%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU626^2 : 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 : n009.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 09:35:42 AM UTC 2026
% Result : Theorem 1.57s 1.32s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 562 ( 142 equ; 0 cnn)
% Maximal formula atoms : 8 ( 12 avg)
% Number of connectives : 650 ( 64 ~; 41 |; 45 &; 466 @)
% ( 4 <=>; 30 =>; 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 : 21 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 114 ( 0 ^; 76 !; 38 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(f55,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f54,f33]) ).
thf(f33,plain,
( ( in @ sK6 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( upairsubunion = $true )
& ( powersetI1 = $true )
& ( ( in @ sK7 @ sK5 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ ( powerset @ ( binunion @ sK4 @ sK5 ) ) ) )
& ( ( in @ sK6 @ sK4 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f21,f23,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( in @ X3 @ sK5 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK6 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK4 @ sK5 ) ) ) ) )
& ( ( in @ sK6 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK5 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK6 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ sK4 @ sK5 ) ) ) ) )
=> ( ( ( in @ sK7 @ sK5 )
= $true )
& ( $true
!= ( in @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ ( powerset @ ( binunion @ sK4 @ sK5 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( upairsubunion = $true )
& ( powersetI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
!= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( upairsubunion = $true )
& ( powersetI1 = $true )
& ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( in @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( upairsubunion = $true )
& ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( powersetI1 = $true )
=> ( ( upairsubunion = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( powersetI1
=> ( upairsubunion
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetI1
=> ( upairsubunion
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetI1
=> ( upairsubunion
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',upairinpowunion) ).
thf(f54,plain,
( ( in @ sK6 @ sK4 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f53,f35]) ).
thf(f35,plain,
( ( in @ sK7 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f53,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK6 @ sK4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( $true != $true )
| ( ( in @ sK6 @ sK4 )
!= $true ) ),
inference(superposition,[status(thm)],[f51,f49]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f37]) ).
thf(f37,plain,
upairsubunion = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X3 @ X2 ) )
| ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
= $true )
| ( upairsubunion != $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
!= ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f19,f18]) ).
thf(f18,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X6 ) )
& ( ( subset @ ( setadjoin @ X4 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ X5 @ X6 ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK2 ) )
& ( ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK2 ) )
& ( ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK3 @ sK2 ) )
& ( $true
!= ( subset @ ( setadjoin @ sK0 @ ( setadjoin @ sK3 @ emptyset ) ) @ ( binunion @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( subset @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( in @ X4 @ X5 )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X6 ) )
& ( ( subset @ ( setadjoin @ X4 @ ( setadjoin @ X7 @ emptyset ) ) @ ( binunion @ X5 @ X6 ) )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) ) )
| ( upairsubunion != $true ) )
& ( ( upairsubunion = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) ) )
<=> ( upairsubunion = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( upairsubunion = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X1 @ X0 ) ) ) )
= upairsubunion ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X0 @ X1 ) ) ) )
= upairsubunion ),
file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',upairsubunion) ).
thf(f51,plain,
( ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ ( binunion @ sK4 @ sK5 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $true != $true )
| ( ( subset @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ ( binunion @ sK4 @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f34,f48]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f40,f36]) ).
thf(f36,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( in @ sK9 @ ( powerset @ sK8 ) )
!= $true )
& ( $true
= ( subset @ sK9 @ sK8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f26,f27]) ).
thf(f27,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
& ( ( subset @ X3 @ X2 )
= $true ) )
=> ( ( ( in @ sK9 @ ( powerset @ sK8 ) )
!= $true )
& ( $true
= ( subset @ sK9 @ sK8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
& ( ( subset @ X3 @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
& ( $true
= ( subset @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( powersetI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetI1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',powersetI1) ).
thf(f34,plain,
( $true
!= ( in @ ( setadjoin @ sK6 @ ( setadjoin @ sK7 @ emptyset ) ) @ ( powerset @ ( binunion @ sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU626^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n009.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 12:28:40 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU626^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Ordered Pairs - Cartesian Products
% 0.16/0.39 % Version : Especial > Reduced > Especial.
