%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU680^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.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 09:36:17 AM UTC 2026
% Result : Theorem 0.32s 1.25s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 532 ( 146 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 738 ( 70 ~; 52 |; 33 &; 550 @)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 11 con; 0-3 aty)
% Number of variables : 167 ( 28 ^; 108 !; 31 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_12,type,
func: $i > $i > $i > $o ).
thf(func_def_13,type,
funcSet: $i > $i > $i ).
thf(func_def_15,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_33,type,
sK4: $i > $i ).
thf(func_def_35,type,
sK6: $i > ( $i > $i ) > $i > $i ).
thf(func_def_37,type,
sK8: $i > $i ).
thf(func_def_40,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f74,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f73,f69]) ).
thf(f69,plain,
( $true
= ( in @ ( sK6 @ sK7 @ sK8 @ sK9 ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true
= ( in @ ( sK6 @ sK7 @ sK8 @ sK9 ) @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f67,f61]) ).
thf(f61,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( func @ X4 @ X6 @ ( lam @ X4 @ X6 @ X5 ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f45,f50]) ).
thf(f50,plain,
lamp = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( $true
!= ( in
@ ( lam @ sK9 @ sK7
@ ^ [Y0: $i] : ( sK8 @ Y0 ) )
@ ( funcSet @ sK9 @ sK7 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK8 @ X3 ) @ sK7 ) )
| ( $true
!= ( in @ X3 @ sK9 ) ) )
& ( lamp = $true )
& ( funcinfuncset = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f28,f40]) ).
thf(f40,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( in
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( funcSet @ X2 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) )
=> ( ( $true
!= ( in
@ ( lam @ sK9 @ sK7
@ ^ [Y0: $i] : ( sK8 @ Y0 ) )
@ ( funcSet @ sK9 @ sK7 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK8 @ X3 ) @ sK7 ) )
| ( $true
!= ( in @ X3 @ sK9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( in
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( funcSet @ X2 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) )
& ( lamp = $true )
& ( funcinfuncset = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( in
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( funcSet @ X2 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) )
& ( lamp = $true )
& ( funcinfuncset = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( ( funcinfuncset = $true )
=> ( ( lamp = $true )
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( X1 @ X3 ) @ X0 ) ) )
=> ( $true
= ( in
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( funcSet @ X2 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( funcinfuncset
=> ( lamp
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X1 @ X3 ) @ X0 ) )
=> ( in
@ ( lam @ X2 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) )
@ ( funcSet @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( funcinfuncset
=> ( lamp
=> ! [X3: $i,X7: $i > $i,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( in
@ ( lam @ X0 @ X3
@ ^ [X1: $i] : ( X7 @ X1 ) )
@ ( funcSet @ X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( funcinfuncset
=> ( lamp
=> ! [X3: $i,X7: $i > $i,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( in
@ ( lam @ X0 @ X3
@ ^ [X1: $i] : ( X7 @ X1 ) )
@ ( funcSet @ X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',lam2p) ).
thf(f45,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) )
| ( lamp != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( lamp = $true )
| ( ( $true
!= ( func @ sK3 @ sK5
@ ( lam @ sK3 @ sK5
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK4 @ X3 ) @ sK5 ) )
| ( ( in @ X3 @ sK3 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $i > $i,X6: $i] :
( ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) ) ) )
| ( lamp != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f36,f38,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
=> ( ( $true
!= ( func @ sK3 @ sK5
@ ( lam @ sK3 @ sK5
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK4 @ X3 ) @ sK5 ) )
| ( ( in @ X3 @ sK3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
! [X4: $i,X5: $i > $i,X6: $i] :
( ? [X7: $i] :
( ( ( in @ ( X5 @ X7 ) @ X6 )
!= $true )
& ( $true
= ( in @ X7 @ X4 ) ) )
=> ( ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) )
& ( $true
= ( in @ ( sK6 @ X6 @ X5 @ X4 ) @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ( ( lamp = $true )
| ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $i > $i,X6: $i] :
( ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ? [X7: $i] :
( ( ( in @ ( X5 @ X7 ) @ X6 )
!= $true )
& ( $true
= ( in @ X7 @ X4 ) ) ) )
| ( lamp != $true ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( lamp = $true )
| ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X1 @ X3 ) @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) )
& ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( $true
!= ( in @ ( X1 @ X3 ) @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ( lamp != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( lamp = $true )
<=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ? [X3: $i] :
( ( $true
!= ( in @ ( X1 @ X3 ) @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( lamp = $true )
<=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( in @ ( X1 @ X3 ) @ X2 ) ) )
=> ( $true
= ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( lamp
= ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X1 @ X3 ) @ X2 ) )
=> ( func @ X0 @ X2
@ ( lam @ X0 @ X2
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( lamp
= ( ! [X0: $i,X7: $i > $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( X7 @ X1 ) @ X3 ) )
=> ( func @ X0 @ X3
@ ( lam @ X0 @ X3
@ ^ [X1: $i] : ( X7 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',lamp) ).
