%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV478^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 09:41:20 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 841 ( 29 ~; 11 |; 13 &; 773 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 4 con; 0-5 aty)
% Number of variables : 115 ( 23 ^; 80 !; 12 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK3: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/ITSET':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > ( X0 > $o ) > X1 > X1 ) ).
thf(func_def_2,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_3,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
'const/sets/CARD':
!>[X0: $tType] : ( ( X0 > $o ) > 'type/nums/num' ) ).
thf(func_def_7,type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_8,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_9,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_10,type,
'const/class/COND':
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_12,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).
thf(func_def_18,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X0 ) ).
thf(func_def_19,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > X1 ) > X1 ) ).
thf(func_def_20,type,
sK4: sK3 ).
thf(func_def_21,type,
sK5: sK3 > $o ).
thf(func_def_23,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f41,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ sK4 @ sK5 ) )
!= ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ sK4 @ sK5 ) ) ),
inference(superposition,[status(thm)],[f22,f39]) ).
thf(f39,plain,
! [X0: sK3] :
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ X0 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) )
= ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ X0 @ sK5 ) ) ),
inference(forward_demodulation,[status(thm)],[f38,f24]) ).
thf(f24,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0] : 'const/nums/SUC'
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [Y0: X0,Y1: 'type/nums/num'] : ( 'const/nums/SUC' @ Y1 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/CARD' @ X0 @ X1 )
= ( 'const/sets/ITSET' @ X0 @ 'type/nums/num'
@ ^ [X2: X0,X3: 'type/nums/num'] : ( 'const/nums/SUC' @ X3 )
@ X1
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/CARD_') ).
thf(f38,plain,
! [X0: sK3] :
( ( 'const/sets/ITSET' @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK3 @ X0 @ sK5 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ X0 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: sK3] :
( ( ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sK2 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' ) ) )
!= ( 'const/nums/SUC'
@ ( 'const/nums/SUC'
@ ( sK2 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' ) ) ) )
| ( ( 'const/sets/ITSET' @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK3 @ X0 @ sK5 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ X0 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: sK3] :
( ( ( 'const/sets/ITSET' @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC'
@ ( 'const/sets/INSERT' @ sK3 @ X0 @ sK5 )
@ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ X0 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 )
@ ( ^ [Y0: sK3] : 'const/nums/SUC'
@ X0
@ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) ) )
| ( ( ^ [Y0: sK3] : 'const/nums/SUC'
@ ( sK1 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' )
@ ( ^ [Y0: sK3] : 'const/nums/SUC'
@ ( sK0 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' )
@ ( sK2 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' ) ) )
!= ( ^ [Y0: sK3] : 'const/nums/SUC'
@ ( sK0 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' )
@ ( ^ [Y0: sK3] : 'const/nums/SUC'
@ ( sK1 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' )
@ ( sK2 @ sK3 @ 'type/nums/num'
@ ^ [Y0: sK3] : 'const/nums/SUC' ) ) ) ) ),
inference(superposition,[status(thm)],[f33,f24]) ).
thf(f33,plain,
! [X0: $tType,X2: sK3 > X0 > X0,X3: X0,X1: sK3] :
( ( ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ ( 'const/sets/INSERT' @ sK3 @ X1 @ sK5 ) @ X3 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK3 @ X1 @ sK5 ) @ ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3 ) @ ( X2 @ X1 @ ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3 ) ) ) )
| ( ( X2 @ ( sK1 @ sK3 @ X0 @ X2 ) @ ( X2 @ ( sK0 @ sK3 @ X0 @ X2 ) @ ( sK2 @ sK3 @ X0 @ X2 ) ) )
!= ( X2 @ ( sK0 @ sK3 @ X0 @ X2 ) @ ( X2 @ ( sK1 @ sK3 @ X0 @ X2 ) @ ( sK2 @ sK3 @ X0 @ X2 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $tType,X2: sK3 > X0 > X0,X3: X0,X1: sK3] :
( ( ( X2 @ ( sK1 @ sK3 @ X0 @ X2 ) @ ( X2 @ ( sK0 @ sK3 @ X0 @ X2 ) @ ( sK2 @ sK3 @ X0 @ X2 ) ) )
!= ( X2 @ ( sK0 @ sK3 @ X0 @ X2 ) @ ( X2 @ ( sK1 @ sK3 @ X0 @ X2 ) @ ( sK2 @ sK3 @ X0 @ X2 ) ) ) )
| ( $true != $true )
| ( ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ ( 'const/sets/INSERT' @ sK3 @ X1 @ sK5 ) @ X3 )
= ( 'const/class/COND' @ X0 @ ( 'const/sets/IN' @ sK3 @ X1 @ sK5 ) @ ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3 ) @ ( X2 @ X1 @ ( 'const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3 ) ) ) ) ),
inference(superposition,[status(thm)],[f17,f23]) ).
