%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU553^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:35:14 AM UTC 2026
% Result : Theorem 0.30s 1.43s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 34 ( 8 ~; 0 |; 5 &; 18 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 4 !; 6 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
powerset: $i > $i ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( powerset @ sK0 )
!= ( powerset @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f9,f8]) ).
thf(f8,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( powerset @ sK1 )
!= ( powerset @ sK0 ) )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6]) ).
thf(f6,plain,
( ? [X0: $i,X1: $i] :
( ( ( powerset @ X0 )
!= ( powerset @ X1 ) )
& ( X0 = X1 ) )
=> ( ( ( powerset @ sK1 )
!= ( powerset @ sK0 ) )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
? [X0: $i,X1: $i] :
( ( ( powerset @ X0 )
!= ( powerset @ X1 ) )
& ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,plain,
? [X1: $i,X0: $i] :
( ( ( powerset @ X0 )
!= ( powerset @ X1 ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( powerset @ X0 )
= ( powerset @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( powerset @ X0 )
= ( powerset @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8Lq8WkAdZy/DTF2THF_8415.p',powerset__Cong) ).
thf(f9,plain,
( ( powerset @ sK1 )
!= ( powerset @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU553^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:26:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU553^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : A simple congruence property of powerset
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (forall A:i.forall B:i.A = B -> powerset A = powerset B)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC055l [Bro08]
% 0.30/0.46 % : ZFC056l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.30/0.46 % Number of types : 1 ( 0 usr)
% 0.30/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.30/0.46 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=32
% 0.30/0.46 % : v4.0.0 - Added powerset type
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(powerset,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong,conjecture,
% 0.30/0.46 ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( powerset @ A )
% 0.30/0.46 = ( powerset @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.30/1.40 ---- Embedded in THF ---
% 0.30/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.40 %%% Generated on Tue Feb 24 12:26:11 EST 2026
% 0.30/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.40 %%% Logic specification used:
% 0.30/1.40 %%% thf(spec, logic, $$dhol).
% 0.30/1.40
% 0.30/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8Lq8WkAdZy/DTF2DTF8415.p
% See solution above
% 0.30/1.40 ------------------------
% 0.30/1.41 ---- Cleaned THF ---
% 0.30/1.41 thf(powerset,type,
% 0.30/1.41 powerset: $i > $i ).
% 0.30/1.41
% 0.30/1.41 thf(powerset__Cong,conjecture,
% 0.30/1.41 ! [A: $i,B: $i] :
% 0.30/1.41 ( ( A = B )
% 0.30/1.41 => ( ( powerset @ A )
% 0.30/1.41 = ( powerset @ B ) ) ) ).
% 0.30/1.41 ------------------------
% 0.30/1.43 % (8512)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8415 for (3000ds/183Mi)
% 0.30/1.43 % (8514)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_8415 for (3000ds/27Mi)
% 0.30/1.43 % (8517)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_8415 for (3000ds/275Mi)
% 0.30/1.43 % (8513)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_8415 for (3000ds/4Mi)
% 0.30/1.43 % (8518)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8415 for (3000ds/18Mi)
% 0.30/1.43 % (8515)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8415 for (3000ds/2Mi)
% 0.30/1.43 % (8516)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_8415 for (3000ds/2Mi)
% 0.30/1.43 % (8515)First to succeed.
% 0.30/1.43 % (8513)Also succeeded, but the first one will report.
% 0.30/1.43 % (8512)Also succeeded, but the first one will report.
% 0.30/1.43 % (8515)Refutation found. Thanks to Tanya!
% 0.30/1.43 % SZS status Theorem for DTF2THF_8415
% 0.30/1.43 % SZS output start Proof for DTF2THF_8415
% 0.30/1.43 thf(func_def_0, type, powerset: $i > $i).
% 0.30/1.43 thf(f11,plain,(
% 0.30/1.43 $false),
% 0.30/1.43 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 0.30/1.43 thf(f10,plain,(
% 0.30/1.43 ((powerset @ sK0) != (powerset @ sK0))),
% 0.30/1.43 inference(definition_unfolding,[status(thm)],[f9,f8])).
% 0.30/1.43 thf(f8,plain,(
% 0.30/1.43 (sK1 = sK0)),
% 0.30/1.43 inference(cnf_transformation,[status(thm)],[f7])).
% 0.30/1.43 thf(f7,plain,(
% 0.30/1.43 ((powerset @ sK1) != (powerset @ sK0)) & (sK1 = sK0)),
% 0.30/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6])).
% 0.30/1.43 thf(f6,plain,(
% 0.30/1.43 ? [X0 : $i,X1 : $i] : (((powerset @ X0) != (powerset @ X1)) & (X0 = X1)) => (((powerset @ sK1) != (powerset @ sK0)) & (sK1 = sK0))),
% 0.30/1.43 introduced(definition,[],[choice_axiom])).
% 0.30/1.43 thf(f5,plain,(
% 0.30/1.43 ? [X0 : $i,X1 : $i] : (((powerset @ X0) != (powerset @ X1)) & (X0 = X1))),
% 0.30/1.43 inference(rectify,[status(thm)],[f4])).
% 0.30/1.43 thf(f4,plain,(
% 0.30/1.43 ? [X1 : $i,X0 : $i] : (((powerset @ X0) != (powerset @ X1)) & (X0 = X1))),
% 0.30/1.43 inference(ennf_transformation,[status(thm)],[f2])).
% 0.30/1.43 thf(f2,negated_conjecture,(
% 0.30/1.43 ~! [X1 : $i,X0 : $i] : ((X0 = X1) => ((powerset @ X0) = (powerset @ X1)))),
% 0.30/1.43 inference(negated_conjecture,[status(cth)],[f1])).
% 0.30/1.43 thf(f1,conjecture,(
% 0.30/1.43 ! [X1 : $i,X0 : $i] : ((X0 = X1) => ((powerset @ X0) = (powerset @ X1)))),
% 0.30/1.43 file('/export/starexec/sandbox/tmp/tmp.8Lq8WkAdZy/DTF2THF_8415.p',powerset__Cong)).
% 0.30/1.43 thf(f9,plain,(
% 0.30/1.43 ((powerset @ sK1) != (powerset @ sK0))),
% 0.30/1.43 inference(cnf_transformation,[status(thm)],[f7])).
% 0.30/1.43 % SZS output end Proof for DTF2THF_8415
% 0.30/1.43 % (8515)------------------------------
% 0.30/1.43 % (8515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.43 % (8515)Termination reason: Refutation
% 0.30/1.43
% 0.30/1.43 % (8515)Memory used [KB]: 5373
% 0.30/1.43 % (8515)Time elapsed: 0.003 s
% 0.30/1.43 % (8515)Instructions burned: 1 (million)
% 0.30/1.43 % (8515)------------------------------
% 0.30/1.43 % (8515)------------------------------
% 0.30/1.43 % (8511)Success in time 0.018 s
%------------------------------------------------------------------------------