thf(f67,plain,
( $true
!= ( func @ sK9 @ sK7 @ ( lam @ sK9 @ sK7 @ sK8 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true
!= ( func @ sK9 @ sK7 @ ( lam @ sK9 @ sK7 @ sK8 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f62,f65]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( func @ X2 @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f44,f49]) ).
thf(f49,plain,
funcinfuncset = $true,
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) )
| ( funcinfuncset != $true ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ( ( $true
!= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
& ( $true
= ( func @ sK2 @ sK0 @ sK1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f32,f33]) ).
thf(f33,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
& ( ( func @ X5 @ X3 @ X4 )
= $true ) )
=> ( ( $true
!= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
& ( $true
= ( func @ sK2 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( funcSet @ X5 @ X3 ) ) )
& ( ( func @ X5 @ X3 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ( $true
= ( func @ X2 @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
| ( $true
!= ( func @ X2 @ X0 @ X1 ) ) )
<=> ( funcinfuncset = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( funcinfuncset = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X0 @ X1 ) )
=> ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( funcinfuncset
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( funcinfuncset
= ( ! [X3: $i,X7: $i,X0: $i] :
( ( func @ X0 @ X3 @ X7 )
=> ( in @ X7 @ ( funcSet @ X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',funcinfuncset) ).
thf(f62,plain,
( $true
!= ( in @ ( lam @ sK9 @ sK7 @ sK8 ) @ ( funcSet @ sK9 @ sK7 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
!= ( in
@ ( lam @ sK9 @ sK7
@ ^ [Y0: $i] : ( sK8 @ Y0 ) )
@ ( funcSet @ sK9 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f73,plain,
( $true
!= ( in @ ( sK6 @ sK7 @ sK8 @ sK9 ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( $true != $true )
| ( $true
!= ( in @ ( sK6 @ sK7 @ sK8 @ sK9 ) @ sK9 ) ) ),
inference(superposition,[status(thm)],[f71,f51]) ).
thf(f51,plain,
! [X3: $i] :
( ( $true
= ( in @ ( sK8 @ X3 ) @ sK7 ) )
| ( $true
!= ( in @ X3 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f71,plain,
( ( in @ ( sK8 @ ( sK6 @ sK7 @ sK8 @ sK9 ) ) @ sK7 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( in @ ( sK8 @ ( sK6 @ sK7 @ sK8 @ sK9 ) ) @ sK7 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f67,f64]) ).
thf(f64,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( func @ X4 @ X6 @ ( lam @ X4 @ X6 @ X5 ) ) )
| ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) )
| ( $true != $true )
| ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f46,f50]) ).
thf(f46,plain,
! [X6: $i,X4: $i,X5: $i > $i] :
( ( $true
= ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( $true
!= ( in @ ( X5 @ ( sK6 @ X6 @ X5 @ X4 ) ) @ X6 ) )
| ( lamp != $true ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU680^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 12:30:54 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU680^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Functions - Lambda Abstraction
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.31/0.46 % in (lam A B (^ x:i.f x)) (funcSet A B))
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC182l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 24 ( 7 unt; 16 typ; 7 def)
% 0.31/0.46 % Number of atoms : 32 ( 9 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 5 ( 4 avg)
% 0.31/0.46 % Number of connectives : 69 ( 0 ~; 0 |; 2 &; 59 @)
% 0.31/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 12 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 17 ( 16 usr; 3 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 31 ( 18 ^; 12 !; 1 ?; 31 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=238
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(in_type,type,
% 0.31/0.46 in: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptyset_type,type,
% 0.31/0.46 emptyset: $i ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoin_type,type,
% 0.31/0.46 setadjoin: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstr_type,type,
% 0.31/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(subset_type,type,
% 0.31/0.46 subset: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(kpair_type,type,
% 0.31/0.46 kpair: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(cartprod_type,type,
% 0.31/0.46 cartprod: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_type,type,
% 0.31/0.46 singleton: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(singleton,definition,
% 0.31/0.46 ( singleton
% 0.31/0.46 = ( ^ [A: $i] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 & ( A
% 0.31/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(ex1_type,type,
% 0.31/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(ex1,definition,
% 0.31/0.46 ( ex1
% 0.31/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.31/0.46 ( singleton
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(breln_type,type,
% 0.31/0.46 breln: $i > $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(breln,definition,
% 0.31/0.46 ( breln
% 0.31/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(dpsetconstr_type,type,
% 0.31/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(func_type,type,
% 0.31/0.46 func: $i > $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(func,definition,
% 0.31/0.46 ( func
% 0.31/0.46 = ( ^ [A: $i,B: $i,R: $i] :
% 0.31/0.46 ( ( breln @ A @ B @ R )
% 0.31/0.46 & ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( ex1 @ B
% 0.31/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(funcSet_type,type,
% 0.31/0.46 funcSet: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(funcinfuncset_type,type,
% 0.31/0.46 funcinfuncset: $o ).