% 0.16/0.39 % English : (! A:i.! B:i.! x:i.in x A -> (! y:i.in y B -> in (setadjoin x
% 0.16/0.39 % (setadjoin y emptyset)) (powerset (binunion A B))))
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC128l [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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
% 0.16/0.39 % Syntax : Number of formulae : 11 ( 2 unt; 8 typ; 2 def)
% 0.16/0.39 % Number of atoms : 14 ( 2 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 5 ( 4 avg)
% 0.16/0.39 % Number of connectives : 37 ( 0 ~; 0 |; 0 &; 30 @)
% 0.16/0.39 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 14 ( 5 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=183
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(subset_type,type,
% 0.16/0.39 subset: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1_type,type,
% 0.16/0.39 powersetI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetI1,definition,
% 0.16/0.39 ( powersetI1
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( subset @ B @ A )
% 0.16/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(binunion_type,type,
% 0.16/0.39 binunion: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion_type,type,
% 0.16/0.39 upairsubunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion,definition,
% 0.16/0.39 ( upairsubunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairinpowunion,conjecture,
% 0.16/0.39 ( powersetI1
% 0.16/0.39 => ( upairsubunion
% 0.16/0.39 => ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.40/1.28 ---- Embedded in THF ---
% 1.40/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.28 %%% Generated on Tue Feb 24 12:28:41 EST 2026
% 1.40/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.28 %%% Logic specification used:
% 1.40/1.28 %%% thf(spec, logic, $$dhol).
% 1.40/1.28
% 1.40/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2DTF15948.p
% See solution above
% 1.40/1.28 ------------------------
% 1.40/1.29 ---- Cleaned THF ---
% 1.40/1.29 thf(in_type,type,
% 1.40/1.29 in: $i > $i > $o ).
% 1.40/1.29
% 1.40/1.29 thf(emptyset_type,type,
% 1.40/1.29 emptyset: $i ).
% 1.40/1.29
% 1.40/1.29 thf(setadjoin_type,type,
% 1.40/1.29 setadjoin: $i > $i > $i ).
% 1.40/1.29
% 1.40/1.29 thf(powerset_type,type,
% 1.40/1.29 powerset: $i > $i ).
% 1.40/1.29
% 1.40/1.29 thf(subset_type,type,
% 1.40/1.29 subset: $i > $i > $o ).
% 1.40/1.29
% 1.40/1.29 thf(powersetI1_type,type,
% 1.40/1.29 powersetI1: $o ).
% 1.40/1.29
% 1.40/1.29 thf(powersetI1,definition,
% 1.40/1.29 ( powersetI1
% 1.40/1.29 = ( ! [A: $i,B: $i] :
% 1.40/1.29 ( ( subset @ B @ A )
% 1.40/1.29 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(binunion_type,type,
% 1.40/1.29 binunion: $i > $i > $i ).
% 1.40/1.29
% 1.40/1.29 thf(upairsubunion_type,type,
% 1.40/1.29 upairsubunion: $o ).
% 1.40/1.29
% 1.40/1.29 thf(upairsubunion,definition,
% 1.40/1.29 ( upairsubunion
% 1.40/1.29 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.40/1.29 ( ( in @ Xx @ A )
% 1.40/1.29 => ! [Xy: $i] :
% 1.40/1.29 ( ( in @ Xy @ B )
% 1.40/1.29 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(upairinpowunion,conjecture,
% 1.40/1.29 ( powersetI1
% 1.40/1.29 => ( upairsubunion
% 1.40/1.29 => ! [A: $i,B: $i,Xx: $i] :
% 1.40/1.29 ( ( in @ Xx @ A )
% 1.40/1.29 => ! [Xy: $i] :
% 1.40/1.29 ( ( in @ Xy @ B )
% 1.40/1.29 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 1.40/1.29 ------------------------
% 1.57/1.31 % (16047)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_15948 for (2999ds/4Mi)
% 1.57/1.31 % (16048)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_15948 for (2999ds/27Mi)
% 1.57/1.31 % (16049)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15948 for (2999ds/2Mi)
% 1.57/1.31 % (16046)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15948 for (2999ds/183Mi)
% 1.57/1.31 % (16050)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_15948 for (2999ds/2Mi)
% 1.57/1.31 % (16052)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15948 for (2999ds/18Mi)
% 1.57/1.31 % (16051)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_15948 for (2999ds/275Mi)
% 1.57/1.31 % (16049)Instruction limit reached!
% 1.57/1.31 % (16049)------------------------------
% 1.57/1.31 % (16049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (16049)Termination reason: Unknown
% 1.57/1.31 % (16050)Instruction limit reached!
