%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU513^2 : 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 : n011.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 09:35:01 AM UTC 2026
% Result : Theorem 1.64s 1.33s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 30 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 114 ( 16 ~; 8 |; 4 &; 80 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 18 !; 6 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$true != $true,
inference(superposition,[status(thm)],[f15,f20]) ).
thf(f20,plain,
! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f16,f14]) ).
thf(f14,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( setadjoinIL = $true )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZmwmRNBSwP/DTF2THF_29116.p',emptyinunitempty) ).
thf(f16,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( setadjoinIL = $true )
| ( ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
=> ( ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( setadjoinIL = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZmwmRNBSwP/DTF2THF_29116.p',setadjoinIL) ).
thf(f15,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SEU513^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.15 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Feb 24 12:24:47 EST 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.48 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SEU513^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.49 % Domain : Set Theory
% 0.28/0.49 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.28/0.49 % Version : Especial > Reduced > Especial.
% 0.28/0.49 % English : in emptyset (setadjoin emptyset emptyset)
% 0.28/0.49
% 0.28/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.49 % Source : [Bro08]
% 0.28/0.49 % Names : ZFC015l [Bro08]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.28/0.49 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.28/0.49 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 2 ( 2 avg)
% 0.28/0.49 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 8 @)
% 0.28/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 5 ( 3 avg)
% 0.28/0.49 % Number of types : 2 ( 0 usr)
% 0.28/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.28/0.49 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.28/0.49 % SPC : TH0_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : http://mathgate.info/detsetitem.php?id=390
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(in_type,type,
% 0.28/0.49 in: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyset_type,type,
% 0.28/0.49 emptyset: $i ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoin_type,type,
% 0.28/0.49 setadjoin: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIL_type,type,
% 0.28/0.49 setadjoinIL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIL,definition,
% 0.28/0.49 ( setadjoinIL
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyinunitempty,conjecture,
% 0.28/0.49 ( setadjoinIL
% 0.28/0.49 => ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.64/1.30 ---- Embedded in THF ---
% 1.64/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.31 %%% Generated on Tue Feb 24 12:24:48 EST 2026
% 1.64/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.31 %%% Logic specification used:
% 1.64/1.31 %%% thf(spec, logic, $$dhol).
% 1.64/1.31
% 1.64/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ZmwmRNBSwP/DTF2DTF29116.p
% See solution above
% 1.64/1.31 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(in_type,type,
% 1.64/1.32 in: $i > $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(emptyset_type,type,
% 1.64/1.32 emptyset: $i ).
% 1.64/1.32
% 1.64/1.32 thf(setadjoin_type,type,
% 1.64/1.32 setadjoin: $i > $i > $i ).
% 1.64/1.32
% 1.64/1.32 thf(setadjoinIL_type,type,
% 1.64/1.32 setadjoinIL: $o ).
% 1.64/1.32
% 1.64/1.32 thf(setadjoinIL,definition,
% 1.64/1.32 ( setadjoinIL
% 1.64/1.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(emptyinunitempty,conjecture,
% 1.64/1.32 ( setadjoinIL
% 1.64/1.32 => ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.64/1.32 ------------------------
% 1.64/1.33 % (29274)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29116 for (3000ds/18Mi)
% 1.64/1.33 % (29272)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_29116 for (3000ds/2Mi)
% 1.64/1.33 % (29271)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29116 for (3000ds/2Mi)
% 1.64/1.33 % (29270)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_29116 for (3000ds/27Mi)
% 1.64/1.33 % (29272)Instruction limit reached!
% 1.64/1.33 % (29272)------------------------------
% 1.64/1.33 % (29272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29272)Termination reason: Unknown
% 1.64/1.33 % (29272)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (29272)Memory used [KB]: 5500
% 1.64/1.33 % (29272)Time elapsed: 0.002 s
% 1.64/1.33 % (29272)Instructions burned: 2 (million)
% 1.64/1.33 % (29272)------------------------------
% 1.64/1.33 % (29272)------------------------------
% 1.64/1.33 % (29274)First to succeed.
% 1.64/1.33 % (29270)Also succeeded, but the first one will report.