% 0.31/0.46
% 0.31/0.46 thf(funcinfuncset,definition,
% 0.31/0.46 ( funcinfuncset
% 0.31/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.46 ( ( func @ A @ B @ Xf )
% 0.31/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lam_type,type,
% 0.31/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(lam,definition,
% 0.31/0.46 ( lam
% 0.31/0.46 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( dpsetconstr @ A @ B
% 0.31/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.46 ( ( Xf @ Xx )
% 0.31/0.46 = Xy ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lamp_type,type,
% 0.31/0.46 lamp: $o ).
% 0.31/0.46
% 0.31/0.46 thf(lamp,definition,
% 0.31/0.46 ( lamp
% 0.31/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.46 => ( func @ A @ B
% 0.31/0.46 @ ( lam @ A @ B
% 0.31/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(lam2p,conjecture,
% 0.31/0.46 ( funcinfuncset
% 0.31/0.46 => ( lamp
% 0.31/0.46 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.46 => ( in
% 0.31/0.46 @ ( lam @ A @ B
% 0.31/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.31/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 0.32/1.21 ---- Embedded in THF ---
% 0.32/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.21 %%% Generated on Tue Feb 24 12:30:54 EST 2026
% 0.32/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.21 %%% Logic specification used:
% 0.32/1.21 %%% thf(spec, logic, $$dhol).
% 0.32/1.21
% 0.32/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2DTF26743.p
% See solution above
% 0.32/1.21 ------------------------
% 0.32/1.22 ---- Cleaned THF ---
% 0.32/1.22 thf(in_type,type,
% 0.32/1.22 in: $i > $i > $o ).
% 0.32/1.22
% 0.32/1.22 thf(emptyset_type,type,
% 0.32/1.22 emptyset: $i ).
% 0.32/1.22
% 0.32/1.22 thf(setadjoin_type,type,
% 0.32/1.22 setadjoin: $i > $i > $i ).
% 0.32/1.22
% 0.32/1.22 thf(dsetconstr_type,type,
% 0.32/1.22 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/1.22
% 0.32/1.22 thf(subset_type,type,
% 0.32/1.22 subset: $i > $i > $o ).
% 0.32/1.22
% 0.32/1.22 thf(kpair_type,type,
% 0.32/1.22 kpair: $i > $i > $i ).
% 0.32/1.22
% 0.32/1.22 thf(cartprod_type,type,
% 0.32/1.22 cartprod: $i > $i > $i ).
% 0.32/1.22
% 0.32/1.22 thf(singleton_type,type,
% 0.32/1.22 singleton: $i > $o ).
% 0.32/1.22
% 0.32/1.22 thf(singleton,definition,
% 0.32/1.22 ( singleton
% 0.32/1.22 = ( ^ [A: $i] :
% 0.32/1.22 ? [Xx: $i] :
% 0.32/1.22 ( ( in @ Xx @ A )
% 0.32/1.22 & ( A
% 0.32/1.22 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(ex1_type,type,
% 0.32/1.22 ex1: $i > ( $i > $o ) > $o ).
% 0.32/1.22
% 0.32/1.22 thf(ex1,definition,
% 0.32/1.22 ( ex1
% 0.32/1.22 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.32/1.22 ( singleton
% 0.32/1.22 @ ( dsetconstr @ A
% 0.32/1.22 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(breln_type,type,
% 0.32/1.22 breln: $i > $i > $i > $o ).
% 0.32/1.22
% 0.32/1.22 thf(breln,definition,
% 0.32/1.22 ( breln
% 0.32/1.22 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(dpsetconstr_type,type,
% 0.32/1.22 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.32/1.22
% 0.32/1.22 thf(func_type,type,
% 0.32/1.22 func: $i > $i > $i > $o ).