thf(f23,plain,
( ( 'const/sets/FINITE' @ sK3 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( 'const/sets/FINITE' @ sK3 @ sK5 )
= $true )
& ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ sK4 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) )
!= ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ sK4 @ sK5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f11,f15]) ).
thf(f15,plain,
( ? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) )
=> ( ( ( 'const/sets/FINITE' @ sK3 @ sK5 )
= $true )
& ( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ sK4 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) )
!= ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ sK4 @ sK5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
!= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/sets/CARD' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ X2 ) )
= ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ X0 @ X1 @ X2 ) @ ( 'const/sets/CARD' @ X0 @ X2 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/CARD_CLAUSES_1') ).
thf(f17,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1,X3: X1,X8: X0 > $o,X7: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
= ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) )
| ( ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ( ( ( sK0 @ X0 @ X1 @ X2 )
!= ( sK1 @ X0 @ X1 @ X2 ) )
& ( ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) ) ) )
| ( ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 )
& ! [X7: X0,X8: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
= ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > X1] :
( ? [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
& ( ( X2 @ X4 @ ( X2 @ X5 @ X6 ) )
!= ( X2 @ X5 @ ( X2 @ X4 @ X6 ) ) ) )
=> ( ( ( sK0 @ X0 @ X1 @ X2 )
!= ( sK1 @ X0 @ X1 @ X2 ) )
& ( ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) )
!= ( X2 @ ( sK0 @ X0 @ X1 @ X2 ) @ ( X2 @ ( sK1 @ X0 @ X1 @ X2 ) @ ( sK2 @ X0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ? [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
& ( ( X2 @ X4 @ ( X2 @ X5 @ X6 ) )
!= ( X2 @ X5 @ ( X2 @ X4 @ X6 ) ) ) )
| ( ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 )
& ! [X7: X0,X8: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
!= $true )
| ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
= ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ! [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
=> ( ( X2 @ X4 @ ( X2 @ X5 @ X6 ) )
= ( X2 @ X5 @ ( X2 @ X4 @ X6 ) ) ) )
=> ( ! [X7: X0,X8: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X8 )
= $true )
=> ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
= ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > X1,X3: X1] :
( ! [X4: X0,X5: X0,X6: X1] :
( ( X4 != X5 )
=> ( ( X2 @ X4 @ ( X2 @ X5 @ X6 ) )
= ( X2 @ X5 @ ( X2 @ X4 @ X6 ) ) ) )
=> ( ! [X7: X0,X8: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X8 )
=> ( ( 'const/class/COND' @ X1 @ ( 'const/sets/IN' @ X0 @ X7 @ X8 ) @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) @ ( X2 @ X7 @ ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3 ) ) )
= ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X7 @ X8 ) @ X3 ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3 )
= X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X4: $tType,X1: X0 > X4 > X4,X2: X4] :
( ! [X3: X0,X5: X0,X6: X4] :
( ( X3 != X5 )
=> ( ( X1 @ X3 @ ( X1 @ X5 @ X6 ) )
= ( X1 @ X5 @ ( X1 @ X3 @ X6 ) ) ) )
=> ( ! [X3: X0,X5: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X5 )
=> ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X5 ) @ X2 )
= ( 'const/class/COND' @ X4 @ ( 'const/sets/IN' @ X0 @ X3 @ X5 ) @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) @ ( X1 @ X3 @ ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2 ) ) ) ) )
& ( ( 'const/sets/ITSET' @ X0 @ X4 @ X1 @ 'const/sets/EMPTY' @ X0 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/FINITE_RECURSION_') ).
