%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU673^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.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 09:36:07 AM UTC 2026
% Result : Theorem 0.33s 1.34s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 714 ( 189 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 818 ( 86 ~; 61 |; 52 &; 575 @)
% ( 6 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 16 con; 0-3 aty)
% Number of variables : 191 ( 46 ^; 105 !; 40 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_11,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_13,type,
breln: $i > $i > $i > $o ).
thf(func_def_14,type,
func: $i > $i > $i > $o ).
thf(func_def_38,type,
sK10: $i > $o ).
thf(func_def_42,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f87,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f86,f52]) ).
thf(f52,plain,
( ( in @ sK7 @ sK6 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( theprop = $true )
& ( dsetconstrEL = $true )
& ( ( func @ sK6 @ sK5 @ sK4 )
= $true )
& ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ sK5 ) )
& ( ( in @ sK7 @ sK6 )
= $true )
& ( funcImageSingleton = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f28,f37,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( ( ( func @ sK6 @ sK5 @ sK4 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ sK4 ) ) )
@ sK5 ) )
& ( $true
= ( in @ X3 @ sK6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ sK4 ) ) )
@ sK5 ) )
& ( $true
= ( in @ X3 @ sK6 ) ) )
=> ( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ sK5 ) )
& ( ( in @ sK7 @ sK6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( theprop = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
& ( funcImageSingleton = $true ) ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
& ( funcImageSingleton = $true )
& ( theprop = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( theprop = $true )
=> ( ( funcImageSingleton = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X0 ) ) )
@ X1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
@ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,negated_conjecture,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X8: $i,X5: $i,X0: $i] :
( ( func @ X0 @ X5 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X8 ) ) )
@ X5 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f8,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [X8: $i,X5: $i,X0: $i] :
( ( func @ X0 @ X5 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X8 ) ) )
@ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',apProp) ).
thf(f86,plain,
( ( in @ sK7 @ sK6 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( in @ sK7 @ sK6 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f84,f54]) ).
thf(f54,plain,
( ( func @ sK6 @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f84,plain,
! [X0: $i] :
( ( $true
!= ( func @ X0 @ sK5 @ sK4 ) )
| ( ( in @ sK7 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( func @ X0 @ sK5 @ sK4 ) )
| ( ( in @ sK7 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f82,f74]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
!= ( func @ X0 @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f50,f51]) ).
thf(f51,plain,
funcImageSingleton = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( funcImageSingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
| ( funcImageSingleton != $true ) )
& ( ( funcImageSingleton = $true )
| ( ( $true
= ( func @ sK0 @ sK2 @ sK1 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f32,f34,f33]) ).
thf(f33,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X4 @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X5 ) ) ) )
& ( ( in @ X7 @ X4 )
= $true ) ) )
=> ( ( $true
= ( func @ sK0 @ sK2 @ sK1 ) )
& ? [X7: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ sK1 ) ) ) )
& ( ( in @ X7 @ sK0 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X7: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ sK1 ) ) ) )
& ( ( in @ X7 @ sK0 )
= $true ) )
=> ( ( $true
!= ( singleton
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( in @ ( kpair @ sK3 @ Y0 ) @ sK1 ) ) ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
| ( funcImageSingleton != $true ) )
& ( ( funcImageSingleton = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X4 @ X6 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X7 @ Y0 ) @ X5 ) ) ) )
& ( ( in @ X7 @ X4 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
| ( funcImageSingleton != $true ) )
& ( ( funcImageSingleton = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X0 @ X2 @ X1 ) )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) ) )
<=> ( funcImageSingleton = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ X3 @ Y0 ) @ X1 ) ) ) ) ) )
<=> ( funcImageSingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) )
= funcImageSingleton ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X0: $i,X8: $i,X5: $i] :
( ( ( func @ X0 @ X5 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X8 ) ) ) ) )
= funcImageSingleton ),
file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',funcImageSingleton) ).
thf(f82,plain,
( $true
!= ( singleton
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true != $true )
| ( $true
!= ( singleton
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) ) ) ),
inference(superposition,[status(thm)],[f53,f78]) ).
thf(f78,plain,
! [X0: $i,X1: $i > $o] :
( ( ( in @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) @ X0 )
= $true )
| ( $true
!= ( singleton @ ( dsetconstr @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: $i,X1: $i > $o] :
( ( ( in @ ( setunion @ ( dsetconstr @ X0 @ X1 ) ) @ X0 )
= $true )
| ( $true
!= ( singleton @ ( dsetconstr @ X0 @ X1 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f76,f73]) ).