% 1.57/1.31 % (16050)------------------------------
% 1.57/1.31 % (16050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (16049)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (16049)Memory used [KB]: 5500
% 1.57/1.31 % (16049)Time elapsed: 0.003 s
% 1.57/1.31 % (16049)Instructions burned: 3 (million)
% 1.57/1.31 % (16049)------------------------------
% 1.57/1.31 % (16049)------------------------------
% 1.57/1.31 % (16050)Termination reason: Unknown
% 1.57/1.31 % (16050)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (16050)Memory used [KB]: 5500
% 1.57/1.31 % (16050)Time elapsed: 0.003 s
% 1.57/1.31 % (16050)Instructions burned: 3 (million)
% 1.57/1.31 % (16050)------------------------------
% 1.57/1.31 % (16050)------------------------------
% 1.57/1.31 % (16047)Instruction limit reached!
% 1.57/1.31 % (16047)------------------------------
% 1.57/1.31 % (16047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (16047)Termination reason: Unknown
% 1.57/1.31 % (16047)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (16047)Memory used [KB]: 5500
% 1.57/1.31 % (16047)Time elapsed: 0.004 s
% 1.57/1.31 % (16047)Instructions burned: 4 (million)
% 1.57/1.31 % (16047)------------------------------
% 1.57/1.31 % (16047)------------------------------
% 1.57/1.31 % (16051)First to succeed.
% 1.57/1.32 % (16046)Also succeeded, but the first one will report.
% 1.57/1.32 % (16048)Also succeeded, but the first one will report.
% 1.57/1.32 % (16051)Refutation found. Thanks to Tanya!
% 1.57/1.32 % SZS status Theorem for DTF2THF_15948
% 1.57/1.32 % SZS output start Proof for DTF2THF_15948
% 1.57/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.57/1.32 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.57/1.32 thf(func_def_3, type, powerset: $i > $i).
% 1.57/1.32 thf(func_def_4, type, subset: $i > $i > $o).
% 1.57/1.32 thf(func_def_7, type, binunion: $i > $i > $i).
% 1.57/1.32 thf(f55,plain,(
% 1.57/1.32 $false),
% 1.57/1.32 inference(subsumption_resolution,[status(thm)],[f54,f33])).
% 1.57/1.32 thf(f33,plain,(
% 1.57/1.32 ((in @ sK6 @ sK4) = $true)),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.57/1.32 thf(f24,plain,(
% 1.57/1.32 (upairsubunion = $true) & (powersetI1 = $true) & ((((in @ sK7 @ sK5) = $true) & ($true != (in @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ (powerset @ (binunion @ sK4 @ sK5))))) & ((in @ sK6 @ sK4) = $true))),
% 1.57/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f21,f23,f22])).
% 1.57/1.32 thf(f22,plain,(
% 1.57/1.32 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true)) & ((in @ X2 @ X0) = $true)) => (? [X3 : $i] : (((in @ X3 @ sK5) = $true) & ($true != (in @ (setadjoin @ sK6 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ sK4 @ sK5))))) & ((in @ sK6 @ sK4) = $true))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f23,plain,(
% 1.57/1.32 ? [X3 : $i] : (((in @ X3 @ sK5) = $true) & ($true != (in @ (setadjoin @ sK6 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ sK4 @ sK5))))) => (((in @ sK7 @ sK5) = $true) & ($true != (in @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ (powerset @ (binunion @ sK4 @ sK5)))))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f21,plain,(
% 1.57/1.32 (upairsubunion = $true) & (powersetI1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true)) & ((in @ X2 @ X0) = $true))),
% 1.57/1.32 inference(rectify,[status(thm)],[f13])).
% 1.57/1.32 thf(f13,plain,(
% 1.57/1.32 (upairsubunion = $true) & (powersetI1 = $true) & ? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))) & ($true = (in @ X0 @ X1)))),
% 1.57/1.32 inference(flattening,[status(thm)],[f12])).
% 1.57/1.32 thf(f12,plain,(
% 1.57/1.32 (? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X2)) & ($true != (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))) & ($true = (in @ X0 @ X1))) & (upairsubunion = $true)) & (powersetI1 = $true)),
% 1.57/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.57/1.32 thf(f11,plain,(
% 1.57/1.32 ~((powersetI1 = $true) => ((upairsubunion = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : (($true = (in @ X0 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X2)) => ($true = (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))))))),
% 1.57/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.57/1.32 thf(f10,plain,(
% 1.57/1.32 ~(powersetI1 => (upairsubunion => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X2)))))))),
% 1.57/1.32 inference(rectify,[status(thm)],[f4])).
