%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU841^5 : 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 : n018.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 09:37:33 AM UTC 2026
% Result : Theorem 1.66s 1.47s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 29 ( 10 ~; 0 |; 15 &; 0 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 9 !; 12 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
sK2 != sK2,
inference(definition_unfolding,[status(thm)],[f10,f13]) ).
thf(f13,plain,
sK1 = sK2,
inference(definition_unfolding,[status(thm)],[f11,f12]) ).
thf(f12,plain,
sK0 = sK2,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sK0 = sK2 )
& ( sK1 = sK0 )
& ( sK1 != sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( X0 = X2 )
& ( X0 = X1 )
& ( X1 != X2 ) )
=> ( ( sK0 = sK2 )
& ( sK1 = sK0 )
& ( sK1 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( X0 = X2 )
& ( X0 = X1 )
& ( X1 != X2 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( X1 = X2 )
& ( X0 = X2 )
& ( X0 != X1 ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( X0 != X1 )
& ( X0 = X2 )
& ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ( X0 = X2 )
& ( X1 = X2 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( X1 = X2 )
& ( X0 = X1 ) )
=> ( X0 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ( X1 = X2 )
& ( X0 = X1 ) )
=> ( X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.V7fV0iNxpv/DTF2THF_15608.p',cGAZING_THM7) ).
thf(f11,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
sK1 != sK2,
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU841^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n018.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:35:16 EST 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.41 ---- Original DTF file ---
% 0.19/0.41 thf(spec,logic,$$dhol).
% 0.19/0.41 %------------------------------------------------------------------------------
% 0.19/0.41 % File : SEU841^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.41 % Domain : Set Theory
% 0.19/0.41 % Problem : TPS problem GAZING-THM7
% 0.19/0.41 % Version : Especial.
% 0.19/0.41 % English :
% 0.19/0.41
% 0.19/0.41 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.19/0.41 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.41 % Source : [Bro09]
% 0.19/0.41 % Names : tps_0186 [Bro09]
% 0.19/0.41 % : 7 [Bar92]
% 0.19/0.41 % : GAZING-THM7 [TPS]
% 0.19/0.41
% 0.19/0.41 % Status : Theorem
% 0.19/0.41 % 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
% 0.19/0.41 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.41 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.19/0.41 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.41 % Number of connectives : 2 ( 0 ~; 0 |; 1 &; 0 @)
% 0.19/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.41 % Maximal formula depth : 6 ( 6 avg)
% 0.19/0.41 % Number of types : 2 ( 1 usr)
% 0.19/0.41 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.41 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.41 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.41 % SPC : TH0_THM_EQU_NAR
% 0.19/0.41
% 0.19/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.41 %------------------------------------------------------------------------------
% 0.19/0.41 thf(a_type,type,
% 0.19/0.41 a: $tType ).
% 0.19/0.41
% 0.19/0.41 thf(cGAZING_THM7,conjecture,
% 0.19/0.41 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.19/0.41 ( ( ( S = T )
% 0.19/0.41 & ( T = U ) )
% 0.19/0.41 => ( S = U ) ) ).
% 0.19/0.41
% 0.19/0.41 %------------------------------------------------------------------------------
% 0.19/0.41 ------------------------
% 1.66/1.44 ---- Embedded in THF ---
% 1.66/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.44 %%% Generated on Tue Feb 24 12:35:17 EST 2026
% 1.66/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.44 %%% Logic specification used:
% 1.66/1.44 %%% thf(spec, logic, $$dhol).
% 1.66/1.44
% 1.66/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.V7fV0iNxpv/DTF2DTF15608.p
% See solution above
% 1.66/1.44 ------------------------
% 1.66/1.45 ---- Cleaned THF ---
% 1.66/1.45 thf(a_type,type,
% 1.66/1.45 a: $tType ).
% 1.66/1.45
% 1.66/1.45 thf(cGAZING_THM7,conjecture,
% 1.66/1.45 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.66/1.45 ( ( ( S = T )
% 1.66/1.45 & ( T = U ) )
% 1.66/1.45 => ( S = U ) ) ).
% 1.66/1.45 ------------------------
% 1.66/1.47 % (15708)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15608 for (3000ds/2Mi)
% 1.66/1.47 % (15705)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15608 for (3000ds/183Mi)
% 1.66/1.47 % (15710)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_15608 for (3000ds/275Mi)
% 1.66/1.47 % (15711)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15608 for (3000ds/18Mi)
% 1.66/1.47 % (15707)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_15608 for (3000ds/27Mi)
% 1.66/1.47 % (15705)First to succeed.