thf(f73,plain,
! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $true
!= ( singleton @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( singleton @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f57,f56]) ).
thf(f56,plain,
theprop = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f57,plain,
! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $true
!= ( singleton @ X1 ) )
| ( theprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( theprop = $true )
| ( ( ( in @ ( setunion @ sK8 ) @ sK8 )
!= $true )
& ( $true
= ( singleton @ sK8 ) ) ) )
& ( ! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $true
!= ( singleton @ X1 ) ) )
| ( theprop != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f40,f41]) ).
thf(f41,plain,
( ? [X0: $i] :
( ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) )
& ( $true
= ( singleton @ X0 ) ) )
=> ( ( ( in @ ( setunion @ sK8 ) @ sK8 )
!= $true )
& ( $true
= ( singleton @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) )
& ( $true
= ( singleton @ X0 ) ) ) )
& ( ! [X1: $i] :
( ( ( in @ ( setunion @ X1 ) @ X1 )
= $true )
| ( $true
!= ( singleton @ X1 ) ) )
| ( theprop != $true ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) )
& ( $true
= ( singleton @ X0 ) ) ) )
& ( ! [X0: $i] :
( ( $true
= ( in @ ( setunion @ X0 ) @ X0 ) )
| ( $true
!= ( singleton @ X0 ) ) )
| ( theprop != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( theprop = $true )
<=> ! [X0: $i] :
( ( $true
= ( in @ ( setunion @ X0 ) @ X0 ) )
| ( $true
!= ( singleton @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
=> ( $true
= ( in @ ( setunion @ X0 ) @ X0 ) ) )
<=> ( theprop = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X4: $i] :
( ( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) )
= theprop ),
file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',theprop) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ ( dsetconstr @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f62,f55]) ).
thf(f55,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( ( in @ sK9
@ ( dsetconstr @ sK11
@ ^ [Y0: $i] : ( sK10 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK9 @ sK11 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f44,f45]) ).
thf(f45,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
& ( $true
!= ( in @ X3 @ X5 ) ) )
=> ( ( ( in @ sK9
@ ( dsetconstr @ sK11
@ ^ [Y0: $i] : ( sK10 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK9 @ sK11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) )
& ( $true
!= ( in @ X3 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ( in @ X0 @ X2 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X2: $i,X1: $i > $o,X0: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',dsetconstrEL) ).
thf(f53,plain,
( $true
!= ( in
@ ( setunion
@ ( dsetconstr @ sK5
@ ^ [Y0: $i] : ( in @ ( kpair @ sK7 @ Y0 ) @ sK4 ) ) )
@ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU673^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:30:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU673^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Functions - Application
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! A:i.! B:i.! f:i.func A B f -> (! x:i.in x A -> in (setunion
% 0.20/0.46 % (dsetconstr B (^ y:i.in (kpair x y) f))) B))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC175l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 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
% 0.20/0.46 % Syntax : Number of formulae : 23 ( 7 unt; 15 typ; 7 def)
% 0.20/0.46 % Number of atoms : 37 ( 8 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 7 ( 4 avg)
% 0.20/0.46 % Number of connectives : 72 ( 0 ~; 0 |; 2 &; 60 @)
% 0.20/0.46 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 19 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 16 ( 15 usr; 4 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 28 ( 14 ^; 13 !; 1 ?; 28 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=224
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setunion_type,type,
% 0.20/0.46 setunion: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL_type,type,
% 0.20/0.46 dsetconstrEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL,definition,
% 0.20/0.46 ( dsetconstrEL
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset_type,type,
% 0.20/0.47 subset: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(kpair_type,type,
% 0.20/0.47 kpair: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(cartprod_type,type,
% 0.20/0.47 cartprod: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(singleton_type,type,
% 0.20/0.47 singleton: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(singleton,definition,
% 0.20/0.47 ( singleton
% 0.20/0.47 = ( ^ [A: $i] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( A
% 0.20/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ex1_type,type,
% 0.20/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ex1,definition,
% 0.20/0.47 ( ex1
% 0.20/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( singleton
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(theprop_type,type,
% 0.20/0.47 theprop: $o ).
