%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU718^2 : 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 : n014.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 09:36:38 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 624 ( 171 equ; 0 cnn)
% Maximal formula atoms : 12 ( 13 avg)
% Number of connectives : 593 ( 65 ~; 44 |; 66 &; 371 @)
% ( 5 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 104 ( 0 ^; 71 !; 33 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(f65,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f64,f39]) ).
thf(f39,plain,
( ( in @ sK8 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ( $true
= ( in @ sK8 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ sK8 @ sK7 )
!= $true )
& ( ( in @ sK8 @ sK5 )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK6 ) )
= $true )
& ( subsetE = $true )
& ( powersetE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f16,f27,f26,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ sK5 )
= $true ) ) )
& ( ( in @ sK5 @ ( powerset @ sK6 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ sK5 )
= $true ) ) )
=> ( ( ( in @ sK7 @ ( powerset @ sK6 ) )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ sK7 ) )
= $true )
& ( $true
!= ( in @ X3 @ sK7 ) )
& ( ( in @ X3 @ sK5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ sK7 ) )
= $true )
& ( $true
!= ( in @ X3 @ sK7 ) )
& ( ( in @ X3 @ sK5 )
= $true ) )
=> ( ( $true
= ( in @ sK8 @ sK6 ) )
& ( ( in @ sK5 @ ( powerset @ sK7 ) )
= $true )
& ( ( in @ sK8 @ sK7 )
!= $true )
& ( ( in @ sK8 @ sK5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( subsetE = $true )
& ( powersetE1 = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X0 @ ( powerset @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( powersetE1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( subsetE = $true )
=> ( ( powersetE1 = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X0 @ ( powerset @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( subsetE
=> ( powersetE1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X0 @ ( powerset @ X2 ) )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetE
=> ( powersetE1
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X3 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetE
=> ( powersetE1
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X3 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',powersetTE1) ).
thf(f64,plain,
( ( in @ sK8 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( in @ sK8 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f61,f56]) ).
thf(f56,plain,
( ( subset @ sK5 @ sK7 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $true != $true )
| ( ( subset @ sK5 @ sK7 )
= $true ) ),
inference(superposition,[status(thm)],[f52,f41]) ).
thf(f41,plain,
( ( in @ sK5 @ ( powerset @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f52,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
| ( ( subset @ X3 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( $true != $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f36]) ).
thf(f36,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f29,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( powersetE1 = $true )
| ( ( ( subset @ sK1 @ sK0 )
!= $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ( ( subset @ sK1 @ sK0 )
!= $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( powersetE1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( powersetE1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',powersetE1) ).
thf(f61,plain,
! [X0: $i] :
( ( ( subset @ X0 @ sK7 )
!= $true )
| ( ( in @ sK8 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK8 @ X0 )
!= $true )
| ( ( subset @ X0 @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f40,f51]) ).
thf(f51,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( subset @ X2 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X1 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f37]) ).
thf(f37,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( subset @ sK4 @ sK2 )
= $true )
& ( ( in @ sK3 @ sK2 )
!= $true )
& ( ( in @ sK3 @ sK4 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f22,f23]) ).
thf(f23,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
= $true )
& ( ( in @ X4 @ X3 )
!= $true )
& ( ( in @ X4 @ X5 )
= $true ) )
=> ( ( ( subset @ sK4 @ sK2 )
= $true )
& ( ( in @ sK3 @ sK2 )
!= $true )
& ( ( in @ sK3 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
= $true )
& ( ( in @ X4 @ X3 )
!= $true )
& ( ( in @ X4 @ X5 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( subsetE = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X2 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( subsetE
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',subsetE) ).
thf(f40,plain,
( ( in @ sK8 @ sK7 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU718^2 : 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 : n014.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 12:31:57 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
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SEU718^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.49 % Domain : Set Theory
% 0.29/0.49 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.29/0.49 % Version : Especial > Reduced > Especial.
