%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV486^1 : 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 : n005.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 09:41:21 AM UTC 2026
% Result : Theorem 1.69s 1.47s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 187 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 316 ( 10 ~; 13 |; 6 &; 274 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 4 con; 0-4 aty)
% ( 0 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 79 ( 29 ^; 43 !; 7 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/SETSPEC':
!>[X0: $tType] : ( X0 > $o > X0 > $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/GSPEC':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_6,type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK0: 'type/nums/num' ).
thf(func_def_19,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f51,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
$false = $true,
inference(superposition,[status(thm)],[f30,f42]) ).
thf(f42,plain,
( $false
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f15,f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $false = $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f20,f33]) ).
thf(f33,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ ( 'const/sets/CARD' @ X0 @ X1 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(equality_resolution,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/CARD' @ X0 @ X1 )
!= X2 )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( $false
= ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
& ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
= ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/HAS_SIZE_') ).
thf(f20,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X2: 'type/nums/num',X1: X0 > $o] :
( ( $true
= ( ( ( 'const/sets/CARD' @ X0 @ X1 )
= X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) ) )
| ( ( 'const/sets/HAS_SIZE' @ X0 @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f15,plain,
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) )
!= $true )
=> ( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ sK0 ) @ Y1 ) ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) )
!= $true ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/FINITE_NUMSEG_LT_') ).
thf(f30,plain,
! [X0: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) ) )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f20,f16]) ).
thf(f16,plain,
! [X0: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
@ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ?? @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ( 'const/arith/<' @ Y1 @ X0 ) @ Y1 ) ) )
@ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
@ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [X1: 'type/nums/num'] :
? [X2: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ( 'const/arith/<' @ X2 @ X0 ) @ X2 ) )
@ X0 ),
file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV486^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:47:44 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SEV486^1 : TPTP v9.2.1. Released v7.0.0.
% 0.28/0.49 % Domain : Analysis
% 0.28/0.49 % Problem : FINITE_NUMSEG_LT
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English :
% 0.28/0.49
% 0.28/0.49 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.28/0.49 % Source : [Kal16]
% 0.28/0.49 % Names : FINITE_NUMSEG_LT_.p [Kal16]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : 0.00 v7.1.0
% 0.28/0.49 % Syntax : Number of formulae : 10 ( 1 unt; 7 typ; 0 def)
% 0.28/0.49 % Number of atoms : 12 ( 2 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.49 % Number of connectives : 29 ( 0 ~; 0 |; 1 &; 28 @)
% 0.28/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 11 ( 8 avg)
% 0.28/0.49 % Number of types : 2 ( 1 usr)
% 0.28/0.49 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 7 ( 6 usr; 0 con; 2-4 aty)
% 0.28/0.49 % Number of variables : 14 ( 2 ^; 5 !; 2 ?; 14 :)
% 0.28/0.49 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.49 % SPC : TH1_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : Exported from core HOL Light.
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf('thf_type_type/nums/num',type,
% 0.28/0.49 'type/nums/num': $tType ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/sets/SETSPEC',type,
% 0.28/0.49 'const/sets/SETSPEC':
% 0.28/0.49 !>[A: $tType] : ( A > $o > A > $o ) ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/sets/HAS_SIZE',type,
% 0.28/0.49 'const/sets/HAS_SIZE':
% 0.28/0.49 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/sets/GSPEC',type,
% 0.28/0.49 'const/sets/GSPEC':
% 0.28/0.49 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/sets/FINITE',type,
% 0.28/0.49 'const/sets/FINITE':
% 0.28/0.49 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/sets/CARD',type,
% 0.28/0.49 'const/sets/CARD':
% 0.28/0.49 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.28/0.49
% 0.28/0.49 thf('thf_const_const/arith/<',type,
% 0.28/0.49 'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.28/0.49
% 0.28/0.49 thf('thm/sets/HAS_SIZE_NUMSEG_LT_',axiom,
% 0.28/0.49 ! [A: 'type/nums/num'] :
% 0.28/0.49 ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
% 0.28/0.49 @ ( 'const/sets/GSPEC' @ 'type/nums/num'
% 0.28/0.49 @ ^ [A0: 'type/nums/num'] :
% 0.28/0.49 ? [A1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) )
% 0.28/0.49 @ A ) ).
