%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU847^5 : 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 : n009.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 09:37:34 AM UTC 2026
% Result : Theorem 1.50s 1.22s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 91 ( 33 ~; 12 |; 21 &; 24 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 13 ^; 4 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
sK0 != sK0,
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [Y0: a] : ( sK0 @ Y0 ) )
!= sK0 ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( $false
| ( sK0 @ Y0 ) ) )
!= sK0 ),
inference(boolean_simplification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( sK0 @ Y0 ) ) )
!= sK0 ),
inference(boolean_simplification,[status(thm)],[f10]) ).
thf(f10,plain,
( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( $true
& ( sK0 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) )
!= sK0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& $false )
| ( ~ $false
& ( X0 @ Y0 ) ) ) )
!= X0 )
=> ( ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& $false )
| ( ~ $false
& ( X0 @ Y0 ) ) ) )
!= X0 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& $false )
| ( ~ $false
& ( X0 @ Y0 ) ) ) )
= X0 ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ $false )
| ( $false
& ~ ( X0 @ X1 ) ) ) )
= X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ $false )
| ( $false
& ~ ( X0 @ X1 ) ) ) )
= X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ $false )
| ( $false
& ~ ( X0 @ X1 ) ) ) )
= X0 ),
file('/export/starexec/sandbox2/tmp/tmp.cJ9tgqgdgr/DTF2THF_5757.p',cGAZING_THM41_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU847^5 : 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
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:35:25 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEU847^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : TPS problem GAZING-THM41
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.18/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Bro09]
% 0.18/0.44 % Names : tps_0279 [Bro09]
% 0.18/0.44 % : 41 [Bar92]
% 0.18/0.44 % : GAZING-THM41 [TPS]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 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, 0.14 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
% 0.18/0.44 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.18/0.44 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 1 ( 3 avg)
% 0.18/0.44 % Number of connectives : 7 ( 2 ~; 1 |; 2 &; 2 @)
% 0.18/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 2 ( 2 avg)
% 0.18/0.44 % Number of types : 2 ( 1 usr)
% 0.18/0.44 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.18/0.44 % Number of variables : 2 ( 1 ^; 1 !; 0 ?; 2 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.44 % : Polymorphic definitions expanded.
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(a_type,type,
% 0.18/0.44 a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(cGAZING_THM41_pme,conjecture,
% 0.18/0.44 ! [S: a > $o] :
% 0.18/0.44 ( ( ^ [Xz: a] :
% 0.18/0.44 ( ( ( S @ Xz )
% 0.18/0.44 & ~ $false )
% 0.18/0.44 | ( $false
% 0.18/0.44 & ~ ( S @ Xz ) ) ) )
% 0.18/0.44 = S ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.33/1.19 ---- Embedded in THF ---
% 1.33/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.33/1.19 %%% Generated on Tue Feb 24 12:35:26 EST 2026
% 1.33/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.33/1.19 %%% Logic specification used:
% 1.33/1.19 %%% thf(spec, logic, $$dhol).
% 1.33/1.19
% 1.33/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.cJ9tgqgdgr/DTF2DTF5757.p
% See solution above
% 1.33/1.19 ------------------------
% 1.50/1.20 ---- Cleaned THF ---
% 1.50/1.20 thf(a_type,type,
% 1.50/1.20 a: $tType ).
% 1.50/1.20
% 1.50/1.20 thf(cGAZING_THM41_pme,conjecture,
% 1.50/1.20 ! [S: a > $o] :
% 1.50/1.20 ( ( ^ [Xz: a] :
% 1.50/1.20 ( ( ( S @ Xz )
% 1.50/1.20 & ~ $false )
% 1.50/1.20 | ( $false
% 1.50/1.20 & ~ ( S @ Xz ) ) ) )
% 1.50/1.20 = S ) ).
% 1.50/1.20 ------------------------
% 1.50/1.22 % (5908)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5757 for (2999ds/18Mi)
% 1.50/1.22 % (5903)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_5757 for (2999ds/4Mi)
% 1.50/1.22 % (5904)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_5757 for (2999ds/27Mi)
% 1.50/1.22 % (5908)First to succeed.
% 1.50/1.22 % (5904)Also succeeded, but the first one will report.
% 1.50/1.22 % (5903)Also succeeded, but the first one will report.
% 1.50/1.22 % (5908)Refutation found. Thanks to Tanya!
% 1.50/1.22 % SZS status Theorem for DTF2THF_5757
% 1.50/1.22 % SZS output start Proof for DTF2THF_5757
% 1.50/1.22 thf(type_def_5, type, a: $tType).
