%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU524^2 : 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 : n017.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 09:35:05 AM UTC 2026
% Result : Theorem 1.53s 1.31s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 162 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 578 ( 75 ~; 61 |; 41 &; 368 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 116 ( 0 ^; 89 !; 27 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
setunion: $i > $i ).
thf(func_def_15,type,
sK7: $i > $i > $i ).
thf(f70,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f67,f35]) ).
thf(f35,plain,
( $true
= ( in @ sK4 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ ( setunion @ sK3 ) ) ) )
& ( $true
= ( in @ sK4 @ sK3 ) )
& ( powersetI = $true )
& ( setunionI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( in @ sK4 @ ( powerset @ ( setunion @ sK3 ) ) ) )
& ( $true
= ( in @ sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( powersetI = $true )
& ( setunionI = $true ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( powersetI = $true )
& ( setunionI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( setunionI = $true )
& ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( powersetI = $true )
=> ( ( setunionI = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( powersetI
=> ( setunionI
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI
=> ( setunionI
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI
=> ( setunionI
=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',subPowSU) ).
thf(f67,plain,
( $true
!= ( in @ sK4 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true
!= ( in @ sK4 @ sK3 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f36,f63]) ).
thf(f63,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f56,f49]) ).
thf(f49,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true != $true )
| ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f34]) ).
thf(f34,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f38,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( powersetI = $true )
| ( ( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK6 )
!= $true )
| ( ( in @ X2 @ sK5 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
& ( $true
!= ( in @ ( sK7 @ X4 @ X3 ) @ X3 ) ) ) )
| ( powersetI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( ( in @ sK6 @ ( powerset @ sK5 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK6 )
!= $true )
| ( ( in @ X2 @ sK5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) ) )
=> ( ( $true
= ( in @ ( sK7 @ X4 @ X3 ) @ X4 ) )
& ( $true
!= ( in @ ( sK7 @ X4 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) ) ) )
| ( powersetI != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( powersetI = $true )
| ? [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
| ( powersetI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( powersetI = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( powersetI = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',powersetI) ).
thf(f56,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK7 @ X0 @ ( setunion @ X1 ) ) @ X2 )
!= $true )
| ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ ( sK7 @ X0 @ ( setunion @ X1 ) ) @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f50,f51]) ).
thf(f51,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setunion @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true != $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setunion @ X5 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f29,f33]) ).
thf(f33,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f29,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setunion @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( setunionI != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( setunionI = $true )
| ( ( ( in @ sK0 @ ( setunion @ sK2 ) )
!= $true )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setunion @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).
thf(f19,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setunion @ X2 ) )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ( ( in @ sK0 @ ( setunion @ sK2 ) )
!= $true )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ( setunionI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setunion @ X2 ) )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setunion @ X5 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( setunionI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setunionI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( in @ X1 @ ( setunion @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setunionI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X0 )
=> ( in @ X2 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',setunionI) ).
thf(f50,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK7 @ X4 @ X3 ) @ X3 ) )
| ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK7 @ X4 @ X3 ) @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f37,f34]) ).
thf(f37,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
= $true )
| ( $true
!= ( in @ ( sK7 @ X4 @ X3 ) @ X3 ) )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f36,plain,
( $true
!= ( in @ sK4 @ ( powerset @ ( setunion @ sK3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU524^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n017.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:24:11 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.38 ---- Original DTF file ---
% 0.15/0.38 thf(spec,logic,$$dhol).
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 % File : SEU524^2 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.38 % Domain : Set Theory
% 0.15/0.38 % Problem : Preliminary Notions - Power Sets and Unions
% 0.15/0.38 % Version : Especial > Reduced > Especial.
