%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV051^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 09:40:10 AM UTC 2026
% Result : Theorem 1.44s 1.28s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 50 ( 20 ~; 7 |; 18 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 28 ( 12 !; 16 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(func_def_0,type,
a: $tType ).
tff(func_def_1,type,
sK0: a ).
tff(func_def_2,type,
sK1: a ).
tff(func_def_3,type,
sK2: a ).
tff(func_def_4,type,
sK3: a ).
tff(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f13]) ).
tff(f13,plain,
sK2 = sK1,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
tff(f10,plain,
( ( sK0 != sK0 )
| ( sK2 = sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f9,plain,
( ( sK0 != sK0 )
| ( ( sK2 = sK3 )
& ( sK3 != sK1 )
& ( sK2 = sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7]) ).
tff(f7,plain,
( ? [X0: a] : ( X0 != X0 )
=> ( sK0 != sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f8,plain,
( ? [X1: a,X2: a,X3: a] :
( ( X2 = X3 )
& ( X1 != X3 )
& ( X1 = X2 ) )
=> ( ( sK2 = sK3 )
& ( sK3 != sK1 )
& ( sK2 = sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f6,plain,
( ? [X0: a] : ( X0 != X0 )
| ? [X1: a,X2: a,X3: a] :
( ( X2 = X3 )
& ( X1 != X3 )
& ( X1 = X2 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
tff(f5,plain,
( ? [X0: a] : ( X0 != X0 )
| ? [X2: a,X1: a,X3: a] :
( ( X1 = X3 )
& ( X2 != X3 )
& ( X1 = X2 ) ) ),
inference(flattening,[status(thm)],[f4]) ).
tff(f4,plain,
( ? [X1: a,X2: a,X3: a] :
( ( X2 != X3 )
& ( X1 = X3 )
& ( X1 = X2 ) )
| ? [X0: a] : ( X0 != X0 ) ),
inference(ennf_transformation,[status(thm)],[f3]) ).
tff(f3,plain,
~ ( ! [X1: a,X2: a,X3: a] :
( ( ( X1 = X3 )
& ( X1 = X2 ) )
=> ( X2 = X3 ) )
& ! [X0: a] : ( X0 = X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ( ! [X0: a] : ( X0 = X0 )
& ! [X3: a,X1: a,X2: a] :
( ( ( X1 = X3 )
& ( X2 = X3 ) )
=> ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
( ! [X0: a] : ( X0 = X0 )
& ! [X3: a,X1: a,X2: a] :
( ( ( X1 = X3 )
& ( X2 = X3 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.03BQ8dpW1A/DTF2THF_18268.p',cTHM557_pme) ).
tff(f16,plain,
sK2 != sK1,
inference(superposition,[status(thm)],[f14,f15]) ).
tff(f15,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
tff(f12,plain,
( ( sK0 != sK0 )
| ( sK2 = sK3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f14,plain,
sK3 != sK1,
inference(trivial_inequality_removal,[status(thm)],[f11]) ).
tff(f11,plain,
( ( sK0 != sK0 )
| ( sK3 != sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV051^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n017.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 12:37:56 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEV051^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Set Theory (Relations)
% 0.30/0.46 % Problem : TPS problem THM557
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : Equality is an LC-relation.
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0210 [Bro09]
% 0.30/0.46 % : THM557 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 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 : 4 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.46 % Number of connectives : 3 ( 0 ~; 0 |; 2 &; 0 @)
% 0.30/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.30/0.46 % Number of types : 1 ( 1 usr)
% 0.30/0.46 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 % : Polymorphic definitions expanded.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(a_type,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM557_pme,conjecture,
% 0.30/0.46 ( ! [Xx: a] : ( Xx = Xx )
% 0.30/0.46 & ! [Xu: a,Xv: a,Xw: a] :
% 0.30/0.46 ( ( ( Xu = Xw )
% 0.30/0.46 & ( Xv = Xw ) )
% 0.30/0.46 => ( Xu = Xv ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.44/1.26 ---- Embedded in THF ---
% 1.44/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.26 %%% Generated on Tue Feb 24 12:37:56 EST 2026
% 1.44/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.26 %%% Logic specification used:
% 1.44/1.26 %%% thf(spec, logic, $$dhol).
% 1.44/1.26
% 1.44/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.03BQ8dpW1A/DTF2DTF18268.p
% See solution above
% 1.44/1.26 ------------------------
% 1.44/1.27 ---- Cleaned THF ---
% 1.44/1.27 thf(a_type,type,
% 1.44/1.27 a: $tType ).
% 1.44/1.27
% 1.44/1.27 thf(cTHM557_pme,conjecture,
% 1.44/1.27 ( ! [Xx: a] : ( Xx = Xx )
% 1.44/1.27 & ! [Xu: a,Xv: a,Xw: a] :
% 1.44/1.27 ( ( ( Xu = Xw )
% 1.44/1.27 & ( Xv = Xw ) )
% 1.44/1.27 => ( Xu = Xv ) ) ) ).
% 1.44/1.27 ------------------------
% 1.44/1.28 % (18486)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18268 for (3000ds/183Mi)
% 1.44/1.28 % (18486)First to succeed.