thf(f22,plain,
( ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ sK3 @ sK4 @ sK5 ) @ ( 'const/sets/CARD' @ sK3 @ sK5 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ sK3 @ sK5 ) ) )
!= ( 'const/sets/CARD' @ sK3 @ ( 'const/sets/INSERT' @ sK3 @ sK4 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV478^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:47:18 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SEV478^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.43 % Domain : Analysis
% 0.16/0.43 % Problem : CARD_CLAUSES_
% 0.16/0.43 % Version : Especial.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.16/0.43 % Source : [Kal16]
% 0.16/0.43 % Names : CARD_CLAUSES_1.p [Kal16]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.16/0.43 % Syntax : Number of formulae : 14 ( 1 unt; 11 typ; 0 def)
% 0.16/0.43 % Number of atoms : 13 ( 6 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 5 ( 4 avg)
% 0.16/0.43 % Number of connectives : 77 ( 1 ~; 0 |; 1 &; 71 @)
% 0.16/0.43 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 12 ( 7 avg)
% 0.16/0.43 % Number of types : 2 ( 1 usr)
% 0.16/0.43 % Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 11 ( 10 usr; 1 con; 0-5 aty)
% 0.16/0.43 % Number of variables : 24 ( 2 ^; 14 !; 0 ?; 24 :)
% 0.16/0.43 % ( 8 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.43 % SPC : TH1_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : Exported from core HOL Light.
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf('thf_type_type/nums/num',type,
% 0.16/0.43 'type/nums/num': $tType ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/ITSET',type,
% 0.16/0.43 'const/sets/ITSET':
% 0.16/0.43 !>[A: $tType,A0: $tType] : ( ( A > A0 > A0 ) > ( A > $o ) > A0 > A0 ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/INSERT',type,
% 0.16/0.43 'const/sets/INSERT':
% 0.16/0.43 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/IN',type,
% 0.16/0.43 'const/sets/IN':
% 0.16/0.43 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/FINITE',type,
% 0.16/0.43 'const/sets/FINITE':
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/EMPTY',type,
% 0.16/0.43 'const/sets/EMPTY':
% 0.16/0.43 !>[A: $tType] : ( A > $o ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/sets/CARD',type,
% 0.16/0.43 'const/sets/CARD':
% 0.16/0.43 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/nums/SUC',type,
% 0.16/0.43 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/nums/NUMERAL',type,
% 0.16/0.43 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/nums/_0',type,
% 0.16/0.43 'const/nums/_0': 'type/nums/num' ).
% 0.16/0.43
% 0.16/0.43 thf('thf_const_const/class/COND',type,
% 0.16/0.43 'const/class/COND':
% 0.16/0.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.43
% 0.16/0.43 thf('thm/sets/CARD_',axiom,
% 0.16/0.43 ! [A: $tType,A0: A > $o] :
% 0.16/0.43 ( ( 'const/sets/CARD' @ A @ A0 )
% 0.16/0.43 = ( 'const/sets/ITSET' @ A @ 'type/nums/num'
% 0.16/0.43 @ ^ [A1: A,A2: 'type/nums/num'] : ( 'const/nums/SUC' @ A2 )
% 0.16/0.43 @ A0
% 0.16/0.43 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf('thm/sets/FINITE_RECURSION_',axiom,
% 0.16/0.43 ! [A: $tType,B: $tType,A0: A > B > B,A1: B] :
% 0.16/0.43 ( ! [A2: A,A3: A,A4: B] :
% 0.16/0.43 ( ( A2 != A3 )
% 0.16/0.43 => ( ( A0 @ A2 @ ( A0 @ A3 @ A4 ) )
% 0.16/0.43 = ( A0 @ A3 @ ( A0 @ A2 @ A4 ) ) ) )
% 0.16/0.43 => ( ( ( 'const/sets/ITSET' @ A @ B @ A0 @ ( 'const/sets/EMPTY' @ A ) @ A1 )