% 0.15/0.38 % English : (! A:i.! x:i.in x A -> in x (powerset (setunion A)))
% 0.15/0.38
% 0.15/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.38 % Source : [Bro08]
% 0.15/0.38 % Names : ZFC026l [Bro08]
% 0.15/0.38
% 0.15/0.38 % Status : Theorem
% 0.15/0.38 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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
% 0.15/0.38 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.15/0.38 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.15/0.38 % Maximal formula atoms : 4 ( 4 avg)
% 0.15/0.38 % Number of connectives : 27 ( 0 ~; 0 |; 0 &; 20 @)
% 0.15/0.38 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.15/0.38 % Maximal formula depth : 9 ( 4 avg)
% 0.15/0.38 % Number of types : 2 ( 0 usr)
% 0.15/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.38 % Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% 0.15/0.38 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.15/0.38 % SPC : TH0_THM_EQU_NAR
% 0.15/0.38
% 0.15/0.38 % Comments : http://mathgate.info/detsetitem.php?id=473
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 thf(in_type,type,
% 0.15/0.38 in: $i > $i > $o ).
% 0.15/0.38
% 0.15/0.38 thf(powerset_type,type,
% 0.15/0.38 powerset: $i > $i ).
% 0.15/0.38
% 0.15/0.38 thf(setunion_type,type,
% 0.15/0.38 setunion: $i > $i ).
% 0.15/0.38
% 0.15/0.38 thf(powersetI_type,type,
% 0.15/0.38 powersetI: $o ).
% 0.15/0.38
% 0.15/0.38 thf(powersetI,definition,
% 0.15/0.38 ( powersetI
% 0.15/0.38 = ( ! [A: $i,B: $i] :
% 0.15/0.38 ( ! [Xx: $i] :
% 0.15/0.38 ( ( in @ Xx @ B )
% 0.15/0.38 => ( in @ Xx @ A ) )
% 0.15/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(setunionI_type,type,
% 0.15/0.38 setunionI: $o ).
% 0.15/0.38
% 0.15/0.38 thf(setunionI,definition,
% 0.15/0.38 ( setunionI
% 0.15/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.15/0.38 ( ( in @ Xx @ B )
% 0.15/0.38 => ( ( in @ B @ A )
% 0.15/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(subPowSU,conjecture,
% 0.15/0.38 ( powersetI
% 0.15/0.38 => ( setunionI
% 0.15/0.38 => ! [A: $i,Xx: $i] :
% 0.15/0.38 ( ( in @ Xx @ A )
% 0.15/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 ------------------------
% 1.35/1.27 ---- Embedded in THF ---
% 1.35/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.35/1.27 %%% Generated on Tue Feb 24 12:24:11 EST 2026
% 1.35/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.35/1.27 %%% Logic specification used:
% 1.35/1.27 %%% thf(spec, logic, $$dhol).
% 1.35/1.27
% 1.35/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2DTF4959.p
% See solution above
% 1.35/1.27 ------------------------
% 1.35/1.28 ---- Cleaned THF ---
% 1.35/1.28 thf(in_type,type,
% 1.35/1.28 in: $i > $i > $o ).
% 1.35/1.28
% 1.35/1.28 thf(powerset_type,type,
% 1.35/1.28 powerset: $i > $i ).
% 1.35/1.28
% 1.35/1.28 thf(setunion_type,type,
% 1.35/1.28 setunion: $i > $i ).
% 1.35/1.28
% 1.35/1.28 thf(powersetI_type,type,
% 1.35/1.28 powersetI: $o ).
% 1.35/1.28
% 1.35/1.28 thf(powersetI,definition,
% 1.35/1.28 ( powersetI
% 1.35/1.28 = ( ! [A: $i,B: $i] :
% 1.35/1.28 ( ! [Xx: $i] :
% 1.35/1.28 ( ( in @ Xx @ B )
% 1.35/1.28 => ( in @ Xx @ A ) )
% 1.35/1.28 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.35/1.28
% 1.35/1.28 thf(setunionI_type,type,
% 1.35/1.28 setunionI: $o ).
