%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU512^2 : 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 : n003.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 09:35:00 AM UTC 2026
% Result : Theorem 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 287 ( 97 equ; 0 cnn)
% Maximal formula atoms : 14 ( 12 avg)
% Number of connectives : 325 ( 48 ~; 46 |; 27 &; 194 @)
% ( 4 <=>; 6 =>; 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 : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 39 !; 18 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ) ),
inference(equality_resolution,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( X0 != X2 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f23,f18]) ).
thf(f18,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) )
!= $true )
& ( setadjoinAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
=> ( ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
& ( setadjoinAx = $true ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( setadjoinAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setadjoinAx = $true )
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X0: $i,X2: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X0: $i,X2: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BghactM7qu/DTF2THF_3124.p',setadjoinIL) ).
thf(f23,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( X0 != X2 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true )
| ( ( ( in @ sK2 @ sK3 )
!= $true )
& ( sK4 != sK2 ) ) )
& ( ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
= $true )
| ( ( in @ sK2 @ sK3 )
= $true )
| ( sK4 = sK2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f15,f16]) ).
thf(f16,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( $true
!= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( $true
!= ( in @ X3 @ X4 ) )
& ( X3 != X5 ) ) )
& ( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X4 ) )
| ( X3 = X5 ) ) )
=> ( ( ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true )
| ( ( ( in @ sK2 @ sK3 )
!= $true )
& ( sK4 != sK2 ) ) )
& ( ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
= $true )
| ( ( in @ sK2 @ sK3 )
= $true )
| ( sK4 = sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( $true
!= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( $true
!= ( in @ X3 @ X4 ) )
& ( X3 != X5 ) ) )
& ( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X4 ) )
| ( X3 = X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( in @ X2 @ X0 ) )
| ( X1 = X2 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( $true
!= ( in @ X2 @ X0 ) )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( $true
!= ( in @ X2 @ X0 ) )
& ( X1 != X2 ) ) )
& ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( X1 = X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( in @ X2 @ X0 ) )
| ( X1 = X2 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( $true
!= ( in @ X2 @ X0 ) )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( $true
!= ( in @ X2 @ X0 ) )
& ( X1 != X2 ) ) )
& ( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
= ( in @ X2 @ X0 ) )
| ( X1 = X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( $true
= ( in @ X2 @ X0 ) )
| ( X1 = X2 ) )
<=> ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
| ( X1 = X2 ) )
<=> ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinAx
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
| ( X0 = X2 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BghactM7qu/DTF2THF_3124.p',setadjoinAx) ).
thf(f19,plain,
( ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU512^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n003.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:24:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SEU512^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.46 % Domain : Set Theory
% 0.26/0.46 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.26/0.46 % Version : Especial > Reduced > Especial.
% 0.26/0.46 % English : (! x:i.! y:i.in x (setadjoin x y))
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.46 % Source : [Bro08]
% 0.26/0.46 % Names : ZFC014l [Bro08]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.29 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
% 0.26/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.26/0.46 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 2 ( 3 avg)
% 0.26/0.46 % Number of connectives : 13 ( 0 ~; 1 |; 0 &; 10 @)
% 0.26/0.46 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.26/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : http://mathgate.info/detsetitem.php?id=80
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(in_type,type,
% 0.26/0.46 in: $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(setadjoin_type,type,
% 0.26/0.46 setadjoin: $i > $i > $i ).
% 0.26/0.46
% 0.26/0.46 thf(setadjoinAx_type,type,
% 0.26/0.46 setadjoinAx: $o ).
% 0.26/0.46
% 0.26/0.46 thf(setadjoinAx,definition,
% 0.26/0.46 ( setadjoinAx
% 0.26/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.26/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.26/0.46 <=> ( ( Xy = Xx )
% 0.26/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(setadjoinIL,conjecture,
% 0.26/0.46 ( setadjoinAx
% 0.26/0.46 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 12:24:56 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BghactM7qu/DTF2DTF3124.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.28 thf(in_type,type,
% 1.45/1.28 in: $i > $i > $o ).
% 1.45/1.28
% 1.45/1.28 thf(setadjoin_type,type,
% 1.45/1.28 setadjoin: $i > $i > $i ).
