%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU713^2 : 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 : n020.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 09:36:36 AM UTC 2026
% Result : Theorem 1.55s 1.28s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 538 ( 123 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 769 ( 12 ~; 28 |; 21 &; 585 @)
% ( 0 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 9 con; 0-2 aty)
% ( 46 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 165 ( 55 ^; 99 !; 11 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_5,type,
setminus: $i > $i > $i ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_20,type,
sK4: $i > $i > $i ).
thf(f175,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
$false = $true,
inference(superposition,[status(thm)],[f144,f103]) ).
thf(f103,plain,
( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( $false
= ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f26,f87]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $false
= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f46,f61]) ).
thf(f61,plain,
! [X0: $i] :
( $true
= ( in @ X0 @ ( powerset @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f54,f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK4 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK4 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK4 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK4 @ X1 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( in @ X1 @ ( powerset @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( in @ X1 @ ( powerset @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f28,f20]) ).
thf(f20,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',powersetI) ).
thf(f28,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( powersetI = $true )
& ( setminusEL = $true )
& ( ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK1 ) )
!= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) )
& ( powersetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ sK0 @ X2 ) @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) ) )
& ( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ sK0 @ X2 ) @ ( powerset @ sK1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) ) )
=> ( ( ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK1 ) )
!= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( powersetI = $true )
& ( setminusEL = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X1 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( powersetI = $true )
=> ( ( powersetE = $true )
=> ( ( setminusEL = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( $true
= ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X3 @ X4 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X3 @ X4 ) @ ( powerset @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',setminusT_lem) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK4 @ X1 @ X2 ) @ X2 )
= $false )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ X3 ) )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( in @ X2 @ Y0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f21]) ).
thf(f21,plain,
( powersetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( powersetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( powersetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( powerset @ X2 ) )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( powersetE
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',powersetE) ).
thf(f23,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f26,plain,
( ( in @ ( setminus @ sK0 @ sK2 ) @ ( powerset @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f144,plain,
! [X0: $i] :
( $true
= ( in @ ( setminus @ sK0 @ X0 ) @ ( powerset @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( in @ ( setminus @ sK0 @ X0 ) @ ( powerset @ sK1 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f133]) ).
thf(f133,plain,
! [X0: $i] :
( ( $true
= ( in @ ( setminus @ sK0 @ X0 ) @ ( powerset @ sK1 ) ) )
| ( $false = $true )
| ( $true
= ( in @ ( setminus @ sK0 @ X0 ) @ ( powerset @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f62,f91]) ).
thf(f91,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK4 @ X0 @ sK1 ) @ sK0 ) )
| ( ( in @ X0 @ ( powerset @ sK1 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK1 ) )
= $true )
| ( $false = $true )
| ( $false
= ( in @ ( sK4 @ X0 @ sK1 ) @ sK0 ) ) ),
inference(superposition,[status(thm)],[f54,f76]) ).
thf(f76,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f24,f46]) ).
thf(f24,plain,
( $true
= ( in @ sK0 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK4 @ ( setminus @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ ( sK4 @ ( setminus @ X0 @ X1 ) @ X2 ) @ X0 )
= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f55,f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setminus @ X1 @ X2 ) )
=> ( in @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setminus @ X1 @ Y0 ) )
=> ( in @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f27,f22]) ).
thf(f22,plain,
( setminusEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( setminusEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setminus @ Y0 @ Y1 ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ( in @ X0 @ X2 ) )
= setminusEL ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) )
= setminusEL ),
file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',setminusEL) ).
thf(f27,plain,
setminusEL = $true,
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU713^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:36:42 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.45 ---- Original DTF file ---
% 0.21/0.45 thf(spec,logic,$$dhol).
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 % File : SEU713^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.45 % Domain : Set Theory
% 0.21/0.45 % Problem : Typed Set Theory - Types of Set Operators
% 0.21/0.45 % Version : Especial > Reduced > Especial.