% 1.35/1.28
% 1.35/1.28 thf(setunionI,definition,
% 1.35/1.28 ( setunionI
% 1.35/1.28 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.35/1.28 ( ( in @ Xx @ B )
% 1.35/1.28 => ( ( in @ B @ A )
% 1.35/1.28 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.35/1.28
% 1.35/1.28 thf(subPowSU,conjecture,
% 1.35/1.28 ( powersetI
% 1.35/1.28 => ( setunionI
% 1.35/1.28 => ! [A: $i,Xx: $i] :
% 1.35/1.28 ( ( in @ Xx @ A )
% 1.35/1.28 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.35/1.28 ------------------------
% 1.53/1.30 % (5062)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_4959 for (2999ds/275Mi)
% 1.53/1.30 % (5061)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_4959 for (2999ds/2Mi)
% 1.53/1.30 % (5060)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4959 for (2999ds/2Mi)
% 1.53/1.30 % (5057)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4959 for (2999ds/183Mi)
% 1.53/1.30 % (5059)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_4959 for (2999ds/27Mi)
% 1.53/1.30 % (5063)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4959 for (2999ds/18Mi)
% 1.53/1.30 % (5058)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_4959 for (2999ds/4Mi)
% 1.53/1.30 % (5060)Instruction limit reached!
% 1.53/1.30 % (5060)------------------------------
% 1.53/1.30 % (5060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (5060)Termination reason: Unknown
% 1.53/1.30 % (5060)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (5060)Memory used [KB]: 895
% 1.53/1.30 % (5060)Time elapsed: 0.003 s
% 1.53/1.30 % (5060)Instructions burned: 2 (million)
% 1.53/1.30 % (5060)------------------------------
% 1.53/1.30 % (5060)------------------------------
% 1.53/1.30 % (5061)Instruction limit reached!
% 1.53/1.30 % (5061)------------------------------
% 1.53/1.30 % (5061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (5061)Termination reason: Unknown
% 1.53/1.30 % (5061)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (5061)Memory used [KB]: 5500
% 1.53/1.30 % (5061)Time elapsed: 0.004 s
% 1.53/1.30 % (5061)Instructions burned: 3 (million)
% 1.53/1.30 % (5061)------------------------------
% 1.53/1.30 % (5061)------------------------------
% 1.53/1.30 % (5058)Instruction limit reached!
% 1.53/1.30 % (5058)------------------------------
% 1.53/1.30 % (5058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.30 % (5058)Termination reason: Unknown
% 1.53/1.30 % (5058)Termination phase: Saturation
% 1.53/1.30
% 1.53/1.30 % (5058)Memory used [KB]: 5500
% 1.53/1.30 % (5058)Time elapsed: 0.004 s
% 1.53/1.30 % (5058)Instructions burned: 4 (million)
% 1.53/1.30 % (5058)------------------------------
% 1.53/1.30 % (5058)------------------------------
% 1.53/1.30 % (5062)First to succeed.
% 1.53/1.31 % (5063)Also succeeded, but the first one will report.
% 1.53/1.31 % (5057)Also succeeded, but the first one will report.
% 1.53/1.31 % (5062)Refutation found. Thanks to Tanya!
% 1.53/1.31 % SZS status Theorem for DTF2THF_4959
% 1.53/1.31 % SZS output start Proof for DTF2THF_4959
% 1.53/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.53/1.31 thf(func_def_1, type, powerset: $i > $i).
% 1.53/1.31 thf(func_def_2, type, setunion: $i > $i).
% 1.53/1.31 thf(func_def_15, type, sK7: $i > $i > $i).
% 1.53/1.31 thf(f70,plain,(
% 1.53/1.31 $false),
% 1.53/1.31 inference(subsumption_resolution,[status(thm)],[f67,f35])).
% 1.53/1.31 thf(f35,plain,(
% 1.53/1.31 ($true = (in @ sK4 @ sK3))),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.53/1.31 thf(f23,plain,(
% 1.53/1.31 (($true != (in @ sK4 @ (powerset @ (setunion @ sK3)))) & ($true = (in @ sK4 @ sK3))) & (powersetI = $true) & (setunionI = $true)),
% 1.53/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22])).