% 0.29/0.49 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.29/0.49 % (! x:i.in x A -> in X (powerset Y) -> in x X -> in x Y)))
% 0.29/0.49
% 0.29/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.49 % Source : [Bro08]
% 0.29/0.49 % Names : ZFC220l [Bro08]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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 v4.1.0, 0.00 v3.7.0
% 0.29/0.49 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.29/0.49 % Number of atoms : 17 ( 2 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 8 ( 5 avg)
% 0.29/0.49 % Number of connectives : 36 ( 0 ~; 0 |; 0 &; 26 @)
% 0.29/0.49 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 14 ( 5 avg)
% 0.29/0.49 % Number of types : 2 ( 0 usr)
% 0.29/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.29/0.49 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : http://mathgate.info/detsetitem.php?id=276
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(in_type,type,
% 0.29/0.49 in: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(powerset_type,type,
% 0.29/0.49 powerset: $i > $i ).
% 0.29/0.49
% 0.29/0.49 thf(subset_type,type,
% 0.29/0.49 subset: $i > $i > $o ).
% 0.29/0.49
% 0.29/0.49 thf(subsetE_type,type,
% 0.29/0.49 subsetE: $o ).
% 0.29/0.49
% 0.29/0.49 thf(subsetE,definition,
% 0.29/0.49 ( subsetE
% 0.29/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.49 ( ( subset @ A @ B )
% 0.29/0.49 => ( ( in @ Xx @ A )
% 0.29/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(powersetE1_type,type,
% 0.29/0.49 powersetE1: $o ).
% 0.29/0.49
% 0.29/0.49 thf(powersetE1,definition,
% 0.29/0.49 ( powersetE1
% 0.29/0.49 = ( ! [A: $i,B: $i] :
% 0.29/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(powersetTE1,conjecture,
% 0.29/0.49 ( subsetE
% 0.29/0.49 => ( powersetE1
% 0.29/0.49 => ! [A: $i,X: $i] :
% 0.29/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.49 => ! [Y: $i] :
% 0.29/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.49 => ! [Xx: $i] :
% 0.29/0.49 ( ( in @ Xx @ A )
% 0.29/0.49 => ( ( in @ X @ ( powerset @ Y ) )
% 0.29/0.49 => ( ( in @ Xx @ X )
% 0.29/0.49 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 12:31:58 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2DTF4764.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(in_type,type,
% 1.66/1.43 in: $i > $i > $o ).
% 1.66/1.43
% 1.66/1.43 thf(powerset_type,type,
% 1.66/1.43 powerset: $i > $i ).
% 1.66/1.43
% 1.66/1.43 thf(subset_type,type,
% 1.66/1.43 subset: $i > $i > $o ).
% 1.66/1.43
% 1.66/1.43 thf(subsetE_type,type,
% 1.66/1.43 subsetE: $o ).
% 1.66/1.43
% 1.66/1.43 thf(subsetE,definition,
% 1.66/1.43 ( subsetE
% 1.66/1.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.43 ( ( subset @ A @ B )
% 1.66/1.43 => ( ( in @ Xx @ A )
% 1.66/1.43 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.66/1.43
% 1.66/1.43 thf(powersetE1_type,type,
% 1.66/1.43 powersetE1: $o ).
% 1.66/1.43
% 1.66/1.43 thf(powersetE1,definition,
% 1.66/1.43 ( powersetE1
% 1.66/1.43 = ( ! [A: $i,B: $i] :
% 1.66/1.43 ( ( in @ B @ ( powerset @ A ) )
% 1.66/1.43 => ( subset @ B @ A ) ) ) ) ).
% 1.66/1.43
% 1.66/1.43 thf(powersetTE1,conjecture,
% 1.66/1.43 ( subsetE
% 1.66/1.43 => ( powersetE1
% 1.66/1.43 => ! [A: $i,X: $i] :
% 1.66/1.43 ( ( in @ X @ ( powerset @ A ) )
% 1.66/1.43 => ! [Y: $i] :
% 1.66/1.43 ( ( in @ Y @ ( powerset @ A ) )
% 1.66/1.43 => ! [Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ A )
% 1.66/1.43 => ( ( in @ X @ ( powerset @ Y ) )
% 1.66/1.43 => ( ( in @ Xx @ X )
% 1.66/1.43 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (4865)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4764 for (2999ds/2Mi)
% 1.66/1.45 % (4863)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_4764 for (2999ds/4Mi)
% 1.66/1.45 % (4866)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_4764 for (2999ds/2Mi)
% 1.66/1.45 % (4864)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_4764 for (2999ds/27Mi)
% 1.66/1.45 % (4867)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_4764 for (2999ds/275Mi)
% 1.66/1.45 % (4868)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4764 for (2999ds/18Mi)
% 1.66/1.45 % (4862)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4764 for (2999ds/183Mi)
% 1.66/1.45 % (4865)Instruction limit reached!
