%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU923^5 : 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 : n024.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 09:37:45 AM UTC 2026
% Result : Theorem 1.54s 1.30s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 13 ~; 5 |; 8 &; 34 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 21 !; 6 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cF: b > a ).
thf(func_def_6,type,
sK0: b ).
thf(func_def_7,type,
sK1: b ).
thf(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f9]) ).
thf(f9,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: b,X1: b] :
( ( X0 = X1 )
| ( ( cF @ X0 )
!= ( cF @ X1 ) ) )
& ( ( cF @ sK1 )
= ( cF @ sK0 ) )
& ( sK0 != sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X2: b,X3: b] :
( ( ( cF @ X2 )
= ( cF @ X3 ) )
& ( X2 != X3 ) )
=> ( ( ( cF @ sK1 )
= ( cF @ sK0 ) )
& ( sK0 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: b,X1: b] :
( ( X0 = X1 )
| ( ( cF @ X0 )
!= ( cF @ X1 ) ) )
& ? [X2: b,X3: b] :
( ( ( cF @ X2 )
= ( cF @ X3 ) )
& ( X2 != X3 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
( ! [X0: b,X1: b] :
( ( X0 = X1 )
| ( ( cF @ X0 )
!= ( cF @ X1 ) ) )
& ? [X3: b,X2: b] :
( ( ( cF @ X2 )
= ( cF @ X3 ) )
& ( X2 != X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X1: b,X0: b] :
( ( ( cF @ X0 )
= ( cF @ X1 ) )
=> ( X0 = X1 ) )
=> ! [X3: b,X2: b] :
( ( ( cF @ X2 )
= ( cF @ X3 ) )
=> ( X2 = X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: b,X0: b] :
( ( ( cF @ X0 )
= ( cF @ X1 ) )
=> ( X0 = X1 ) )
=> ! [X0: b,X1: b] :
( ( ( cF @ X0 )
= ( cF @ X1 ) )
=> ( X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: b,X0: b] :
( ( ( cF @ X0 )
= ( cF @ X1 ) )
=> ( X0 = X1 ) )
=> ! [X0: b,X1: b] :
( ( ( cF @ X0 )
= ( cF @ X1 ) )
=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KXfYTfDejh/DTF2THF_23340.p',cTHM54_pme) ).
thf(f16,plain,
sK0 = sK1,
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: b] :
( ( ( cF @ X0 )
!= ( cF @ sK0 ) )
| ( sK1 = X0 ) ),
inference(superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( ( cF @ sK1 )
= ( cF @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f11,plain,
! [X0: b,X1: b] :
( ( ( cF @ X0 )
!= ( cF @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU923^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n024.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 07:37:10 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU923^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.38 % Domain : Set Theory (Functions)
% 0.18/0.38 % Problem : TPS problem THM54
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Bro09]
% 0.18/0.38 % Names : tps_0134 [Bro09]
% 0.18/0.38 % : THM54 [TPS]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % 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 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.18/0.38 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.18/0.38 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.38 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.18/0.38 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 5 ( 5 avg)
% 0.18/0.38 % Number of types : 2 ( 2 usr)
% 0.18/0.38 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.18/0.38 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.38 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.38 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.38 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.38 % : Polymorphic definitions expanded.
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(b_type,type,
% 0.18/0.38 b: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(a_type,type,
% 0.18/0.38 a: $tType ).
% 0.18/0.38
% 0.18/0.38 thf(cF,type,
% 0.18/0.38 cF: b > a ).
% 0.18/0.38
% 0.18/0.38 thf(cTHM54_pme,conjecture,
% 0.18/0.38 ( ! [Xx: b,Xy: b] :
% 0.18/0.38 ( ( ( cF @ Xx )
% 0.18/0.38 = ( cF @ Xy ) )
% 0.18/0.38 => ( Xx = Xy ) )
% 0.18/0.38 => ! [Xx: b,Xy: b] :
% 0.18/0.38 ( ( ( cF @ Xx )
% 0.18/0.38 = ( cF @ Xy ) )
% 0.18/0.38 => ( Xx = Xy ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.37/1.27 ---- Embedded in THF ---
% 1.37/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.27 %%% Generated on Tue Feb 24 07:37:11 EST 2026
% 1.37/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.27 %%% Logic specification used:
% 1.37/1.27 %%% thf(spec, logic, $$dhol).
% 1.37/1.27
% 1.37/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KXfYTfDejh/DTF2DTF23340.p
% See solution above
% 1.37/1.27 ------------------------
% 1.37/1.28 ---- Cleaned THF ---
% 1.37/1.28 thf(b_type,type,
% 1.37/1.28 b: $tType ).
% 1.37/1.28
% 1.37/1.28 thf(a_type,type,
% 1.37/1.28 a: $tType ).
% 1.37/1.28
% 1.37/1.28 thf(cF,type,
% 1.37/1.28 cF: b > a ).
% 1.37/1.28
% 1.37/1.28 thf(cTHM54_pme,conjecture,
% 1.37/1.28 ( ! [Xx: b,Xy: b] :
% 1.37/1.28 ( ( ( cF @ Xx )
% 1.37/1.28 = ( cF @ Xy ) )
% 1.37/1.28 => ( Xx = Xy ) )
% 1.37/1.28 => ! [Xx: b,Xy: b] :
% 1.37/1.28 ( ( ( cF @ Xx )
% 1.37/1.28 = ( cF @ Xy ) )
% 1.37/1.28 => ( Xx = Xy ) ) ) ).