% 1.53/1.31 thf(f22,plain,(
% 1.53/1.31 ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ (setunion @ X0)))) & ((in @ X1 @ X0) = $true)) => (($true != (in @ sK4 @ (powerset @ (setunion @ sK3)))) & ($true = (in @ sK4 @ sK3)))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f21,plain,(
% 1.53/1.31 ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ (setunion @ X0)))) & ((in @ X1 @ X0) = $true)) & (powersetI = $true) & (setunionI = $true)),
% 1.53/1.31 inference(rectify,[status(thm)],[f13])).
% 1.53/1.31 thf(f13,plain,(
% 1.53/1.31 ? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ (setunion @ X1))) != $true) & ((in @ X0 @ X1) = $true)) & (powersetI = $true) & (setunionI = $true)),
% 1.53/1.31 inference(flattening,[status(thm)],[f12])).
% 1.53/1.31 thf(f12,plain,(
% 1.53/1.31 (? [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ (setunion @ X1))) != $true) & ((in @ X0 @ X1) = $true)) & (setunionI = $true)) & (powersetI = $true)),
% 1.53/1.31 inference(ennf_transformation,[status(thm)],[f11])).
% 1.53/1.31 thf(f11,plain,(
% 1.53/1.31 ~((powersetI = $true) => ((setunionI = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ X1) = $true) => ((in @ X0 @ (powerset @ (setunion @ X1))) = $true))))),
% 1.53/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.53/1.31 thf(f10,plain,(
% 1.53/1.31 ~(powersetI => (setunionI => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (powerset @ (setunion @ X1))))))),
% 1.53/1.31 inference(rectify,[status(thm)],[f4])).
% 1.53/1.31 thf(f4,negated_conjecture,(
% 1.53/1.31 ~(powersetI => (setunionI => ! [X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (powerset @ (setunion @ X0))))))),
% 1.53/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.53/1.31 thf(f3,conjecture,(
% 1.53/1.31 powersetI => (setunionI => ! [X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (powerset @ (setunion @ X0)))))),
% 1.53/1.31 file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',subPowSU)).
% 1.53/1.31 thf(f67,plain,(
% 1.53/1.31 ($true != (in @ sK4 @ sK3))),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.53/1.31 thf(f64,plain,(
% 1.53/1.31 ($true != (in @ sK4 @ sK3)) | ($true != $true)),
% 1.53/1.31 inference(superposition,[status(thm)],[f36,f63])).
% 1.53/1.31 thf(f63,plain,(
% 1.53/1.31 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ (setunion @ X1))) = $true) | ((in @ X0 @ X1) != $true)) )),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.53/1.31 thf(f62,plain,(
% 1.53/1.31 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ (setunion @ X1))) = $true)) )),
% 1.53/1.31 inference(duplicate_literal_removal,[status(thm)],[f57])).
% 1.53/1.31 thf(f57,plain,(
% 1.53/1.31 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ (powerset @ (setunion @ X1))) = $true) | ((in @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ (setunion @ X1))) = $true)) )),
% 1.53/1.31 inference(superposition,[status(thm)],[f56,f49])).
% 1.53/1.31 thf(f49,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK7 @ X4 @ X3) @ X4)) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.53/1.31 thf(f47,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true != $true) | ($true = (in @ (sK7 @ X4 @ X3) @ X4))) )),
% 1.53/1.31 inference(definition_unfolding,[status(thm)],[f38,f34])).
% 1.53/1.31 thf(f34,plain,(
% 1.53/1.31 (powersetI = $true)),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.53/1.31 thf(f38,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true = (in @ (sK7 @ X4 @ X3) @ X4)) | (powersetI != $true)) )),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f28])).
