%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU617^2 : 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 : n001.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 09:35:39 AM UTC 2026
% Result : Theorem 1.52s 1.26s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 415 ( 106 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 482 ( 54 ~; 36 |; 24 &; 347 @)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 61 !; 23 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(f48,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f47,f42]) ).
thf(f42,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f33]) ).
thf(f33,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
!= ( in @ sK5 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
=> ( $true
!= ( in @ sK5 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setunionI = $true )
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setadjoinIL
=> ( setunionI
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( setunionI
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setadjoinIL
=> ( setunionI
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setukpairIL) ).
thf(f32,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22]) ).
thf(f22,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
=> ( ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setadjoinIL) ).
thf(f47,plain,
( ( in @ sK5 @ ( setadjoin @ sK5 @ emptyset ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true != $true )
| ( ( in @ sK5 @ ( setadjoin @ sK5 @ emptyset ) )
!= $true ) ),
inference(superposition,[status(thm)],[f45,f42]) ).
thf(f45,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( ( in @ sK5 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i] :
( ( ( in @ sK5 @ X0 )
!= $true )
| ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f35,f43]) ).
thf(f43,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) )
| ( $true != $true )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f27,f34]) ).
thf(f34,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f27,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( setunionI != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( setunionI = $true )
| ( ( $true
!= ( in @ sK1 @ ( setunion @ sK2 ) ) )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK0 @ sK2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X2 ) ) )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) )
=> ( ( $true
!= ( in @ sK1 @ ( setunion @ sK2 ) ) )
& ( ( in @ sK1 @ sK0 )
= $true )
& ( ( in @ sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ( setunionI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X2 ) ) )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( setunion @ X5 ) ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setunionI != $true ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( setunionI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X2 ) ) )
& ( ( in @ X1 @ X0 )
= $true )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( setunionI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setunionI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( setunionI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( setunionI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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
= ( ! [X3: $i,X0: $i,X2: $i] :
( ( in @ X0 @ X3 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X0 @ ( setunion @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setunionI) ).
thf(f35,plain,
( $true
!= ( in @ sK5 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK5 @ ( setadjoin @ sK6 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU617^2 : 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
% 0.19/0.35 % Computer : n001.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue Feb 24 12:29:05 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SEU617^2 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Set Theory
% 0.21/0.46 % Problem : Ordered Pairs - Kuratowski Pairs
% 0.21/0.46 % Version : Especial > Reduced > Especial.
% 0.21/0.46 % English : (! x:i.! y:i.in x (setunion (setadjoin (setadjoin x emptyset)
% 0.21/0.46 % (setadjoin (setadjoin x (setadjoin y emptyset)) emptyset))))
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.46 % Source : [Bro08]
% 0.21/0.46 % Names : ZFC119l [Bro08]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 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
% 0.21/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.21/0.46 % Number of atoms : 11 ( 2 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.21/0.46 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 24 @)
% 0.21/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 13 ( 5 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.21/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : http://mathgate.info/detsetitem.php?id=172
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(in_type,type,
% 0.21/0.46 in: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset_type,type,
% 0.21/0.46 emptyset: $i ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin_type,type,
% 0.21/0.46 setadjoin: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setunion_type,type,
% 0.21/0.46 setunion: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL_type,type,
% 0.21/0.46 setadjoinIL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL,definition,
% 0.21/0.46 ( setadjoinIL
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI_type,type,
% 0.21/0.46 setunionI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI,definition,
% 0.21/0.46 ( setunionI
% 0.21/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( ( in @ B @ A )
% 0.21/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setukpairIL,conjecture,
% 0.21/0.46 ( setadjoinIL
% 0.21/0.46 => ( setunionI
% 0.21/0.46 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.52/1.23 ---- Embedded in THF ---
% 1.52/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.23 %%% Generated on Tue Feb 24 12:29:06 EST 2026
% 1.52/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.23 %%% Logic specification used:
% 1.52/1.23 %%% thf(spec, logic, $$dhol).
% 1.52/1.23
% 1.52/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2DTF20808.p
% See solution above
% 1.52/1.23 ------------------------
% 1.52/1.24 ---- Cleaned THF ---
% 1.52/1.24 thf(in_type,type,
% 1.52/1.24 in: $i > $i > $o ).