% 1.66/1.45 % (4865)------------------------------
% 1.66/1.45 % (4865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (4865)Termination reason: Unknown
% 1.66/1.45 % (4865)Termination phase: Saturation
% 1.66/1.45 % (4866)Instruction limit reached!
% 1.66/1.45 % (4866)------------------------------
% 1.66/1.45 % (4866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (4866)Termination reason: Unknown
% 1.66/1.45 % (4866)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (4866)Memory used [KB]: 5500
% 1.66/1.45 % (4866)Time elapsed: 0.003 s
% 1.66/1.45 % (4866)Instructions burned: 3 (million)
% 1.66/1.45 % (4866)------------------------------
% 1.66/1.45 % (4866)------------------------------
% 1.66/1.45
% 1.66/1.45 % (4865)Memory used [KB]: 5500
% 1.66/1.45 % (4865)Time elapsed: 0.003 s
% 1.66/1.45 % (4865)Instructions burned: 3 (million)
% 1.66/1.45 % (4865)------------------------------
% 1.66/1.45 % (4865)------------------------------
% 1.66/1.45 % (4863)Instruction limit reached!
% 1.66/1.45 % (4863)------------------------------
% 1.66/1.45 % (4863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (4863)Termination reason: Unknown
% 1.66/1.45 % (4863)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (4863)Memory used [KB]: 5500
% 1.66/1.45 % (4863)Time elapsed: 0.004 s
% 1.66/1.45 % (4863)Instructions burned: 4 (million)
% 1.66/1.45 % (4863)------------------------------
% 1.66/1.45 % (4863)------------------------------
% 1.66/1.45 % (4867)First to succeed.
% 1.66/1.45 % (4868)Also succeeded, but the first one will report.
% 1.66/1.45 % (4867)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_4764
% 1.66/1.45 % SZS output start Proof for DTF2THF_4764
% 1.66/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.45 thf(func_def_1, type, powerset: $i > $i).
% 1.66/1.45 thf(func_def_2, type, subset: $i > $i > $o).
% 1.66/1.45 thf(f65,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(subsumption_resolution,[status(thm)],[f64,f39])).
% 1.66/1.45 thf(f39,plain,(
% 1.66/1.45 ((in @ sK8 @ sK5) = $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.45 thf(f28,plain,(
% 1.66/1.45 ((((in @ sK7 @ (powerset @ sK6)) = $true) & (($true = (in @ sK8 @ sK6)) & ((in @ sK5 @ (powerset @ sK7)) = $true) & ((in @ sK8 @ sK7) != $true) & ((in @ sK8 @ sK5) = $true))) & ((in @ sK5 @ (powerset @ sK6)) = $true)) & (subsetE = $true) & (powersetE1 = $true)),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f16,f27,f26,f25])).
% 1.66/1.45 thf(f25,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X0 @ (powerset @ X2)) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK6))) & ? [X3 : $i] : (($true = (in @ X3 @ sK6)) & ((in @ sK5 @ (powerset @ X2)) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ sK5) = $true))) & ((in @ sK5 @ (powerset @ sK6)) = $true))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f26,plain,(
% 1.66/1.45 ? [X2 : $i] : (($true = (in @ X2 @ (powerset @ sK6))) & ? [X3 : $i] : (($true = (in @ X3 @ sK6)) & ((in @ sK5 @ (powerset @ X2)) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ sK5) = $true))) => (((in @ sK7 @ (powerset @ sK6)) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ sK6)) & ((in @ sK5 @ (powerset @ sK7)) = $true) & ($true != (in @ X3 @ sK7)) & ((in @ X3 @ sK5) = $true)))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f27,plain,(
% 1.66/1.45 ? [X3 : $i] : (($true = (in @ X3 @ sK6)) & ((in @ sK5 @ (powerset @ sK7)) = $true) & ($true != (in @ X3 @ sK7)) & ((in @ X3 @ sK5) = $true)) => (($true = (in @ sK8 @ sK6)) & ((in @ sK5 @ (powerset @ sK7)) = $true) & ((in @ sK8 @ sK7) != $true) & ((in @ sK8 @ sK5) = $true))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f16,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X0 @ (powerset @ X2)) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true))) & ($true = (in @ X0 @ (powerset @ X1)))) & (subsetE = $true) & (powersetE1 = $true)),
% 1.66/1.45 inference(flattening,[status(thm)],[f15])).