% 0.21/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.45 % in (setminus X Y) (powerset A)))
% 0.21/0.45
% 0.21/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.45 % Source : [Bro08]
% 0.21/0.45 % Names : ZFC215l [Bro08]
% 0.21/0.45 % : ZFC212l [Bro08]
% 0.21/0.45
% 0.21/0.45 % Status : Theorem
% 0.21/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.21/0.45 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.21/0.45 % Number of atoms : 20 ( 3 equ; 0 cnn)
% 0.21/0.45 % Maximal formula atoms : 6 ( 5 avg)
% 0.21/0.45 % Number of connectives : 41 ( 0 ~; 0 |; 0 &; 31 @)
% 0.21/0.45 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.45 % Maximal formula depth : 13 ( 4 avg)
% 0.21/0.45 % Number of types : 2 ( 0 usr)
% 0.21/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.21/0.45 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.21/0.45 % Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 0.21/0.45 % SPC : TH0_THM_EQU_NAR
% 0.21/0.45
% 0.21/0.45 % Comments : http://mathgate.info/detsetitem.php?id=271
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 thf(in_type,type,
% 0.21/0.45 in: $i > $i > $o ).
% 0.21/0.45
% 0.21/0.45 thf(powerset_type,type,
% 0.21/0.45 powerset: $i > $i ).
% 0.21/0.45
% 0.21/0.45 thf(powersetI_type,type,
% 0.21/0.45 powersetI: $o ).
% 0.21/0.45
% 0.21/0.45 thf(powersetI,definition,
% 0.21/0.45 ( powersetI
% 0.21/0.45 = ( ! [A: $i,B: $i] :
% 0.21/0.45 ( ! [Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ B )
% 0.21/0.45 => ( in @ Xx @ A ) )
% 0.21/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(powersetE_type,type,
% 0.21/0.45 powersetE: $o ).
% 0.21/0.45
% 0.21/0.45 thf(powersetE,definition,
% 0.21/0.45 ( powersetE
% 0.21/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.45 => ( ( in @ Xx @ B )
% 0.21/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(setminus_type,type,
% 0.21/0.45 setminus: $i > $i > $i ).
% 0.21/0.45
% 0.21/0.45 thf(setminusEL_type,type,
% 0.21/0.45 setminusEL: $o ).
% 0.21/0.45
% 0.21/0.45 thf(setminusEL,definition,
% 0.21/0.45 ( setminusEL
% 0.21/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.21/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 thf(setminusT_lem,conjecture,
% 0.21/0.45 ( powersetI
% 0.21/0.45 => ( powersetE
% 0.21/0.45 => ( setminusEL
% 0.21/0.45 => ! [A: $i,X: $i] :
% 0.21/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.21/0.45 => ! [Y: $i] :
% 0.21/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.21/0.45 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ).
% 0.21/0.45
% 0.21/0.45 %------------------------------------------------------------------------------
% 0.21/0.45 ------------------------
% 1.55/1.24 ---- Embedded in THF ---
% 1.55/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.24 %%% Generated on Tue Feb 24 12:36:43 EST 2026
% 1.55/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.24 %%% Logic specification used:
% 1.55/1.24 %%% thf(spec, logic, $$dhol).
% 1.55/1.24
% 1.55/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2DTF26584.p
% See solution above
% 1.55/1.24 ------------------------
% 1.55/1.25 ---- Cleaned THF ---
% 1.55/1.25 thf(in_type,type,
% 1.55/1.25 in: $i > $i > $o ).
% 1.55/1.25
% 1.55/1.25 thf(powerset_type,type,
% 1.55/1.25 powerset: $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(powersetI_type,type,
% 1.55/1.25 powersetI: $o ).
% 1.55/1.25
% 1.55/1.25 thf(powersetI,definition,
% 1.55/1.25 ( powersetI
% 1.55/1.25 = ( ! [A: $i,B: $i] :
% 1.55/1.25 ( ! [Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ B )
% 1.55/1.25 => ( in @ Xx @ A ) )
% 1.55/1.25 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(powersetE_type,type,
% 1.55/1.25 powersetE: $o ).
% 1.55/1.25
% 1.55/1.25 thf(powersetE,definition,
% 1.55/1.25 ( powersetE
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( in @ B @ ( powerset @ A ) )
% 1.55/1.25 => ( ( in @ Xx @ B )
% 1.55/1.25 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(setminus_type,type,
% 1.55/1.25 setminus: $i > $i > $i ).
