%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET630^5 : 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 : n005.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 09:31:59 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 133 ( 54 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 167 ( 35 ~; 13 |; 44 &; 72 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 10 !; 17 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a ).
thf(f30,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f28,f29]) ).
thf(f29,plain,
spl3_2,
inference(avatar_split_clause,[status(thm)],[f12,f23]) ).
thf(f23,definition,
( spl3_2
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f12,plain,
( ( sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( ( sK1 @ sK2 )
!= $true )
& ( ( sK0 @ sK2 )
= $true ) )
| ( ( ( sK0 @ sK2 )
!= $true )
& ( ( sK1 @ sK2 )
= $true ) ) )
& ( ( sK0 @ sK2 )
= $true )
& ( ( sK1 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a] :
( ( ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( ( ( ( ( sK1 @ sK2 )
!= $true )
& ( ( sK0 @ sK2 )
= $true ) )
| ( ( ( sK0 @ sK2 )
!= $true )
& ( ( sK1 @ sK2 )
= $true ) ) )
& ( ( sK0 @ sK2 )
= $true )
& ( ( sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a] :
( ( ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a] :
( ( ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
~ ? [X2: a] :
( ( ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
~ ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) )
& ( ( X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
~ ? [X2: a] :
( ( X1 @ X2 )
& ( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) )
& ( X0 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
~ ? [X2: a] :
( ( X0 @ X2 )
& ( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
& ( X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
~ ? [X2: a] :
( ( X0 @ X2 )
& ( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
& ( X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.hkDaw6MZRp/DTF2THF_12714.p',cBOOL_PROP_112_pme) ).
thf(f28,plain,
spl3_1,
inference(avatar_split_clause,[status(thm)],[f13,f19]) ).
thf(f19,definition,
( spl3_1
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f13,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f27,plain,
( ~ spl3_2
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f19,f23]) ).
thf(f17,plain,
( ( ( sK0 @ sK2 )
!= $true )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET630^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:00:59 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET630^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-112
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 112th Boolean property of sets.
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0291 [Bro09]
% 0.19/0.45 % : BOOL-PROP-112 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.45 % Number of connectives : 14 ( 3 ~; 1 |; 4 &; 6 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.45 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_112_pme,conjecture,
% 0.19/0.45 ! [X: a > $o,Y: a > $o] :
% 0.19/0.45 ~ ? [Xx: a] :
% 0.19/0.45 ( ( X @ Xx )
% 0.19/0.45 & ( Y @ Xx )
% 0.19/0.45 & ( ( ( X @ Xx )
% 0.19/0.45 & ~ ( Y @ Xx ) )
% 0.19/0.45 | ( ( Y @ Xx )
% 0.19/0.45 & ~ ( X @ Xx ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 12:01:00 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hkDaw6MZRp/DTF2DTF12714.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(a_type,type,
% 1.47/1.26 a: $tType ).
% 1.47/1.26
% 1.47/1.26 thf(cBOOL_PROP_112_pme,conjecture,
% 1.47/1.26 ! [X: a > $o,Y: a > $o] :
% 1.47/1.26 ~ ? [Xx: a] :
% 1.47/1.26 ( ( X @ Xx )
% 1.47/1.26 & ( Y @ Xx )
% 1.47/1.26 & ( ( ( X @ Xx )
% 1.47/1.26 & ~ ( Y @ Xx ) )
% 1.47/1.26 | ( ( Y @ Xx )
% 1.47/1.26 & ~ ( X @ Xx ) ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.28 % (12834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12714 for (3000ds/18Mi)
% 1.47/1.28 % (12834)First to succeed.
% 1.47/1.28 % (12831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12714 for (3000ds/2Mi)
% 1.47/1.28 % (12831)Also succeeded, but the first one will report.
% 1.47/1.28 % (12834)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_12714
% 1.47/1.28 % SZS output start Proof for DTF2THF_12714
% 1.47/1.28 thf(type_def_5, type, a: $tType).
% 1.47/1.28 thf(func_def_0, type, a: $tType).
% 1.47/1.28 thf(func_def_4, type, sK0: a > $o).
% 1.47/1.28 thf(func_def_5, type, sK1: a > $o).
% 1.47/1.28 thf(func_def_6, type, sK2: a).
% 1.47/1.28 thf(f30,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(avatar_sat_refutation,[status(thm)],[f27,f28,f29])).
% 1.47/1.28 thf(f29,plain,(
% 1.47/1.28 spl3_2),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f12,f23])).