% 0.16/0.43 = A1 )
% 0.16/0.43 & ! [A2: A,A3: A > $o] :
% 0.16/0.43 ( ( 'const/sets/FINITE' @ A @ A3 )
% 0.16/0.43 => ( ( 'const/sets/ITSET' @ A @ B @ A0 @ ( 'const/sets/INSERT' @ A @ A2 @ A3 ) @ A1 )
% 0.16/0.43 = ( 'const/class/COND' @ B @ ( 'const/sets/IN' @ A @ A2 @ A3 ) @ ( 'const/sets/ITSET' @ A @ B @ A0 @ A3 @ A1 ) @ ( A0 @ A2 @ ( 'const/sets/ITSET' @ A @ B @ A0 @ A3 @ A1 ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf('thm/sets/CARD_CLAUSES_1',conjecture,
% 0.16/0.43 ! [A: $tType,A0: A,A1: A > $o] :
% 0.16/0.43 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.16/0.43 => ( ( 'const/sets/CARD' @ A @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 0.16/0.43 = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ A @ A0 @ A1 ) @ ( 'const/sets/CARD' @ A @ A1 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ A @ A1 ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:47:19 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2DTF2889.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf('thf_type_type/nums/num',type,
% 1.49/1.26 'type/nums/num': $tType ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/ITSET',type,
% 1.49/1.26 'const/sets/ITSET':
% 1.49/1.26 !>[A: $tType,A0: $tType] : ( ( A > A0 > A0 ) > ( A > $o ) > A0 > A0 ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/INSERT',type,
% 1.49/1.26 'const/sets/INSERT':
% 1.49/1.26 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/IN',type,
% 1.49/1.26 'const/sets/IN':
% 1.49/1.26 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/FINITE',type,
% 1.49/1.26 'const/sets/FINITE':
% 1.49/1.26 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/EMPTY',type,
% 1.49/1.26 'const/sets/EMPTY':
% 1.49/1.26 !>[A: $tType] : ( A > $o ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/sets/CARD',type,
% 1.49/1.26 'const/sets/CARD':
% 1.49/1.26 !>[A: $tType] : ( ( A > $o ) > 'type/nums/num' ) ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/nums/SUC',type,
% 1.49/1.26 'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/nums/NUMERAL',type,
% 1.49/1.26 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/nums/_0',type,
% 1.49/1.26 'const/nums/_0': 'type/nums/num' ).
% 1.49/1.26
% 1.49/1.26 thf('thf_const_const/class/COND',type,
% 1.49/1.26 'const/class/COND':
% 1.49/1.26 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.49/1.26
% 1.49/1.26 thf('thm/sets/CARD_',axiom,
% 1.49/1.26 ! [A: $tType,A0: A > $o] :
% 1.49/1.26 ( ( 'const/sets/CARD' @ A @ A0 )
% 1.49/1.26 = ( 'const/sets/ITSET' @ A @ 'type/nums/num'
% 1.49/1.26 @ ^ [A1: A,A2: 'type/nums/num'] : ( 'const/nums/SUC' @ A2 )
% 1.49/1.26 @ A0
% 1.49/1.26 @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf('thm/sets/FINITE_RECURSION_',axiom,
% 1.49/1.26 ! [A: $tType,B: $tType,A0: A > B > B,A1: B] :
% 1.49/1.26 ( ! [A2: A,A3: A,A4: B] :
% 1.49/1.26 ( ( A2 != A3 )
% 1.49/1.26 => ( ( A0 @ A2 @ ( A0 @ A3 @ A4 ) )
% 1.49/1.26 = ( A0 @ A3 @ ( A0 @ A2 @ A4 ) ) ) )
% 1.49/1.26 => ( ( ( 'const/sets/ITSET' @ A @ B @ A0 @ ( 'const/sets/EMPTY' @ A ) @ A1 )
% 1.49/1.26 = A1 )
% 1.49/1.26 & ! [A2: A,A3: A > $o] :
% 1.49/1.26 ( ( 'const/sets/FINITE' @ A @ A3 )
% 1.49/1.26 => ( ( 'const/sets/ITSET' @ A @ B @ A0 @ ( 'const/sets/INSERT' @ A @ A2 @ A3 ) @ A1 )
% 1.49/1.26 = ( 'const/class/COND' @ B @ ( 'const/sets/IN' @ A @ A2 @ A3 ) @ ( 'const/sets/ITSET' @ A @ B @ A0 @ A3 @ A1 ) @ ( A0 @ A2 @ ( 'const/sets/ITSET' @ A @ B @ A0 @ A3 @ A1 ) ) ) ) ) ) ) ).