% 0.20/0.47
% 0.20/0.47 thf(theprop,definition,
% 0.20/0.47 ( theprop
% 0.20/0.47 = ( ! [X: $i] :
% 0.20/0.47 ( ( singleton @ X )
% 0.20/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln_type,type,
% 0.20/0.47 breln: $i > $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln,definition,
% 0.20/0.47 ( breln
% 0.20/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(func_type,type,
% 0.20/0.47 func: $i > $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(func,definition,
% 0.20/0.47 ( func
% 0.20/0.47 = ( ^ [A: $i,B: $i,R: $i] :
% 0.20/0.47 ( ( breln @ A @ B @ R )
% 0.20/0.47 & ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ex1 @ B
% 0.20/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(funcImageSingleton_type,type,
% 0.20/0.47 funcImageSingleton: $o ).
% 0.20/0.47
% 0.20/0.47 thf(funcImageSingleton,definition,
% 0.20/0.47 ( funcImageSingleton
% 0.20/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.47 ( ( func @ A @ B @ Xf )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( singleton
% 0.20/0.47 @ ( dsetconstr @ B
% 0.20/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(apProp,conjecture,
% 0.20/0.47 ( dsetconstrEL
% 0.20/0.47 => ( theprop
% 0.20/0.47 => ( funcImageSingleton
% 0.20/0.47 => ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.47 ( ( func @ A @ B @ Xf )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in
% 0.20/0.47 @ ( setunion
% 0.20/0.47 @ ( dsetconstr @ B
% 0.20/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.20/0.47 @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.33/1.30 ---- Embedded in THF ---
% 0.33/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.30 %%% Generated on Tue Feb 24 12:30:42 EST 2026
% 0.33/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.30 %%% Logic specification used:
% 0.33/1.30 %%% thf(spec, logic, $$dhol).
% 0.33/1.30
% 0.33/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2DTF19262.p
% See solution above
% 0.33/1.30 ------------------------
% 0.33/1.31 ---- Cleaned THF ---
% 0.33/1.31 thf(in_type,type,
% 0.33/1.31 in: $i > $i > $o ).
% 0.33/1.31
% 0.33/1.31 thf(emptyset_type,type,
% 0.33/1.31 emptyset: $i ).
% 0.33/1.31
% 0.33/1.31 thf(setadjoin_type,type,
% 0.33/1.31 setadjoin: $i > $i > $i ).
% 0.33/1.31
% 0.33/1.31 thf(setunion_type,type,
% 0.33/1.31 setunion: $i > $i ).
% 0.33/1.31
% 0.33/1.31 thf(dsetconstr_type,type,
% 0.33/1.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.33/1.31
% 0.33/1.31 thf(dsetconstrEL_type,type,
% 0.33/1.31 dsetconstrEL: $o ).
% 0.33/1.31
% 0.33/1.31 thf(dsetconstrEL,definition,
% 0.33/1.31 ( dsetconstrEL
% 0.33/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.31 ( ( in @ Xx
% 0.33/1.31 @ ( dsetconstr @ A
% 0.33/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/1.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(subset_type,type,
% 0.33/1.31 subset: $i > $i > $o ).
% 0.33/1.31
% 0.33/1.31 thf(kpair_type,type,
% 0.33/1.31 kpair: $i > $i > $i ).
% 0.33/1.31
% 0.33/1.31 thf(cartprod_type,type,
% 0.33/1.31 cartprod: $i > $i > $i ).
% 0.33/1.31
% 0.33/1.31 thf(singleton_type,type,
% 0.33/1.31 singleton: $i > $o ).
% 0.33/1.31
% 0.33/1.31 thf(singleton,definition,
% 0.33/1.31 ( singleton
% 0.33/1.31 = ( ^ [A: $i] :
% 0.33/1.31 ? [Xx: $i] :
% 0.33/1.31 ( ( in @ Xx @ A )
% 0.33/1.31 & ( A
% 0.33/1.31 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(ex1_type,type,
% 0.33/1.31 ex1: $i > ( $i > $o ) > $o ).
% 0.33/1.31
% 0.33/1.31 thf(ex1,definition,
% 0.33/1.31 ( ex1
% 0.33/1.31 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.33/1.31 ( singleton
% 0.33/1.31 @ ( dsetconstr @ A
% 0.33/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(theprop_type,type,
% 0.33/1.31 theprop: $o ).