% 1.52/1.24
% 1.52/1.24 thf(emptyset_type,type,
% 1.52/1.24 emptyset: $i ).
% 1.52/1.24
% 1.52/1.24 thf(setadjoin_type,type,
% 1.52/1.24 setadjoin: $i > $i > $i ).
% 1.52/1.24
% 1.52/1.24 thf(setunion_type,type,
% 1.52/1.24 setunion: $i > $i ).
% 1.52/1.24
% 1.52/1.24 thf(setadjoinIL_type,type,
% 1.52/1.24 setadjoinIL: $o ).
% 1.52/1.24
% 1.52/1.24 thf(setadjoinIL,definition,
% 1.52/1.24 ( setadjoinIL
% 1.52/1.24 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.52/1.24
% 1.52/1.24 thf(setunionI_type,type,
% 1.52/1.24 setunionI: $o ).
% 1.52/1.24
% 1.52/1.24 thf(setunionI,definition,
% 1.52/1.24 ( setunionI
% 1.52/1.24 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.52/1.24 ( ( in @ Xx @ B )
% 1.52/1.24 => ( ( in @ B @ A )
% 1.52/1.24 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.52/1.24
% 1.52/1.24 thf(setukpairIL,conjecture,
% 1.52/1.24 ( setadjoinIL
% 1.52/1.24 => ( setunionI
% 1.52/1.24 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 1.52/1.24 ------------------------
% 1.52/1.26 % (21141)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_20808 for (2999ds/275Mi)
% 1.52/1.26 % (21139)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20808 for (2999ds/2Mi)
% 1.52/1.26 % (21139)Instruction limit reached!
% 1.52/1.26 % (21139)------------------------------
% 1.52/1.26 % (21139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (21139)Termination reason: Unknown
% 1.52/1.26 % (21139)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (21139)Memory used [KB]: 5500
% 1.52/1.26 % (21139)Time elapsed: 0.002 s
% 1.52/1.26 % (21139)Instructions burned: 3 (million)
% 1.52/1.26 % (21139)------------------------------
% 1.52/1.26 % (21139)------------------------------
% 1.52/1.26 % (21141)First to succeed.
% 1.52/1.26 % (21141)Refutation found. Thanks to Tanya!
% 1.52/1.26 % SZS status Theorem for DTF2THF_20808
% 1.52/1.26 % SZS output start Proof for DTF2THF_20808
% 1.52/1.26 thf(func_def_0, type, in: $i > $i > $o).
% 1.52/1.26 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.52/1.26 thf(func_def_3, type, setunion: $i > $i).
% 1.52/1.26 thf(f48,plain,(
% 1.52/1.26 $false),
% 1.52/1.26 inference(subsumption_resolution,[status(thm)],[f47,f42])).
% 1.52/1.26 thf(f42,plain,(
% 1.52/1.26 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0)))) )),
% 1.52/1.26 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.52/1.26 thf(f40,plain,(
% 1.52/1.26 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | ($true != $true)) )),
% 1.52/1.26 inference(definition_unfolding,[status(thm)],[f32,f33])).
% 1.52/1.26 thf(f33,plain,(
% 1.52/1.26 (setadjoinIL = $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f26])).
% 1.52/1.26 thf(f26,plain,(
% 1.52/1.26 ($true != (in @ sK5 @ (setunion @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK6 @ emptyset)) @ emptyset))))) & (setunionI = $true) & (setadjoinIL = $true)),
% 1.52/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f24,f25])).
% 1.52/1.26 thf(f25,plain,(
% 1.52/1.26 ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) != $true) => ($true != (in @ sK5 @ (setunion @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK6 @ emptyset)) @ emptyset)))))),
% 1.52/1.26 introduced(definition,[],[choice_axiom])).
% 1.52/1.26 thf(f24,plain,(
% 1.52/1.26 ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) != $true) & (setunionI = $true) & (setadjoinIL = $true)),
% 1.52/1.26 inference(rectify,[status(thm)],[f15])).
% 1.52/1.26 thf(f15,plain,(
% 1.52/1.26 ? [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) != $true) & (setunionI = $true) & (setadjoinIL = $true)),
% 1.52/1.26 inference(flattening,[status(thm)],[f14])).
% 1.52/1.26 thf(f14,plain,(
% 1.52/1.26 (? [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) != $true) & (setunionI = $true)) & (setadjoinIL = $true)),
% 1.52/1.26 inference(ennf_transformation,[status(thm)],[f11])).