% 0.32/1.22
% 0.32/1.22 thf(func,definition,
% 0.32/1.22 ( func
% 0.32/1.22 = ( ^ [A: $i,B: $i,R: $i] :
% 0.32/1.22 ( ( breln @ A @ B @ R )
% 0.32/1.22 & ! [Xx: $i] :
% 0.32/1.22 ( ( in @ Xx @ A )
% 0.32/1.22 => ( ex1 @ B
% 0.32/1.22 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(funcSet_type,type,
% 0.32/1.22 funcSet: $i > $i > $i ).
% 0.32/1.22
% 0.32/1.22 thf(funcinfuncset_type,type,
% 0.32/1.22 funcinfuncset: $o ).
% 0.32/1.22
% 0.32/1.22 thf(funcinfuncset,definition,
% 0.32/1.22 ( funcinfuncset
% 0.32/1.22 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/1.22 ( ( func @ A @ B @ Xf )
% 0.32/1.22 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(lam_type,type,
% 0.32/1.22 lam: $i > $i > ( $i > $i ) > $i ).
% 0.32/1.22
% 0.32/1.22 thf(lam,definition,
% 0.32/1.22 ( lam
% 0.32/1.22 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.32/1.22 ( dpsetconstr @ A @ B
% 0.32/1.22 @ ^ [Xx: $i,Xy: $i] :
% 0.32/1.22 ( ( Xf @ Xx )
% 0.32/1.22 = Xy ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(lamp_type,type,
% 0.32/1.22 lamp: $o ).
% 0.32/1.22
% 0.32/1.22 thf(lamp,definition,
% 0.32/1.22 ( lamp
% 0.32/1.22 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/1.22 ( ! [Xx: $i] :
% 0.32/1.22 ( ( in @ Xx @ A )
% 0.32/1.22 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/1.22 => ( func @ A @ B
% 0.32/1.22 @ ( lam @ A @ B
% 0.32/1.22 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/1.22
% 0.32/1.22 thf(lam2p,conjecture,
% 0.32/1.22 ( funcinfuncset
% 0.32/1.22 => ( lamp
% 0.32/1.22 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/1.22 ( ! [Xx: $i] :
% 0.32/1.22 ( ( in @ Xx @ A )
% 0.32/1.22 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/1.22 => ( in
% 0.32/1.22 @ ( lam @ A @ B
% 0.32/1.22 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/1.22 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/1.22 ------------------------
% 0.32/1.23 % (26840)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26743 for (2999ds/183Mi)
% 0.32/1.23 % (26841)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_26743 for (2999ds/4Mi)
% 0.32/1.23 % (26841)Instruction limit reached!
% 0.32/1.23 % (26841)------------------------------
% 0.32/1.23 % (26841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.23 % (26841)Termination reason: Unknown
% 0.32/1.23 % (26841)Termination phase: Saturation
% 0.32/1.23
% 0.32/1.23 % (26841)Memory used [KB]: 5500
% 0.32/1.23 % (26841)Time elapsed: 0.003 s
% 0.32/1.23 % (26841)Instructions burned: 6 (million)
% 0.32/1.23 % (26841)------------------------------
% 0.32/1.23 % (26841)------------------------------
% 0.32/1.24 % (26842)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_26743 for (2999ds/27Mi)
% 0.32/1.24 % (26843)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26743 for (2999ds/2Mi)
% 0.32/1.24 % (26844)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_26743 for (2999ds/2Mi)
% 0.32/1.24 % (26845)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_26743 for (2999ds/275Mi)
% 0.32/1.24 % (26846)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26743 for (2999ds/18Mi)
% 0.32/1.24 % (26843)Instruction limit reached!
% 0.32/1.24 % (26843)------------------------------
% 0.32/1.24 % (26843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.24 % (26843)Termination reason: Unknown
% 0.32/1.24 % (26843)Termination phase: shuffling
% 0.32/1.24
% 0.32/1.24 % (26843)Memory used [KB]: 1023
% 0.32/1.24 % (26843)Time elapsed: 0.003 s
% 0.32/1.24 % (26843)Instructions burned: 2 (million)
% 0.32/1.24 % (26843)------------------------------
% 0.32/1.24 % (26843)------------------------------
% 0.32/1.24 % (26844)Instruction limit reached!