% 0.33/1.31
% 0.33/1.31 thf(theprop,definition,
% 0.33/1.31 ( theprop
% 0.33/1.31 = ( ! [X: $i] :
% 0.33/1.31 ( ( singleton @ X )
% 0.33/1.31 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(breln_type,type,
% 0.33/1.31 breln: $i > $i > $i > $o ).
% 0.33/1.31
% 0.33/1.31 thf(breln,definition,
% 0.33/1.31 ( breln
% 0.33/1.31 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(func_type,type,
% 0.33/1.31 func: $i > $i > $i > $o ).
% 0.33/1.31
% 0.33/1.31 thf(func,definition,
% 0.33/1.31 ( func
% 0.33/1.31 = ( ^ [A: $i,B: $i,R: $i] :
% 0.33/1.31 ( ( breln @ A @ B @ R )
% 0.33/1.31 & ! [Xx: $i] :
% 0.33/1.31 ( ( in @ Xx @ A )
% 0.33/1.31 => ( ex1 @ B
% 0.33/1.31 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(funcImageSingleton_type,type,
% 0.33/1.31 funcImageSingleton: $o ).
% 0.33/1.31
% 0.33/1.31 thf(funcImageSingleton,definition,
% 0.33/1.31 ( funcImageSingleton
% 0.33/1.31 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.31 ( ( func @ A @ B @ Xf )
% 0.33/1.31 => ! [Xx: $i] :
% 0.33/1.31 ( ( in @ Xx @ A )
% 0.33/1.31 => ( singleton
% 0.33/1.31 @ ( dsetconstr @ B
% 0.33/1.31 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.33/1.31
% 0.33/1.31 thf(apProp,conjecture,
% 0.33/1.31 ( dsetconstrEL
% 0.33/1.31 => ( theprop
% 0.33/1.31 => ( funcImageSingleton
% 0.33/1.31 => ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.31 ( ( func @ A @ B @ Xf )
% 0.33/1.31 => ! [Xx: $i] :
% 0.33/1.31 ( ( in @ Xx @ A )
% 0.33/1.31 => ( in
% 0.33/1.31 @ ( setunion
% 0.33/1.31 @ ( dsetconstr @ B
% 0.33/1.31 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.33/1.31 @ B ) ) ) ) ) ) ).
% 0.33/1.31 ------------------------
% 0.33/1.32 % (19592)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19262 for (2999ds/2Mi)
% 0.33/1.32 % (19590)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_19262 for (2999ds/4Mi)
% 0.33/1.32 % (19592)Instruction limit reached!
% 0.33/1.32 % (19592)------------------------------
% 0.33/1.32 % (19592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.32 % (19592)Termination reason: Unknown
% 0.33/1.32 % (19592)Termination phase: Preprocessing 3
% 0.33/1.32
% 0.33/1.32 % (19592)Memory used [KB]: 1023
% 0.33/1.32 % (19592)Time elapsed: 0.002 s
% 0.33/1.32 % (19592)Instructions burned: 3 (million)
% 0.33/1.32 % (19592)------------------------------
% 0.33/1.32 % (19592)------------------------------
% 0.33/1.33 % (19590)Instruction limit reached!
% 0.33/1.33 % (19590)------------------------------
% 0.33/1.33 % (19590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.33 % (19590)Termination reason: Unknown
% 0.33/1.33 % (19590)Termination phase: Saturation
% 0.33/1.33
% 0.33/1.33 % (19590)Memory used [KB]: 5500
% 0.33/1.33 % (19590)Time elapsed: 0.003 s
% 0.33/1.33 % (19590)Instructions burned: 6 (million)
% 0.33/1.33 % (19590)------------------------------
% 0.33/1.33 % (19590)------------------------------
% 0.33/1.33 % (19589)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19262 for (2999ds/183Mi)
% 0.33/1.33 % (19591)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_19262 for (2999ds/27Mi)
% 0.33/1.33 % (19593)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_19262 for (2999ds/2Mi)
% 0.33/1.33 % (19594)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_19262 for (2999ds/275Mi)
% 0.33/1.33 % (19595)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19262 for (2999ds/18Mi)
% 0.33/1.33 % (19593)Instruction limit reached!