% 1.52/1.26 thf(f11,plain,(
% 1.52/1.26 ~((setadjoinIL = $true) => ((setunionI = $true) => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = $true)))),
% 1.52/1.26 inference(fool_elimination,[status(thm)],[f10])).
% 1.52/1.26 thf(f10,plain,(
% 1.52/1.26 ~(setadjoinIL => (setunionI => ! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))))),
% 1.52/1.26 inference(rectify,[status(thm)],[f4])).
% 1.52/1.26 thf(f4,negated_conjecture,(
% 1.52/1.26 ~(setadjoinIL => (setunionI => ! [X1 : $i,X0 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))),
% 1.52/1.26 inference(negated_conjecture,[status(cth)],[f3])).
% 1.52/1.26 thf(f3,conjecture,(
% 1.52/1.26 setadjoinIL => (setunionI => ! [X1 : $i,X0 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 1.52/1.26 file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setukpairIL)).
% 1.52/1.26 thf(f32,plain,(
% 1.52/1.26 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) )),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f23])).
% 1.52/1.26 thf(f23,plain,(
% 1.52/1.26 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ((in @ sK4 @ (setadjoin @ sK4 @ sK3)) != $true))),
% 1.52/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f21,f22])).
% 1.52/1.26 thf(f22,plain,(
% 1.52/1.26 ? [X2 : $i,X3 : $i] : ($true != (in @ X3 @ (setadjoin @ X3 @ X2))) => ((in @ sK4 @ (setadjoin @ sK4 @ sK3)) != $true)),
% 1.52/1.26 introduced(definition,[],[choice_axiom])).
% 1.52/1.26 thf(f21,plain,(
% 1.52/1.26 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X3 @ (setadjoin @ X3 @ X2))))),
% 1.52/1.26 inference(rectify,[status(thm)],[f20])).
% 1.52/1.26 thf(f20,plain,(
% 1.52/1.26 (! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true))),
% 1.52/1.26 inference(nnf_transformation,[status(thm)],[f7])).
% 1.52/1.26 thf(f7,plain,(
% 1.52/1.26 ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) <=> (setadjoinIL = $true)),
% 1.52/1.26 inference(fool_elimination,[status(thm)],[f6])).
% 1.52/1.26 thf(f6,plain,(
% 1.52/1.26 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.52/1.26 inference(rectify,[status(thm)],[f1])).
% 1.52/1.26 thf(f1,axiom,(
% 1.52/1.26 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.52/1.26 file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setadjoinIL)).
% 1.52/1.26 thf(f47,plain,(
% 1.52/1.26 ((in @ sK5 @ (setadjoin @ sK5 @ emptyset)) != $true)),
% 1.52/1.26 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.52/1.26 thf(f46,plain,(
% 1.52/1.26 ($true != $true) | ((in @ sK5 @ (setadjoin @ sK5 @ emptyset)) != $true)),
% 1.52/1.26 inference(superposition,[status(thm)],[f45,f42])).
% 1.52/1.26 thf(f45,plain,(
% 1.52/1.26 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK6 @ emptyset)) @ emptyset))) != $true) | ((in @ sK5 @ X0) != $true)) )),
% 1.52/1.26 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.52/1.26 thf(f44,plain,(
% 1.52/1.26 ( ! [X0 : $i] : (((in @ sK5 @ X0) != $true) | ((in @ X0 @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK6 @ emptyset)) @ emptyset))) != $true) | ($true != $true)) )),
% 1.52/1.26 inference(superposition,[status(thm)],[f35,f43])).
% 1.52/1.26 thf(f43,plain,(
% 1.52/1.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setunion @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X3 @ X5) != $true)) )),
% 1.52/1.26 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.52/1.26 thf(f39,plain,(
% 1.52/1.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ($true = (in @ X4 @ (setunion @ X5))) | ($true != $true) | ((in @ X4 @ X3) != $true)) )),
% 1.52/1.26 inference(definition_unfolding,[status(thm)],[f27,f34])).
% 1.52/1.26 thf(f34,plain,(
% 1.52/1.26 (setunionI = $true)),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f26])).
% 1.52/1.26 thf(f27,plain,(
% 1.52/1.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setunion @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X3 @ X5) != $true) | (setunionI != $true)) )),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f19])).