% 1.55/1.25
% 1.55/1.25 thf(setminusEL_type,type,
% 1.55/1.25 setminusEL: $o ).
% 1.55/1.25
% 1.55/1.25 thf(setminusEL,definition,
% 1.55/1.25 ( setminusEL
% 1.55/1.25 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.55/1.25 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.55/1.25 => ( in @ Xx @ A ) ) ) ) ).
% 1.55/1.25
% 1.55/1.25 thf(setminusT_lem,conjecture,
% 1.55/1.25 ( powersetI
% 1.55/1.25 => ( powersetE
% 1.55/1.25 => ( setminusEL
% 1.55/1.25 => ! [A: $i,X: $i] :
% 1.55/1.25 ( ( in @ X @ ( powerset @ A ) )
% 1.55/1.25 => ! [Y: $i] :
% 1.55/1.25 ( ( in @ Y @ ( powerset @ A ) )
% 1.55/1.25 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ).
% 1.55/1.25 ------------------------
% 1.55/1.27 % (26727)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_26584 for (2999ds/27Mi)
% 1.55/1.27 % (26728)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26584 for (2999ds/2Mi)
% 1.55/1.27 % (26728)Instruction limit reached!
% 1.55/1.27 % (26728)------------------------------
% 1.55/1.27 % (26728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (26726)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_26584 for (2999ds/4Mi)
% 1.55/1.27 % (26728)Termination reason: Unknown
% 1.55/1.27 % (26728)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.27 % (26728)Memory used [KB]: 5500
% 1.55/1.27 % (26728)Time elapsed: 0.002 s
% 1.55/1.27 % (26728)Instructions burned: 3 (million)
% 1.55/1.27 % (26728)------------------------------
% 1.55/1.27 % (26728)------------------------------
% 1.55/1.27 % (26726)Instruction limit reached!
% 1.55/1.27 % (26726)------------------------------
% 1.55/1.27 % (26726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (26726)Termination reason: Unknown
% 1.55/1.27 % (26726)Termination phase: Saturation
% 1.55/1.27
% 1.55/1.27 % (26726)Memory used [KB]: 5500
% 1.55/1.27 % (26726)Time elapsed: 0.003 s
% 1.55/1.27 % (26726)Instructions burned: 5 (million)
% 1.55/1.27 % (26726)------------------------------
% 1.55/1.27 % (26726)------------------------------
% 1.55/1.27 % (26725)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26584 for (2999ds/183Mi)
% 1.55/1.27 % (26727)First to succeed.
% 1.55/1.27 % (26729)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_26584 for (2999ds/2Mi)
% 1.55/1.28 % (26729)Instruction limit reached!
% 1.55/1.28 % (26729)------------------------------
% 1.55/1.28 % (26729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (26729)Termination reason: Unknown
% 1.55/1.28 % (26729)Termination phase: Property scanning
% 1.55/1.28
% 1.55/1.28 % (26729)Memory used [KB]: 895
% 1.55/1.28 % (26729)Time elapsed: 0.003 s
% 1.55/1.28 % (26729)Instructions burned: 3 (million)
% 1.55/1.28 % (26729)------------------------------
% 1.55/1.28 % (26729)------------------------------
% 1.55/1.28 % (26727)Refutation found. Thanks to Tanya!
% 1.55/1.28 % SZS status Theorem for DTF2THF_26584
% 1.55/1.28 % SZS output start Proof for DTF2THF_26584
% 1.55/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.28 thf(func_def_1, type, powerset: $i > $i).
% 1.55/1.28 thf(func_def_5, type, setminus: $i > $i > $i).
% 1.55/1.28 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.55/1.28 thf(func_def_20, type, sK4: $i > $i > $i).
% 1.55/1.28 thf(f175,plain,(
% 1.55/1.28 $false),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.55/1.28 thf(f171,plain,(
% 1.55/1.28 ($false = $true)),
% 1.55/1.28 inference(superposition,[status(thm)],[f144,f103])).