% 0.33/1.33 % (19593)------------------------------
% 0.33/1.33 % (19593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.33 % (19593)Termination reason: Unknown
% 0.33/1.33 % (19593)Termination phase: shuffling
% 0.33/1.33
% 0.33/1.33 % (19593)Memory used [KB]: 1023
% 0.33/1.33 % (19593)Time elapsed: 0.003 s
% 0.33/1.33 % (19593)Instructions burned: 2 (million)
% 0.33/1.33 % (19593)------------------------------
% 0.33/1.33 % (19593)------------------------------
% 0.33/1.33 % (19596)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19262 for (2999ds/3Mi)
% 0.33/1.33 % (19596)Instruction limit reached!
% 0.33/1.33 % (19596)------------------------------
% 0.33/1.33 % (19596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.33 % (19596)Termination reason: Unknown
% 0.33/1.33 % (19596)Termination phase: Function definition elimination
% 0.33/1.33
% 0.33/1.33 % (19596)Memory used [KB]: 1023
% 0.33/1.33 % (19596)Time elapsed: 0.002 s
% 0.33/1.33 % (19596)Instructions burned: 4 (million)
% 0.33/1.33 % (19596)------------------------------
% 0.33/1.33 % (19596)------------------------------
% 0.33/1.34 % (19597)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_19262 for (2999ds/37Mi)
% 0.33/1.34 % (19594)First to succeed.
% 0.33/1.34 % (19594)Refutation found. Thanks to Tanya!
% 0.33/1.34 % SZS status Theorem for DTF2THF_19262
% 0.33/1.34 % SZS output start Proof for DTF2THF_19262
% 0.33/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 0.33/1.34 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.33/1.34 thf(func_def_3, type, setunion: $i > $i).
% 0.33/1.34 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.33/1.34 thf(func_def_7, type, subset: $i > $i > $o).
% 0.33/1.34 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.33/1.34 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.33/1.34 thf(func_def_10, type, singleton: $i > $o).
% 0.33/1.34 thf(func_def_11, type, ex1: $i > ($i > $o) > $o).
% 0.33/1.34 thf(func_def_13, type, breln: $i > $i > $i > $o).
% 0.33/1.34 thf(func_def_14, type, func: $i > $i > $i > $o).
% 0.33/1.34 thf(func_def_38, type, sK10: $i > $o).
% 0.33/1.34 thf(func_def_42, type, ph13: !>[X0: $tType]:(X0)).
% 0.33/1.34 thf(f87,plain,(
% 0.33/1.34 $false),
% 0.33/1.34 inference(subsumption_resolution,[status(thm)],[f86,f52])).
% 0.33/1.34 thf(f52,plain,(
% 0.33/1.34 ((in @ sK7 @ sK6) = $true)),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 thf(f38,plain,(
% 0.33/1.34 (theprop = $true) & (dsetconstrEL = $true) & (((func @ sK6 @ sK5 @ sK4) = $true) & (($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK4)))) @ sK5)) & ((in @ sK7 @ sK6) = $true))) & (funcImageSingleton = $true)),
% 0.33/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f28,f37,f36])).
% 0.33/1.34 thf(f36,plain,(
% 0.33/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X0)))) @ X1)) & ($true = (in @ X3 @ X2)))) => (((func @ sK6 @ sK5 @ sK4) = $true) & ? [X3 : $i] : (($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK4)))) @ sK5)) & ($true = (in @ X3 @ sK6))))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f37,plain,(
% 0.33/1.34 ? [X3 : $i] : (($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK4)))) @ sK5)) & ($true = (in @ X3 @ sK6))) => (($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK4)))) @ sK5)) & ((in @ sK7 @ sK6) = $true))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f28,plain,(
% 0.33/1.34 (theprop = $true) & (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X0)))) @ X1)) & ($true = (in @ X3 @ X2)))) & (funcImageSingleton = $true)),
% 0.33/1.34 inference(flattening,[status(thm)],[f27])).
% 0.33/1.34 thf(f27,plain,(
% 0.33/1.34 ((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) & ? [X3 : $i] : (($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X0)))) @ X1)) & ($true = (in @ X3 @ X2)))) & (funcImageSingleton = $true)) & (theprop = $true)) & (dsetconstrEL = $true)),
% 0.33/1.34 inference(ennf_transformation,[status(thm)],[f19])).
% 0.33/1.34 thf(f19,plain,(
% 0.33/1.34 ~((dsetconstrEL = $true) => ((theprop = $true) => ((funcImageSingleton = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X2 @ X1 @ X0)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ($true = (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X0)))) @ X1)))))))),
% 0.33/1.34 inference(fool_elimination,[status(thm)],[f18])).
