%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU547^2 : 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 : n031.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 09:35:12 AM UTC 2026
% Result : Theorem 1.48s 1.23s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 105 ( 13 ~; 0 |; 22 &; 56 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 16 !; 20 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(f18,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( ( in @ sK3 @ sK1 )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f15]) ).
thf(f15,plain,
sK0 = sK1,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK0 = sK1 )
& ( sK2 = sK3 )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
!= ( in @ sK2 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X2 @ X1 ) ) ) )
=> ( ( sK0 = sK1 )
& ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( ( in @ X2 @ sK1 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( $true
= ( in @ X3 @ sK0 ) )
& ( ( in @ X2 @ sK1 )
!= $true ) )
=> ( ( sK2 = sK3 )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
!= ( in @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( $true
= ( in @ X3 @ X0 ) )
& ( $true
!= ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: $i,X0: $i] :
( ( X0 = X1 )
& ? [X3: $i,X2: $i] :
( ( X2 = X3 )
& ( $true
= ( in @ X2 @ X1 ) )
& ( $true
!= ( in @ X3 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) )
& ( X2 = X3 ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X3 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X3 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X3 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CYGcBzffoz/DTF2THF_5105.p',inCongP) ).
thf(f13,plain,
( ( in @ sK3 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f17,plain,
( ( in @ sK3 @ sK1 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f12,f14]) ).
thf(f14,plain,
sK2 = sK3,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
( $true
!= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU547^2 : 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:27:33 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU547^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Preliminary Notions - Equality Laws
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! A:i.! B:i.A = B -> (! x:i.! y:i.x = y -> in x A -> in y B))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC049l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 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
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.18/0.45 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=128
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(inCongP,conjecture,
% 0.18/0.45 ! [A: $i,B: $i] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xy @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.48/1.21 ---- Embedded in THF ---
% 1.48/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.21 %%% Generated on Tue Feb 24 12:27:34 EST 2026
% 1.48/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.21 %%% Logic specification used:
% 1.48/1.21 %%% thf(spec, logic, $$dhol).
% 1.48/1.21
% 1.48/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CYGcBzffoz/DTF2DTF5105.p
% See solution above
% 1.48/1.21 ------------------------
% 1.48/1.22 ---- Cleaned THF ---
% 1.48/1.22 thf(in,type,
% 1.48/1.22 in: $i > $i > $o ).
% 1.48/1.22
% 1.48/1.22 thf(inCongP,conjecture,
% 1.48/1.22 ! [A: $i,B: $i] :
% 1.48/1.22 ( ( A = B )
% 1.48/1.22 => ! [Xx: $i,Xy: $i] :
% 1.48/1.22 ( ( Xx = Xy )
% 1.48/1.22 => ( ( in @ Xx @ A )
% 1.48/1.22 => ( in @ Xy @ B ) ) ) ) ).
% 1.48/1.22 ------------------------
% 1.48/1.23 % (5225)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5105 for (3000ds/18Mi)
% 1.48/1.23 % (5220)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_5105 for (3000ds/4Mi)
% 1.48/1.23 % (5225)First to succeed.
% 1.48/1.23 % (5220)Also succeeded, but the first one will report.
% 1.48/1.23 % (5225)Refutation found. Thanks to Tanya!
% 1.48/1.23 % SZS status Theorem for DTF2THF_5105
% 1.48/1.23 % SZS output start Proof for DTF2THF_5105
% 1.48/1.23 thf(func_def_0, type, in: $i > $i > $o).
% 1.48/1.23 thf(f18,plain,(
% 1.48/1.23 $false),
% 1.48/1.23 inference(subsumption_resolution,[status(thm)],[f17,f16])).
% 1.48/1.23 thf(f16,plain,(
% 1.48/1.23 ((in @ sK3 @ sK1) = $true)),
% 1.48/1.23 inference(definition_unfolding,[status(thm)],[f13,f15])).