% 1.45/1.28
% 1.45/1.28 thf(setadjoinAx_type,type,
% 1.45/1.28 setadjoinAx: $o ).
% 1.45/1.28
% 1.45/1.28 thf(setadjoinAx,definition,
% 1.45/1.28 ( setadjoinAx
% 1.45/1.28 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.45/1.28 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.45/1.28 <=> ( ( Xy = Xx )
% 1.45/1.28 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.45/1.28
% 1.45/1.28 thf(setadjoinIL,conjecture,
% 1.45/1.28 ( setadjoinAx
% 1.45/1.28 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ).
% 1.45/1.28 ------------------------
% 1.45/1.29 % (3345)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3124 for (2999ds/18Mi)
% 1.45/1.29 % (3344)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_3124 for (2999ds/275Mi)
% 1.45/1.29 % (3345)First to succeed.
% 1.45/1.29 % (3344)Also succeeded, but the first one will report.
% 1.45/1.29 % (3345)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_3124
% 1.45/1.29 % SZS output start Proof for DTF2THF_3124
% 1.45/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.45/1.29 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.45/1.29 thf(f36,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f19,f34])).
% 1.45/1.29 thf(f34,plain,(
% 1.45/1.29 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X2 @ X1)))) )),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.45/1.29 thf(f32,plain,(
% 1.45/1.29 ( ! [X2 : $i,X1 : $i] : (($true != $true) | ($true = (in @ X2 @ (setadjoin @ X2 @ X1)))) )),
% 1.45/1.29 inference(equality_resolution,[status(thm)],[f28])).
% 1.45/1.29 thf(f28,plain,(
% 1.45/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (X0 != X2) | ($true != $true)) )),
% 1.45/1.29 inference(definition_unfolding,[status(thm)],[f23,f18])).
% 1.45/1.29 thf(f18,plain,(
% 1.45/1.29 (setadjoinAx = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.45/1.29 thf(f12,plain,(
% 1.45/1.29 ((in @ sK1 @ (setadjoin @ sK1 @ sK0)) != $true) & (setadjoinAx = $true)),
% 1.45/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11])).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) => ((in @ sK1 @ (setadjoin @ sK1 @ sK0)) != $true)),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) & (setadjoinAx = $true)),
% 1.45/1.29 inference(rectify,[status(thm)],[f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ? [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true) & (setadjoinAx = $true)),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ~((setadjoinAx = $true) => ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true))),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ~(setadjoinAx => ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.45/1.29 inference(rectify,[status(thm)],[f3])).
% 1.45/1.29 thf(f3,negated_conjecture,(
% 1.45/1.29 ~(setadjoinAx => ! [X0 : $i,X2 : $i] : (in @ X0 @ (setadjoin @ X0 @ X2)))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.45/1.29 thf(f2,conjecture,(
% 1.45/1.29 setadjoinAx => ! [X0 : $i,X2 : $i] : (in @ X0 @ (setadjoin @ X0 @ X2))),
% 1.45/1.29 file('/export/starexec/sandbox2/tmp/tmp.BghactM7qu/DTF2THF_3124.p',setadjoinIL)).
% 1.45/1.29 thf(f23,plain,(
% 1.45/1.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (X0 != X2) | (setadjoinAx != $true)) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.45/1.29 thf(f17,plain,(
% 1.45/1.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X1)) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (($true != (in @ X0 @ X1)) & (X0 != X2)))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ((((in @ sK2 @ (setadjoin @ sK4 @ sK3)) != $true) | (((in @ sK2 @ sK3) != $true) & (sK4 != sK2))) & (((in @ sK2 @ (setadjoin @ sK4 @ sK3)) = $true) | ((in @ sK2 @ sK3) = $true) | (sK4 = sK2))))),
% 1.45/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f15,f16])).
