%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET585^5 : 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 : n017.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 09:31:49 AM UTC 2026
% Result : Theorem 1.29s 1.18s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 30 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 89 ( 16 ~; 4 |; 22 &; 42 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 16 !; 16 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a > $o ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f13]) ).
thf(f13,plain,
( $true
!= ( sK3 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
!= ( sK2 @ sK0 ) )
& ( $true
!= ( sK3 @ sK0 ) )
& ( $true
= ( sK1 @ sK0 ) )
& ( $true
= ( sK3 @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( $true
!= ( X3 @ X0 ) )
& ( $true
= ( X1 @ X0 ) )
& ( $true
= ( X3 @ X0 ) ) )
=> ( ( $true
!= ( sK2 @ sK0 ) )
& ( $true
!= ( sK3 @ sK0 ) )
& ( $true
= ( sK1 @ sK0 ) )
& ( $true
= ( sK3 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( $true
!= ( X2 @ X0 ) )
& ( $true
!= ( X3 @ X0 ) )
& ( $true
= ( X1 @ X0 ) )
& ( $true
= ( X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a,X2: a > $o,X3: a > $o,X1: a > $o] :
( ( $true
!= ( X3 @ X0 ) )
& ( $true
!= ( X1 @ X0 ) )
& ( $true
= ( X2 @ X0 ) )
& ( $true
= ( X1 @ X0 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X3: a > $o,X2: a > $o,X1: a > $o,X0: a] :
( ( $true
!= ( X1 @ X0 ) )
& ( $true
!= ( X3 @ X0 ) )
& ( $true
= ( X2 @ X0 ) )
& ( $true
= ( X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X3: a > $o,X2: a > $o,X1: a > $o,X0: a] :
( ( ( $true
= ( X2 @ X0 ) )
& ( $true
= ( X1 @ X0 ) ) )
=> ( ( $true
= ( X1 @ X0 ) )
| ( $true
= ( X3 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ( X1 @ X0 )
& ( X2 @ X0 ) )
=> ( ( X1 @ X0 )
| ( X3 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( ( X0 @ X3 )
| ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( ( X0 @ X3 )
| ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yd7fxPpKAE/DTF2THF_20644.p',cBOOL_PROP_38_pme) ).
thf(f11,plain,
( $true
= ( sK3 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET585^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.28 % Computer : n017.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Feb 24 11:58:10 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SET585^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.40 % Domain : Set Theory
% 0.16/0.40 % Problem : TPS problem BOOL-PROP-38
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % English : Trybulec's 38th Boolean property of sets
% 0.16/0.40
% 0.16/0.40 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.40 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Bro09]
% 0.16/0.40 % Names : tps_0097 [Bro09]
% 0.16/0.40 % : BOOL-PROP-38 [TPS]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.16/0.40 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.40 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.40 % Number of connectives : 7 ( 0 ~; 1 |; 1 &; 4 @)
% 0.16/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 8 ( 8 avg)
% 0.16/0.40 % Number of types : 2 ( 1 usr)
% 0.16/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.40 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.16/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.40 % : Polymorphic definitions expanded.
% 0.16/0.40 % :
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(a_type,type,
% 0.16/0.40 a: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(cBOOL_PROP_38_pme,conjecture,
% 0.16/0.40 ! [X: a > $o,Y: a > $o,Z: a > $o,Xx: a] :
% 0.16/0.40 ( ( ( X @ Xx )
% 0.16/0.40 & ( Y @ Xx ) )
% 0.16/0.40 => ( ( X @ Xx )
% 0.16/0.40 | ( Z @ Xx ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.29/1.16 ---- Embedded in THF ---
% 1.29/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.29/1.16 %%% Generated on Tue Feb 24 11:58:11 EST 2026
% 1.29/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.29/1.16 %%% Logic specification used:
% 1.29/1.16 %%% thf(spec, logic, $$dhol).
% 1.29/1.16
% 1.29/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Yd7fxPpKAE/DTF2DTF20644.p
% See solution above
% 1.29/1.16 ------------------------
% 1.29/1.17 ---- Cleaned THF ---
% 1.29/1.17 thf(a_type,type,
% 1.29/1.17 a: $tType ).
% 1.29/1.17
% 1.29/1.17 thf(cBOOL_PROP_38_pme,conjecture,
% 1.29/1.17 ! [X: a > $o,Y: a > $o,Z: a > $o,Xx: a] :
% 1.29/1.17 ( ( ( X @ Xx )
% 1.29/1.17 & ( Y @ Xx ) )
% 1.29/1.17 => ( ( X @ Xx )
% 1.29/1.17 | ( Z @ Xx ) ) ) ).
% 1.29/1.17 ------------------------
% 1.29/1.18 % (20741)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20644 for (3000ds/183Mi)
% 1.29/1.18 % (20743)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_20644 for (3000ds/27Mi)
% 1.29/1.18 % (20741)First to succeed.
% 1.29/1.18 % (20743)Also succeeded, but the first one will report.
% 1.29/1.18 % (20741)Refutation found. Thanks to Tanya!
