%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU888^5 : 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 : n007.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 09:37:40 AM UTC 2026
% Result : Theorem 1.30s 1.14s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 41 ( 10 ~; 9 |; 4 &; 16 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 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,
g: b > a ).
thf(func_def_3,type,
z: a ).
thf(func_def_4,type,
y: b ).
thf(func_def_5,type,
x: b ).
thf(f11,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f10,f8]) ).
thf(f8,plain,
( z
!= ( g @ y ) ),
inference(equality_resolution,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: b] :
( ( z
!= ( g @ X0 ) )
| ( y != X0 ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ! [X0: b] :
( ( z
!= ( g @ X0 ) )
| ( ( y != X0 )
& ( x != X0 ) ) )
& ( ( z
= ( g @ x ) )
| ( z
= ( g @ y ) ) ) ),
inference(ennf_transformation,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( z
= ( g @ x ) )
| ( z
= ( g @ y ) ) )
=> ? [X0: b] :
( ( ( x = X0 )
| ( y = X0 ) )
& ( z
= ( g @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( z
= ( g @ x ) )
| ( z
= ( g @ y ) ) )
=> ? [X0: b] :
( ( ( x = X0 )
| ( y = X0 ) )
& ( z
= ( g @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DOr5pi6mUq/DTF2THF_24982.p',cTHM500C_WFF_pme) ).
thf(f10,plain,
( z
= ( g @ y ) ),
inference(subsumption_resolution,[status(thm)],[f5,f9]) ).
thf(f9,plain,
( z
!= ( g @ x ) ),
inference(equality_resolution,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: b] :
( ( z
!= ( g @ X0 ) )
| ( x != X0 ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f5,plain,
( ( z
= ( g @ x ) )
| ( z
= ( g @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU888^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Feb 24 12:35:23 EST 2026
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.45 ---- Original DTF file ---
% 0.16/0.45 thf(spec,logic,$$dhol).
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 % File : SEU888^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.45 % Domain : Set Theory
% 0.16/0.45 % Problem : TPS problem THM500C-WFF
% 0.16/0.45 % Version : Especial.
% 0.16/0.45 % English :
% 0.16/0.45
% 0.16/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.45 % Source : [Bro09]
% 0.16/0.45 % Names : tps_0287 [Bro09]
% 0.16/0.45 % : THM500C-WFF [TPS]
% 0.16/0.45
% 0.16/0.45 % Status : Theorem
% 0.16/0.45 % Rating : 0.00 v6.1.0, 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
% 0.16/0.45 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.16/0.45 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.16/0.45 % Maximal formula atoms : 5 ( 5 avg)
% 0.16/0.45 % Number of connectives : 7 ( 0 ~; 2 |; 1 &; 3 @)
% 0.16/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.45 % Maximal formula depth : 5 ( 5 avg)
% 0.16/0.45 % Number of types : 2 ( 2 usr)
% 0.16/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.45 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.16/0.45 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.16/0.45 % SPC : TH0_THM_EQU_NAR
% 0.16/0.45
% 0.16/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.45 % : Polymorphic definitions expanded.
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 thf(b_type,type,
% 0.16/0.45 b: $tType ).
% 0.16/0.45
% 0.16/0.45 thf(a_type,type,
% 0.16/0.45 a: $tType ).
% 0.16/0.45
% 0.16/0.45 thf(g,type,
% 0.16/0.45 g: b > a ).
% 0.16/0.45
% 0.16/0.45 thf(z,type,
% 0.16/0.45 z: a ).
% 0.16/0.45
% 0.16/0.45 thf(y,type,
% 0.16/0.45 y: b ).
% 0.16/0.45
% 0.16/0.45 thf(x,type,
% 0.16/0.45 x: b ).
% 0.16/0.45
% 0.16/0.45 thf(cTHM500C_WFF_pme,conjecture,
% 0.16/0.45 ( ( ( z
% 0.16/0.45 = ( g @ x ) )
% 0.16/0.45 | ( z
% 0.16/0.45 = ( g @ y ) ) )
% 0.16/0.45 => ? [Xt: b] :
% 0.16/0.45 ( ( ( Xt = x )
% 0.16/0.45 | ( Xt = y ) )
% 0.16/0.45 & ( z
% 0.16/0.45 = ( g @ Xt ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 ------------------------
% 1.10/1.11 ---- Embedded in THF ---
% 1.30/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.30/1.11 %%% Generated on Tue Feb 24 12:35:24 EST 2026
% 1.30/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.30/1.11 %%% Logic specification used:
% 1.30/1.11 %%% thf(spec, logic, $$dhol).
% 1.30/1.11
% 1.30/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DOr5pi6mUq/DTF2DTF24982.p
% See solution above
% 1.30/1.11 ------------------------
% 1.30/1.12 ---- Cleaned THF ---
% 1.30/1.12 thf(b_type,type,
% 1.30/1.12 b: $tType ).
% 1.30/1.12
% 1.30/1.12 thf(a_type,type,
% 1.30/1.12 a: $tType ).