% 1.52/1.26 thf(f19,plain,(
% 1.52/1.26 ((setunionI = $true) | (($true != (in @ sK1 @ (setunion @ sK2))) & ((in @ sK1 @ sK0) = $true) & ((in @ sK0 @ sK2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setunion @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X3 @ X5) != $true)) | (setunionI != $true))),
% 1.52/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18])).
% 1.52/1.26 thf(f18,plain,(
% 1.52/1.26 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setunion @ X2))) & ((in @ X1 @ X0) = $true) & ($true = (in @ X0 @ X2))) => (($true != (in @ sK1 @ (setunion @ sK2))) & ((in @ sK1 @ sK0) = $true) & ((in @ sK0 @ sK2) = $true))),
% 1.52/1.26 introduced(definition,[],[choice_axiom])).
% 1.52/1.26 thf(f17,plain,(
% 1.52/1.26 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setunion @ X2))) & ((in @ X1 @ X0) = $true) & ($true = (in @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setunion @ X5))) | ((in @ X4 @ X3) != $true) | ((in @ X3 @ X5) != $true)) | (setunionI != $true))),
% 1.52/1.26 inference(rectify,[status(thm)],[f16])).
% 1.52/1.26 thf(f16,plain,(
% 1.52/1.26 ((setunionI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setunion @ X2))) & ((in @ X1 @ X0) = $true) & ($true = (in @ X0 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setunion @ X2))) | ((in @ X1 @ X0) != $true) | ($true != (in @ X0 @ X2))) | (setunionI != $true))),
% 1.52/1.26 inference(nnf_transformation,[status(thm)],[f13])).
% 1.52/1.26 thf(f13,plain,(
% 1.52/1.26 (setunionI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setunion @ X2))) | ((in @ X1 @ X0) != $true) | ($true != (in @ X0 @ X2)))),
% 1.52/1.26 inference(flattening,[status(thm)],[f12])).
% 1.52/1.26 thf(f12,plain,(
% 1.52/1.26 (setunionI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((($true = (in @ X1 @ (setunion @ X2))) | ($true != (in @ X0 @ X2))) | ((in @ X1 @ X0) != $true))),
% 1.52/1.26 inference(ennf_transformation,[status(thm)],[f9])).
% 1.52/1.26 thf(f9,plain,(
% 1.52/1.26 (setunionI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X1 @ X0) = $true) => (($true = (in @ X0 @ X2)) => ($true = (in @ X1 @ (setunion @ X2)))))),
% 1.52/1.26 inference(fool_elimination,[status(thm)],[f8])).
% 1.52/1.26 thf(f8,plain,(
% 1.52/1.26 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X2) => (in @ X1 @ (setunion @ X2)))))),
% 1.52/1.26 inference(rectify,[status(thm)],[f2])).
% 1.52/1.26 thf(f2,axiom,(
% 1.52/1.26 (setunionI = ! [X3 : $i,X0 : $i,X2 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X2) => (in @ X0 @ (setunion @ X2)))))),
% 1.52/1.26 file('/export/starexec/sandbox/tmp/tmp.Uj4uAKyNcV/DTF2THF_20808.p',setunionI)).
% 1.52/1.26 thf(f35,plain,(
% 1.52/1.26 ($true != (in @ sK5 @ (setunion @ (setadjoin @ (setadjoin @ sK5 @ emptyset) @ (setadjoin @ (setadjoin @ sK5 @ (setadjoin @ sK6 @ emptyset)) @ emptyset)))))),
% 1.52/1.26 inference(cnf_transformation,[status(thm)],[f26])).
% 1.52/1.26 % SZS output end Proof for DTF2THF_20808
% 1.52/1.26 % (21141)------------------------------
% 1.52/1.26 % (21141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (21141)Termination reason: Refutation
% 1.52/1.26
% 1.52/1.26 % (21141)Memory used [KB]: 5500
% 1.52/1.26 % (21141)Time elapsed: 0.004 s
% 1.52/1.26 % (21141)Instructions burned: 4 (million)
% 1.52/1.26 % (21141)------------------------------
% 1.52/1.26 % (21141)------------------------------
% 1.52/1.26 % (21135)Success in time 0.013 s
%------------------------------------------------------------------------------