%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV286^5 : 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 : n010.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 09:40:45 AM UTC 2026
% Result : Theorem 1.59s 1.36s
% Output : Refutation 1.59s
% 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 : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 8 ~; 0 |; 5 &; 18 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 6 !; 9 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_5,type,
sK0: a ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_7,type,
sK2: a > b ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK2 @ sK0 )
!= ( sK2 @ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f9,f8]) ).
thf(f8,plain,
sK1 = sK0,
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( sK2 @ sK1 )
!= ( sK2 @ sK0 ) )
& ( sK1 = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5,f6]) ).
thf(f6,plain,
( ? [X0: a,X1: a,X2: a > b] :
( ( ( X2 @ X1 )
!= ( X2 @ X0 ) )
& ( X0 = X1 ) )
=> ( ( ( sK2 @ sK1 )
!= ( sK2 @ sK0 ) )
& ( sK1 = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
? [X0: a,X1: a,X2: a > b] :
( ( ( X2 @ X1 )
!= ( X2 @ X0 ) )
& ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,plain,
? [X2: a,X1: a,X0: a > b] :
( ( ( X0 @ X1 )
!= ( X0 @ X2 ) )
& ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > b,X1: a,X2: a] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
= ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > b,X1: a,X2: a] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
= ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjWhQsc73M/DTF2THF_18064.p',cEC_eq_) ).
thf(f9,plain,
( ( sK2 @ sK1 )
!= ( sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n010.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 12:42:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEV286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : TPS problem from TTTP-NATS-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0088 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 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
% 0.19/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.47 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.19/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.19/0.47 % Number of types : 2 ( 2 usr)
% 0.19/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.47 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(a_type,type,
% 0.19/0.47 a: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(b_type,type,
% 0.19/0.47 b: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(cEC_eq_,conjecture,
% 0.19/0.47 ! [F: a > b,A: a,B: a] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ( ( F @ A )
% 0.19/0.47 = ( F @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.59/1.33 ---- Embedded in THF ---
% 1.59/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.33 %%% Generated on Tue Feb 24 12:42:49 EST 2026
% 1.59/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.33 %%% Logic specification used:
% 1.59/1.33 %%% thf(spec, logic, $$dhol).
% 1.59/1.33
% 1.59/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.GjWhQsc73M/DTF2DTF18064.p
% See solution above
% 1.59/1.33 ------------------------
% 1.59/1.34 ---- Cleaned THF ---
% 1.59/1.34 thf(a_type,type,
% 1.59/1.34 a: $tType ).
% 1.59/1.34
% 1.59/1.34 thf(b_type,type,
% 1.59/1.34 b: $tType ).
% 1.59/1.34
% 1.59/1.34 thf(cEC_eq_,conjecture,
% 1.59/1.34 ! [F: a > b,A: a,B: a] :
% 1.59/1.34 ( ( A = B )
% 1.59/1.34 => ( ( F @ A )
% 1.59/1.34 = ( F @ B ) ) ) ).
% 1.59/1.34 ------------------------
% 1.59/1.36 % (18239)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18064 for (3000ds/2Mi)
% 1.59/1.36 % (18241)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_18064 for (3000ds/275Mi)
% 1.59/1.36 % (18239)First to succeed.
% 1.59/1.36 % (18241)Also succeeded, but the first one will report.
% 1.59/1.36 % (18242)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18064 for (3000ds/18Mi)
% 1.59/1.36 % (18242)Also succeeded, but the first one will report.
% 1.59/1.36 % (18239)Refutation found. Thanks to Tanya!
% 1.59/1.36 % SZS status Theorem for DTF2THF_18064
% 1.59/1.36 % SZS output start Proof for DTF2THF_18064
% 1.59/1.36 thf(type_def_5, type, a: $tType).
% 1.59/1.36 thf(type_def_6, type, b: $tType).
% 1.59/1.36 thf(func_def_0, type, a: $tType).
% 1.59/1.36 thf(func_def_1, type, b: $tType).
% 1.59/1.36 thf(func_def_5, type, sK0: a).
% 1.59/1.36 thf(func_def_6, type, sK1: a).
% 1.59/1.36 thf(func_def_7, type, sK2: a > b).
% 1.59/1.36 thf(f11,plain,(
% 1.59/1.36 $false),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.59/1.36 thf(f10,plain,(
% 1.59/1.36 ((sK2 @ sK0) != (sK2 @ sK0))),
% 1.59/1.36 inference(definition_unfolding,[status(thm)],[f9,f8])).
% 1.59/1.36 thf(f8,plain,(
% 1.59/1.36 (sK1 = sK0)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f7])).
% 1.59/1.36 thf(f7,plain,(
% 1.59/1.36 ((sK2 @ sK1) != (sK2 @ sK0)) & (sK1 = sK0)),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5,f6])).
% 1.59/1.36 thf(f6,plain,(
% 1.59/1.36 ? [X0 : a,X1 : a,X2 : a > b] : (((X2 @ X1) != (X2 @ X0)) & (X0 = X1)) => (((sK2 @ sK1) != (sK2 @ sK0)) & (sK1 = sK0))),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f5,plain,(
% 1.59/1.36 ? [X0 : a,X1 : a,X2 : a > b] : (((X2 @ X1) != (X2 @ X0)) & (X0 = X1))),
% 1.59/1.36 inference(rectify,[status(thm)],[f4])).
% 1.59/1.36 thf(f4,plain,(
% 1.59/1.36 ? [X2 : a,X1 : a,X0 : a > b] : (((X0 @ X1) != (X0 @ X2)) & (X1 = X2))),
% 1.59/1.36 inference(ennf_transformation,[status(thm)],[f2])).
% 1.59/1.36 thf(f2,negated_conjecture,(
% 1.59/1.36 ~! [X0 : a > b,X1 : a,X2 : a] : ((X1 = X2) => ((X0 @ X1) = (X0 @ X2)))),
% 1.59/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.36 thf(f1,conjecture,(
% 1.59/1.36 ! [X0 : a > b,X1 : a,X2 : a] : ((X1 = X2) => ((X0 @ X1) = (X0 @ X2)))),
% 1.59/1.36 file('/export/starexec/sandbox2/tmp/tmp.GjWhQsc73M/DTF2THF_18064.p',cEC_eq_)).
% 1.59/1.36 thf(f9,plain,(
% 1.59/1.36 ((sK2 @ sK1) != (sK2 @ sK0))),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f7])).
% 1.59/1.36 % SZS output end Proof for DTF2THF_18064
% 1.59/1.36 % (18239)------------------------------
% 1.59/1.36 % (18239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (18239)Termination reason: Refutation
% 1.59/1.36
% 1.59/1.36 % (18239)Memory used [KB]: 5373
% 1.59/1.36 % (18239)Time elapsed: 0.002 s
% 1.59/1.36 % (18239)Instructions burned: 1 (million)
% 1.59/1.36 % (18239)------------------------------
% 1.59/1.36 % (18239)------------------------------
% 1.59/1.36 % (18233)Success in time 0.017 s
%------------------------------------------------------------------------------