% 1.50/1.22 thf(func_def_0, type, a: $tType).
% 1.50/1.22 thf(func_def_9, type, sK0: a > $o).
% 1.50/1.22 thf(f15,plain,(
% 1.50/1.22 $false),
% 1.50/1.22 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.50/1.22 thf(f14,plain,(
% 1.50/1.22 (sK0 != sK0)),
% 1.50/1.22 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.50/1.22 thf(f13,plain,(
% 1.50/1.22 ((^[Y0 : a]: (sK0 @ Y0)) != sK0)),
% 1.50/1.22 inference(boolean_simplification,[status(thm)],[f12])).
% 1.50/1.22 thf(f12,plain,(
% 1.50/1.22 ((^[Y0 : a]: ($false | (sK0 @ Y0))) != sK0)),
% 1.50/1.22 inference(boolean_simplification,[status(thm)],[f11])).
% 1.50/1.22 thf(f11,plain,(
% 1.50/1.22 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & $false) | (sK0 @ Y0))) != sK0)),
% 1.50/1.22 inference(boolean_simplification,[status(thm)],[f10])).
% 1.50/1.22 thf(f10,plain,(
% 1.50/1.22 (sK0 != (^[Y0 : a]: (((~ (sK0 @ Y0)) & $false) | ($true & (sK0 @ Y0)))))),
% 1.50/1.22 inference(boolean_simplification,[status(thm)],[f9])).
% 1.50/1.22 thf(f9,plain,(
% 1.50/1.22 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & $false) | ((~ $false) & (sK0 @ Y0)))) != sK0)),
% 1.50/1.22 inference(cnf_transformation,[status(thm)],[f8])).
% 1.50/1.22 thf(f8,plain,(
% 1.50/1.22 ((^[Y0 : a]: (((~ (sK0 @ Y0)) & $false) | ((~ $false) & (sK0 @ Y0)))) != sK0)),
% 1.50/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.50/1.22 thf(f7,plain,(
% 1.50/1.22 ? [X0 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & $false) | ((~ $false) & (X0 @ Y0)))) != X0) => ((^[Y0 : a]: (((~ (sK0 @ Y0)) & $false) | ((~ $false) & (sK0 @ Y0)))) != sK0)),
% 1.50/1.22 introduced(definition,[],[choice_axiom])).
% 1.50/1.22 thf(f6,plain,(
% 1.50/1.22 ? [X0 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & $false) | ((~ $false) & (X0 @ Y0)))) != X0)),
% 1.50/1.22 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.22 thf(f5,plain,(
% 1.50/1.22 ~! [X0 : a > $o] : ((^[Y0 : a]: (((~ (X0 @ Y0)) & $false) | ((~ $false) & (X0 @ Y0)))) = X0)),
% 1.50/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.22 thf(f4,plain,(
% 1.50/1.22 ~! [X0 : a > $o] : ((^[X1 : a] : (((X0 @ X1) & ~$false) | ($false & ~(X0 @ X1)))) = X0)),
% 1.50/1.22 inference(rectify,[status(thm)],[f2])).
% 1.50/1.22 thf(f2,negated_conjecture,(
% 1.50/1.22 ~! [X0 : a > $o] : ((^[X1 : a] : (((X0 @ X1) & ~$false) | ($false & ~(X0 @ X1)))) = X0)),
% 1.50/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.22 thf(f1,conjecture,(
% 1.50/1.22 ! [X0 : a > $o] : ((^[X1 : a] : (((X0 @ X1) & ~$false) | ($false & ~(X0 @ X1)))) = X0)),
% 1.50/1.22 file('/export/starexec/sandbox2/tmp/tmp.cJ9tgqgdgr/DTF2THF_5757.p',cGAZING_THM41_pme)).
% 1.50/1.22 % SZS output end Proof for DTF2THF_5757
% 1.50/1.22 % (5908)------------------------------
% 1.50/1.22 % (5908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (5908)Termination reason: Refutation
% 1.50/1.22
% 1.50/1.22 % (5908)Memory used [KB]: 5373
% 1.50/1.22 % (5908)Time elapsed: 0.002 s
% 1.50/1.22 % (5908)Instructions burned: 1 (million)
% 1.50/1.22 % (5908)------------------------------
% 1.50/1.22 % (5908)------------------------------
% 1.50/1.22 % (5901)Success in time 0.012 s
%------------------------------------------------------------------------------