%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET629^5 : 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 : n018.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 09:31:58 AM UTC 2026
% Result : Theorem 1.44s 1.28s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 102 ( 22 ~; 0 |; 33 &; 46 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 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_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_7,type,
sK2: a > $o ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f15]) ).
thf(f15,plain,
( ( sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK0 @ sK1 )
= $true )
& ( ( sK2 @ sK1 )
= $true )
& ( ( sK0 @ sK1 )
!= $true )
& ( ( sK2 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a,X2: a > $o] :
( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X2 @ X1 ) )
& ( $true
!= ( X0 @ X1 ) )
& ( $true
= ( X2 @ X1 ) ) )
=> ( ( ( sK0 @ sK1 )
= $true )
& ( ( sK2 @ sK1 )
= $true )
& ( ( sK0 @ sK1 )
!= $true )
& ( ( sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a,X2: a > $o] :
( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X2 @ X1 ) )
& ( $true
!= ( X0 @ X1 ) )
& ( $true
= ( X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X2: a,X1: a > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: a > $o,X0: a > $o] :
~ ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
~ ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 )
& ~ ( X0 @ X2 )
& ( X1 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
~ ? [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 )
& ~ ( X1 @ X2 )
& ( X0 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
~ ? [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 )
& ~ ( X1 @ X2 )
& ( X0 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.cfrPQvQGBH/DTF2THF_26133.p',cBOOL_PROP_111_pme) ).
thf(f13,plain,
( ( sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET629^5 : 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
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:01:01 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SET629^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : TPS problem BOOL-PROP-111
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Trybulec's 111th Boolean property of sets
% 0.31/0.47
% 0.31/0.47 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0190 [Bro09]
% 0.31/0.47 % : BOOL-PROP-111 [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.47 % Number of connectives : 9 ( 2 ~; 0 |; 3 &; 4 @)
% 0.31/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 10 ( 10 avg)
% 0.31/0.47 % Number of types : 2 ( 1 usr)
% 0.31/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.47 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 % : Polymorphic definitions expanded.
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(a_type,type,
% 0.31/0.47 a: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(cBOOL_PROP_111_pme,conjecture,
% 0.31/0.47 ! [X: a > $o,Y: a > $o] :
% 0.31/0.47 ~ ? [Xx: a] :
% 0.31/0.47 ( ( X @ Xx )
% 0.31/0.47 & ( Y @ Xx )
% 0.31/0.47 & ( X @ Xx )
% 0.31/0.47 & ~ ( Y @ Xx ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.44/1.26 ---- Embedded in THF ---
% 1.44/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.26 %%% Generated on Tue Feb 24 12:01:02 EST 2026
% 1.44/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.26 %%% Logic specification used:
% 1.44/1.26 %%% thf(spec, logic, $$dhol).
% 1.44/1.26
% 1.44/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.cfrPQvQGBH/DTF2DTF26133.p
% See solution above
% 1.44/1.26 ------------------------
% 1.44/1.27 ---- Cleaned THF ---
% 1.44/1.27 thf(a_type,type,
% 1.44/1.27 a: $tType ).
% 1.44/1.27
% 1.44/1.27 thf(cBOOL_PROP_111_pme,conjecture,
% 1.44/1.27 ! [X: a > $o,Y: a > $o] :
% 1.44/1.27 ~ ? [Xx: a] :
% 1.44/1.27 ( ( X @ Xx )
% 1.44/1.27 & ( Y @ Xx )
% 1.44/1.27 & ( X @ Xx )
% 1.44/1.27 & ~ ( Y @ Xx ) ) ).
% 1.44/1.27 ------------------------
% 1.44/1.28 % (26475)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_26133 for (2999ds/27Mi)
% 1.44/1.28 % (26473)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26133 for (2999ds/183Mi)
% 1.44/1.28 % (26475)First to succeed.
% 1.44/1.28 % (26473)Also succeeded, but the first one will report.
% 1.44/1.28 % (26475)Refutation found. Thanks to Tanya!
% 1.44/1.28 % SZS status Theorem for DTF2THF_26133
% 1.44/1.28 % SZS output start Proof for DTF2THF_26133
% 1.44/1.28 thf(type_def_5, type, a: $tType).
% 1.44/1.28 thf(func_def_0, type, a: $tType).
% 1.44/1.28 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.44/1.28 thf(func_def_5, type, sK0: a > $o).
% 1.44/1.28 thf(func_def_6, type, sK1: a).
% 1.44/1.28 thf(func_def_7, type, sK2: a > $o).