% 1.49/1.26
% 1.49/1.26 thf('thm/sets/CARD_CLAUSES_1',conjecture,
% 1.49/1.26 ! [A: $tType,A0: A,A1: A > $o] :
% 1.49/1.26 ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.49/1.26 => ( ( 'const/sets/CARD' @ A @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) )
% 1.49/1.26 = ( 'const/class/COND' @ 'type/nums/num' @ ( 'const/sets/IN' @ A @ A0 @ A1 ) @ ( 'const/sets/CARD' @ A @ A1 ) @ ( 'const/nums/SUC' @ ( 'const/sets/CARD' @ A @ A1 ) ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (2987)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_2889 for (2999ds/4Mi)
% 1.49/1.28 % (2991)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_2889 for (2999ds/275Mi)
% 1.49/1.28 % (2989)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2889 for (2999ds/2Mi)
% 1.49/1.28 % (2990)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_2889 for (2999ds/2Mi)
% 1.49/1.28 % (2988)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_2889 for (2999ds/27Mi)
% 1.49/1.28 % (2992)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2889 for (2999ds/18Mi)
% 1.49/1.28 % Exception at run slice level
% 1.49/1.28 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.49/1.28 % (2989)Instruction limit reached!
% 1.49/1.28 % (2989)------------------------------
% 1.49/1.28 % (2989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (2989)Termination reason: Unknown
% 1.49/1.28 % (2989)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (2989)Memory used [KB]: 5500
% 1.49/1.28 % (2989)Time elapsed: 0.003 s
% 1.49/1.28 % (2989)Instructions burned: 3 (million)
% 1.49/1.28 % (2989)------------------------------
% 1.49/1.28 % (2989)------------------------------
% 1.49/1.28 % (2991)Refutation not found, incomplete strategy
% 1.49/1.28 % (2991)------------------------------
% 1.49/1.28 % (2991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (2991)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.28
% 1.49/1.28
% 1.49/1.28 % (2991)Memory used [KB]: 5500
% 1.49/1.28 % (2991)Time elapsed: 0.003 s
% 1.49/1.28 % (2991)Instructions burned: 2 (million)
% 1.49/1.28 % (2991)------------------------------
% 1.49/1.28 % (2991)------------------------------
% 1.49/1.28 % (2987)Instruction limit reached!
% 1.49/1.28 % (2987)------------------------------
% 1.49/1.28 % (2987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (2987)Termination reason: Unknown
% 1.49/1.28 % (2987)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (2987)Memory used [KB]: 5500
% 1.49/1.28 % (2987)Time elapsed: 0.004 s
% 1.49/1.28 % (2987)Instructions burned: 4 (million)
% 1.49/1.28 % (2987)------------------------------
% 1.49/1.28 % (2987)------------------------------
% 1.49/1.28 % (2986)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2889 for (2999ds/183Mi)
% 1.49/1.29 % (2992)Instruction limit reached!
% 1.49/1.29 % (2992)------------------------------
% 1.49/1.29 % (2992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (2992)Termination reason: Unknown
% 1.49/1.29 % (2992)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (2992)Memory used [KB]: 5756
% 1.49/1.29 % (2992)Time elapsed: 0.011 s
% 1.49/1.29 % (2992)Instructions burned: 19 (million)
% 1.49/1.29 % (2992)------------------------------
% 1.49/1.29 % (2992)------------------------------
% 1.49/1.29 % (2988)First to succeed.
% 1.49/1.29 % (2988)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_2889
% 1.49/1.29 % SZS output start Proof for DTF2THF_2889
% 1.49/1.29 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.49/1.29 thf(type_def_7, type, sK3: $tType).
% 1.49/1.29 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.49/1.29 thf(func_def_1, type, 'const/sets/ITSET': !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X0 > $o) > X1 > X1)).
% 1.49/1.29 thf(func_def_2, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.49/1.29 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.49/1.29 thf(func_def_4, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.49/1.29 thf(func_def_5, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.49/1.29 thf(func_def_6, type, 'const/sets/CARD': !>[X0: $tType]:((X0 > $o) > 'type/nums/num')).
