%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU842^5 : 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 : n012.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 1.02s 0.91s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 63 ( 8 ~; 0 |; 18 &; 36 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 18 ^; 8 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(f10,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
=> ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lFxGdCGhDn/DTF2THF_26782.p',cGAZING_THM25_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU842^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:35:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEU842^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Set Theory
% 0.07/0.31 % Problem : TPS problem GAZING-THM25
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.07/0.31 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0195 [Bro09]
% 0.07/0.31 % : 25 [Bar92]
% 0.07/0.31 % : GAZING-THM25 [TPS]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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 v4.0.1, 0.33 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.07/0.31 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.31 % Number of connectives : 6 ( 0 ~; 0 |; 2 &; 4 @)
% 0.07/0.31 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 3 ( 3 avg)
% 0.07/0.31 % Number of types : 2 ( 1 usr)
% 0.07/0.31 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.31 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 % : Polymorphic definitions expanded.
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(a_type,type,
% 0.07/0.31 a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(cGAZING_THM25_pme,conjecture,
% 0.07/0.31 ! [S: a > $o,T: a > $o] :
% 0.07/0.31 ( ( ^ [Xx: a] :
% 0.07/0.31 ( ( S @ Xx )
% 0.07/0.31 & ( T @ Xx ) ) )
% 0.07/0.31 = ( ^ [Xx: a] :
% 0.07/0.31 ( ( T @ Xx )
% 0.07/0.31 & ( S @ Xx ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.83/0.89 ---- Embedded in THF ---
% 0.83/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.89 %%% Generated on Tue Feb 24 12:35:16 EST 2026
% 0.83/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.89 %%% Logic specification used:
% 0.83/0.89 %%% thf(spec, logic, $$dhol).
% 0.83/0.89
% 0.83/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lFxGdCGhDn/DTF2DTF26782.p
% See solution above
% 0.83/0.89 ------------------------
% 1.02/0.90 ---- Cleaned THF ---
% 1.02/0.90 thf(a_type,type,
% 1.02/0.90 a: $tType ).
% 1.02/0.90
% 1.02/0.90 thf(cGAZING_THM25_pme,conjecture,
% 1.02/0.90 ! [S: a > $o,T: a > $o] :
% 1.02/0.90 ( ( ^ [Xx: a] :
% 1.02/0.90 ( ( S @ Xx )
% 1.02/0.90 & ( T @ Xx ) ) )
% 1.02/0.90 = ( ^ [Xx: a] :
% 1.02/0.90 ( ( T @ Xx )
% 1.02/0.90 & ( S @ Xx ) ) ) ) ).
% 1.02/0.90 ------------------------
% 1.02/0.91 % (26882)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_26782 for (3000ds/27Mi)
% 1.02/0.91 % (26886)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26782 for (3000ds/18Mi)
% 1.02/0.91 % (26882)First to succeed.
% 1.02/0.91 % (26880)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26782 for (3000ds/183Mi)
% 1.02/0.91 % (26886)Also succeeded, but the first one will report.
% 1.02/0.91 % (26882)Refutation found. Thanks to Tanya!
% 1.02/0.91 % SZS status Theorem for DTF2THF_26782
% 1.02/0.91 % SZS output start Proof for DTF2THF_26782
% 1.02/0.91 thf(type_def_5, type, a: $tType).
% 1.02/0.91 thf(func_def_0, type, a: $tType).
% 1.02/0.91 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.02/0.91 thf(func_def_8, type, sK0: a > $o).
% 1.02/0.91 thf(func_def_9, type, sK1: a > $o).
% 1.02/0.91 thf(f10,plain,(
% 1.02/0.91 $false),
% 1.02/0.91 inference(trivial_inequality_removal,[status(thm)],[f9])).
% 1.02/0.91 thf(f9,plain,(
% 1.02/0.91 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.02/0.91 inference(cnf_transformation,[status(thm)],[f8])).
% 1.02/0.91 thf(f8,plain,(
% 1.02/0.91 ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.02/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.02/0.91 thf(f7,plain,(
% 1.02/0.91 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) => ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.02/0.91 introduced(definition,[],[choice_axiom])).
% 1.02/0.91 thf(f6,plain,(
% 1.02/0.91 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))),
% 1.02/0.91 inference(ennf_transformation,[status(thm)],[f5])).
% 1.02/0.91 thf(f5,plain,(
% 1.02/0.91 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))))),
% 1.02/0.91 inference(fool_elimination,[status(thm)],[f4])).
% 1.02/0.91 thf(f4,plain,(
% 1.02/0.91 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3))))),
% 1.02/0.91 inference(rectify,[status(thm)],[f2])).
% 1.02/0.91 thf(f2,negated_conjecture,(
% 1.02/0.91 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = (^[X2 : a] : ((X1 @ X2) & (X0 @ X2))))),
% 1.02/0.91 inference(negated_conjecture,[status(cth)],[f1])).
% 1.02/0.91 thf(f1,conjecture,(
% 1.02/0.91 ! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = (^[X2 : a] : ((X1 @ X2) & (X0 @ X2))))),
% 1.02/0.91 file('/export/starexec/sandbox/tmp/tmp.lFxGdCGhDn/DTF2THF_26782.p',cGAZING_THM25_pme)).
% 1.02/0.91 % SZS output end Proof for DTF2THF_26782
% 1.02/0.91 % (26882)------------------------------
% 1.02/0.91 % (26882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.91 % (26882)Termination reason: Refutation
% 1.02/0.91
% 1.02/0.91 % (26882)Memory used [KB]: 5373
% 1.02/0.91 % (26882)Time elapsed: 0.002 s
% 1.02/0.91 % (26882)------------------------------
% 1.02/0.91 % (26882)------------------------------
% 1.02/0.91 % (26879)Success in time 0.01 s
%------------------------------------------------------------------------------