% 1.57/1.32 thf(f4,negated_conjecture,(
% 1.57/1.32 ~(powersetI1 => (upairsubunion => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1)))))))),
% 1.57/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.57/1.32 thf(f3,conjecture,(
% 1.57/1.32 powersetI1 => (upairsubunion => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))))),
% 1.57/1.32 file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',upairinpowunion)).
% 1.57/1.32 thf(f54,plain,(
% 1.57/1.32 ((in @ sK6 @ sK4) != $true)),
% 1.57/1.32 inference(subsumption_resolution,[status(thm)],[f53,f35])).
% 1.57/1.32 thf(f35,plain,(
% 1.57/1.32 ((in @ sK7 @ sK5) = $true)),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.57/1.32 thf(f53,plain,(
% 1.57/1.32 ((in @ sK7 @ sK5) != $true) | ((in @ sK6 @ sK4) != $true)),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.57/1.32 thf(f52,plain,(
% 1.57/1.32 ((in @ sK7 @ sK5) != $true) | ($true != $true) | ((in @ sK6 @ sK4) != $true)),
% 1.57/1.32 inference(superposition,[status(thm)],[f51,f49])).
% 1.57/1.32 thf(f49,plain,(
% 1.57/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)) = $true) | ($true != (in @ X0 @ X1)) | ($true != (in @ X3 @ X2))) )),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.57/1.32 thf(f41,plain,(
% 1.57/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != $true) | ($true != (in @ X3 @ X2)) | ((subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)) = $true)) )),
% 1.57/1.32 inference(definition_unfolding,[status(thm)],[f32,f37])).
% 1.57/1.32 thf(f37,plain,(
% 1.57/1.32 (upairsubunion = $true)),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.57/1.32 thf(f32,plain,(
% 1.57/1.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != (in @ X3 @ X2)) | ((subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)) = $true) | (upairsubunion != $true)) )),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f20])).
% 1.57/1.32 thf(f20,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)) = $true))) | (upairsubunion != $true)) & ((upairsubunion = $true) | (($true = (in @ sK0 @ sK1)) & (($true = (in @ sK3 @ sK2)) & ($true != (subset @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK1 @ sK2))))))),
% 1.57/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f19,f18])).
% 1.57/1.32 thf(f18,plain,(
% 1.57/1.32 ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X4 @ X5) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X6)) & ((subset @ (setadjoin @ X4 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ X5 @ X6)) != $true))) => (($true = (in @ sK0 @ sK1)) & ? [X7 : $i] : (($true = (in @ X7 @ sK2)) & ((subset @ (setadjoin @ sK0 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ sK1 @ sK2)) != $true)))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f19,plain,(
% 1.57/1.32 ? [X7 : $i] : (($true = (in @ X7 @ sK2)) & ((subset @ (setadjoin @ sK0 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ sK1 @ sK2)) != $true)) => (($true = (in @ sK3 @ sK2)) & ($true != (subset @ (setadjoin @ sK0 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK1 @ sK2))))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f17,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) | ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)) = $true))) | (upairsubunion != $true)) & ((upairsubunion = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (((in @ X4 @ X5) = $true) & ? [X7 : $i] : (($true = (in @ X7 @ X6)) & ((subset @ (setadjoin @ X4 @ (setadjoin @ X7 @ emptyset)) @ (binunion @ X5 @ X6)) != $true))))),
% 1.57/1.32 inference(rectify,[status(thm)],[f16])).
% 1.57/1.32 thf(f16,plain,(
% 1.57/1.32 (! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0))))) | (upairsubunion != $true)) & ((upairsubunion = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) & ? [X3 : $i] : (($true = (in @ X3 @ X0)) & ($true != (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0))))))),
% 1.57/1.32 inference(nnf_transformation,[status(thm)],[f15])).
% 1.57/1.32 thf(f15,plain,(
% 1.57/1.32 ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0))))) <=> (upairsubunion = $true)),
% 1.57/1.32 inference(ennf_transformation,[status(thm)],[f9])).