% 0.33/1.34 thf(f18,plain,(
% 0.33/1.34 ~(dsetconstrEL => (theprop => (funcImageSingleton => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X0)))) @ X1))))))),
% 0.33/1.34 inference(rectify,[status(thm)],[f9])).
% 0.33/1.34 thf(f9,negated_conjecture,(
% 0.33/1.34 ~(dsetconstrEL => (theprop => (funcImageSingleton => ! [X8 : $i,X5 : $i,X0 : $i] : ((func @ X0 @ X5 @ X8) => ! [X2 : $i] : ((in @ X2 @ X0) => (in @ (setunion @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))) @ X5))))))),
% 0.33/1.34 inference(negated_conjecture,[status(cth)],[f8])).
% 0.33/1.34 thf(f8,conjecture,(
% 0.33/1.34 dsetconstrEL => (theprop => (funcImageSingleton => ! [X8 : $i,X5 : $i,X0 : $i] : ((func @ X0 @ X5 @ X8) => ! [X2 : $i] : ((in @ X2 @ X0) => (in @ (setunion @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))) @ X5)))))),
% 0.33/1.34 file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',apProp)).
% 0.33/1.34 thf(f86,plain,(
% 0.33/1.34 ((in @ sK7 @ sK6) != $true)),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 0.33/1.34 thf(f85,plain,(
% 0.33/1.34 ((in @ sK7 @ sK6) != $true) | ($true != $true)),
% 0.33/1.34 inference(superposition,[status(thm)],[f84,f54])).
% 0.33/1.34 thf(f54,plain,(
% 0.33/1.34 ((func @ sK6 @ sK5 @ sK4) = $true)),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 thf(f84,plain,(
% 0.33/1.34 ( ! [X0 : $i] : (($true != (func @ X0 @ sK5 @ sK4)) | ((in @ sK7 @ X0) != $true)) )),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 0.33/1.34 thf(f83,plain,(
% 0.33/1.34 ( ! [X0 : $i] : (($true != $true) | ($true != (func @ X0 @ sK5 @ sK4)) | ((in @ sK7 @ X0) != $true)) )),
% 0.33/1.34 inference(superposition,[status(thm)],[f82,f74])).
% 0.33/1.34 thf(f74,plain,(
% 0.33/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)) | ($true != (func @ X0 @ X2 @ X1))) )),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 0.33/1.34 thf(f63,plain,(
% 0.33/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ($true != (in @ X3 @ X0)) | ($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != $true)) )),
% 0.33/1.34 inference(definition_unfolding,[status(thm)],[f50,f51])).
% 0.33/1.34 thf(f51,plain,(
% 0.33/1.34 (funcImageSingleton = $true)),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 thf(f50,plain,(
% 0.33/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)) | (funcImageSingleton != $true)) )),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f35])).
% 0.33/1.34 thf(f35,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | (($true = (func @ sK0 @ sK2 @ sK1)) & (($true != (singleton @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1))))) & ((in @ sK3 @ sK0) = $true))))),
% 0.33/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f32,f34,f33])).
% 0.33/1.34 thf(f33,plain,(
% 0.33/1.34 ? [X4 : $i,X5 : $i,X6 : $i] : (((func @ X4 @ X6 @ X5) = $true) & ? [X7 : $i] : (($true != (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X5))))) & ((in @ X7 @ X4) = $true))) => (($true = (func @ sK0 @ sK2 @ sK1)) & ? [X7 : $i] : (($true != (singleton @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ sK1))))) & ((in @ X7 @ sK0) = $true)))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f34,plain,(
% 0.33/1.34 ? [X7 : $i] : (($true != (singleton @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ sK1))))) & ((in @ X7 @ sK0) = $true)) => (($true != (singleton @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1))))) & ((in @ sK3 @ sK0) = $true))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f32,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (((func @ X4 @ X6 @ X5) = $true) & ? [X7 : $i] : (($true != (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X5))))) & ((in @ X7 @ X4) = $true))))),
% 0.33/1.34 inference(rectify,[status(thm)],[f31])).
% 0.33/1.34 thf(f31,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) & ($true = (in @ X3 @ X0)))))),
% 0.33/1.34 inference(nnf_transformation,[status(thm)],[f29])).