% 1.53/1.31 thf(f28,plain,(
% 1.53/1.31 ((powersetI = $true) | (((in @ sK6 @ (powerset @ sK5)) != $true) & ! [X2 : $i] : (((in @ X2 @ sK6) != $true) | ((in @ X2 @ sK5) = $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | (($true = (in @ (sK7 @ X4 @ X3) @ X4)) & ($true != (in @ (sK7 @ X4 @ X3) @ X3)))) | (powersetI != $true))),
% 1.53/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f25,f27,f26])).
% 1.53/1.31 thf(f26,plain,(
% 1.53/1.31 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))) => (((in @ sK6 @ (powerset @ sK5)) != $true) & ! [X2 : $i] : (((in @ X2 @ sK6) != $true) | ((in @ X2 @ sK5) = $true)))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f27,plain,(
% 1.53/1.31 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X3))) => (($true = (in @ (sK7 @ X4 @ X3) @ X4)) & ($true != (in @ (sK7 @ X4 @ X3) @ X3))))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f25,plain,(
% 1.53/1.31 ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)))) & (! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ? [X5 : $i] : (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X3)))) | (powersetI != $true))),
% 1.53/1.31 inference(rectify,[status(thm)],[f24])).
% 1.53/1.31 thf(f24,plain,(
% 1.53/1.31 ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)))) & (! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (powersetI != $true))),
% 1.53/1.31 inference(nnf_transformation,[status(thm)],[f16])).
% 1.53/1.31 thf(f16,plain,(
% 1.53/1.31 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)))),
% 1.53/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.53/1.31 thf(f9,plain,(
% 1.53/1.31 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ($true = (in @ X0 @ (powerset @ X1)))) <=> (powersetI = $true)),
% 1.53/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.53/1.31 thf(f8,plain,(
% 1.53/1.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 1.53/1.31 inference(rectify,[status(thm)],[f1])).
% 1.53/1.31 thf(f1,axiom,(
% 1.53/1.31 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 1.53/1.31 file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',powersetI)).
% 1.53/1.31 thf(f56,plain,(
% 1.53/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK7 @ X0 @ (setunion @ X1)) @ X2) != $true) | ((in @ X0 @ (powerset @ (setunion @ X1))) = $true) | ((in @ X2 @ X1) != $true)) )),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.53/1.31 thf(f55,plain,(
% 1.53/1.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ (powerset @ (setunion @ X1))) = $true) | ((in @ X2 @ X1) != $true) | ((in @ (sK7 @ X0 @ (setunion @ X1)) @ X2) != $true)) )),
% 1.53/1.31 inference(superposition,[status(thm)],[f50,f51])).
% 1.53/1.31 thf(f51,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setunion @ X5)) = $true) | ((in @ X4 @ X5) != $true) | ((in @ X3 @ X4) != $true)) )),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.53/1.31 thf(f44,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ($true != $true) | ((in @ X4 @ X5) != $true) | ((in @ X3 @ (setunion @ X5)) = $true)) )),
% 1.53/1.31 inference(definition_unfolding,[status(thm)],[f29,f33])).
% 1.53/1.31 thf(f33,plain,(
% 1.53/1.31 (setunionI = $true)),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.53/1.31 thf(f29,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setunion @ X5)) = $true) | ((in @ X4 @ X5) != $true) | ((in @ X3 @ X4) != $true) | (setunionI != $true)) )),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.53/1.31 thf(f20,plain,(
% 1.53/1.31 ((setunionI = $true) | (((in @ sK0 @ (setunion @ sK2)) != $true) & ($true = (in @ sK1 @ sK2)) & ($true = (in @ sK0 @ sK1)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setunion @ X5)) = $true) | ((in @ X4 @ X5) != $true) | ((in @ X3 @ X4) != $true)) | (setunionI != $true))),
% 1.53/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19])).
% 1.53/1.31 thf(f19,plain,(
% 1.53/1.31 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setunion @ X2)) != $true) & ($true = (in @ X1 @ X2)) & ((in @ X0 @ X1) = $true)) => (((in @ sK0 @ (setunion @ sK2)) != $true) & ($true = (in @ sK1 @ sK2)) & ($true = (in @ sK0 @ sK1)))),
% 1.53/1.31 introduced(definition,[],[choice_axiom])).