% 1.47/1.28 thf(f23,definition,(
% 1.47/1.28 spl3_2 <=> ((sK1 @ sK2) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 ((sK1 @ sK2) = $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 ((((sK1 @ sK2) != $true) & ((sK0 @ sK2) = $true)) | (((sK0 @ sK2) != $true) & ((sK1 @ sK2) = $true))) & ((sK0 @ sK2) = $true) & ((sK1 @ sK2) = $true)),
% 1.47/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10])).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a] : (((((X1 @ X2) != $true) & ((X0 @ X2) = $true)) | (((X0 @ X2) != $true) & ((X1 @ X2) = $true))) & ((X0 @ X2) = $true) & ((X1 @ X2) = $true)) => (((((sK1 @ sK2) != $true) & ((sK0 @ sK2) = $true)) | (((sK0 @ sK2) != $true) & ((sK1 @ sK2) = $true))) & ((sK0 @ sK2) = $true) & ((sK1 @ sK2) = $true))),
% 1.47/1.28 introduced(definition,[],[choice_axiom])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a] : (((((X1 @ X2) != $true) & ((X0 @ X2) = $true)) | (((X0 @ X2) != $true) & ((X1 @ X2) = $true))) & ((X0 @ X2) = $true) & ((X1 @ X2) = $true))),
% 1.47/1.28 inference(rectify,[status(thm)],[f8])).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 ? [X1 : a > $o,X0 : a > $o,X2 : a] : (((((X0 @ X2) != $true) & ((X1 @ X2) = $true)) | (((X1 @ X2) != $true) & ((X0 @ X2) = $true))) & ((X1 @ X2) = $true) & ((X0 @ X2) = $true))),
% 1.47/1.28 inference(flattening,[status(thm)],[f7])).
% 1.47/1.28 thf(f7,plain,(
% 1.47/1.28 ? [X0 : a > $o,X1 : a > $o] : ? [X2 : a] : (((((X0 @ X2) != $true) & ((X1 @ X2) = $true)) | (((X1 @ X2) != $true) & ((X0 @ X2) = $true))) & ((X1 @ X2) = $true) & ((X0 @ X2) = $true))),
% 1.47/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.28 thf(f6,plain,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ~? [X2 : a] : (((((X0 @ X2) != $true) & ((X1 @ X2) = $true)) | (((X1 @ X2) != $true) & ((X0 @ X2) = $true))) & ((X1 @ X2) = $true) & ((X0 @ X2) = $true))),
% 1.47/1.28 inference(flattening,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,plain,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ~? [X2 : a] : (((X1 @ X2) = $true) & ((~((X1 @ X2) = $true) & ((X0 @ X2) = $true)) | (~((X0 @ X2) = $true) & ((X1 @ X2) = $true))) & ((X0 @ X2) = $true))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.28 thf(f4,plain,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ~? [X2 : a] : ((X1 @ X2) & ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2))) & (X0 @ X2))),
% 1.47/1.28 inference(rectify,[status(thm)],[f2])).
% 1.47/1.28 thf(f2,negated_conjecture,(
% 1.47/1.28 ~! [X1 : a > $o,X0 : a > $o] : ~? [X2 : a] : ((X0 @ X2) & ((~(X0 @ X2) & (X1 @ X2)) | (~(X1 @ X2) & (X0 @ X2))) & (X1 @ X2))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 ! [X1 : a > $o,X0 : a > $o] : ~? [X2 : a] : ((X0 @ X2) & ((~(X0 @ X2) & (X1 @ X2)) | (~(X1 @ X2) & (X0 @ X2))) & (X1 @ X2))),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.hkDaw6MZRp/DTF2THF_12714.p',cBOOL_PROP_112_pme)).
% 1.47/1.28 thf(f28,plain,(
% 1.47/1.28 spl3_1),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f13,f19])).
% 1.47/1.28 thf(f19,definition,(
% 1.47/1.28 spl3_1 <=> ((sK0 @ sK2) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.47/1.28 thf(f13,plain,(
% 1.47/1.28 ((sK0 @ sK2) = $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.28 thf(f27,plain,(
% 1.47/1.28 ~spl3_2 | ~spl3_1),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f17,f19,f23])).
% 1.47/1.28 thf(f17,plain,(
% 1.47/1.28 ((sK0 @ sK2) != $true) | ((sK1 @ sK2) != $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.28 % SZS output end Proof for DTF2THF_12714
% 1.47/1.28 % (12834)------------------------------
% 1.47/1.28 % (12834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (12834)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (12834)Memory used [KB]: 5500
% 1.47/1.28 % (12834)Time elapsed: 0.002 s
% 1.47/1.28 % (12834)Instructions burned: 1 (million)
% 1.47/1.28 % (12834)------------------------------
% 1.47/1.28 % (12834)------------------------------
% 1.47/1.28 % (12827)Success in time 0.002 s
%------------------------------------------------------------------------------