% 1.66/1.45 thf(f15,plain,(
% 1.66/1.45 (? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X0 @ (powerset @ X2)) = $true)) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ($true = (in @ X0 @ (powerset @ X1)))) & (powersetE1 = $true)) & (subsetE = $true)),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f9])).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 ~((subsetE = $true) => ((powersetE1 = $true) => ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X0 @ (powerset @ X2)) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))))))))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 ~(subsetE => (powersetE1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X0 @ (powerset @ X2)) => ((in @ X3 @ X0) => (in @ X3 @ X2))))))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f4])).
% 1.66/1.45 thf(f4,negated_conjecture,(
% 1.66/1.45 ~(subsetE => (powersetE1 => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X3 @ (powerset @ X4)) => ((in @ X2 @ X3) => (in @ X2 @ X4))))))))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.45 thf(f3,conjecture,(
% 1.66/1.45 subsetE => (powersetE1 => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X3 @ (powerset @ X4)) => ((in @ X2 @ X3) => (in @ X2 @ X4)))))))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',powersetTE1)).
% 1.66/1.45 thf(f64,plain,(
% 1.66/1.45 ((in @ sK8 @ sK5) != $true)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.66/1.45 thf(f63,plain,(
% 1.66/1.45 ((in @ sK8 @ sK5) != $true) | ($true != $true)),
% 1.66/1.45 inference(superposition,[status(thm)],[f61,f56])).
% 1.66/1.45 thf(f56,plain,(
% 1.66/1.45 ((subset @ sK5 @ sK7) = $true)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 1.66/1.45 thf(f54,plain,(
% 1.66/1.45 ($true != $true) | ((subset @ sK5 @ sK7) = $true)),
% 1.66/1.45 inference(superposition,[status(thm)],[f52,f41])).
% 1.66/1.45 thf(f41,plain,(
% 1.66/1.45 ((in @ sK5 @ (powerset @ sK7)) = $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.45 thf(f52,plain,(
% 1.66/1.45 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) != $true) | ((subset @ X3 @ X2) = $true)) )),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.66/1.45 thf(f46,plain,(
% 1.66/1.45 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ($true != $true) | ((in @ X3 @ (powerset @ X2)) != $true)) )),
% 1.66/1.45 inference(definition_unfolding,[status(thm)],[f29,f36])).
% 1.66/1.45 thf(f36,plain,(
% 1.66/1.45 (powersetE1 = $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.45 thf(f29,plain,(
% 1.66/1.45 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ((in @ X3 @ (powerset @ X2)) != $true) | (powersetE1 != $true)) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f20])).
% 1.66/1.45 thf(f20,plain,(
% 1.66/1.45 ((powersetE1 = $true) | (((subset @ sK1 @ sK0) != $true) & ((in @ sK1 @ (powerset @ sK0)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (powersetE1 != $true))),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19])).
% 1.66/1.45 thf(f19,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ (powerset @ X0)) = $true)) => (((subset @ sK1 @ sK0) != $true) & ((in @ sK1 @ (powerset @ sK0)) = $true))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f18,plain,(
% 1.66/1.45 ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (powersetE1 != $true))),
% 1.66/1.45 inference(rectify,[status(thm)],[f17])).
% 1.66/1.45 thf(f17,plain,(
% 1.66/1.45 ((powersetE1 = $true) | ? [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) != $true) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ($true != (in @ X0 @ (powerset @ X1)))) | (powersetE1 != $true))),
% 1.66/1.45 inference(nnf_transformation,[status(thm)],[f14])).