% 0.28/0.49
% 0.28/0.49 thf('thm/sets/HAS_SIZE_',axiom,
% 0.28/0.49 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 0.28/0.49 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 0.28/0.49 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.28/0.49 & ( ( 'const/sets/CARD' @ A @ A0 )
% 0.28/0.49 = A1 ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf('thm/sets/FINITE_NUMSEG_LT_',conjecture,
% 0.28/0.49 ! [A: 'type/nums/num'] :
% 0.28/0.49 ( 'const/sets/FINITE' @ 'type/nums/num'
% 0.28/0.49 @ ( 'const/sets/GSPEC' @ 'type/nums/num'
% 0.28/0.49 @ ^ [A0: 'type/nums/num'] :
% 0.28/0.49 ? [A1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.69/1.43 ---- Embedded in THF ---
% 1.69/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.43 %%% Generated on Tue Feb 24 12:47:45 EST 2026
% 1.69/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.43 %%% Logic specification used:
% 1.69/1.43 %%% thf(spec, logic, $$dhol).
% 1.69/1.43
% 1.69/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2DTF8000.p
% See solution above
% 1.69/1.43 ------------------------
% 1.69/1.44 ---- Cleaned THF ---
% 1.69/1.44 thf('thf_type_type/nums/num',type,
% 1.69/1.44 'type/nums/num': $tType ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/sets/SETSPEC',type,
% 1.69/1.44 'const/sets/SETSPEC':
% 1.69/1.44 !>[A: $tType] : ( A > $o > A > $o ) ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/sets/HAS_SIZE',type,
% 1.69/1.44 'const/sets/HAS_SIZE':
% 1.69/1.44 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' > $o ) ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/sets/GSPEC',type,
% 1.69/1.44 'const/sets/GSPEC':
% 1.69/1.44 !>[A: $tType] : ( ( A > $o ) > A > $o ) ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/sets/FINITE',type,
% 1.69/1.44 'const/sets/FINITE':
% 1.69/1.44 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/sets/CARD',type,
% 1.69/1.44 'const/sets/CARD':
% 1.69/1.44 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.69/1.44
% 1.69/1.44 thf('thf_const_const/arith/<',type,
% 1.69/1.44 'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.69/1.44
% 1.69/1.44 thf('thm/sets/HAS_SIZE_NUMSEG_LT_',axiom,
% 1.69/1.44 ! [A: 'type/nums/num'] :
% 1.69/1.44 ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
% 1.69/1.44 @ ( 'const/sets/GSPEC' @ 'type/nums/num'
% 1.69/1.44 @ ^ [A0: 'type/nums/num'] :
% 1.69/1.44 ? [A1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) )
% 1.69/1.44 @ A ) ).
% 1.69/1.44
% 1.69/1.44 thf('thm/sets/HAS_SIZE_',axiom,
% 1.69/1.44 ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
% 1.69/1.44 ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
% 1.69/1.44 = ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.69/1.44 & ( ( 'const/sets/CARD' @ A @ A0 )
% 1.69/1.44 = A1 ) ) ) ).
% 1.69/1.44
% 1.69/1.44 thf('thm/sets/FINITE_NUMSEG_LT_',conjecture,
% 1.69/1.44 ! [A: 'type/nums/num'] :
% 1.69/1.44 ( 'const/sets/FINITE' @ 'type/nums/num'
% 1.69/1.44 @ ( 'const/sets/GSPEC' @ 'type/nums/num'
% 1.69/1.44 @ ^ [A0: 'type/nums/num'] :
% 1.69/1.44 ? [A1: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A0 @ ( 'const/arith/<' @ A1 @ A ) @ A1 ) ) ) ).