% 0.32/1.24 % (26844)------------------------------
% 0.32/1.24 % (26844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.24 % (26844)Termination reason: Unknown
% 0.32/1.24 % (26844)Termination phase: shuffling
% 0.32/1.24
% 0.32/1.24 % (26844)Memory used [KB]: 1023
% 0.32/1.24 % (26844)Time elapsed: 0.003 s
% 0.32/1.24 % (26844)Instructions burned: 2 (million)
% 0.32/1.24 % (26844)------------------------------
% 0.32/1.24 % (26844)------------------------------
% 0.32/1.24 % (26847)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26743 for (2999ds/3Mi)
% 0.32/1.24 % (26847)Instruction limit reached!
% 0.32/1.24 % (26847)------------------------------
% 0.32/1.24 % (26847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.24 % (26847)Termination reason: Unknown
% 0.32/1.24 % (26847)Termination phase: Function definition elimination
% 0.32/1.24
% 0.32/1.24 % (26847)Memory used [KB]: 1023
% 0.32/1.24 % (26847)Time elapsed: 0.002 s
% 0.32/1.24 % (26847)Instructions burned: 4 (million)
% 0.32/1.24 % (26847)------------------------------
% 0.32/1.24 % (26847)------------------------------
% 0.32/1.24 % (26845)First to succeed.
% 0.32/1.25 % (26845)Refutation found. Thanks to Tanya!
% 0.32/1.25 % SZS status Theorem for DTF2THF_26743
% 0.32/1.25 % SZS output start Proof for DTF2THF_26743
% 0.32/1.25 thf(func_def_0, type, in: $i > $i > $o).
% 0.32/1.25 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.32/1.25 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.32/1.25 thf(func_def_4, type, subset: $i > $i > $o).
% 0.32/1.25 thf(func_def_5, type, kpair: $i > $i > $i).
% 0.32/1.25 thf(func_def_6, type, cartprod: $i > $i > $i).
% 0.32/1.25 thf(func_def_7, type, singleton: $i > $o).
% 0.32/1.25 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.32/1.25 thf(func_def_10, type, breln: $i > $i > $i > $o).
% 0.32/1.25 thf(func_def_11, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.32/1.25 thf(func_def_12, type, func: $i > $i > $i > $o).
% 0.32/1.25 thf(func_def_13, type, funcSet: $i > $i > $i).
% 0.32/1.25 thf(func_def_15, type, lam: $i > $i > ($i > $i) > $i).
% 0.32/1.25 thf(func_def_33, type, sK4: $i > $i).
% 0.32/1.25 thf(func_def_35, type, sK6: $i > ($i > $i) > $i > $i).
% 0.32/1.25 thf(func_def_37, type, sK8: $i > $i).
% 0.32/1.25 thf(func_def_40, type, ph11: !>[X0: $tType]:(X0)).
% 0.32/1.25 thf(f74,plain,(
% 0.32/1.25 $false),
% 0.32/1.25 inference(subsumption_resolution,[status(thm)],[f73,f69])).
% 0.32/1.25 thf(f69,plain,(
% 0.32/1.25 ($true = (in @ (sK6 @ sK7 @ sK8 @ sK9) @ sK9))),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 0.32/1.25 thf(f68,plain,(
% 0.32/1.25 ($true = (in @ (sK6 @ sK7 @ sK8 @ sK9) @ sK9)) | ($true != $true)),
% 0.32/1.25 inference(superposition,[status(thm)],[f67,f61])).
% 0.32/1.25 thf(f61,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ X5))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4))) )),
% 0.32/1.25 inference(beta_eta_normalization,[status(thm)],[f60])).
% 0.32/1.25 thf(f60,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) )),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 0.32/1.25 thf(f59,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | ($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true != $true)) )),
% 0.32/1.25 inference(definition_unfolding,[status(thm)],[f45,f50])).
% 0.32/1.25 thf(f50,plain,(
% 0.32/1.25 (lamp = $true)),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f41])).
% 0.32/1.25 thf(f41,plain,(
% 0.32/1.25 (($true != (in @ (lam @ sK9 @ sK7 @ (^[Y0 : $i]: (sK8 @ Y0))) @ (funcSet @ sK9 @ sK7))) & ! [X3 : $i] : (($true = (in @ (sK8 @ X3) @ sK7)) | ($true != (in @ X3 @ sK9)))) & (lamp = $true) & (funcinfuncset = $true)),
% 0.32/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f28,f40])).
