%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU529^2 : 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 : n020.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 09:35:06 AM UTC 2026
% Result : Theorem 1.62s 1.30s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 127 ( 10 ~; 0 |; 6 &; 94 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 32 ( 10 ^; 18 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
$true != $true,
inference(superposition,[status(thm)],[f17,f21]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f12]) ).
thf(f12,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,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/sandbox2/tmp/tmp.B6l83KFmvG/DTF2THF_15821.p',setadjoinIL) ).
thf(f15,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setadjoinIL = $true )
& ( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
!= $true )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 = X1 ) )
=> ( ( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
!= $true )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( setadjoinIL = $true )
& ? [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setadjoinIL = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setadjoinIL
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinIL
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinIL
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.B6l83KFmvG/DTF2THF_15821.p',eqinunit) ).
thf(f17,plain,
( ( in @ sK0 @ ( setadjoin @ sK0 @ emptyset ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f14,f13]) ).
thf(f13,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU529^2 : 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
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:25:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU529^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Preliminary Notions - Equality Laws
% 0.30/0.47 % Version : Especial > Reduced > Especial.
% 0.30/0.47 % English : (! x:i.! y:i.x = y -> in x (setadjoin y emptyset))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC031l [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % 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
% 0.30/0.47 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.30/0.47 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.30/0.47 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 8 @)
% 0.30/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 8 ( 5 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=94
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyset_type,type,
% 0.30/0.47 emptyset: $i ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoin_type,type,
% 0.30/0.47 setadjoin: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL_type,type,
% 0.30/0.47 setadjoinIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL,definition,
% 0.30/0.47 ( setadjoinIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit,conjecture,
% 0.30/0.47 ( setadjoinIL
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:25:58 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.B6l83KFmvG/DTF2DTF15821.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(in_type,type,
% 1.46/1.28 in: $i > $i > $o ).
% 1.46/1.28
% 1.46/1.28 thf(emptyset_type,type,
% 1.46/1.28 emptyset: $i ).
% 1.46/1.28
% 1.46/1.28 thf(setadjoin_type,type,
% 1.46/1.28 setadjoin: $i > $i > $i ).
% 1.46/1.28
% 1.46/1.28 thf(setadjoinIL_type,type,
% 1.46/1.28 setadjoinIL: $o ).
% 1.46/1.28
% 1.46/1.28 thf(setadjoinIL,definition,
% 1.46/1.28 ( setadjoinIL
% 1.46/1.28 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.46/1.28
% 1.46/1.28 thf(eqinunit,conjecture,
% 1.46/1.28 ( setadjoinIL
% 1.46/1.28 => ! [Xx: $i,Xy: $i] :
% 1.46/1.28 ( ( Xx = Xy )
% 1.46/1.28 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ).
% 1.46/1.28 ------------------------
% 1.62/1.30 % (15935)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15821 for (3000ds/183Mi)
% 1.62/1.30 % (15941)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15821 for (3000ds/18Mi)
% 1.62/1.30 % (15935)First to succeed.
% 1.62/1.30 % (15941)Also succeeded, but the first one will report.
% 1.62/1.30 % (15935)Refutation found. Thanks to Tanya!
% 1.62/1.30 % SZS status Theorem for DTF2THF_15821
% 1.62/1.30 % SZS output start Proof for DTF2THF_15821
% 1.62/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.62/1.30 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.62/1.30 thf(f23,plain,(
% 1.62/1.30 $false),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.62/1.30 thf(f22,plain,(
% 1.62/1.30 ($true != $true)),
% 1.62/1.30 inference(superposition,[status(thm)],[f17,f21])).
% 1.62/1.30 thf(f21,plain,(
% 1.62/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X2 @ X1)))) )),
% 1.62/1.30 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.62/1.30 thf(f20,plain,(
% 1.62/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2))) )),
% 1.62/1.30 inference(pi_clausification,[status(thm)],[f19])).
% 1.62/1.30 thf(f19,plain,(
% 1.62/1.30 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))))) )),
% 1.62/1.30 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.62/1.30 thf(f18,plain,(
% 1.62/1.30 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.62/1.30 inference(pi_clausification,[status(thm)],[f16])).
% 1.62/1.30 thf(f16,plain,(
% 1.62/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.62/1.30 inference(definition_unfolding,[status(thm)],[f15,f12])).
% 1.62/1.30 thf(f12,plain,(
% 1.62/1.30 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.62/1.30 thf(f6,plain,(
% 1.62/1.30 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.62/1.30 thf(f5,plain,(
% 1.62/1.30 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.62/1.30 inference(rectify,[status(thm)],[f1])).
% 1.62/1.30 thf(f1,axiom,(
% 1.62/1.30 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.62/1.30 file('/export/starexec/sandbox2/tmp/tmp.B6l83KFmvG/DTF2THF_15821.p',setadjoinIL)).
% 1.62/1.30 thf(f15,plain,(
% 1.62/1.30 (setadjoinIL = $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f11,plain,(
% 1.62/1.30 (setadjoinIL = $true) & (((in @ sK1 @ (setadjoin @ sK0 @ emptyset)) != $true) & (sK1 = sK0))),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.62/1.30 thf(f10,plain,(
% 1.62/1.30 ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 = X1)) => (((in @ sK1 @ (setadjoin @ sK0 @ emptyset)) != $true) & (sK1 = sK0))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f9,plain,(
% 1.62/1.30 (setadjoinIL = $true) & ? [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 = X1))),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.62/1.30 thf(f8,plain,(
% 1.62/1.30 ~((setadjoinIL = $true) => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ($true = (in @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.62/1.30 thf(f7,plain,(
% 1.62/1.30 ~(setadjoinIL => ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.62/1.30 inference(rectify,[status(thm)],[f3])).
% 1.62/1.30 thf(f3,negated_conjecture,(
% 1.62/1.30 ~(setadjoinIL => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.62/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.62/1.30 thf(f2,conjecture,(
% 1.62/1.30 setadjoinIL => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset)))),
% 1.62/1.30 file('/export/starexec/sandbox2/tmp/tmp.B6l83KFmvG/DTF2THF_15821.p',eqinunit)).
% 1.62/1.30 thf(f17,plain,(
% 1.62/1.30 ((in @ sK0 @ (setadjoin @ sK0 @ emptyset)) != $true)),
% 1.62/1.30 inference(definition_unfolding,[status(thm)],[f14,f13])).
% 1.62/1.30 thf(f13,plain,(
% 1.62/1.30 (sK1 = sK0)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f14,plain,(
% 1.62/1.30 ((in @ sK1 @ (setadjoin @ sK0 @ emptyset)) != $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 % SZS output end Proof for DTF2THF_15821
% 1.62/1.30 % (15935)------------------------------
% 1.62/1.30 % (15935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (15935)Termination reason: Refutation
% 1.62/1.30
% 1.62/1.30 % (15935)Memory used [KB]: 5500
% 1.62/1.30 % (15935)Time elapsed: 0.003 s
% 1.62/1.30 % (15935)Instructions burned: 1 (million)
% 1.62/1.30 % (15935)------------------------------
% 1.62/1.30 % (15935)------------------------------
% 1.62/1.30 % (15934)Success in time 0.002 s
%------------------------------------------------------------------------------