% 1.69/1.44 ------------------------
% 1.69/1.46 % (8101)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8000 for (2999ds/2Mi)
% 1.69/1.46 % (8098)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8000 for (2999ds/183Mi)
% 1.69/1.46 % (8099)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_8000 for (2999ds/4Mi)
% 1.69/1.46 % (8100)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_8000 for (2999ds/27Mi)
% 1.69/1.46 % (8102)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_8000 for (2999ds/2Mi)
% 1.69/1.46 % (8103)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_8000 for (2999ds/275Mi)
% 1.69/1.46 % (8104)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8000 for (2999ds/18Mi)
% 1.69/1.46 % (8101)Instruction limit reached!
% 1.69/1.46 % (8101)------------------------------
% 1.69/1.46 % (8101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (8101)Termination reason: Unknown
% 1.69/1.46 % (8102)Instruction limit reached!
% 1.69/1.46 % (8102)------------------------------
% 1.69/1.46 % (8102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (8101)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (8101)Memory used [KB]: 5500
% 1.69/1.46 % (8101)Time elapsed: 0.003 s
% 1.69/1.46 % (8101)Instructions burned: 2 (million)
% 1.69/1.46 % (8101)------------------------------
% 1.69/1.46 % (8101)------------------------------
% 1.69/1.46 % (8103)Refutation not found, incomplete strategy
% 1.69/1.46 % (8103)------------------------------
% 1.69/1.46 % (8103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (8103)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.46
% 1.69/1.46
% 1.69/1.46 % (8103)Memory used [KB]: 5500
% 1.69/1.46 % (8103)Time elapsed: 0.002 s
% 1.69/1.46 % (8103)Instructions burned: 1 (million)
% 1.69/1.46 % (8103)------------------------------
% 1.69/1.46 % (8103)------------------------------
% 1.69/1.46 % (8102)Termination reason: Unknown
% 1.69/1.46 % (8102)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (8102)Memory used [KB]: 5500
% 1.69/1.46 % (8102)Time elapsed: 0.003 s
% 1.69/1.46 % (8102)Instructions burned: 2 (million)
% 1.69/1.46 % (8102)------------------------------
% 1.69/1.46 % (8102)------------------------------
% 1.69/1.46 % (8099)Instruction limit reached!
% 1.69/1.46 % (8099)------------------------------
% 1.69/1.46 % (8099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.46 % (8099)Termination reason: Unknown
% 1.69/1.46 % (8099)Termination phase: Saturation
% 1.69/1.46
% 1.69/1.46 % (8099)Memory used [KB]: 5500
% 1.69/1.46 % (8099)Time elapsed: 0.004 s
% 1.69/1.46 % (8099)Instructions burned: 4 (million)
% 1.69/1.46 % (8099)------------------------------
% 1.69/1.46 % (8099)------------------------------
% 1.69/1.47 % (8100)First to succeed.
% 1.69/1.47 % (8100)Refutation found. Thanks to Tanya!
% 1.69/1.47 % SZS status Theorem for DTF2THF_8000
% 1.69/1.47 % SZS output start Proof for DTF2THF_8000
% 1.69/1.47 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.69/1.47 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.69/1.47 thf(func_def_1, type, 'const/sets/SETSPEC': !>[X0: $tType]:(X0 > $o > X0 > $o)).
% 1.69/1.47 thf(func_def_2, type, 'const/sets/HAS_SIZE': !>[X0: $tType]:((X0 > $o) > 'type/nums/num' > $o)).
% 1.69/1.47 thf(func_def_3, type, 'const/sets/GSPEC': !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 1.69/1.47 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.69/1.47 thf(func_def_5, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.69/1.47 thf(func_def_6, type, 'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o).
% 1.69/1.47 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.69/1.47 thf(func_def_17, type, sK0: 'type/nums/num').