% 1.44/1.28 % (18486)Refutation found. Thanks to Tanya!
% 1.44/1.28 % SZS status Theorem for DTF2THF_18268
% 1.44/1.28 % SZS output start Proof for DTF2THF_18268
% 1.44/1.28 tff(type_def_5, type, a: $tType).
% 1.44/1.28 tff(func_def_0, type, a: $tType).
% 1.44/1.28 tff(func_def_1, type, sK0: a).
% 1.44/1.28 tff(func_def_2, type, sK1: a).
% 1.44/1.28 tff(func_def_3, type, sK2: a).
% 1.44/1.28 tff(func_def_4, type, sK3: a).
% 1.44/1.28 tff(f17,plain,(
% 1.44/1.28 $false),
% 1.44/1.28 inference(subsumption_resolution,[status(thm)],[f16,f13])).
% 1.44/1.28 tff(f13,plain,(
% 1.44/1.28 sK2 = sK1),
% 1.44/1.28 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.44/1.28 tff(f10,plain,(
% 1.44/1.28 sK0 != sK0 | sK2 = sK1),
% 1.44/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.44/1.28 tff(f9,plain,(
% 1.44/1.28 sK0 != sK0 | (sK2 = sK3 & sK3 != sK1 & sK2 = sK1)),
% 1.44/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f6,f8,f7])).
% 1.44/1.28 tff(f7,plain,(
% 1.44/1.28 ? [X0 : a] : X0 != X0 => sK0 != sK0),
% 1.44/1.28 introduced(definition,[],[choice_axiom])).
% 1.44/1.28 tff(f8,plain,(
% 1.44/1.28 ? [X1 : a,X2 : a,X3 : a] : (X2 = X3 & X1 != X3 & X1 = X2) => (sK2 = sK3 & sK3 != sK1 & sK2 = sK1)),
% 1.44/1.28 introduced(definition,[],[choice_axiom])).
% 1.44/1.28 tff(f6,plain,(
% 1.44/1.28 ? [X0 : a] : X0 != X0 | ? [X1 : a,X2 : a,X3 : a] : (X2 = X3 & X1 != X3 & X1 = X2)),
% 1.44/1.28 inference(rectify,[status(thm)],[f5])).
% 1.44/1.28 tff(f5,plain,(
% 1.44/1.28 ? [X0 : a] : X0 != X0 | ? [X2 : a,X1 : a,X3 : a] : (X1 = X3 & X2 != X3 & X1 = X2)),
% 1.44/1.28 inference(flattening,[status(thm)],[f4])).
% 1.44/1.28 tff(f4,plain,(
% 1.44/1.28 ? [X1 : a,X2 : a,X3 : a] : (X2 != X3 & (X1 = X3 & X1 = X2)) | ? [X0 : a] : X0 != X0),
% 1.44/1.28 inference(ennf_transformation,[status(thm)],[f3])).
% 1.44/1.28 tff(f3,plain,(
% 1.44/1.28 ~(! [X1 : a,X2 : a,X3 : a] : ((X1 = X3 & X1 = X2) => X2 = X3) & ! [X0 : a] : X0 = X0)),
% 1.44/1.28 inference(rectify,[status(thm)],[f2])).
% 1.44/1.28 tff(f2,negated_conjecture,(
% 1.44/1.28 ~(! [X0 : a] : X0 = X0 & ! [X3 : a,X1 : a,X2 : a] : ((X1 = X3 & X2 = X3) => X1 = X2))),
% 1.44/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.44/1.28 tff(f1,conjecture,(
% 1.44/1.28 ! [X0 : a] : X0 = X0 & ! [X3 : a,X1 : a,X2 : a] : ((X1 = X3 & X2 = X3) => X1 = X2)),
% 1.44/1.28 file('/export/starexec/sandbox2/tmp/tmp.03BQ8dpW1A/DTF2THF_18268.p',cTHM557_pme)).
% 1.44/1.28 tff(f16,plain,(
% 1.44/1.28 sK2 != sK1),
% 1.44/1.28 inference(superposition,[status(thm)],[f14,f15])).
% 1.44/1.28 tff(f15,plain,(
% 1.44/1.28 sK2 = sK3),
% 1.44/1.28 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.44/1.28 tff(f12,plain,(
% 1.44/1.28 sK0 != sK0 | sK2 = sK3),
% 1.44/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.44/1.28 tff(f14,plain,(
% 1.44/1.28 sK3 != sK1),
% 1.44/1.28 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.44/1.28 tff(f11,plain,(
% 1.44/1.28 sK0 != sK0 | sK3 != sK1),
% 1.44/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.44/1.28 % SZS output end Proof for DTF2THF_18268
% 1.44/1.28 % (18486)------------------------------
% 1.44/1.28 % (18486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (18486)Termination reason: Refutation
% 1.44/1.28
% 1.44/1.28 % (18486)Memory used [KB]: 5373
% 1.44/1.28 % (18486)Time elapsed: 0.002 s
% 1.44/1.28 % (18486)------------------------------
% 1.44/1.28 % (18486)------------------------------
% 1.44/1.28 % (18485)Success in time 0.011 s
%------------------------------------------------------------------------------