% 1.45/1.29 thf(f16,plain,(
% 1.45/1.29 ? [X3 : $i,X4 : $i,X5 : $i] : ((($true != (in @ X3 @ (setadjoin @ X5 @ X4))) | (($true != (in @ X3 @ X4)) & (X3 != X5))) & (($true = (in @ X3 @ (setadjoin @ X5 @ X4))) | ($true = (in @ X3 @ X4)) | (X3 = X5))) => ((((in @ sK2 @ (setadjoin @ sK4 @ sK3)) != $true) | (((in @ sK2 @ sK3) != $true) & (sK4 != sK2))) & (((in @ sK2 @ (setadjoin @ sK4 @ sK3)) = $true) | ((in @ sK2 @ sK3) = $true) | (sK4 = sK2)))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f15,plain,(
% 1.45/1.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X1)) | (X0 = X2) | ($true != (in @ X0 @ (setadjoin @ X2 @ X1)))) & (($true = (in @ X0 @ (setadjoin @ X2 @ X1))) | (($true != (in @ X0 @ X1)) & (X0 != X2)))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((($true != (in @ X3 @ (setadjoin @ X5 @ X4))) | (($true != (in @ X3 @ X4)) & (X3 != X5))) & (($true = (in @ X3 @ (setadjoin @ X5 @ X4))) | ($true = (in @ X3 @ X4)) | (X3 = X5))))),
% 1.45/1.29 inference(rectify,[status(thm)],[f14])).
% 1.45/1.29 thf(f14,plain,(
% 1.45/1.29 (! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (in @ X2 @ X0)) | (X1 = X2) | ($true != (in @ X2 @ (setadjoin @ X1 @ X0)))) & (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | (($true != (in @ X2 @ X0)) & (X1 != X2)))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | (($true != (in @ X2 @ X0)) & (X1 != X2))) & (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | ($true = (in @ X2 @ X0)) | (X1 = X2))))),
% 1.45/1.29 inference(flattening,[status(thm)],[f13])).
% 1.45/1.29 thf(f13,plain,(
% 1.45/1.29 (! [X2 : $i,X0 : $i,X1 : $i] : (((($true = (in @ X2 @ X0)) | (X1 = X2)) | ($true != (in @ X2 @ (setadjoin @ X1 @ X0)))) & (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | (($true != (in @ X2 @ X0)) & (X1 != X2)))) | (setadjoinAx != $true)) & ((setadjoinAx = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((($true != (in @ X2 @ (setadjoin @ X1 @ X0))) | (($true != (in @ X2 @ X0)) & (X1 != X2))) & (($true = (in @ X2 @ (setadjoin @ X1 @ X0))) | (($true = (in @ X2 @ X0)) | (X1 = X2)))))),
% 1.45/1.29 inference(nnf_transformation,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 ! [X2 : $i,X0 : $i,X1 : $i] : ((($true = (in @ X2 @ X0)) | (X1 = X2)) <=> ($true = (in @ X2 @ (setadjoin @ X1 @ X0)))) <=> (setadjoinAx = $true)),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 (setadjoinAx = ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) | (X1 = X2)) <=> (in @ X2 @ (setadjoin @ X1 @ X0))))),
% 1.45/1.29 inference(rectify,[status(thm)],[f1])).
% 1.45/1.29 thf(f1,axiom,(
% 1.45/1.29 (setadjoinAx = ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X2 @ X1) | (X0 = X2)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))))),
% 1.45/1.29 file('/export/starexec/sandbox2/tmp/tmp.BghactM7qu/DTF2THF_3124.p',setadjoinAx)).
% 1.45/1.29 thf(f19,plain,(
% 1.45/1.29 ((in @ sK1 @ (setadjoin @ sK1 @ sK0)) != $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.45/1.29 % SZS output end Proof for DTF2THF_3124
% 1.45/1.29 % (3345)------------------------------
% 1.45/1.29 % (3345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (3345)Termination reason: Refutation
% 1.45/1.29
% 1.45/1.29 % (3345)Memory used [KB]: 5500
% 1.45/1.29 % (3345)Time elapsed: 0.003 s
% 1.45/1.29 % (3345)Instructions burned: 1 (million)
% 1.45/1.29 % (3345)------------------------------
% 1.45/1.29 % (3345)------------------------------
% 1.45/1.29 % (3338)Success in time 0.013 s
%------------------------------------------------------------------------------