% 1.69/1.47 thf(func_def_19, type, ph2: !>[X0: $tType]:(X0)).
% 1.69/1.47 thf(f51,plain,(
% 1.69/1.47 $false),
% 1.69/1.47 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.69/1.47 thf(f49,plain,(
% 1.69/1.47 ($false = $true)),
% 1.69/1.47 inference(superposition,[status(thm)],[f30,f42])).
% 1.69/1.47 thf(f42,plain,(
% 1.69/1.47 ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ sK0) @ Y1)))))))),
% 1.69/1.47 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.69/1.47 thf(f40,plain,(
% 1.69/1.47 ($true != $true) | ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ sK0) @ Y1)))))))),
% 1.69/1.47 inference(superposition,[status(thm)],[f15,f38])).
% 1.69/1.47 thf(f38,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.69/1.47 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.69/1.47 thf(f37,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = $true) | (('const/sets/FINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.69/1.47 inference(superposition,[status(thm)],[f20,f33])).
% 1.69/1.47 thf(f33,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ ('const/sets/CARD' @ X0 @ X1)) = $true) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.69/1.47 inference(equality_resolution,[status(thm)],[f24])).
% 1.69/1.47 thf(f24,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/CARD' @ X0 @ X1) != X2) | (('const/sets/FINITE' @ X0 @ X1) = $false) | (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.47 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.69/1.47 thf(f23,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true) | (('const/sets/FINITE' @ X0 @ X1) = $false) | ($false = (('const/sets/CARD' @ X0 @ X1) = X2))) )),
% 1.69/1.47 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.69/1.47 thf(f18,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $true) | ($false = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1)))) )),
% 1.69/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.69/1.47 thf(f17,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1)))) )),
% 1.69/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.69/1.47 thf(f7,plain,(
% 1.69/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1)))),
% 1.69/1.47 inference(fool_elimination,[status(thm)],[f6])).
% 1.69/1.47 thf(f6,plain,(
% 1.69/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2) = ('const/sets/HAS_SIZE' @ X0 @ X1 @ X2))),
% 1.69/1.47 inference(rectify,[status(thm)],[f2])).
% 1.69/1.47 thf(f2,axiom,(
% 1.69/1.47 ! [X0 : $tType,X1 : X0 > $o,X2 : 'type/nums/num'] : (('const/sets/FINITE' @ X0 @ X1) & (('const/sets/CARD' @ X0 @ X1) = X2) = ('const/sets/HAS_SIZE' @ X0 @ X1 @ X2))),
% 1.69/1.47 file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/HAS_SIZE_')).
% 1.69/1.47 thf(f20,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $false) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.69/1.47 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.69/1.47 thf(f19,plain,(
% 1.69/1.47 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : X0 > $o] : (($true = ((('const/sets/CARD' @ X0 @ X1) = X2) & ('const/sets/FINITE' @ X0 @ X1))) | (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2) = $false)) )),
% 1.69/1.47 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.69/1.47 thf(f15,plain,(
% 1.69/1.47 (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ sK0) @ Y1)))))) != $true)),
% 1.69/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.47 thf(f14,plain,(
% 1.69/1.47 (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ sK0) @ Y1)))))) != $true)),
% 1.69/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 1.69/1.47 thf(f13,plain,(
% 1.69/1.47 ? [X0 : 'type/nums/num'] : (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1)))))) != $true) => (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ sK0) @ Y1)))))) != $true)),
% 1.69/1.47 introduced(definition,[],[choice_axiom])).
% 1.69/1.47 thf(f12,plain,(
% 1.69/1.47 ? [X0 : 'type/nums/num'] : (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1)))))) != $true)),
% 1.69/1.47 inference(ennf_transformation,[status(thm)],[f9])).
% 1.69/1.47 thf(f9,plain,(
% 1.69/1.47 ~! [X0 : 'type/nums/num'] : (('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1)))))) = $true)),
% 1.69/1.47 inference(fool_elimination,[status(thm)],[f8])).