% 1.57/1.32 thf(f9,plain,(
% 1.57/1.32 (upairsubunion = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0)))))),
% 1.57/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.57/1.32 thf(f8,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0)))) = upairsubunion)),
% 1.57/1.32 inference(rectify,[status(thm)],[f2])).
% 1.57/1.32 thf(f2,axiom,(
% 1.57/1.32 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))) = upairsubunion)),
% 1.57/1.32 file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',upairsubunion)).
% 1.57/1.32 thf(f51,plain,(
% 1.57/1.32 ((subset @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ (binunion @ sK4 @ sK5)) != $true)),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.57/1.32 thf(f50,plain,(
% 1.57/1.32 ($true != $true) | ((subset @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ (binunion @ sK4 @ sK5)) != $true)),
% 1.57/1.32 inference(superposition,[status(thm)],[f34,f48])).
% 1.57/1.32 thf(f48,plain,(
% 1.57/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) )),
% 1.57/1.32 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.57/1.32 thf(f45,plain,(
% 1.57/1.32 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 1.57/1.32 inference(definition_unfolding,[status(thm)],[f40,f36])).
% 1.57/1.32 thf(f36,plain,(
% 1.57/1.32 (powersetI1 = $true)),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.57/1.32 thf(f40,plain,(
% 1.57/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true) | (powersetI1 != $true)) )),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f28])).
% 1.57/1.32 thf(f28,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | (((in @ sK9 @ (powerset @ sK8)) != $true) & ($true = (subset @ sK9 @ sK8))))),
% 1.57/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f26,f27])).
% 1.57/1.32 thf(f27,plain,(
% 1.57/1.32 ? [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) != $true) & ((subset @ X3 @ X2) = $true)) => (((in @ sK9 @ (powerset @ sK8)) != $true) & ($true = (subset @ sK9 @ sK8)))),
% 1.57/1.32 introduced(definition,[],[choice_axiom])).
% 1.57/1.32 thf(f26,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) != $true) & ((subset @ X3 @ X2) = $true)))),
% 1.57/1.32 inference(rectify,[status(thm)],[f25])).
% 1.57/1.32 thf(f25,plain,(
% 1.57/1.32 (! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ($true != (subset @ X0 @ X1))) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X1 : $i,X0 : $i] : (($true != (in @ X0 @ (powerset @ X1))) & ($true = (subset @ X0 @ X1))))),
% 1.57/1.32 inference(nnf_transformation,[status(thm)],[f14])).
% 1.57/1.32 thf(f14,plain,(
% 1.57/1.32 ! [X1 : $i,X0 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ($true != (subset @ X0 @ X1))) <=> (powersetI1 = $true)),
% 1.57/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.57/1.32 thf(f7,plain,(
% 1.57/1.32 ! [X1 : $i,X0 : $i] : (($true = (subset @ X0 @ X1)) => ($true = (in @ X0 @ (powerset @ X1)))) <=> (powersetI1 = $true)),
% 1.57/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.57/1.32 thf(f6,plain,(
% 1.57/1.32 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = powersetI1)),
% 1.57/1.32 inference(rectify,[status(thm)],[f1])).
% 1.57/1.32 thf(f1,axiom,(
% 1.57/1.32 (! [X1 : $i,X0 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = powersetI1)),
% 1.57/1.32 file('/export/starexec/sandbox2/tmp/tmp.JQ6tlp4zFu/DTF2THF_15948.p',powersetI1)).
% 1.57/1.32 thf(f34,plain,(
% 1.57/1.32 ($true != (in @ (setadjoin @ sK6 @ (setadjoin @ sK7 @ emptyset)) @ (powerset @ (binunion @ sK4 @ sK5))))),
% 1.57/1.32 inference(cnf_transformation,[status(thm)],[f24])).
% 1.57/1.32 % SZS output end Proof for DTF2THF_15948
% 1.57/1.32 % (16051)------------------------------
% 1.57/1.32 % (16051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (16051)Termination reason: Refutation
% 1.57/1.32
% 1.57/1.32 % (16051)Memory used [KB]: 5500
% 1.57/1.32 % (16051)Time elapsed: 0.006 s
% 1.57/1.32 % (16051)Instructions burned: 4 (million)
% 1.57/1.32 % (16051)------------------------------
% 1.57/1.32 % (16051)------------------------------
% 1.57/1.32 % (16045)Success in time 0.01 s
%------------------------------------------------------------------------------