% 1.55/1.28 thf(f103,plain,(
% 1.55/1.28 ($false = (in @ (setminus @ sK0 @ sK2) @ (powerset @ sK1)))),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.55/1.28 thf(f97,plain,(
% 1.55/1.28 ($true != $true) | ($false = (in @ (setminus @ sK0 @ sK2) @ (powerset @ sK1)))),
% 1.55/1.28 inference(superposition,[status(thm)],[f26,f87])).
% 1.55/1.28 thf(f87,plain,(
% 1.55/1.28 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) | ($false = (in @ X1 @ X0))) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.55/1.28 thf(f86,plain,(
% 1.55/1.28 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (in @ X1 @ X0)) | ($true = (in @ X1 @ X0))) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f46,f61])).
% 1.55/1.28 thf(f61,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($true = (in @ X0 @ (powerset @ X0)))) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.55/1.28 thf(f60,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($false = $true) | ($true = (in @ X0 @ (powerset @ X0)))) )),
% 1.55/1.28 inference(duplicate_literal_removal,[status(thm)],[f59])).
% 1.55/1.28 thf(f59,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($true = (in @ X0 @ (powerset @ X0))) | ($true = (in @ X0 @ (powerset @ X0))) | ($false = $true)) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f54,f55])).
% 1.55/1.28 thf(f55,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK4 @ X1 @ X2) @ X1)) | ($true = (in @ X1 @ (powerset @ X2)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.55/1.28 thf(f53,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X2))) | ($false = ((in @ (sK4 @ X1 @ X2) @ X1) => (in @ (sK4 @ X1 @ X2) @ X2)))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.55/1.28 thf(f52,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK4 @ X1 @ X2)))) )),
% 1.55/1.28 inference(sigma_clausification,[status(thm)],[f51])).
% 1.55/1.28 thf(f51,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))) | ($true = (in @ X1 @ (powerset @ X2)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.55/1.28 thf(f50,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (in @ X1 @ (powerset @ X2))) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.55/1.28 thf(f49,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (in @ X1 @ (powerset @ Y0)))) @ X2))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f48])).
% 1.55/1.28 thf(f48,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (in @ X1 @ (powerset @ Y0))))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.55/1.28 thf(f47,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))) @ X1))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f29])).
% 1.55/1.28 thf(f29,plain,(
% 1.55/1.28 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))),
% 1.55/1.28 inference(definition_unfolding,[status(thm)],[f28,f20])).
% 1.55/1.28 thf(f20,plain,(
% 1.55/1.28 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.28 thf(f8,plain,(
% 1.55/1.28 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.55/1.28 thf(f7,plain,(
% 1.55/1.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.55/1.28 inference(rectify,[status(thm)],[f1])).
% 1.55/1.28 thf(f1,axiom,(
% 1.55/1.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.55/1.28 file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',powersetI)).
% 1.55/1.28 thf(f28,plain,(
% 1.55/1.28 (powersetI = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.55/1.28 thf(f19,plain,(
% 1.55/1.28 (powersetI = $true) & (setminusEL = $true) & ((((in @ (setminus @ sK0 @ sK2) @ (powerset @ sK1)) != $true) & ($true = (in @ sK2 @ (powerset @ sK1)))) & ($true = (in @ sK0 @ (powerset @ sK1)))) & (powersetE = $true)),
% 1.55/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f18,f17])).
% 1.55/1.28 thf(f17,plain,(
% 1.55/1.28 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true != (in @ (setminus @ X0 @ X2) @ (powerset @ X1))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (($true != (in @ (setminus @ sK0 @ X2) @ (powerset @ sK1))) & ($true = (in @ X2 @ (powerset @ sK1)))) & ($true = (in @ sK0 @ (powerset @ sK1))))),
% 1.55/1.28 introduced(definition,[],[choice_axiom])).
% 1.55/1.28 thf(f18,plain,(
% 1.55/1.28 ? [X2 : $i] : (($true != (in @ (setminus @ sK0 @ X2) @ (powerset @ sK1))) & ($true = (in @ X2 @ (powerset @ sK1)))) => (((in @ (setminus @ sK0 @ sK2) @ (powerset @ sK1)) != $true) & ($true = (in @ sK2 @ (powerset @ sK1))))),
% 1.55/1.28 introduced(definition,[],[choice_axiom])).
