%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU551^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 09:35:13 AM UTC 2026
% Result : Theorem 1.40s 1.28s
% Output : Refutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f4]) ).
fof(f4,plain,
emptyset != emptyset,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f3,plain,
emptyset != emptyset,
inference(flattening,[status(thm)],[f2]) ).
fof(f2,negated_conjecture,
emptyset != emptyset,
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1,conjecture,
emptyset = emptyset,
file('/export/starexec/sandbox2/tmp/tmp.SaTlfDTq0a/DTF2THF_9733.p',emptyset__Cong) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU551^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:26:40 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU551^2 : TPTP v9.2.1. Bugfixed v4.0.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : A simple congruence property of emptyset
% 0.17/0.38 % Version : Especial > Reduced > Especial.
% 0.17/0.38 % English :
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC053l [Bro08]
% 0.17/0.38 % : ZFC057l [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.17/0.38 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.17/0.38 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.38 % Number of connectives : 0 ( 0 ~; 0 |; 0 &; 0 @)
% 0.17/0.38 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 1 ( 1 avg)
% 0.17/0.38 % Number of types : 1 ( 0 usr)
% 0.17/0.38 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 2 ( 1 usr; 1 con; 0-2 aty)
% 0.17/0.38 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=27
% 0.17/0.38 % : v4.0.0 - Added emptyset type
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(emptyset,type,
% 0.17/0.38 emptyset: $i ).
% 0.17/0.38
% 0.17/0.38 thf(emptyset__Cong,conjecture,
% 0.17/0.38 emptyset = emptyset ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.40/1.25 ---- Embedded in THF ---
% 1.40/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.25 %%% Generated on Tue Feb 24 12:26:41 EST 2026
% 1.40/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.25 %%% Logic specification used:
% 1.40/1.25 %%% thf(spec, logic, $$dhol).
% 1.40/1.25
% 1.40/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SaTlfDTq0a/DTF2DTF9733.p
% See solution above
% 1.40/1.25 ------------------------
% 1.40/1.25 ---- Cleaned THF ---
% 1.40/1.26 thf(emptyset,type,
% 1.40/1.26 emptyset: $i ).
% 1.40/1.26
% 1.40/1.26 thf(emptyset__Cong,conjecture,
% 1.40/1.26 emptyset = emptyset ).
% 1.40/1.26 ------------------------
% 1.40/1.28 % (9832)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_9733 for (3000ds/27Mi)
% 1.40/1.28 % (9830)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9733 for (3000ds/183Mi)
% 1.40/1.28 % (9831)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_9733 for (3000ds/4Mi)
% 1.40/1.28 % (9833)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9733 for (3000ds/2Mi)
% 1.40/1.28 % (9834)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_9733 for (3000ds/2Mi)
% 1.40/1.28 % (9835)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_9733 for (3000ds/275Mi)
% 1.40/1.28 % (9836)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9733 for (3000ds/18Mi)
% 1.40/1.28 % (9831)First to succeed.
% 1.40/1.28 % (9833)Also succeeded, but the first one will report.
% 1.40/1.28 % (9830)Also succeeded, but the first one will report.
% 1.40/1.28 % (9831)Refutation found. Thanks to Tanya!
% 1.40/1.28 % SZS status Theorem for DTF2THF_9733
% 1.40/1.28 % SZS output start Proof for DTF2THF_9733
% 1.40/1.28 fof(f5,plain,(
% 1.40/1.28 $false),
% 1.40/1.28 inference(trivial_inequality_removal,[status(thm)],[f4])).
% 1.40/1.28 fof(f4,plain,(
% 1.40/1.28 emptyset != emptyset),
% 1.40/1.28 inference(cnf_transformation,[status(thm)],[f3])).
% 1.40/1.28 fof(f3,plain,(
% 1.40/1.28 emptyset != emptyset),
% 1.40/1.28 inference(flattening,[status(thm)],[f2])).
% 1.40/1.28 fof(f2,negated_conjecture,(
% 1.40/1.28 ~emptyset = emptyset),
% 1.40/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.40/1.28 fof(f1,conjecture,(
% 1.40/1.28 emptyset = emptyset),
% 1.40/1.28 file('/export/starexec/sandbox2/tmp/tmp.SaTlfDTq0a/DTF2THF_9733.p',emptyset__Cong)).
% 1.40/1.28 % SZS output end Proof for DTF2THF_9733
% 1.40/1.28 % (9831)------------------------------
% 1.40/1.28 % (9831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.28 % (9831)Termination reason: Refutation
% 1.40/1.28
% 1.40/1.28 % (9831)Memory used [KB]: 5373
% 1.40/1.28 % (9831)Time elapsed: 0.002 s
% 1.40/1.28 % (9831)Instructions burned: 1 (million)
% 1.40/1.28 % (9831)------------------------------
% 1.40/1.28 % (9831)------------------------------
% 1.40/1.28 % (9829)Success in time 0.017 s
%------------------------------------------------------------------------------