%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET604^5 : 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 : n016.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 09:31:53 AM UTC 2026
% Result : Theorem 0.31s 1.33s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 10 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 37 ( 18 ~; 0 |; 9 &; 9 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 20 ^; 4 !; 2 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] : $false ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( $false
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( $false
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o] :
( ( ^ [Y0: a] :
( $false
& ~ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
=> ( ( ^ [Y0: a] :
( $false
& ~ ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ^ [Y0: a] :
( $false
& ~ ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ( ^ [Y0: a] :
( $false
& ~ ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ~ ( X0 @ X1 )
& $false ) )
= ( ^ [X2: a] : $false ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( ^ [X1: a] :
( ~ ( X0 @ X1 )
& $false ) )
= ( ^ [X1: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( ^ [X1: a] :
( ~ ( X0 @ X1 )
& $false ) )
= ( ^ [X1: a] : $false ) ),
file('/export/starexec/sandbox/tmp/tmp.oOQT2vjYX5/DTF2THF_28983.p',cBOOL_PROP_75_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET604^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:01:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET604^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem BOOL-PROP-75
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : Trybulec's 75th Boolean property of sets
% 0.31/0.46
% 0.31/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0177 [Bro09]
% 0.31/0.46 % : BOOL-PROP-75 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % 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, 0.14 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
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 1 ( 3 avg)
% 0.31/0.46 % Number of connectives : 3 ( 1 ~; 0 |; 1 &; 1 @)
% 0.31/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 2 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cBOOL_PROP_75_pme,conjecture,
% 0.31/0.46 ! [X: a > $o] :
% 0.31/0.46 ( ( ^ [Xx: a] :
% 0.31/0.46 ( $false
% 0.31/0.46 & ~ ( X @ Xx ) ) )
% 0.31/0.46 = ( ^ [Xx: a] : $false ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:01:07 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oOQT2vjYX5/DTF2DTF28983.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(a_type,type,
% 0.31/1.31 a: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(cBOOL_PROP_75_pme,conjecture,
% 0.31/1.31 ! [X: a > $o] :
% 0.31/1.31 ( ( ^ [Xx: a] :
% 0.31/1.31 ( $false
% 0.31/1.31 & ~ ( X @ Xx ) ) )
% 0.31/1.31 = ( ^ [Xx: a] : $false ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.33 % (29172)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_28983 for (2999ds/4Mi)
% 0.31/1.33 % (29172)First to succeed.
% 0.31/1.33 % (29177)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28983 for (2999ds/18Mi)
% 0.31/1.33 % (29177)Also succeeded, but the first one will report.
% 0.31/1.33 % (29172)Refutation found. Thanks to Tanya!
% 0.31/1.33 % SZS status Theorem for DTF2THF_28983
% 0.31/1.33 % SZS output start Proof for DTF2THF_28983
% 0.31/1.33 thf(type_def_5, type, a: $tType).
% 0.31/1.33 thf(func_def_0, type, a: $tType).
% 0.31/1.33 thf(func_def_8, type, sK0: a > $o).
% 0.31/1.33 thf(f11,plain,(
% 0.31/1.33 $false),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 0.31/1.33 thf(f10,plain,(
% 0.31/1.33 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ($false)))),
% 0.31/1.33 inference(boolean_simplification,[status(thm)],[f9])).
% 0.31/1.33 thf(f9,plain,(
% 0.31/1.33 ((^[Y0 : a]: ($false & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ($false)))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f8])).
% 0.31/1.33 thf(f8,plain,(
% 0.31/1.33 ((^[Y0 : a]: ($false & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ($false)))),
% 0.31/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 0.31/1.33 thf(f7,plain,(
% 0.31/1.33 ? [X0 : a > $o] : ((^[Y0 : a]: ($false & (~ (X0 @ Y0)))) != (^[Y0 : a]: ($false))) => ((^[Y0 : a]: ($false & (~ (sK0 @ Y0)))) != (^[Y0 : a]: ($false)))),
% 0.31/1.33 introduced(definition,[],[choice_axiom])).
% 0.31/1.33 thf(f6,plain,(
% 0.31/1.33 ? [X0 : a > $o] : ((^[Y0 : a]: ($false & (~ (X0 @ Y0)))) != (^[Y0 : a]: ($false)))),
% 0.31/1.33 inference(ennf_transformation,[status(thm)],[f5])).
% 0.31/1.33 thf(f5,plain,(
% 0.31/1.33 ~! [X0 : a > $o] : ((^[Y0 : a]: ($false & (~ (X0 @ Y0)))) = (^[Y0 : a]: ($false)))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.31/1.33 thf(f4,plain,(
% 0.31/1.33 ~! [X0 : a > $o] : ((^[X1 : a] : (~(X0 @ X1) & $false)) = (^[X2 : a] : ($false)))),
% 0.31/1.33 inference(rectify,[status(thm)],[f2])).
% 0.31/1.33 thf(f2,negated_conjecture,(
% 0.31/1.33 ~! [X0 : a > $o] : ((^[X1 : a] : (~(X0 @ X1) & $false)) = (^[X1 : a] : ($false)))),
% 0.31/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.31/1.33 thf(f1,conjecture,(
% 0.31/1.33 ! [X0 : a > $o] : ((^[X1 : a] : (~(X0 @ X1) & $false)) = (^[X1 : a] : ($false)))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.oOQT2vjYX5/DTF2THF_28983.p',cBOOL_PROP_75_pme)).
% 0.31/1.33 % SZS output end Proof for DTF2THF_28983
% 0.31/1.33 % (29172)------------------------------
% 0.31/1.33 % (29172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (29172)Termination reason: Refutation
% 0.31/1.33
% 0.31/1.33 % (29172)Memory used [KB]: 5373
% 0.31/1.33 % (29172)Time elapsed: 0.002 s
% 0.31/1.33 % (29172)------------------------------
% 0.31/1.33 % (29172)------------------------------
% 0.31/1.33 % (29170)Success in time 0.003 s
%------------------------------------------------------------------------------