% 1.55/1.28 thf(f16,plain,(
% 1.55/1.28 (powersetI = $true) & (setminusEL = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true != (in @ (setminus @ X0 @ X2) @ (powerset @ X1))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (powersetE = $true)),
% 1.55/1.28 inference(flattening,[status(thm)],[f15])).
% 1.55/1.28 thf(f15,plain,(
% 1.55/1.28 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true != (in @ (setminus @ X0 @ X2) @ (powerset @ X1))) & ($true = (in @ X2 @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (setminusEL = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 1.55/1.28 inference(ennf_transformation,[status(thm)],[f10])).
% 1.55/1.28 thf(f10,plain,(
% 1.55/1.28 ~((powersetI = $true) => ((powersetE = $true) => ((setminusEL = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ($true = (in @ (setminus @ X0 @ X2) @ (powerset @ X1))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.55/1.28 thf(f9,plain,(
% 1.55/1.28 ~(powersetI => (powersetE => (setminusEL => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X0 @ X2) @ (powerset @ X1)))))))),
% 1.55/1.28 inference(rectify,[status(thm)],[f5])).
% 1.55/1.28 thf(f5,negated_conjecture,(
% 1.55/1.28 ~(powersetI => (powersetE => (setminusEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (in @ (setminus @ X3 @ X4) @ (powerset @ X0)))))))),
% 1.55/1.28 inference(negated_conjecture,[status(cth)],[f4])).
% 1.55/1.28 thf(f4,conjecture,(
% 1.55/1.28 powersetI => (powersetE => (setminusEL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (in @ (setminus @ X3 @ X4) @ (powerset @ X0))))))),
% 1.55/1.28 file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',setminusT_lem)).
% 1.55/1.28 thf(f54,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (((in @ (sK4 @ X1 @ X2) @ X2) = $false) | ($true = (in @ X1 @ (powerset @ X2)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.55/1.28 thf(f46,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (powerset @ X1))) | ($false = (in @ X2 @ X3)) | ((in @ X2 @ X1) = $true)) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.55/1.28 thf(f45,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => (in @ X2 @ X1))) | ($false = (in @ X3 @ (powerset @ X1)))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.55/1.28 thf(f44,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (powerset @ X1)) => ((in @ X2 @ X3) => (in @ X2 @ X1))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.55/1.28 thf(f43,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((in @ X2 @ Y0) => (in @ X2 @ X1)))) @ X3))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f42])).
% 1.55/1.28 thf(f42,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => ((in @ X2 @ Y0) => (in @ X2 @ X1))))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.55/1.28 thf(f41,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((in @ Y0 @ Y1) => (in @ Y0 @ X1)))))) @ X2))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f40])).
% 1.55/1.28 thf(f40,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => ((in @ Y0 @ Y1) => (in @ Y0 @ X1))))))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.55/1.28 thf(f39,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0)))))))) @ X1))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f31])).
% 1.55/1.28 thf(f31,plain,(
% 1.55/1.28 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.55/1.28 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.55/1.28 thf(f21,plain,(
% 1.55/1.28 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.55/1.28 thf(f14,plain,(
% 1.55/1.28 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f13])).
% 1.55/1.28 thf(f13,plain,(
% 1.55/1.28 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X2)) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 1.55/1.28 inference(rectify,[status(thm)],[f2])).
% 1.55/1.28 thf(f2,axiom,(
% 1.55/1.28 (powersetE = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 1.55/1.28 file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',powersetE)).
% 1.55/1.28 thf(f23,plain,(
% 1.55/1.28 (powersetE = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.55/1.28 thf(f26,plain,(
% 1.55/1.28 ((in @ (setminus @ sK0 @ sK2) @ (powerset @ sK1)) != $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.55/1.28 thf(f144,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($true = (in @ (setminus @ sK0 @ X0) @ (powerset @ sK1)))) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.55/1.28 thf(f143,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($false = $true) | ($true = (in @ (setminus @ sK0 @ X0) @ (powerset @ sK1)))) )),
% 1.55/1.28 inference(duplicate_literal_removal,[status(thm)],[f133])).