% 0.32/1.25 thf(f40,plain,(
% 0.32/1.25 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (in @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (funcSet @ X2 @ X0))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X0)) | ($true != (in @ X3 @ X2)))) => (($true != (in @ (lam @ sK9 @ sK7 @ (^[Y0 : $i]: (sK8 @ Y0))) @ (funcSet @ sK9 @ sK7))) & ! [X3 : $i] : (($true = (in @ (sK8 @ X3) @ sK7)) | ($true != (in @ X3 @ sK9))))),
% 0.32/1.25 introduced(definition,[],[choice_axiom])).
% 0.32/1.25 thf(f28,plain,(
% 0.32/1.25 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (in @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (funcSet @ X2 @ X0))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X0)) | ($true != (in @ X3 @ X2)))) & (lamp = $true) & (funcinfuncset = $true)),
% 0.32/1.25 inference(flattening,[status(thm)],[f27])).
% 0.32/1.25 thf(f27,plain,(
% 0.32/1.25 (? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (in @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (funcSet @ X2 @ X0))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X0)) | ($true != (in @ X3 @ X2)))) & (lamp = $true)) & (funcinfuncset = $true)),
% 0.32/1.25 inference(ennf_transformation,[status(thm)],[f26])).
% 0.32/1.25 thf(f26,plain,(
% 0.32/1.25 ~((funcinfuncset = $true) => ((lamp = $true) => ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : (($true = (in @ X3 @ X2)) => ($true = (in @ (X1 @ X3) @ X0))) => ($true = (in @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (funcSet @ X2 @ X0))))))),
% 0.32/1.25 inference(fool_elimination,[status(thm)],[f25])).
% 0.32/1.25 thf(f25,plain,(
% 0.32/1.25 ~(funcinfuncset => (lamp => ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (in @ (lam @ X2 @ X0 @ (^[X4 : $i] : (X1 @ X4))) @ (funcSet @ X2 @ X0)))))),
% 0.32/1.25 inference(rectify,[status(thm)],[f9])).
% 0.32/1.25 thf(f9,negated_conjecture,(
% 0.32/1.25 ~(funcinfuncset => (lamp => ! [X3 : $i,X7 : $i > $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (in @ (lam @ X0 @ X3 @ (^[X1 : $i] : (X7 @ X1))) @ (funcSet @ X0 @ X3)))))),
% 0.32/1.25 inference(negated_conjecture,[status(cth)],[f8])).
% 0.32/1.25 thf(f8,conjecture,(
% 0.32/1.25 funcinfuncset => (lamp => ! [X3 : $i,X7 : $i > $i,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (in @ (lam @ X0 @ X3 @ (^[X1 : $i] : (X7 @ X1))) @ (funcSet @ X0 @ X3))))),
% 0.32/1.25 file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',lam2p)).
% 0.32/1.25 thf(f45,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)) | (lamp != $true)) )),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f39])).
% 0.32/1.25 thf(f39,plain,(
% 0.32/1.25 ((lamp = $true) | (($true != (func @ sK3 @ sK5 @ (lam @ sK3 @ sK5 @ (^[Y0 : $i]: (sK4 @ Y0))))) & ! [X3 : $i] : (($true = (in @ (sK4 @ X3) @ sK5)) | ((in @ X3 @ sK3) != $true)))) & (! [X4 : $i,X5 : $i > $i,X6 : $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | (($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4)))) | (lamp != $true))),
% 0.32/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f36,f38,f37])).
% 0.32/1.25 thf(f37,plain,(
% 0.32/1.25 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X2)) | ((in @ X3 @ X0) != $true))) => (($true != (func @ sK3 @ sK5 @ (lam @ sK3 @ sK5 @ (^[Y0 : $i]: (sK4 @ Y0))))) & ! [X3 : $i] : (($true = (in @ (sK4 @ X3) @ sK5)) | ((in @ X3 @ sK3) != $true)))),
% 0.32/1.25 introduced(definition,[],[choice_axiom])).
% 0.32/1.25 thf(f38,plain,(
% 0.32/1.25 ! [X4 : $i,X5 : $i > $i,X6 : $i] : (? [X7 : $i] : (((in @ (X5 @ X7) @ X6) != $true) & ($true = (in @ X7 @ X4))) => (($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6)) & ($true = (in @ (sK6 @ X6 @ X5 @ X4) @ X4))))),
% 0.32/1.25 introduced(definition,[],[choice_axiom])).
% 0.32/1.25 thf(f36,plain,(
% 0.32/1.25 ((lamp = $true) | ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X2)) | ((in @ X3 @ X0) != $true)))) & (! [X4 : $i,X5 : $i > $i,X6 : $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ? [X7 : $i] : (((in @ (X5 @ X7) @ X6) != $true) & ($true = (in @ X7 @ X4)))) | (lamp != $true))),
% 0.32/1.25 inference(rectify,[status(thm)],[f35])).