% 1.69/1.47 thf(f8,plain,(
% 1.69/1.47 ~! [X0 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[X1 : 'type/nums/num'] : (? [X2 : 'type/nums/num'] : ('const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ('const/arith/<' @ X2 @ X0) @ X2)))))),
% 1.69/1.47 inference(rectify,[status(thm)],[f4])).
% 1.69/1.47 thf(f4,negated_conjecture,(
% 1.69/1.47 ~! [X0 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[X1 : 'type/nums/num'] : (? [X2 : 'type/nums/num'] : ('const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ('const/arith/<' @ X2 @ X0) @ X2)))))),
% 1.69/1.47 inference(negated_conjecture,[status(cth)],[f3])).
% 1.69/1.47 thf(f3,conjecture,(
% 1.69/1.47 ! [X0 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[X1 : 'type/nums/num'] : (? [X2 : 'type/nums/num'] : ('const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ('const/arith/<' @ X2 @ X0) @ X2)))))),
% 1.69/1.47 file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/FINITE_NUMSEG_LT_')).
% 1.69/1.47 thf(f30,plain,(
% 1.69/1.47 ( ! [X0 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1)))))) = $true)) )),
% 1.69/1.47 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.69/1.47 thf(f28,plain,(
% 1.69/1.47 ( ! [X0 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1)))))) = $true) | ($false = $true)) )),
% 1.69/1.47 inference(superposition,[status(thm)],[f20,f16])).
% 1.69/1.47 thf(f16,plain,(
% 1.69/1.47 ( ! [X0 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1))))) @ X0) = $true)) )),
% 1.69/1.47 inference(cnf_transformation,[status(thm)],[f11])).
% 1.69/1.47 thf(f11,plain,(
% 1.69/1.47 ! [X0 : 'type/nums/num'] : (('const/sets/HAS_SIZE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (?? @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/SETSPEC' @ 'type/nums/num' @ Y0 @ ('const/arith/<' @ Y1 @ X0) @ Y1))))) @ X0) = $true)),
% 1.69/1.47 inference(fool_elimination,[status(thm)],[f10])).
% 1.69/1.47 thf(f10,plain,(
% 1.69/1.47 ! [X0 : 'type/nums/num'] : ('const/sets/HAS_SIZE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[X1 : 'type/nums/num'] : (? [X2 : 'type/nums/num'] : ('const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ('const/arith/<' @ X2 @ X0) @ X2)))) @ X0)),
% 1.69/1.47 inference(rectify,[status(thm)],[f1])).
% 1.69/1.47 thf(f1,axiom,(
% 1.69/1.47 ! [X0 : 'type/nums/num'] : ('const/sets/HAS_SIZE' @ 'type/nums/num' @ ('const/sets/GSPEC' @ 'type/nums/num' @ (^[X1 : 'type/nums/num'] : (? [X2 : 'type/nums/num'] : ('const/sets/SETSPEC' @ 'type/nums/num' @ X1 @ ('const/arith/<' @ X2 @ X0) @ X2)))) @ X0)),
% 1.69/1.47 file('/export/starexec/sandbox/tmp/tmp.hgaX80bx12/DTF2THF_8000.p','thm/sets/HAS_SIZE_NUMSEG_LT_')).
% 1.69/1.47 % SZS output end Proof for DTF2THF_8000
% 1.69/1.47 % (8100)------------------------------
% 1.69/1.47 % (8100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.47 % (8100)Termination reason: Refutation
% 1.69/1.47
% 1.69/1.47 % (8100)Memory used [KB]: 5500
% 1.69/1.47 % (8100)Time elapsed: 0.008 s
% 1.69/1.47 % (8100)Instructions burned: 7 (million)
% 1.69/1.47 % (8100)------------------------------
% 1.69/1.47 % (8100)------------------------------
% 1.69/1.47 % (8097)Success in time 0.022 s
%------------------------------------------------------------------------------