% 1.55/1.28 thf(f133,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($true = (in @ (setminus @ sK0 @ X0) @ (powerset @ sK1))) | ($false = $true) | ($true = (in @ (setminus @ sK0 @ X0) @ (powerset @ sK1)))) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f62,f91])).
% 1.55/1.28 thf(f91,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($false = (in @ (sK4 @ X0 @ sK1) @ sK0)) | ((in @ X0 @ (powerset @ sK1)) = $true)) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.55/1.28 thf(f90,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK1)) = $true) | ($false = $true) | ($false = (in @ (sK4 @ X0 @ sK1) @ sK0))) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f54,f76])).
% 1.55/1.28 thf(f76,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($true = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK0))) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.55/1.28 thf(f69,plain,(
% 1.55/1.28 ( ! [X0 : $i] : (($false = $true) | ($true = (in @ X0 @ sK1)) | ($false = (in @ X0 @ sK0))) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f24,f46])).
% 1.55/1.28 thf(f24,plain,(
% 1.55/1.28 ($true = (in @ sK0 @ (powerset @ sK1)))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.55/1.28 thf(f62,plain,(
% 1.55/1.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK4 @ (setminus @ X0 @ X1) @ X2) @ X0) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X2)) = $true)) )),
% 1.55/1.28 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.55/1.28 thf(f56,plain,(
% 1.55/1.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ((in @ (sK4 @ (setminus @ X0 @ X1) @ X2) @ X0) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X2)) = $true)) )),
% 1.55/1.28 inference(superposition,[status(thm)],[f55,f38])).
% 1.55/1.28 thf(f38,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (setminus @ X1 @ X2))) | ($true = (in @ X3 @ X1))) )),
% 1.55/1.28 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.55/1.28 thf(f37,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (setminus @ X1 @ X2)) => (in @ X3 @ X1)) = $true)) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.55/1.28 thf(f36,plain,(
% 1.55/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (in @ Y0 @ X1))) @ X3))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f35])).
% 1.55/1.28 thf(f35,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setminus @ X1 @ X2)) => (in @ Y0 @ X1)))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.55/1.28 thf(f34,plain,(
% 1.55/1.28 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (in @ Y1 @ X1))))) @ X2))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f33])).
% 1.55/1.28 thf(f33,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setminus @ X1 @ Y0)) => (in @ Y1 @ X1)))))))) )),
% 1.55/1.28 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.55/1.28 thf(f32,plain,(
% 1.55/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))) @ X1))) )),
% 1.55/1.28 inference(pi_clausification,[status(thm)],[f30])).
% 1.55/1.28 thf(f30,plain,(
% 1.55/1.28 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 1.55/1.28 inference(definition_unfolding,[status(thm)],[f27,f22])).
% 1.55/1.28 thf(f22,plain,(
% 1.55/1.28 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f12])).
% 1.55/1.28 thf(f12,plain,(
% 1.55/1.28 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 1.55/1.28 inference(fool_elimination,[status(thm)],[f11])).
% 1.55/1.28 thf(f11,plain,(
% 1.55/1.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)) = setminusEL)),
% 1.55/1.28 inference(rectify,[status(thm)],[f3])).
% 1.55/1.28 thf(f3,axiom,(
% 1.55/1.28 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 1.55/1.28 file('/export/starexec/sandbox2/tmp/tmp.JQbkK6wljv/DTF2THF_26584.p',setminusEL)).
% 1.55/1.28 thf(f27,plain,(
% 1.55/1.28 (setminusEL = $true)),
% 1.55/1.28 inference(cnf_transformation,[status(thm)],[f19])).
% 1.55/1.28 % SZS output end Proof for DTF2THF_26584
% 1.55/1.28 % (26727)------------------------------
% 1.55/1.28 % (26727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (26727)Termination reason: Refutation
% 1.55/1.28
% 1.55/1.28 % (26727)Memory used [KB]: 5628
% 1.55/1.28 % (26727)Time elapsed: 0.011 s
% 1.55/1.28 % (26727)Instructions burned: 23 (million)
% 1.55/1.28 % (26727)------------------------------
% 1.55/1.28 % (26727)------------------------------
% 1.55/1.28 % (26724)Success in time 0.03 s
%------------------------------------------------------------------------------