% 0.32/1.25 thf(f35,plain,(
% 0.32/1.25 ((lamp = $true) | ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true != (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) & ! [X3 : $i] : (($true = (in @ (X1 @ X3) @ X2)) | ((in @ X3 @ X0) != $true)))) & (! [X0 : $i,X1 : $i > $i,X2 : $i] : (($true = (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ? [X3 : $i] : (($true != (in @ (X1 @ X3) @ X2)) & ((in @ X3 @ X0) = $true))) | (lamp != $true))),
% 0.32/1.25 inference(nnf_transformation,[status(thm)],[f30])).
% 0.32/1.25 thf(f30,plain,(
% 0.32/1.25 (lamp = $true) <=> ! [X0 : $i,X1 : $i > $i,X2 : $i] : (($true = (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ? [X3 : $i] : (($true != (in @ (X1 @ X3) @ X2)) & ((in @ X3 @ X0) = $true)))),
% 0.32/1.25 inference(ennf_transformation,[status(thm)],[f24])).
% 0.32/1.25 thf(f24,plain,(
% 0.32/1.25 (lamp = $true) <=> ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) = $true) => ($true = (in @ (X1 @ X3) @ X2))) => ($true = (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))))),
% 0.32/1.25 inference(fool_elimination,[status(thm)],[f23])).
% 0.32/1.25 thf(f23,plain,(
% 0.32/1.25 (lamp = ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X1 @ X3) @ X2)) => (func @ X0 @ X2 @ (lam @ X0 @ X2 @ (^[X4 : $i] : (X1 @ X4))))))),
% 0.32/1.25 inference(rectify,[status(thm)],[f7])).
% 0.32/1.25 thf(f7,axiom,(
% 0.32/1.25 (lamp = ! [X0 : $i,X7 : $i > $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (in @ (X7 @ X1) @ X3)) => (func @ X0 @ X3 @ (lam @ X0 @ X3 @ (^[X1 : $i] : (X7 @ X1))))))),
% 0.32/1.25 file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',lamp)).
% 0.32/1.25 thf(f67,plain,(
% 0.32/1.25 ($true != (func @ sK9 @ sK7 @ (lam @ sK9 @ sK7 @ sK8)))),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 0.32/1.25 thf(f66,plain,(
% 0.32/1.25 ($true != (func @ sK9 @ sK7 @ (lam @ sK9 @ sK7 @ sK8))) | ($true != $true)),
% 0.32/1.25 inference(superposition,[status(thm)],[f62,f65])).
% 0.32/1.25 thf(f65,plain,(
% 0.32/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1))) )),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 0.32/1.25 thf(f53,plain,(
% 0.32/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (func @ X2 @ X0 @ X1)) | ($true != $true) | ($true = (in @ X1 @ (funcSet @ X2 @ X0)))) )),
% 0.32/1.25 inference(definition_unfolding,[status(thm)],[f44,f49])).
% 0.32/1.25 thf(f49,plain,(
% 0.32/1.25 (funcinfuncset = $true)),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f41])).
% 0.32/1.25 thf(f44,plain,(
% 0.32/1.25 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1)) | (funcinfuncset != $true)) )),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f34])).
% 0.32/1.25 thf(f34,plain,(
% 0.32/1.25 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1))) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | (($true != (in @ sK1 @ (funcSet @ sK2 @ sK0))) & ($true = (func @ sK2 @ sK0 @ sK1))))),
% 0.32/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f32,f33])).
% 0.32/1.25 thf(f33,plain,(
% 0.32/1.25 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) & ((func @ X5 @ X3 @ X4) = $true)) => (($true != (in @ sK1 @ (funcSet @ sK2 @ sK0))) & ($true = (func @ sK2 @ sK0 @ sK1)))),
% 0.32/1.25 introduced(definition,[],[choice_axiom])).
% 0.32/1.25 thf(f32,plain,(
% 0.32/1.25 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1))) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (funcSet @ X5 @ X3))) & ((func @ X5 @ X3 @ X4) = $true)))),
% 0.32/1.25 inference(rectify,[status(thm)],[f31])).
% 0.32/1.25 thf(f31,plain,(
% 0.32/1.25 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1))) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (funcSet @ X2 @ X0))) & ($true = (func @ X2 @ X0 @ X1))))),
% 0.32/1.25 inference(nnf_transformation,[status(thm)],[f29])).