% 1.49/1.29 thf(func_def_7, type, 'const/nums/SUC': 'type/nums/num' > 'type/nums/num').
% 1.49/1.29 thf(func_def_8, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.49/1.29 thf(func_def_9, type, 'const/nums/_0': 'type/nums/num').
% 1.49/1.29 thf(func_def_10, type, 'const/class/COND': !>[X0: $tType]:($o > X0 > X0 > X0)).
% 1.49/1.29 thf(func_def_12, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.29 thf(func_def_17, type, sK0: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > X0)).
% 1.49/1.29 thf(func_def_18, type, sK1: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > X0)).
% 1.49/1.29 thf(func_def_19, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > X1)).
% 1.49/1.29 thf(func_def_20, type, sK4: sK3).
% 1.49/1.29 thf(func_def_21, type, sK5: sK3 > $o).
% 1.49/1.29 thf(func_def_23, type, ph7: !>[X0: $tType]:(X0)).
% 1.49/1.29 thf(f41,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.49/1.29 thf(f40,plain,(
% 1.49/1.29 (('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5)) != ('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5)))),
% 1.49/1.29 inference(superposition,[status(thm)],[f22,f39])).
% 1.49/1.29 thf(f39,plain,(
% 1.49/1.29 ( ! [X0 : sK3] : ((('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))) = ('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5)))) )),
% 1.49/1.29 inference(forward_demodulation,[status(thm)],[f38,f24])).
% 1.49/1.29 thf(f24,plain,(
% 1.49/1.29 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/CARD' @ X0 @ X1) = ('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ('const/nums/SUC')) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 1.49/1.29 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.49/1.29 thf(f21,plain,(
% 1.49/1.29 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/CARD' @ X0 @ X1) = ('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ((^[Y1 : 'type/nums/num']: ('const/nums/SUC' @ Y1)))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/CARD' @ X0 @ X1) = ('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[Y0 : X0]: ((^[Y1 : 'type/nums/num']: ('const/nums/SUC' @ Y1)))) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f1])).
% 1.49/1.29 thf(f1,axiom,(
% 1.49/1.29 ! [X0 : $tType,X1 : X0 > $o] : (('const/sets/CARD' @ X0 @ X1) = ('const/sets/ITSET' @ X0 @ 'type/nums/num' @ (^[X2 : X0, X3 : 'type/nums/num'] : ('const/nums/SUC' @ X3)) @ X1 @ ('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/CARD_')).
% 1.49/1.29 thf(f38,plain,(
% 1.49/1.29 ( ! [X0 : sK3] : ((('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))))) )),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.49/1.29 thf(f37,plain,(
% 1.49/1.29 ( ! [X0 : sK3] : ((('const/nums/SUC' @ ('const/nums/SUC' @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))))) != ('const/nums/SUC' @ ('const/nums/SUC' @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')))))) | (('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))))) )),
% 1.49/1.29 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.49/1.29 thf(f36,plain,(
% 1.49/1.29 ( ! [X0 : sK3] : ((('const/sets/ITSET' @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC')) @ ('const/sets/INSERT' @ sK3 @ X0 @ sK5) @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ X0 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ X0 @ ('const/sets/CARD' @ sK3 @ sK5)))) | (((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK1 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK0 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))))) != ((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK0 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ ((^[Y0 : sK3]: ('const/nums/SUC')) @ (sK1 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))) @ (sK2 @ sK3 @ 'type/nums/num' @ (^[Y0 : sK3]: ('const/nums/SUC'))))))) )),
% 1.49/1.29 inference(superposition,[status(thm)],[f33,f24])).