% 1.44/1.28 thf(f17,plain,(
% 1.44/1.28 $false),
% 1.44/1.28 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.44/1.28 thf(f16,plain,(
% 1.44/1.28 ($true != $true)),
% 1.44/1.28 inference(superposition,[status(thm)],[f13,f15])).
% 1.44/1.28 thf(f15,plain,(
% 1.44/1.28 ((sK0 @ sK1) = $true)),
% 1.44/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.44/1.28 thf(f11,plain,(
% 1.44/1.28 ((sK0 @ sK1) = $true) & ((sK2 @ sK1) = $true) & ((sK0 @ sK1) != $true) & ((sK2 @ sK1) = $true)),
% 1.44/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10])).
% 1.44/1.28 thf(f10,plain,(
% 1.44/1.28 ? [X0 : a > $o,X1 : a,X2 : a > $o] : (($true = (X0 @ X1)) & ($true = (X2 @ X1)) & ($true != (X0 @ X1)) & ($true = (X2 @ X1))) => (((sK0 @ sK1) = $true) & ((sK2 @ sK1) = $true) & ((sK0 @ sK1) != $true) & ((sK2 @ sK1) = $true))),
% 1.44/1.28 introduced(definition,[],[choice_axiom])).
% 1.44/1.28 thf(f9,plain,(
% 1.44/1.28 ? [X0 : a > $o,X1 : a,X2 : a > $o] : (($true = (X0 @ X1)) & ($true = (X2 @ X1)) & ($true != (X0 @ X1)) & ($true = (X2 @ X1)))),
% 1.44/1.28 inference(rectify,[status(thm)],[f8])).
% 1.44/1.28 thf(f8,plain,(
% 1.44/1.28 ? [X0 : a > $o,X2 : a,X1 : a > $o] : (((X0 @ X2) = $true) & ((X1 @ X2) = $true) & ((X0 @ X2) != $true) & ((X1 @ X2) = $true))),
% 1.44/1.28 inference(flattening,[status(thm)],[f7])).
% 1.44/1.28 thf(f7,plain,(
% 1.44/1.28 ? [X1 : a > $o,X0 : a > $o] : ? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) = $true) & ((X0 @ X2) != $true) & ((X1 @ X2) = $true))),
% 1.44/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.44/1.28 thf(f6,plain,(
% 1.44/1.28 ~! [X1 : a > $o,X0 : a > $o] : ~? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) = $true) & ((X0 @ X2) != $true) & ((X1 @ X2) = $true))),
% 1.44/1.28 inference(flattening,[status(thm)],[f5])).
% 1.44/1.28 thf(f5,plain,(
% 1.44/1.28 ~! [X0 : a > $o,X1 : a > $o] : ~? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) = $true) & ~((X0 @ X2) = $true) & ((X1 @ X2) = $true))),
% 1.44/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.44/1.28 thf(f4,plain,(
% 1.44/1.28 ~! [X0 : a > $o,X1 : a > $o] : ~? [X2 : a] : ((X1 @ X2) & (X0 @ X2) & ~(X0 @ X2) & (X1 @ X2))),
% 1.44/1.28 inference(rectify,[status(thm)],[f2])).
% 1.44/1.28 thf(f2,negated_conjecture,(
% 1.44/1.28 ~! [X1 : a > $o,X0 : a > $o] : ~? [X2 : a] : ((X0 @ X2) & (X1 @ X2) & ~(X1 @ X2) & (X0 @ X2))),
% 1.44/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.44/1.28 thf(f1,conjecture,(
% 1.44/1.28 ! [X1 : a > $o,X0 : a > $o] : ~? [X2 : a] : ((X0 @ X2) & (X1 @ X2) & ~(X1 @ X2) & (X0 @ X2))),
% 1.44/1.28 file('/export/starexec/sandbox/tmp/tmp.cfrPQvQGBH/DTF2THF_26133.p',cBOOL_PROP_111_pme)).
% 1.44/1.28 thf(f13,plain,(
% 1.44/1.28 ((sK0 @ sK1) != $true)),
% 1.44/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.44/1.28 % SZS output end Proof for DTF2THF_26133
% 1.44/1.28 % (26475)------------------------------
% 1.44/1.28 % (26475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.44/1.28 % (26475)Termination reason: Refutation
% 1.44/1.28
% 1.44/1.28 % (26475)Memory used [KB]: 5500
% 1.44/1.28 % (26475)Time elapsed: 0.002 s
% 1.44/1.28 % (26475)Instructions burned: 1 (million)
% 1.44/1.28 % (26475)------------------------------
% 1.44/1.28 % (26475)------------------------------
% 1.44/1.28 % (26472)Success in time 0.012 s
%------------------------------------------------------------------------------