% 1.53/1.31 thf(f18,plain,(
% 1.53/1.31 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setunion @ X2)) != $true) & ($true = (in @ X1 @ X2)) & ((in @ X0 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setunion @ X5)) = $true) | ((in @ X4 @ X5) != $true) | ((in @ X3 @ X4) != $true)) | (setunionI != $true))),
% 1.53/1.31 inference(rectify,[status(thm)],[f17])).
% 1.53/1.31 thf(f17,plain,(
% 1.53/1.31 ((setunionI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ (setunion @ X2)) != $true) & ($true = (in @ X0 @ X2)) & ((in @ X1 @ X0) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ (setunion @ X2)) = $true) | ($true != (in @ X0 @ X2)) | ((in @ X1 @ X0) != $true)) | (setunionI != $true))),
% 1.53/1.31 inference(nnf_transformation,[status(thm)],[f15])).
% 1.53/1.31 thf(f15,plain,(
% 1.53/1.31 (setunionI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X1 @ (setunion @ X2)) = $true) | ($true != (in @ X0 @ X2)) | ((in @ X1 @ X0) != $true))),
% 1.53/1.31 inference(flattening,[status(thm)],[f14])).
% 1.53/1.31 thf(f14,plain,(
% 1.53/1.31 (setunionI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X2)) = $true) | ($true != (in @ X0 @ X2))) | ((in @ X1 @ X0) != $true))),
% 1.53/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.53/1.31 thf(f7,plain,(
% 1.53/1.31 (setunionI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X1 @ X0) = $true) => (($true = (in @ X0 @ X2)) => ((in @ X1 @ (setunion @ X2)) = $true)))),
% 1.53/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.53/1.31 thf(f6,plain,(
% 1.53/1.31 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X2) => (in @ X1 @ (setunion @ X2)))))),
% 1.53/1.31 inference(rectify,[status(thm)],[f2])).
% 1.53/1.31 thf(f2,axiom,(
% 1.53/1.31 (setunionI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X1) => ((in @ X1 @ X0) => (in @ X2 @ (setunion @ X0)))))),
% 1.53/1.31 file('/export/starexec/sandbox/tmp/tmp.FXJISFW8Rt/DTF2THF_4959.p',setunionI)).
% 1.53/1.31 thf(f50,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK7 @ X4 @ X3) @ X3)) | ((in @ X4 @ (powerset @ X3)) = $true)) )),
% 1.53/1.31 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.53/1.31 thf(f48,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true != $true) | ($true != (in @ (sK7 @ X4 @ X3) @ X3))) )),
% 1.53/1.31 inference(definition_unfolding,[status(thm)],[f37,f34])).
% 1.53/1.31 thf(f37,plain,(
% 1.53/1.31 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ (powerset @ X3)) = $true) | ($true != (in @ (sK7 @ X4 @ X3) @ X3)) | (powersetI != $true)) )),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f28])).
% 1.53/1.31 thf(f36,plain,(
% 1.53/1.31 ($true != (in @ sK4 @ (powerset @ (setunion @ sK3))))),
% 1.53/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.53/1.31 % SZS output end Proof for DTF2THF_4959
% 1.53/1.31 % (5062)------------------------------
% 1.53/1.31 % (5062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.31 % (5062)Termination reason: Refutation
% 1.53/1.31
% 1.53/1.31 % (5062)Memory used [KB]: 5500
% 1.53/1.31 % (5062)Time elapsed: 0.007 s
% 1.53/1.31 % (5062)Instructions burned: 6 (million)
% 1.53/1.31 % (5062)------------------------------
% 1.53/1.31 % (5062)------------------------------
% 1.53/1.31 % (5056)Success in time 0.021 s
%------------------------------------------------------------------------------