% 0.33/1.34 thf(f29,plain,(
% 0.33/1.34 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X2 @ X1)) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))) | ($true != (in @ X3 @ X0)))) <=> (funcImageSingleton = $true)),
% 0.33/1.34 inference(ennf_transformation,[status(thm)],[f15])).
% 0.33/1.34 thf(f15,plain,(
% 0.33/1.34 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1))))))) <=> (funcImageSingleton = $true)),
% 0.33/1.34 inference(fool_elimination,[status(thm)],[f14])).
% 0.33/1.34 thf(f14,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1)))))) = funcImageSingleton)),
% 0.33/1.34 inference(rectify,[status(thm)],[f7])).
% 0.33/1.34 thf(f7,axiom,(
% 0.33/1.34 (! [X0 : $i,X8 : $i,X5 : $i] : ((func @ X0 @ X5 @ X8) => ! [X2 : $i] : ((in @ X2 @ X0) => (singleton @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))))) = funcImageSingleton)),
% 0.33/1.34 file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',funcImageSingleton)).
% 0.33/1.34 thf(f82,plain,(
% 0.33/1.34 ($true != (singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK4)))))),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.33/1.34 thf(f81,plain,(
% 0.33/1.34 ($true != $true) | ($true != (singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK4)))))),
% 0.33/1.34 inference(superposition,[status(thm)],[f53,f78])).
% 0.33/1.34 thf(f78,plain,(
% 0.33/1.34 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (setunion @ (dsetconstr @ X0 @ X1)) @ X0) = $true) | ($true != (singleton @ (dsetconstr @ X0 @ X1)))) )),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 0.33/1.34 thf(f77,plain,(
% 0.33/1.34 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (setunion @ (dsetconstr @ X0 @ X1)) @ X0) = $true) | ($true != (singleton @ (dsetconstr @ X0 @ X1))) | ($true != $true)) )),
% 0.33/1.34 inference(superposition,[status(thm)],[f76,f73])).
% 0.33/1.34 thf(f73,plain,(
% 0.33/1.34 ( ! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != (singleton @ X1))) )),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 0.33/1.34 thf(f69,plain,(
% 0.33/1.34 ( ! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != $true) | ($true != (singleton @ X1))) )),
% 0.33/1.34 inference(definition_unfolding,[status(thm)],[f57,f56])).
% 0.33/1.34 thf(f56,plain,(
% 0.33/1.34 (theprop = $true)),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 thf(f57,plain,(
% 0.33/1.34 ( ! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != (singleton @ X1)) | (theprop != $true)) )),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 0.33/1.34 thf(f42,plain,(
% 0.33/1.34 ((theprop = $true) | (((in @ (setunion @ sK8) @ sK8) != $true) & ($true = (singleton @ sK8)))) & (! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != (singleton @ X1))) | (theprop != $true))),
% 0.33/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f40,f41])).
% 0.33/1.34 thf(f41,plain,(
% 0.33/1.34 ? [X0 : $i] : (($true != (in @ (setunion @ X0) @ X0)) & ($true = (singleton @ X0))) => (((in @ (setunion @ sK8) @ sK8) != $true) & ($true = (singleton @ sK8)))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f40,plain,(
% 0.33/1.34 ((theprop = $true) | ? [X0 : $i] : (($true != (in @ (setunion @ X0) @ X0)) & ($true = (singleton @ X0)))) & (! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != (singleton @ X1))) | (theprop != $true))),
% 0.33/1.34 inference(rectify,[status(thm)],[f39])).
% 0.33/1.34 thf(f39,plain,(
% 0.33/1.34 ((theprop = $true) | ? [X0 : $i] : (($true != (in @ (setunion @ X0) @ X0)) & ($true = (singleton @ X0)))) & (! [X0 : $i] : (($true = (in @ (setunion @ X0) @ X0)) | ($true != (singleton @ X0))) | (theprop != $true))),
% 0.33/1.34 inference(nnf_transformation,[status(thm)],[f30])).
% 0.33/1.34 thf(f30,plain,(
% 0.33/1.34 (theprop = $true) <=> ! [X0 : $i] : (($true = (in @ (setunion @ X0) @ X0)) | ($true != (singleton @ X0)))),
% 0.33/1.34 inference(ennf_transformation,[status(thm)],[f17])).