% 1.37/1.28 ------------------------
% 1.37/1.29 % (23437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23340 for (3000ds/183Mi)
% 1.54/1.30 % (23437)First to succeed.
% 1.54/1.30 % (23437)Refutation found. Thanks to Tanya!
% 1.54/1.30 % SZS status Theorem for DTF2THF_23340
% 1.54/1.30 % SZS output start Proof for DTF2THF_23340
% 1.54/1.30 thf(type_def_5, type, b: $tType).
% 1.54/1.30 thf(type_def_6, type, a: $tType).
% 1.54/1.30 thf(func_def_0, type, b: $tType).
% 1.54/1.30 thf(func_def_1, type, a: $tType).
% 1.54/1.30 thf(func_def_2, type, cF: b > a).
% 1.54/1.30 thf(func_def_6, type, sK0: b).
% 1.54/1.30 thf(func_def_7, type, sK1: b).
% 1.54/1.30 thf(f17,plain,(
% 1.54/1.30 $false),
% 1.54/1.30 inference(subsumption_resolution,[status(thm)],[f16,f9])).
% 1.54/1.30 thf(f9,plain,(
% 1.54/1.30 (sK0 != sK1)),
% 1.54/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.54/1.30 thf(f8,plain,(
% 1.54/1.30 ! [X0 : b,X1 : b] : ((X0 = X1) | ((cF @ X0) != (cF @ X1))) & (((cF @ sK1) = (cF @ sK0)) & (sK0 != sK1))),
% 1.54/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.54/1.30 thf(f7,plain,(
% 1.54/1.30 ? [X2 : b,X3 : b] : (((cF @ X2) = (cF @ X3)) & (X2 != X3)) => (((cF @ sK1) = (cF @ sK0)) & (sK0 != sK1))),
% 1.54/1.30 introduced(definition,[],[choice_axiom])).
% 1.54/1.30 thf(f6,plain,(
% 1.54/1.30 ! [X0 : b,X1 : b] : ((X0 = X1) | ((cF @ X0) != (cF @ X1))) & ? [X2 : b,X3 : b] : (((cF @ X2) = (cF @ X3)) & (X2 != X3))),
% 1.54/1.30 inference(rectify,[status(thm)],[f5])).
% 1.54/1.30 thf(f5,plain,(
% 1.54/1.30 ! [X0 : b,X1 : b] : ((X0 = X1) | ((cF @ X0) != (cF @ X1))) & ? [X3 : b,X2 : b] : (((cF @ X2) = (cF @ X3)) & (X2 != X3))),
% 1.54/1.30 inference(ennf_transformation,[status(thm)],[f4])).
% 1.54/1.30 thf(f4,plain,(
% 1.54/1.30 ~(! [X1 : b,X0 : b] : (((cF @ X0) = (cF @ X1)) => (X0 = X1)) => ! [X3 : b,X2 : b] : (((cF @ X2) = (cF @ X3)) => (X2 = X3)))),
% 1.54/1.30 inference(rectify,[status(thm)],[f2])).
% 1.54/1.30 thf(f2,negated_conjecture,(
% 1.54/1.30 ~(! [X1 : b,X0 : b] : (((cF @ X0) = (cF @ X1)) => (X0 = X1)) => ! [X0 : b,X1 : b] : (((cF @ X0) = (cF @ X1)) => (X0 = X1)))),
% 1.54/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.30 thf(f1,conjecture,(
% 1.54/1.30 ! [X1 : b,X0 : b] : (((cF @ X0) = (cF @ X1)) => (X0 = X1)) => ! [X0 : b,X1 : b] : (((cF @ X0) = (cF @ X1)) => (X0 = X1))),
% 1.54/1.30 file('/export/starexec/sandbox/tmp/tmp.KXfYTfDejh/DTF2THF_23340.p',cTHM54_pme)).
% 1.54/1.30 thf(f16,plain,(
% 1.54/1.30 (sK0 = sK1)),
% 1.54/1.30 inference(equality_resolution,[status(thm)],[f13])).
% 1.54/1.30 thf(f13,plain,(
% 1.54/1.30 ( ! [X0 : b] : (((cF @ X0) != (cF @ sK0)) | (sK1 = X0)) )),
% 1.54/1.30 inference(superposition,[status(thm)],[f11,f10])).
% 1.54/1.30 thf(f10,plain,(
% 1.54/1.30 ((cF @ sK1) = (cF @ sK0))),
% 1.54/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.54/1.30 thf(f11,plain,(
% 1.54/1.30 ( ! [X0 : b,X1 : b] : (((cF @ X0) != (cF @ X1)) | (X0 = X1)) )),
% 1.54/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.54/1.30 % SZS output end Proof for DTF2THF_23340
% 1.54/1.30 % (23437)------------------------------
% 1.54/1.30 % (23437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.30 % (23437)Termination reason: Refutation
% 1.54/1.30
% 1.54/1.30 % (23437)Memory used [KB]: 5500
% 1.54/1.30 % (23437)Time elapsed: 0.002 s
% 1.54/1.30 % (23437)Instructions burned: 2 (million)
% 1.54/1.30 % (23437)------------------------------
% 1.54/1.30 % (23437)------------------------------
% 1.54/1.30 % (23436)Success in time 0.007 s
%------------------------------------------------------------------------------