%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU551^3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 1.61s 1.42s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 4 ( 2 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(func_def_0,type,
a: $tType ).
tff(func_def_1,type,
sK0: a ).
tff(f7,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f6]) ).
tff(f6,plain,
sK0 != sK0,
inference(cnf_transformation,[status(thm)],[f5]) ).
tff(f5,plain,
sK0 != sK0,
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f3,f4]) ).
tff(f4,plain,
( ? [X0: a] : ( X0 != X0 )
=> ( sK0 != sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f3,plain,
? [X0: a] : ( X0 != X0 ),
inference(ennf_transformation,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: a] : ( X0 = X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
! [X0: a] : ( X0 = X0 ),
file('/export/starexec/sandbox/tmp/tmp.Mp9yoZwhri/DTF2THF_11996.p',cER_eq_) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU551^3 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:27:40 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : SEU551^3 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.47 % Domain : Set Theory
% 0.18/0.47 % Problem : A simple congruence property of emptyset
% 0.18/0.47 % Version : Especial.
% 0.18/0.47 % English : Reflexivity.
% 0.18/0.47
% 0.18/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.47 % Source : [Bro09]
% 0.18/0.47 % Names : tps_0010 [Bro09]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 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 v5.1.0
% 0.18/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.18/0.47 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.18/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.18/0.47 % Number of connectives : 0 ( 0 ~; 0 |; 0 &; 0 @)
% 0.18/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 2 ( 2 avg)
% 0.18/0.47 % Number of types : 1 ( 1 usr)
% 0.18/0.47 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.47 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.18/0.47 % SPC : TH0_THM_EQU_NAR
% 0.18/0.47
% 0.18/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.47 % : TPS problem from TTTP-NATS-THMS
% 0.18/0.47 % : Renamed from SEV283^5
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 thf(a_type,type,
% 0.18/0.47 a: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(cER_eq_,conjecture,
% 0.18/0.47 ! [A: a] : ( A = A ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 1.45/1.38 ---- Embedded in THF ---
% 1.45/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.39 %%% Generated on Tue Feb 24 12:27:41 EST 2026
% 1.45/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.39 %%% Logic specification used:
% 1.45/1.39 %%% thf(spec, logic, $$dhol).
% 1.45/1.39
% 1.45/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Mp9yoZwhri/DTF2DTF11996.p
% See solution above
% 1.45/1.39 ------------------------
% 1.45/1.39 ---- Cleaned THF ---
% 1.45/1.39 thf(a_type,type,
% 1.45/1.39 a: $tType ).
% 1.45/1.39
% 1.45/1.39 thf(cER_eq_,conjecture,
% 1.45/1.39 ! [A: a] : ( A = A ) ).
% 1.45/1.39 ------------------------
% 1.61/1.41 % (12099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11996 for (3000ds/18Mi)
% 1.61/1.41 % (12094)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_11996 for (3000ds/4Mi)
% 1.61/1.41 % (12093)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11996 for (3000ds/183Mi)
% 1.61/1.41 % (12095)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_11996 for (3000ds/27Mi)
% 1.61/1.41 % (12097)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_11996 for (3000ds/2Mi)
% 1.61/1.41 % (12096)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11996 for (3000ds/2Mi)
% 1.61/1.41 % (12098)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_11996 for (3000ds/275Mi)
% 1.61/1.41 % (12093)First to succeed.
% 1.61/1.42 % (12094)Also succeeded, but the first one will report.
% 1.61/1.42 % (12095)Also succeeded, but the first one will report.
% 1.61/1.42 % (12093)Refutation found. Thanks to Tanya!
% 1.61/1.42 % SZS status Theorem for DTF2THF_11996
% 1.61/1.42 % SZS output start Proof for DTF2THF_11996
% 1.61/1.42 tff(type_def_5, type, a: $tType).
% 1.61/1.42 tff(func_def_0, type, a: $tType).
% 1.61/1.42 tff(func_def_1, type, sK0: a).
% 1.61/1.42 tff(f7,plain,(
% 1.61/1.42 $false),
% 1.61/1.42 inference(trivial_inequality_removal,[status(thm)],[f6])).
% 1.61/1.42 tff(f6,plain,(
% 1.61/1.42 sK0 != sK0),
% 1.61/1.42 inference(cnf_transformation,[status(thm)],[f5])).
% 1.61/1.42 tff(f5,plain,(
% 1.61/1.42 sK0 != sK0),
% 1.61/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f3,f4])).
% 1.61/1.42 tff(f4,plain,(
% 1.61/1.42 ? [X0 : a] : X0 != X0 => sK0 != sK0),
% 1.61/1.42 introduced(definition,[],[choice_axiom])).
% 1.61/1.42 tff(f3,plain,(
% 1.61/1.42 ? [X0 : a] : X0 != X0),
% 1.61/1.42 inference(ennf_transformation,[status(thm)],[f2])).
% 1.61/1.42 tff(f2,negated_conjecture,(
% 1.61/1.42 ~! [X0 : a] : X0 = X0),
% 1.61/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.42 tff(f1,conjecture,(
% 1.61/1.42 ! [X0 : a] : X0 = X0),
% 1.61/1.42 file('/export/starexec/sandbox/tmp/tmp.Mp9yoZwhri/DTF2THF_11996.p',cER_eq_)).
% 1.61/1.42 % SZS output end Proof for DTF2THF_11996
% 1.61/1.42 % (12093)------------------------------
% 1.61/1.42 % (12093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.42 % (12093)Termination reason: Refutation
% 1.61/1.42
% 1.61/1.42 % (12093)Memory used [KB]: 5373
% 1.61/1.42 % (12093)Time elapsed: 0.003 s
% 1.61/1.42 % (12093)Instructions burned: 1 (million)
% 1.61/1.42 % (12093)------------------------------
% 1.61/1.42 % (12093)------------------------------
% 1.61/1.42 % (12092)Success in time 0.017 s
%------------------------------------------------------------------------------