% 0.33/1.34 thf(f17,plain,(
% 0.33/1.34 ! [X0 : $i] : (($true = (singleton @ X0)) => ($true = (in @ (setunion @ X0) @ X0))) <=> (theprop = $true)),
% 0.33/1.34 inference(fool_elimination,[status(thm)],[f16])).
% 0.33/1.34 thf(f16,plain,(
% 0.33/1.34 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 0.33/1.34 inference(rectify,[status(thm)],[f4])).
% 0.33/1.34 thf(f4,axiom,(
% 0.33/1.34 (! [X4 : $i] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)) = theprop)),
% 0.33/1.34 file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',theprop)).
% 0.33/1.34 thf(f76,plain,(
% 0.33/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ X1)) != $true) | ((in @ X0 @ X2) = $true)) )),
% 0.33/1.34 inference(beta_eta_normalization,[status(thm)],[f75])).
% 0.33/1.34 thf(f75,plain,(
% 0.33/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true)) )),
% 0.33/1.34 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 0.33/1.34 thf(f70,plain,(
% 0.33/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ($true != $true)) )),
% 0.33/1.34 inference(definition_unfolding,[status(thm)],[f62,f55])).
% 0.33/1.34 thf(f55,plain,(
% 0.33/1.34 (dsetconstrEL = $true)),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 thf(f62,plain,(
% 0.33/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true) | (dsetconstrEL != $true)) )),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f46])).
% 0.33/1.34 thf(f46,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK9 @ (dsetconstr @ sK11 @ (^[Y0 : $i]: (sK10 @ Y0)))) = $true) & ($true != (in @ sK9 @ sK11))))),
% 0.33/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f44,f45])).
% 0.33/1.34 thf(f45,plain,(
% 0.33/1.34 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0))))) & ($true != (in @ X3 @ X5))) => (((in @ sK9 @ (dsetconstr @ sK11 @ (^[Y0 : $i]: (sK10 @ Y0)))) = $true) & ($true != (in @ sK9 @ sK11)))),
% 0.33/1.34 introduced(definition,[],[choice_axiom])).
% 0.33/1.34 thf(f44,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0))))) & ($true != (in @ X3 @ X5))))),
% 0.33/1.34 inference(rectify,[status(thm)],[f43])).
% 0.33/1.34 thf(f43,plain,(
% 0.33/1.34 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) & ((in @ X0 @ X2) != $true)))),
% 0.33/1.34 inference(nnf_transformation,[status(thm)],[f26])).
% 0.33/1.34 thf(f26,plain,(
% 0.33/1.34 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) | ((in @ X0 @ X2) = $true)) <=> (dsetconstrEL = $true)),
% 0.33/1.34 inference(ennf_transformation,[status(thm)],[f13])).
% 0.33/1.34 thf(f13,plain,(
% 0.33/1.34 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) => ((in @ X0 @ X2) = $true)) <=> (dsetconstrEL = $true)),
% 0.33/1.34 inference(fool_elimination,[status(thm)],[f12])).
% 0.33/1.34 thf(f12,plain,(
% 0.33/1.34 (dsetconstrEL = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)))),
% 0.33/1.34 inference(rectify,[status(thm)],[f1])).
% 0.33/1.34 thf(f1,axiom,(
% 0.33/1.34 (dsetconstrEL = ! [X2 : $i,X1 : $i > $o,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 0.33/1.34 file('/export/starexec/sandbox/tmp/tmp.m1uC4Wq2WY/DTF2THF_19262.p',dsetconstrEL)).
% 0.33/1.34 thf(f53,plain,(
% 0.33/1.34 ($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK4)))) @ sK5))),
% 0.33/1.34 inference(cnf_transformation,[status(thm)],[f38])).
% 0.33/1.34 % SZS output end Proof for DTF2THF_19262
% 0.33/1.34 % (19594)------------------------------
% 0.33/1.34 % (19594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.34 % (19594)Termination reason: Refutation
% 0.33/1.34
% 0.33/1.34 % (19594)Memory used [KB]: 5500
% 0.33/1.34 % (19594)Time elapsed: 0.010 s
% 0.33/1.34 % (19594)Instructions burned: 7 (million)
% 0.33/1.34 % (19594)------------------------------
% 0.33/1.34 % (19594)------------------------------
% 0.33/1.34 % (19588)Success in time 0.026 s
%------------------------------------------------------------------------------