% 1.66/1.45 thf(f14,plain,(
% 1.66/1.45 (powersetE1 = $true) <=> ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) | ($true != (in @ X0 @ (powerset @ X1))))),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.45 thf(f11,plain,(
% 1.66/1.45 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ((subset @ X0 @ X1) = $true)) <=> (powersetE1 = $true)),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.45 thf(f10,plain,(
% 1.66/1.45 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))),
% 1.66/1.45 inference(rectify,[status(thm)],[f2])).
% 1.66/1.45 thf(f2,axiom,(
% 1.66/1.45 (powersetE1 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',powersetE1)).
% 1.66/1.45 thf(f61,plain,(
% 1.66/1.45 ( ! [X0 : $i] : (((subset @ X0 @ sK7) != $true) | ((in @ sK8 @ X0) != $true)) )),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.66/1.45 thf(f60,plain,(
% 1.66/1.45 ( ! [X0 : $i] : (($true != $true) | ((in @ sK8 @ X0) != $true) | ((subset @ X0 @ sK7) != $true)) )),
% 1.66/1.45 inference(superposition,[status(thm)],[f40,f51])).
% 1.66/1.45 thf(f51,plain,(
% 1.66/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true) | ((subset @ X2 @ X0) != $true)) )),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.66/1.45 thf(f47,plain,(
% 1.66/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X2) != $true) | ((subset @ X2 @ X0) != $true) | ($true != $true) | ((in @ X1 @ X0) = $true)) )),
% 1.66/1.45 inference(definition_unfolding,[status(thm)],[f35,f37])).
% 1.66/1.45 thf(f37,plain,(
% 1.66/1.45 (subsetE = $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.45 thf(f35,plain,(
% 1.66/1.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X0) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true) | (subsetE != $true)) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f24])).
% 1.66/1.45 thf(f24,plain,(
% 1.66/1.45 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (((subset @ sK4 @ sK2) = $true) & ((in @ sK3 @ sK2) != $true) & ((in @ sK3 @ sK4) = $true)))),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f22,f23])).
% 1.66/1.45 thf(f23,plain,(
% 1.66/1.45 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X3) = $true) & ((in @ X4 @ X3) != $true) & ((in @ X4 @ X5) = $true)) => (((subset @ sK4 @ sK2) = $true) & ((in @ sK3 @ sK2) != $true) & ((in @ sK3 @ sK4) = $true))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f22,plain,(
% 1.66/1.45 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) != $true) | ((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X3) = $true) & ((in @ X4 @ X3) != $true) & ((in @ X4 @ X5) = $true)))),
% 1.66/1.45 inference(rectify,[status(thm)],[f21])).
% 1.66/1.45 thf(f21,plain,(
% 1.66/1.45 (! [X2 : $i,X1 : $i,X0 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((subset @ X0 @ X2) = $true) & ((in @ X1 @ X2) != $true) & ((in @ X1 @ X0) = $true)))),
% 1.66/1.45 inference(nnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f13,plain,(
% 1.66/1.45 ! [X2 : $i,X1 : $i,X0 : $i] : (((subset @ X0 @ X2) != $true) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) != $true)) <=> (subsetE = $true)),
% 1.66/1.45 inference(flattening,[status(thm)],[f12])).
% 1.66/1.45 thf(f12,plain,(
% 1.66/1.45 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2) = $true) | ((in @ X1 @ X0) != $true)) | ((subset @ X0 @ X2) != $true))),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f7])).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X2) = $true) => (((in @ X1 @ X0) = $true) => ((in @ X1 @ X2) = $true)))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f1])).
% 1.66/1.45 thf(f1,axiom,(
% 1.66/1.45 (subsetE = ! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.ipE4LhKGWi/DTF2THF_4764.p',subsetE)).
% 1.66/1.45 thf(f40,plain,(
% 1.66/1.45 ((in @ sK8 @ sK7) != $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.45 % SZS output end Proof for DTF2THF_4764
% 1.66/1.45 % (4867)------------------------------
% 1.66/1.45 % (4867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (4867)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (4867)Memory used [KB]: 5500
% 1.66/1.45 % (4867)Time elapsed: 0.006 s
% 1.66/1.45 % (4867)Instructions burned: 6 (million)
% 1.66/1.45 % (4867)------------------------------
% 1.66/1.45 % (4867)------------------------------
% 1.66/1.45 % (4861)Success in time 0.021 s
%------------------------------------------------------------------------------