) | ~spl8_4),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.76/1.51 thf(f125,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3))) ) | ~spl8_4),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.76/1.51 thf(f121,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ((sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) != (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3))) ) | ~spl8_4),
% 1.76/1.51 inference(superposition,[status(thm)],[f37,f116])).
% 1.76/1.51 thf(f116,plain,(
% 1.76/1.51 ((sK5 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) = (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ~spl8_4),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.76/1.51 thf(f115,plain,(
% 1.76/1.51 ($true != $true) | ((sK5 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) = (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ~spl8_4),
% 1.76/1.51 inference(superposition,[status(thm)],[f28,f86])).
% 1.76/1.51 thf(f86,plain,(
% 1.76/1.51 (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | ~spl8_4),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.76/1.51 thf(f28,plain,(
% 1.76/1.51 ( ! [X6 : sK0] : (($true != ('const/sets/IN' @ sK0 @ X6 @ sK2)) | ((sK5 @ (sK4 @ X6)) = X6)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 thf(f37,plain,(
% 1.76/1.51 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X6 : 'type/nums/num',X4 : X0 > X1,X5 : X1 > X0] : (((sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) != (X5 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) | (('const/sets/IN' @ X1 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X3) != $true) | (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ($true = ('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X3))) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.51 thf(f150,plain,(
% 1.76/1.51 ~spl8_4 | spl8_7),
% 1.76/1.51 inference(avatar_contradiction_clause,[status(thm)],[f149])).
% 1.76/1.51 thf(f149,plain,(
% 1.76/1.51 $false | (~spl8_4 | spl8_7)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f148,f86])).
% 1.76/1.51 thf(f148,plain,(
% 1.76/1.51 (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) != $true) | spl8_7),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.76/1.51 thf(f147,plain,(
% 1.76/1.51 (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) != $true) | ($true != $true) | spl8_7),
% 1.76/1.51 inference(superposition,[status(thm)],[f132,f27])).
% 1.76/1.51 thf(f27,plain,(
% 1.76/1.51 ( ! [X6 : sK0] : (($true = ('const/sets/IN' @ sK1 @ (sK4 @ X6) @ sK3)) | ($true != ('const/sets/IN' @ sK0 @ X6 @ sK2))) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 thf(f132,plain,(
% 1.76/1.51 ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | spl8_7),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.76/1.51 thf(f145,plain,(
% 1.76/1.51 ~spl8_8 | ~spl8_7 | spl8_3 | ~spl8_9 | ~spl8_4),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f124,f84,f141,f81,f130,f137])).
% 1.76/1.51 thf(f124,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | ~spl8_4),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.76/1.51 thf(f122,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2))) ) | ~spl8_4),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.76/1.51 thf(f120,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2)) | ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | ((sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) != (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | ~spl8_4),
% 1.76/1.51 inference(superposition,[status(thm)],[f36,f116])).
% 1.76/1.51 thf(f36,plain,(
% 1.76/1.51 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > $o,X3 : X1 > $o,X6 : 'type/nums/num',X4 : X0 > X1,X5 : X1 > X0] : (((sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) != (X5 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) | (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6) = ('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) | ($true != ('const/sets/IN' @ X0 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X2)) | ((X4 @ (X5 @ (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (sK7 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) | (('const/sets/IN' @ X1 @ (X4 @ (sK6 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X3) != $true)) )),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f24])).
% 1.76/1.51 thf(f144,plain,(
% 1.76/1.51 ~spl8_8 | ~spl8_9 | spl8_6 | ~spl8_7 | ~spl8_4),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f123,f84,f130,f92,f141,f137])).
% 1.76/1.51 thf(f123,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ((sK4 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2))) != (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) | ($true != ('const/sets/IN' @ sK0 @ (sK5 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK2)) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3))) ) | ~spl8_4),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.76/1.51 thf(f135,plain,(
% 1.76/1.51 spl8_3 | ~spl8_7 | ~spl8_4 | spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f134,f88,f84,f130,f81])).
% 1.76/1.51 thf(f134,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3)) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false)) ) | (~spl8_4 | spl8_5)),
% 1.76/1.51 inference(subsumption_resolution,[status(thm)],[f127,f90])).
% 1.76/1.51 thf(f90,plain,(
% 1.76/1.51 ($true != ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | spl8_5),
% 1.76/1.51 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.76/1.51 thf(f127,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true = ('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK3)) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0)) | ($true != ('const/sets/IN' @ sK1 @ (sK4 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2)) @ sK3))) ) | ~spl8_4),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.76/1.51 thf(f107,plain,(
% 1.76/1.51 spl8_4 | spl8_3 | spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f105,f88,f81,f84])).
% 1.76/1.51 thf(f105,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $false) | ($true = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | spl8_5),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.76/1.51 thf(f103,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | spl8_5),
% 1.76/1.51 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.76/1.51 thf(f102,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : (($true != $true) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | (('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | spl8_5),
% 1.76/1.51 inference(superposition,[status(thm)],[f90,f35])).
% 1.76/1.51 thf(f106,plain,(
% 1.76/1.51 spl8_6 | spl8_4 | spl8_5),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f104,f88,f84,f92])).
% 1.76/1.51 thf(f104,plain,(
% 1.76/1.51 ( ! [X0 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ sK1 @ sK3 @ X0) = $true) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ sK1 @ sK5 @ sK4 @ sK3 @ sK2) @ sK2) = $true) | ($false = ('const/sets/HAS_SIZE' @ sK0 @ sK2 @ X0))) ) | spl8_5),
% 1.76/1.51 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.76/1.51 thf(f47,plain,(
% 1.76/1.51 spl8_1 | spl8_2),
% 1.76/1.51 inference(avatar_split_clause,[status(thm)],[f29,f44,f40])).
% 1.76/1.51 thf(f29,plain,(
% 1.76/1.51 ($true = ('const/sets/FINITE' @ sK0 @ sK2)) | ($true = ('const/sets/FINITE' @ sK1 @ sK3))),
% 1.76/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.76/1.51 % SZS output end Proof for DTF2THF_8193
% 1.76/1.51 % (8295)------------------------------
% 1.76/1.51 % (8295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.51 % (8295)Termination reason: Refutation
% 1.76/1.51
% 1.76/1.51 % (8295)Memory used [KB]: 5884
% 1.76/1.51 % (8295)Time elapsed: 0.060 s
% 1.76/1.51 % (8295)Instructions burned: 102 (million)
% 1.76/1.51 % (8295)------------------------------
% 1.76/1.51 % (8295)------------------------------
% 1.76/1.51 % (8289)Success in time 0.069 s
%------------------------------------------------------------------------------