% 1.29/1.18 % SZS status Theorem for DTF2THF_20644
% 1.29/1.18 % SZS output start Proof for DTF2THF_20644
% 1.29/1.18 thf(type_def_5, type, a: $tType).
% 1.29/1.18 thf(func_def_0, type, a: $tType).
% 1.29/1.18 thf(func_def_4, type, sK0: a).
% 1.29/1.18 thf(func_def_5, type, sK1: a > $o).
% 1.29/1.18 thf(func_def_6, type, sK2: a > $o).
% 1.29/1.18 thf(func_def_7, type, sK3: a > $o).
% 1.29/1.18 thf(f15,plain,(
% 1.29/1.18 $false),
% 1.29/1.18 inference(subsumption_resolution,[status(thm)],[f11,f13])).
% 1.29/1.18 thf(f13,plain,(
% 1.29/1.18 ($true != (sK3 @ sK0))),
% 1.29/1.18 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.18 thf(f10,plain,(
% 1.29/1.18 ($true != (sK2 @ sK0)) & ($true != (sK3 @ sK0)) & ($true = (sK1 @ sK0)) & ($true = (sK3 @ sK0))),
% 1.29/1.18 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9])).
% 1.29/1.18 thf(f9,plain,(
% 1.29/1.18 ? [X0 : a,X1 : a > $o,X2 : a > $o,X3 : a > $o] : (($true != (X2 @ X0)) & ($true != (X3 @ X0)) & ($true = (X1 @ X0)) & ($true = (X3 @ X0))) => (($true != (sK2 @ sK0)) & ($true != (sK3 @ sK0)) & ($true = (sK1 @ sK0)) & ($true = (sK3 @ sK0)))),
% 1.29/1.18 introduced(definition,[],[choice_axiom])).
% 1.29/1.18 thf(f8,plain,(
% 1.29/1.18 ? [X0 : a,X1 : a > $o,X2 : a > $o,X3 : a > $o] : (($true != (X2 @ X0)) & ($true != (X3 @ X0)) & ($true = (X1 @ X0)) & ($true = (X3 @ X0)))),
% 1.29/1.18 inference(rectify,[status(thm)],[f7])).
% 1.29/1.18 thf(f7,plain,(
% 1.29/1.18 ? [X0 : a,X2 : a > $o,X3 : a > $o,X1 : a > $o] : (($true != (X3 @ X0)) & ($true != (X1 @ X0)) & ($true = (X2 @ X0)) & ($true = (X1 @ X0)))),
% 1.29/1.18 inference(flattening,[status(thm)],[f6])).
% 1.29/1.18 thf(f6,plain,(
% 1.29/1.18 ? [X3 : a > $o,X2 : a > $o,X1 : a > $o,X0 : a] : ((($true != (X1 @ X0)) & ($true != (X3 @ X0))) & (($true = (X2 @ X0)) & ($true = (X1 @ X0))))),
% 1.29/1.18 inference(ennf_transformation,[status(thm)],[f5])).
% 1.29/1.18 thf(f5,plain,(
% 1.29/1.18 ~! [X3 : a > $o,X2 : a > $o,X1 : a > $o,X0 : a] : ((($true = (X2 @ X0)) & ($true = (X1 @ X0))) => (($true = (X1 @ X0)) | ($true = (X3 @ X0))))),
% 1.29/1.18 inference(fool_elimination,[status(thm)],[f4])).
% 1.29/1.18 thf(f4,plain,(
% 1.29/1.18 ~! [X0 : a,X1 : a > $o,X2 : a > $o,X3 : a > $o] : (((X1 @ X0) & (X2 @ X0)) => ((X1 @ X0) | (X3 @ X0)))),
% 1.29/1.18 inference(rectify,[status(thm)],[f2])).
% 1.29/1.18 thf(f2,negated_conjecture,(
% 1.29/1.18 ~! [X3 : a,X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((X0 @ X3) & (X1 @ X3)) => ((X0 @ X3) | (X2 @ X3)))),
% 1.29/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.29/1.18 thf(f1,conjecture,(
% 1.29/1.18 ! [X3 : a,X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((X0 @ X3) & (X1 @ X3)) => ((X0 @ X3) | (X2 @ X3)))),
% 1.29/1.18 file('/export/starexec/sandbox/tmp/tmp.Yd7fxPpKAE/DTF2THF_20644.p',cBOOL_PROP_38_pme)).
% 1.29/1.18 thf(f11,plain,(
% 1.29/1.18 ($true = (sK3 @ sK0))),
% 1.29/1.18 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.18 % SZS output end Proof for DTF2THF_20644
% 1.29/1.18 % (20741)------------------------------
% 1.29/1.18 % (20741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.18 % (20741)Termination reason: Refutation
% 1.29/1.18
% 1.29/1.18 % (20741)Memory used [KB]: 5373
% 1.29/1.18 % (20741)Time elapsed: 0.002 s
% 1.29/1.18 % (20741)------------------------------
% 1.29/1.18 % (20741)------------------------------
% 1.29/1.18 % (20740)Success in time 0.011 s
%------------------------------------------------------------------------------