% 0.32/1.25 thf(f29,plain,(
% 0.32/1.25 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (funcSet @ X2 @ X0))) | ($true != (func @ X2 @ X0 @ X1))) <=> (funcinfuncset = $true)),
% 0.32/1.25 inference(ennf_transformation,[status(thm)],[f12])).
% 0.32/1.25 thf(f12,plain,(
% 0.32/1.25 (funcinfuncset = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X0 @ X1)) => ($true = (in @ X1 @ (funcSet @ X2 @ X0))))),
% 0.32/1.25 inference(fool_elimination,[status(thm)],[f11])).
% 0.32/1.25 thf(f11,plain,(
% 0.32/1.25 (funcinfuncset = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => (in @ X1 @ (funcSet @ X2 @ X0))))),
% 0.32/1.25 inference(rectify,[status(thm)],[f5])).
% 0.32/1.25 thf(f5,axiom,(
% 0.32/1.25 (funcinfuncset = ! [X3 : $i,X7 : $i,X0 : $i] : ((func @ X0 @ X3 @ X7) => (in @ X7 @ (funcSet @ X0 @ X3))))),
% 0.32/1.25 file('/export/starexec/sandbox2/tmp/tmp.QeVQeU3n2D/DTF2THF_26743.p',funcinfuncset)).
% 0.32/1.25 thf(f62,plain,(
% 0.32/1.25 ($true != (in @ (lam @ sK9 @ sK7 @ sK8) @ (funcSet @ sK9 @ sK7)))),
% 0.32/1.25 inference(beta_eta_normalization,[status(thm)],[f52])).
% 0.32/1.25 thf(f52,plain,(
% 0.32/1.25 ($true != (in @ (lam @ sK9 @ sK7 @ (^[Y0 : $i]: (sK8 @ Y0))) @ (funcSet @ sK9 @ sK7)))),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f41])).
% 0.32/1.25 thf(f73,plain,(
% 0.32/1.25 ($true != (in @ (sK6 @ sK7 @ sK8 @ sK9) @ sK9))),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 0.32/1.25 thf(f72,plain,(
% 0.32/1.25 ($true != $true) | ($true != (in @ (sK6 @ sK7 @ sK8 @ sK9) @ sK9))),
% 0.32/1.25 inference(superposition,[status(thm)],[f71,f51])).
% 0.32/1.25 thf(f51,plain,(
% 0.32/1.25 ( ! [X3 : $i] : (($true = (in @ (sK8 @ X3) @ sK7)) | ($true != (in @ X3 @ sK9))) )),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f41])).
% 0.32/1.25 thf(f71,plain,(
% 0.32/1.25 ((in @ (sK8 @ (sK6 @ sK7 @ sK8 @ sK9)) @ sK7) != $true)),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 0.32/1.25 thf(f70,plain,(
% 0.32/1.25 ((in @ (sK8 @ (sK6 @ sK7 @ sK8 @ sK9)) @ sK7) != $true) | ($true != $true)),
% 0.32/1.25 inference(superposition,[status(thm)],[f67,f64])).
% 0.32/1.25 thf(f64,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ X5))) | ($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6))) )),
% 0.32/1.25 inference(beta_eta_normalization,[status(thm)],[f63])).
% 0.32/1.25 thf(f63,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6))) )),
% 0.32/1.25 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 0.32/1.25 thf(f58,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6)) | ($true != $true) | ($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) )),
% 0.32/1.25 inference(definition_unfolding,[status(thm)],[f46,f50])).
% 0.32/1.25 thf(f46,plain,(
% 0.32/1.25 ( ! [X6 : $i,X4 : $i,X5 : $i > $i] : (($true = (func @ X4 @ X6 @ (lam @ X4 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true != (in @ (X5 @ (sK6 @ X6 @ X5 @ X4)) @ X6)) | (lamp != $true)) )),
% 0.32/1.25 inference(cnf_transformation,[status(thm)],[f39])).
% 0.32/1.25 % SZS output end Proof for DTF2THF_26743
% 0.32/1.25 % (26845)------------------------------
% 0.32/1.25 % (26845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.25 % (26845)Termination reason: Refutation
% 0.32/1.25
% 0.32/1.25 % (26845)Memory used [KB]: 5500
% 0.32/1.25 % (26845)Time elapsed: 0.009 s
% 0.32/1.25 % (26845)Instructions burned: 7 (million)
% 0.32/1.25 % (26845)------------------------------
% 0.32/1.25 % (26845)------------------------------
% 0.32/1.25 % (26839)Success in time 0.024 s
%------------------------------------------------------------------------------