%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET008^5 : 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 : n022.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 09:30:54 AM UTC 2026
% Result : Theorem 1.53s 1.34s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 67 ( 19 ~; 0 |; 19 &; 28 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 22 ^; 8 !; 4 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(f12,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] : $false ) ),
inference(boolean_simplification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( $false
& ( sK0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
=> ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] : $false )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ( X1 @ X3 )
& ~ ( X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 )
& ~ ( X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.irf2g1dmp9/DTF2THF_3061.p',cBOOL_PROP_78_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET008^5 : 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
% 0.10/0.29 % Computer : n022.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 11:48:36 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SET008^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : TPS problem BOOL-PROP-78
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Trybulec's 78th Boolean property of sets
% 0.16/0.39
% 0.16/0.39 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0191 [Bro09]
% 0.16/0.39 % : BOOL-PROP-78 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % 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
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 1 ( 2 avg)
% 0.16/0.39 % Number of connectives : 6 ( 1 ~; 0 |; 2 &; 3 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 3 ( 3 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % : Polymorphic definitions expanded.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cBOOL_PROP_78_pme,conjecture,
% 0.16/0.39 ! [X: a > $o,Y: a > $o] :
% 0.16/0.39 ( ( ^ [Xx: a] :
% 0.16/0.39 ( ( X @ Xx )
% 0.16/0.39 & ~ ( Y @ Xx )
% 0.16/0.39 & ( Y @ Xx ) ) )
% 0.16/0.39 = ( ^ [Xx: a] : $false ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.53/1.31 ---- Embedded in THF ---
% 1.53/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.31 %%% Generated on Tue Feb 24 11:48:37 EST 2026
% 1.53/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.31 %%% Logic specification used:
% 1.53/1.31 %%% thf(spec, logic, $$dhol).
% 1.53/1.31
% 1.53/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.irf2g1dmp9/DTF2DTF3061.p
% See solution above
% 1.53/1.31 ------------------------
% 1.53/1.32 ---- Cleaned THF ---
% 1.53/1.32 thf(a_type,type,
% 1.53/1.32 a: $tType ).
% 1.53/1.32
% 1.53/1.32 thf(cBOOL_PROP_78_pme,conjecture,
% 1.53/1.32 ! [X: a > $o,Y: a > $o] :
% 1.53/1.32 ( ( ^ [Xx: a] :
% 1.53/1.32 ( ( X @ Xx )
% 1.53/1.32 & ~ ( Y @ Xx )
% 1.53/1.32 & ( Y @ Xx ) ) )
% 1.53/1.32 = ( ^ [Xx: a] : $false ) ) ).
% 1.53/1.32 ------------------------
% 1.53/1.34 % (3164)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3061 for (3000ds/275Mi)
% 1.53/1.34 % (3161)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_3061 for (3000ds/27Mi)
% 1.53/1.34 % (3159)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3061 for (3000ds/183Mi)
% 1.53/1.34 % (3163)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3061 for (3000ds/2Mi)
% 1.53/1.34 % (3162)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3061 for (3000ds/2Mi)
% 1.53/1.34 % (3165)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3061 for (3000ds/18Mi)
% 1.53/1.34 % (3160)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_3061 for (3000ds/4Mi)
% 1.53/1.34 % (3164)First to succeed.
% 1.53/1.34 % (3163)Instruction limit reached!
% 1.53/1.34 % (3163)------------------------------
% 1.53/1.34 % (3163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (3163)Termination reason: Unknown
% 1.53/1.34 % (3163)Termination phase: Saturation
% 1.53/1.34
% 1.53/1.34 % (3163)Memory used [KB]: 5500
% 1.53/1.34 % (3163)Time elapsed: 0.003 s
% 1.53/1.34 % (3163)Instructions burned: 2 (million)
% 1.53/1.34 % (3163)------------------------------
% 1.53/1.34 % (3163)------------------------------
% 1.53/1.34 % (3159)Also succeeded, but the first one will report.
% 1.53/1.34 % (3165)Also succeeded, but the first one will report.
% 1.53/1.34 % (3164)Refutation found. Thanks to Tanya!
% 1.53/1.34 % SZS status Theorem for DTF2THF_3061
% 1.53/1.34 % SZS output start Proof for DTF2THF_3061
% 1.53/1.34 thf(type_def_5, type, a: $tType).
% 1.53/1.34 thf(func_def_0, type, a: $tType).
% 1.53/1.34 thf(func_def_8, type, sK0: a > $o).
% 1.53/1.34 thf(func_def_9, type, sK1: a > $o).
% 1.53/1.34 thf(f12,plain,(
% 1.53/1.34 $false),
% 1.53/1.34 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.53/1.34 thf(f11,plain,(
% 1.53/1.34 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ($false)))),
% 1.53/1.34 inference(boolean_simplification,[status(thm)],[f10])).
% 1.53/1.34 thf(f10,plain,(
% 1.53/1.34 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ($false & (sK0 @ Y0))))),
% 1.53/1.34 inference(boolean_simplification,[status(thm)],[f9])).
% 1.53/1.34 thf(f9,plain,(
% 1.53/1.34 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK1 @ Y0)) & (sK0 @ Y0))))),
% 1.53/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.53/1.34 thf(f8,plain,(
% 1.53/1.34 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK1 @ Y0)) & (sK0 @ Y0))))),
% 1.53/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.53/1.34 thf(f7,plain,(
% 1.53/1.34 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X1 @ Y0)) & (X0 @ Y0))) != (^[Y0 : a]: ($false))) => ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK1 @ Y0)) & (sK0 @ Y0))))),
% 1.53/1.34 introduced(definition,[],[choice_axiom])).
% 1.53/1.34 thf(f6,plain,(
% 1.53/1.34 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X1 @ Y0)) & (X0 @ Y0))) != (^[Y0 : a]: ($false)))),
% 1.53/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.53/1.34 thf(f5,plain,(
% 1.53/1.34 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X1 @ Y0)) & (X0 @ Y0))) = (^[Y0 : a]: ($false)))),
% 1.53/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.34 thf(f4,plain,(
% 1.53/1.34 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ($false)) = (^[X3 : a] : ((X0 @ X3) & (X1 @ X3) & ~(X1 @ X3))))),
% 1.53/1.34 inference(rectify,[status(thm)],[f2])).
% 1.53/1.34 thf(f2,negated_conjecture,(
% 1.53/1.34 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ($false)) = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2) & ~(X1 @ X2))))),
% 1.53/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.34 thf(f1,conjecture,(
% 1.53/1.34 ! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ($false)) = (^[X2 : a] : ((X0 @ X2) & (X1 @ X2) & ~(X1 @ X2))))),
% 1.53/1.34 file('/export/starexec/sandbox/tmp/tmp.irf2g1dmp9/DTF2THF_3061.p',cBOOL_PROP_78_pme)).
% 1.53/1.34 % SZS output end Proof for DTF2THF_3061
% 1.53/1.34 % (3164)------------------------------
% 1.53/1.34 % (3164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.34 % (3164)Termination reason: Refutation
% 1.53/1.34
% 1.53/1.34 % (3164)Memory used [KB]: 5373
% 1.53/1.34 % (3164)Time elapsed: 0.003 s
% 1.53/1.34 % (3164)Instructions burned: 1 (million)
% 1.53/1.34 % (3164)------------------------------
% 1.53/1.34 % (3164)------------------------------
% 1.53/1.34 % (3158)Success in time 0.017 s
%------------------------------------------------------------------------------