% 1.64/1.33 % (29274)Refutation found. Thanks to Tanya!
% 1.64/1.33 % SZS status Theorem for DTF2THF_29116
% 1.64/1.33 % SZS output start Proof for DTF2THF_29116
% 1.64/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.33 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.64/1.33 thf(f22,plain,(
% 1.64/1.33 $false),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.64/1.33 thf(f21,plain,(
% 1.64/1.33 ($true != $true)),
% 1.64/1.33 inference(superposition,[status(thm)],[f15,f20])).
% 1.64/1.33 thf(f20,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ X2)) = $true)) )),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.64/1.33 thf(f19,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ((in @ X3 @ (setadjoin @ X3 @ X2)) = $true)) )),
% 1.64/1.33 inference(definition_unfolding,[status(thm)],[f16,f14])).
% 1.64/1.33 thf(f14,plain,(
% 1.64/1.33 (setadjoinIL = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.33 thf(f9,plain,(
% 1.64/1.33 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) != $true) & (setadjoinIL = $true)),
% 1.64/1.33 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.33 thf(f6,plain,(
% 1.64/1.33 ~((setadjoinIL = $true) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) = $true))),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f5])).
% 1.64/1.33 thf(f5,plain,(
% 1.64/1.33 ~(setadjoinIL => (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))),
% 1.64/1.33 inference(rectify,[status(thm)],[f3])).
% 1.64/1.33 thf(f3,negated_conjecture,(
% 1.64/1.33 ~(setadjoinIL => (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))),
% 1.64/1.33 inference(negated_conjecture,[status(cth)],[f2])).
% 1.64/1.33 thf(f2,conjecture,(
% 1.64/1.33 setadjoinIL => (in @ emptyset @ (setadjoin @ emptyset @ emptyset))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.ZmwmRNBSwP/DTF2THF_29116.p',emptyinunitempty)).
% 1.64/1.33 thf(f16,plain,(
% 1.64/1.33 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ X2)) = $true) | (setadjoinIL != $true)) )),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.33 thf(f13,plain,(
% 1.64/1.33 ((setadjoinIL = $true) | ((in @ sK1 @ (setadjoin @ sK1 @ sK0)) != $true)) & (! [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X3 @ X2)) = $true) | (setadjoinIL != $true))),
% 1.64/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12])).
% 1.64/1.33 thf(f12,plain,(
% 1.64/1.33 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) => ((in @ sK1 @ (setadjoin @ sK1 @ sK0)) != $true)),
% 1.64/1.33 introduced(definition,[],[choice_axiom])).
% 1.64/1.33 thf(f11,plain,(
% 1.64/1.33 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X2 : $i,X3 : $i] : ((in @ X3 @ (setadjoin @ X3 @ X2)) = $true) | (setadjoinIL != $true))),
% 1.64/1.33 inference(rectify,[status(thm)],[f10])).
% 1.64/1.33 thf(f10,plain,(
% 1.64/1.33 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true))),
% 1.64/1.33 inference(nnf_transformation,[status(thm)],[f8])).
% 1.64/1.33 thf(f8,plain,(
% 1.64/1.33 (setadjoinIL = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.33 thf(f7,plain,(
% 1.64/1.33 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.64/1.33 inference(rectify,[status(thm)],[f1])).
% 1.64/1.33 thf(f1,axiom,(
% 1.64/1.33 (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.ZmwmRNBSwP/DTF2THF_29116.p',setadjoinIL)).
% 1.64/1.33 thf(f15,plain,(
% 1.64/1.33 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) != $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.33 % SZS output end Proof for DTF2THF_29116
% 1.64/1.33 % (29274)------------------------------
% 1.64/1.33 % (29274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (29274)Termination reason: Refutation
% 1.64/1.33
% 1.64/1.33 % (29274)Memory used [KB]: 5500
% 1.64/1.33 % (29274)Time elapsed: 0.003 s
% 1.64/1.33 % (29274)Instructions burned: 2 (million)
% 1.64/1.33 % (29274)------------------------------
% 1.64/1.33 % (29274)------------------------------
% 1.64/1.33 % (29266)Success in time 0.005 s
%------------------------------------------------------------------------------