% 1.48/1.23 thf(f15,plain,(
% 1.48/1.23 (sK0 = sK1)),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.23 thf(f11,plain,(
% 1.48/1.23 (sK0 = sK1) & ((sK2 = sK3) & ((in @ sK3 @ sK0) = $true) & ($true != (in @ sK2 @ sK1)))),
% 1.48/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.48/1.23 thf(f9,plain,(
% 1.48/1.23 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ? [X2 : $i,X3 : $i] : ((X2 = X3) & ($true = (in @ X3 @ X0)) & ($true != (in @ X2 @ X1)))) => ((sK0 = sK1) & ? [X3 : $i,X2 : $i] : ((X2 = X3) & ($true = (in @ X3 @ sK0)) & ((in @ X2 @ sK1) != $true)))),
% 1.48/1.23 introduced(definition,[],[choice_axiom])).
% 1.48/1.23 thf(f10,plain,(
% 1.48/1.23 ? [X3 : $i,X2 : $i] : ((X2 = X3) & ($true = (in @ X3 @ sK0)) & ((in @ X2 @ sK1) != $true)) => ((sK2 = sK3) & ((in @ sK3 @ sK0) = $true) & ($true != (in @ sK2 @ sK1)))),
% 1.48/1.23 introduced(definition,[],[choice_axiom])).
% 1.48/1.23 thf(f8,plain,(
% 1.48/1.23 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ? [X2 : $i,X3 : $i] : ((X2 = X3) & ($true = (in @ X3 @ X0)) & ($true != (in @ X2 @ X1))))),
% 1.48/1.23 inference(rectify,[status(thm)],[f7])).
% 1.48/1.23 thf(f7,plain,(
% 1.48/1.23 ? [X1 : $i,X0 : $i] : ((X0 = X1) & ? [X3 : $i,X2 : $i] : ((X2 = X3) & ($true = (in @ X2 @ X1)) & ($true != (in @ X3 @ X0))))),
% 1.48/1.23 inference(flattening,[status(thm)],[f6])).
% 1.48/1.23 thf(f6,plain,(
% 1.48/1.23 ? [X0 : $i,X1 : $i] : (? [X2 : $i,X3 : $i] : ((($true != (in @ X3 @ X0)) & ($true = (in @ X2 @ X1))) & (X2 = X3)) & (X0 = X1))),
% 1.48/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.23 thf(f5,plain,(
% 1.48/1.23 ~! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => (($true = (in @ X2 @ X1)) => ($true = (in @ X3 @ X0)))))),
% 1.48/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.23 thf(f4,plain,(
% 1.48/1.23 ~! [X0 : $i,X1 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X1) => (in @ X3 @ X0))))),
% 1.48/1.23 inference(rectify,[status(thm)],[f2])).
% 1.48/1.23 thf(f2,negated_conjecture,(
% 1.48/1.23 ~! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1))))),
% 1.48/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.23 thf(f1,conjecture,(
% 1.48/1.23 ! [X1 : $i,X0 : $i] : ((X0 = X1) => ! [X2 : $i,X3 : $i] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1))))),
% 1.48/1.23 file('/export/starexec/sandbox/tmp/tmp.CYGcBzffoz/DTF2THF_5105.p',inCongP)).
% 1.48/1.23 thf(f13,plain,(
% 1.48/1.23 ((in @ sK3 @ sK0) = $true)),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.23 thf(f17,plain,(
% 1.48/1.23 ((in @ sK3 @ sK1) != $true)),
% 1.48/1.23 inference(definition_unfolding,[status(thm)],[f12,f14])).
% 1.48/1.23 thf(f14,plain,(
% 1.48/1.23 (sK2 = sK3)),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.23 thf(f12,plain,(
% 1.48/1.23 ($true != (in @ sK2 @ sK1))),
% 1.48/1.23 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.23 % SZS output end Proof for DTF2THF_5105
% 1.48/1.23 % (5225)------------------------------
% 1.48/1.23 % (5225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.23 % (5225)Termination reason: Refutation
% 1.48/1.23
% 1.48/1.23 % (5225)Memory used [KB]: 5500
% 1.48/1.23 % (5225)Time elapsed: 0.002 s
% 1.48/1.23 % (5225)Instructions burned: 1 (million)
% 1.48/1.23 % (5225)------------------------------
% 1.48/1.23 % (5225)------------------------------
% 1.48/1.23 % (5218)Success in time 0.002 s
%------------------------------------------------------------------------------