% 1.30/1.12
% 1.30/1.12 thf(g,type,
% 1.30/1.12 g: b > a ).
% 1.30/1.12
% 1.30/1.12 thf(z,type,
% 1.30/1.12 z: a ).
% 1.30/1.12
% 1.30/1.12 thf(y,type,
% 1.30/1.12 y: b ).
% 1.30/1.12
% 1.30/1.12 thf(x,type,
% 1.30/1.12 x: b ).
% 1.30/1.12
% 1.30/1.12 thf(cTHM500C_WFF_pme,conjecture,
% 1.30/1.12 ( ( ( z
% 1.30/1.12 = ( g @ x ) )
% 1.30/1.12 | ( z
% 1.30/1.12 = ( g @ y ) ) )
% 1.30/1.12 => ? [Xt: b] :
% 1.30/1.12 ( ( ( Xt = x )
% 1.30/1.12 | ( Xt = y ) )
% 1.30/1.12 & ( z
% 1.30/1.12 = ( g @ Xt ) ) ) ) ).
% 1.30/1.12 ------------------------
% 1.30/1.13 % (25083)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24982 for (3000ds/183Mi)
% 1.30/1.13 % (25083)First to succeed.
% 1.30/1.14 % (25083)Refutation found. Thanks to Tanya!
% 1.30/1.14 % SZS status Theorem for DTF2THF_24982
% 1.30/1.14 % SZS output start Proof for DTF2THF_24982
% 1.30/1.14 thf(type_def_5, type, b: $tType).
% 1.30/1.14 thf(type_def_6, type, a: $tType).
% 1.30/1.14 thf(func_def_0, type, b: $tType).
% 1.30/1.14 thf(func_def_1, type, a: $tType).
% 1.30/1.14 thf(func_def_2, type, g: b > a).
% 1.30/1.14 thf(func_def_3, type, z: a).
% 1.30/1.14 thf(func_def_4, type, y: b).
% 1.30/1.14 thf(func_def_5, type, x: b).
% 1.30/1.14 thf(f11,plain,(
% 1.30/1.14 $false),
% 1.30/1.14 inference(subsumption_resolution,[status(thm)],[f10,f8])).
% 1.30/1.14 thf(f8,plain,(
% 1.30/1.14 (z != (g @ y))),
% 1.30/1.14 inference(equality_resolution,[status(thm)],[f7])).
% 1.30/1.14 thf(f7,plain,(
% 1.30/1.14 ( ! [X0 : b] : ((z != (g @ X0)) | (y != X0)) )),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f4])).
% 1.30/1.14 thf(f4,plain,(
% 1.30/1.14 ! [X0 : b] : ((z != (g @ X0)) | ((y != X0) & (x != X0))) & ((z = (g @ x)) | (z = (g @ y)))),
% 1.30/1.14 inference(ennf_transformation,[status(thm)],[f2])).
% 1.30/1.14 thf(f2,negated_conjecture,(
% 1.30/1.14 ~(((z = (g @ x)) | (z = (g @ y))) => ? [X0 : b] : (((x = X0) | (y = X0)) & (z = (g @ X0))))),
% 1.30/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.30/1.14 thf(f1,conjecture,(
% 1.30/1.14 ((z = (g @ x)) | (z = (g @ y))) => ? [X0 : b] : (((x = X0) | (y = X0)) & (z = (g @ X0)))),
% 1.30/1.14 file('/export/starexec/sandbox2/tmp/tmp.DOr5pi6mUq/DTF2THF_24982.p',cTHM500C_WFF_pme)).
% 1.30/1.14 thf(f10,plain,(
% 1.30/1.14 (z = (g @ y))),
% 1.30/1.14 inference(subsumption_resolution,[status(thm)],[f5,f9])).
% 1.30/1.14 thf(f9,plain,(
% 1.30/1.14 (z != (g @ x))),
% 1.30/1.14 inference(equality_resolution,[status(thm)],[f6])).
% 1.30/1.14 thf(f6,plain,(
% 1.30/1.14 ( ! [X0 : b] : ((z != (g @ X0)) | (x != X0)) )),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f4])).
% 1.30/1.14 thf(f5,plain,(
% 1.30/1.14 (z = (g @ x)) | (z = (g @ y))),
% 1.30/1.14 inference(cnf_transformation,[status(thm)],[f4])).
% 1.30/1.14 % SZS output end Proof for DTF2THF_24982
% 1.30/1.14 % (25083)------------------------------
% 1.30/1.14 % (25083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.14 % (25083)Termination reason: Refutation
% 1.30/1.14
% 1.30/1.14 % (25083)Memory used [KB]: 5373
% 1.30/1.14 % (25083)Time elapsed: 0.002 s
% 1.30/1.14 % (25083)Instructions burned: 1 (million)
% 1.30/1.14 % (25083)------------------------------
% 1.30/1.14 % (25083)------------------------------
% 1.30/1.14 % (25082)Success in time 0.006 s
%------------------------------------------------------------------------------