% 1.49/1.29 thf(f33,plain,(
% 1.49/1.29 ( ! [X0 : $tType,X2 : sK3 > X0 > X0,X3 : X0,X1 : sK3] : ((('const/sets/ITSET' @ sK3 @ X0 @ X2 @ ('const/sets/INSERT' @ sK3 @ X1 @ sK5) @ X3) = ('const/class/COND' @ X0 @ ('const/sets/IN' @ sK3 @ X1 @ sK5) @ ('const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3) @ (X2 @ X1 @ ('const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3)))) | ((X2 @ (sK1 @ sK3 @ X0 @ X2) @ (X2 @ (sK0 @ sK3 @ X0 @ X2) @ (sK2 @ sK3 @ X0 @ X2))) != (X2 @ (sK0 @ sK3 @ X0 @ X2) @ (X2 @ (sK1 @ sK3 @ X0 @ X2) @ (sK2 @ sK3 @ X0 @ X2))))) )),
% 1.49/1.29 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.49/1.29 thf(f32,plain,(
% 1.49/1.29 ( ! [X0 : $tType,X2 : sK3 > X0 > X0,X3 : X0,X1 : sK3] : (((X2 @ (sK1 @ sK3 @ X0 @ X2) @ (X2 @ (sK0 @ sK3 @ X0 @ X2) @ (sK2 @ sK3 @ X0 @ X2))) != (X2 @ (sK0 @ sK3 @ X0 @ X2) @ (X2 @ (sK1 @ sK3 @ X0 @ X2) @ (sK2 @ sK3 @ X0 @ X2)))) | ($true != $true) | (('const/sets/ITSET' @ sK3 @ X0 @ X2 @ ('const/sets/INSERT' @ sK3 @ X1 @ sK5) @ X3) = ('const/class/COND' @ X0 @ ('const/sets/IN' @ sK3 @ X1 @ sK5) @ ('const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3) @ (X2 @ X1 @ ('const/sets/ITSET' @ sK3 @ X0 @ X2 @ sK5 @ X3))))) )),
% 1.49/1.29 inference(superposition,[status(thm)],[f17,f23])).
% 1.49/1.29 thf(f23,plain,(
% 1.49/1.29 (('const/sets/FINITE' @ sK3 @ sK5) = $true)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.29 thf(f16,plain,(
% 1.49/1.29 (('const/sets/FINITE' @ sK3 @ sK5) = $true) & (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ sK4 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))) != ('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5)))),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f11,f15])).
% 1.49/1.29 thf(f15,plain,(
% 1.49/1.29 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) != ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2))))) => ((('const/sets/FINITE' @ sK3 @ sK5) = $true) & (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ sK4 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))) != ('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) != ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2)))))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f10])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X2) = $true) => (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2)))))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2)))))),
% 1.49/1.29 inference(rectify,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,negated_conjecture,(
% 1.49/1.29 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2)))))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.49/1.29 thf(f3,conjecture,(
% 1.49/1.29 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => (('const/sets/CARD' @ X0 @ ('const/sets/INSERT' @ X0 @ X1 @ X2)) = ('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ X0 @ X1 @ X2) @ ('const/sets/CARD' @ X0 @ X2) @ ('const/nums/SUC' @ ('const/sets/CARD' @ X0 @ X2)))))),
% 1.49/1.29 file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/CARD_CLAUSES_1')).
% 1.49/1.29 thf(f17,plain,(
% 1.49/1.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X1,X3 : X1,X8 : X0 > $o,X7 : X0] : ((('const/sets/FINITE' @ X0 @ X8) != $true) | (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))) = ('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)) | ((X2 @ (sK1 @ X0 @ X1 @ X2) @ (X2 @ (sK0 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))) != (X2 @ (sK0 @ X0 @ X1 @ X2) @ (X2 @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))))) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.29 thf(f14,plain,(
% 1.49/1.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X1] : ((((sK0 @ X0 @ X1 @ X2) != (sK1 @ X0 @ X1 @ X2)) & ((X2 @ (sK1 @ X0 @ X1 @ X2) @ (X2 @ (sK0 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))) != (X2 @ (sK0 @ X0 @ X1 @ X2) @ (X2 @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))))) | ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = X3) & ! [X7 : X0,X8 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X8) != $true) | (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))) = ('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)))))),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13])).