% 1.66/1.47 % (15708)Also succeeded, but the first one will report.
% 1.66/1.47 % (15709)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_15608 for (3000ds/2Mi)
% 1.66/1.47 % (15707)Also succeeded, but the first one will report.
% 1.66/1.47 % (15705)Refutation found. Thanks to Tanya!
% 1.66/1.47 % SZS status Theorem for DTF2THF_15608
% 1.66/1.47 % SZS output start Proof for DTF2THF_15608
% 1.66/1.47 thf(type_def_5, type, a: $tType).
% 1.66/1.47 thf(func_def_0, type, a: $tType).
% 1.66/1.47 thf(func_def_3, type, sK0: a > $o).
% 1.66/1.47 thf(func_def_4, type, sK1: a > $o).
% 1.66/1.47 thf(func_def_5, type, sK2: a > $o).
% 1.66/1.47 thf(f15,plain,(
% 1.66/1.47 $false),
% 1.66/1.47 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.66/1.47 thf(f14,plain,(
% 1.66/1.47 (sK2 != sK2)),
% 1.66/1.47 inference(definition_unfolding,[status(thm)],[f10,f13])).
% 1.66/1.47 thf(f13,plain,(
% 1.66/1.47 (sK1 = sK2)),
% 1.66/1.47 inference(definition_unfolding,[status(thm)],[f11,f12])).
% 1.66/1.47 thf(f12,plain,(
% 1.66/1.47 (sK0 = sK2)),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.47 thf(f9,plain,(
% 1.66/1.47 (sK0 = sK2) & (sK1 = sK0) & (sK1 != sK2)),
% 1.66/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f8])).
% 1.66/1.47 thf(f8,plain,(
% 1.66/1.47 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((X0 = X2) & (X0 = X1) & (X1 != X2)) => ((sK0 = sK2) & (sK1 = sK0) & (sK1 != sK2))),
% 1.66/1.47 introduced(definition,[],[choice_axiom])).
% 1.66/1.47 thf(f7,plain,(
% 1.66/1.47 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((X0 = X2) & (X0 = X1) & (X1 != X2))),
% 1.66/1.47 inference(rectify,[status(thm)],[f6])).
% 1.66/1.47 thf(f6,plain,(
% 1.66/1.47 ? [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((X1 = X2) & (X0 = X2) & (X0 != X1))),
% 1.66/1.47 inference(flattening,[status(thm)],[f5])).
% 1.66/1.47 thf(f5,plain,(
% 1.66/1.47 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((X0 != X1) & ((X0 = X2) & (X1 = X2)))),
% 1.66/1.47 inference(ennf_transformation,[status(thm)],[f4])).
% 1.66/1.47 thf(f4,plain,(
% 1.66/1.47 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : (((X0 = X2) & (X1 = X2)) => (X0 = X1))),
% 1.66/1.47 inference(rectify,[status(thm)],[f2])).
% 1.66/1.47 thf(f2,negated_conjecture,(
% 1.66/1.47 ~! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (((X1 = X2) & (X0 = X1)) => (X0 = X2))),
% 1.66/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.47 thf(f1,conjecture,(
% 1.66/1.47 ! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : (((X1 = X2) & (X0 = X1)) => (X0 = X2))),
% 1.66/1.47 file('/export/starexec/sandbox/tmp/tmp.V7fV0iNxpv/DTF2THF_15608.p',cGAZING_THM7)).
% 1.66/1.47 thf(f11,plain,(
% 1.66/1.47 (sK1 = sK0)),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.47 thf(f10,plain,(
% 1.66/1.47 (sK1 != sK2)),
% 1.66/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.47 % SZS output end Proof for DTF2THF_15608
% 1.66/1.47 % (15705)------------------------------
% 1.66/1.47 % (15705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (15705)Termination reason: Refutation
% 1.66/1.47
% 1.66/1.47 % (15705)Memory used [KB]: 5373
% 1.66/1.47 % (15705)Time elapsed: 0.002 s
% 1.66/1.47 % (15705)------------------------------
% 1.66/1.47 % (15705)------------------------------
% 1.66/1.47 % (15704)Success in time 0.017 s
%------------------------------------------------------------------------------