% 1.49/1.29 thf(f13,plain,(
% 1.49/1.29 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X1] : (? [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) & ((X2 @ X4 @ (X2 @ X5 @ X6)) != (X2 @ X5 @ (X2 @ X4 @ X6)))) => (((sK0 @ X0 @ X1 @ X2) != (sK1 @ X0 @ X1 @ X2)) & ((X2 @ (sK1 @ X0 @ X1 @ X2) @ (X2 @ (sK0 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))) != (X2 @ (sK0 @ X0 @ X1 @ X2) @ (X2 @ (sK1 @ X0 @ X1 @ X2) @ (sK2 @ X0 @ X1 @ X2))))))),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X1] : (? [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) & ((X2 @ X4 @ (X2 @ X5 @ X6)) != (X2 @ X5 @ (X2 @ X4 @ X6)))) | ((('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = X3) & ! [X7 : X0,X8 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X8) != $true) | (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))) = ('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3)))))),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.49/1.29 thf(f7,plain,(
% 1.49/1.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X1] : (! [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) => ((X2 @ X4 @ (X2 @ X5 @ X6)) = (X2 @ X5 @ (X2 @ X4 @ X6)))) => (! [X7 : X0,X8 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X8) = $true) => (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))) = ('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3))) & (('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = X3)))),
% 1.49/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.49/1.29 thf(f6,plain,(
% 1.49/1.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X1] : (! [X4 : X0,X5 : X0,X6 : X1] : ((X4 != X5) => ((X2 @ X4 @ (X2 @ X5 @ X6)) = (X2 @ X5 @ (X2 @ X4 @ X6)))) => (! [X7 : X0,X8 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X8) => (('const/class/COND' @ X1 @ ('const/sets/IN' @ X0 @ X7 @ X8) @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3) @ (X2 @ X7 @ ('const/sets/ITSET' @ X0 @ X1 @ X2 @ X8 @ X3))) = ('const/sets/ITSET' @ X0 @ X1 @ X2 @ ('const/sets/INSERT' @ X0 @ X7 @ X8) @ X3))) & (('const/sets/ITSET' @ X0 @ X1 @ X2 @ 'const/sets/EMPTY' @ X0 @ X3) = X3)))),
% 1.49/1.30 inference(rectify,[status(thm)],[f2])).
% 1.49/1.30 thf(f2,axiom,(
% 1.49/1.30 ! [X0 : $tType,X4 : $tType,X1 : X0 > X4 > X4,X2 : X4] : (! [X3 : X0,X5 : X0,X6 : X4] : ((X3 != X5) => ((X1 @ X3 @ (X1 @ X5 @ X6)) = (X1 @ X5 @ (X1 @ X3 @ X6)))) => (! [X3 : X0,X5 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X5) => (('const/sets/ITSET' @ X0 @ X4 @ X1 @ ('const/sets/INSERT' @ X0 @ X3 @ X5) @ X2) = ('const/class/COND' @ X4 @ ('const/sets/IN' @ X0 @ X3 @ X5) @ ('const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2) @ (X1 @ X3 @ ('const/sets/ITSET' @ X0 @ X4 @ X1 @ X5 @ X2))))) & (('const/sets/ITSET' @ X0 @ X4 @ X1 @ 'const/sets/EMPTY' @ X0 @ X2) = X2)))),
% 1.49/1.30 file('/export/starexec/sandbox2/tmp/tmp.YitG1QH8zT/DTF2THF_2889.p','thm/sets/FINITE_RECURSION_')).
% 1.49/1.30 thf(f22,plain,(
% 1.49/1.30 (('const/class/COND' @ 'type/nums/num' @ ('const/sets/IN' @ sK3 @ sK4 @ sK5) @ ('const/sets/CARD' @ sK3 @ sK5) @ ('const/nums/SUC' @ ('const/sets/CARD' @ sK3 @ sK5))) != ('const/sets/CARD' @ sK3 @ ('const/sets/INSERT' @ sK3 @ sK4 @ sK5)))),
% 1.49/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.30 % SZS output end Proof for DTF2THF_2889
% 1.49/1.30 % (2988)------------------------------
% 1.49/1.30 % (2988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.30 % (2988)Termination reason: Refutation
% 1.49/1.30
% 1.49/1.30 % (2988)Memory used [KB]: 5756
% 1.49/1.30 % (2988)Time elapsed: 0.013 s
% 1.49/1.30 % (2988)Instructions burned: 18 (million)
% 1.49/1.30 % (2988)------------------------------
% 1.49/1.30 % (2988)------------------------------
% 1.49/1.30 % (2985)Success in time 0.027 s
%------------------------------------------------------------------------------