%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET063^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 09:31:07 AM UTC 2026
% Result : Theorem 1.60s 1.31s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 52 ( 20 ~; 1 |; 4 &; 16 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 12 ^; 19 !; 2 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_7,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
sK3: a ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f14]) ).
thf(f14,plain,
! [X1: a] :
( $false
= ( sK0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: a] :
( ( $true != $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(fool_paramodulation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: a] :
( $true
!= ( sK0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] : $false )
!= sK0 )
& ! [X1: a] :
( $true
!= ( sK0 @ X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X0 )
& ! [X1: a] :
( ( X0 @ X1 )
!= $true ) )
=> ( ( ( ^ [Y0: a] : $false )
!= sK0 )
& ! [X1: a] :
( $true
!= ( sK0 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X0 )
& ! [X1: a] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
!= $true )
=> ( ( ^ [Y0: a] : $false )
= X0 ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
!= $true )
=> ( ( ^ [Y0: a] : $false )
= X0 ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
=> $false )
=> ( ( ^ [Y0: a] : $false )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> $false )
=> ( X0
= ( ^ [X2: a] : $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> $false )
=> ( X0
= ( ^ [X1: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> $false )
=> ( X0
= ( ^ [X1: a] : $false ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YQAFsEsBvn/DTF2THF_2679.p',cBOOL_PROP_30_pme) ).
thf(f19,plain,
( ( sK0 @ sK3 )
!= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( sK0 @ sK3 )
!= ( ^ [Y0: a] : $false
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a] : $false )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET063^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n004.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 11:50:56 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : SET063^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.49 % Domain : Set Theory
% 0.27/0.49 % Problem : TPS problem BOOL-PROP-30
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : Trybulec's 30th Boolean property of sets
% 0.27/0.49
% 0.27/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.27/0.49 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.27/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : tps_0076 [Bro09]
% 0.27/0.49 % : BOOL-PROP-30 [TPS]
% 0.27/0.49 % : 15 [Bar92]
% 0.27/0.49 % : GAZING-THM15 [TPS]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % 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 v4.0.1, 0.33 v4.0.0
% 0.27/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.27/0.49 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 2 ( 3 avg)
% 0.27/0.49 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 1 @)
% 0.27/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 6 ( 6 avg)
% 0.27/0.49 % Number of types : 2 ( 1 usr)
% 0.27/0.49 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.27/0.49 % Number of variables : 3 ( 1 ^; 2 !; 0 ?; 3 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.49 % : Polymorphic definitions expanded.
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(a_type,type,
% 0.27/0.49 a: $tType ).
% 0.27/0.49
% 0.27/0.49 thf(cBOOL_PROP_30_pme,conjecture,
% 0.27/0.49 ! [X: a > $o] :
% 0.27/0.49 ( ! [Xx: a] :
% 0.27/0.49 ( ( X @ Xx )
% 0.27/0.49 => $false )
% 0.27/0.49 => ( X
% 0.27/0.49 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 11:50:57 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YQAFsEsBvn/DTF2DTF2679.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(a_type,type,
% 1.44/1.29 a: $tType ).
% 1.44/1.29
% 1.44/1.29 thf(cBOOL_PROP_30_pme,conjecture,
% 1.44/1.29 ! [X: a > $o] :
% 1.44/1.29 ( ! [Xx: a] :
% 1.44/1.29 ( ( X @ Xx )
% 1.44/1.29 => $false )
% 1.44/1.29 => ( X
% 1.44/1.29 = ( ^ [Xx: a] : $false ) ) ) ).
% 1.44/1.29 ------------------------
% 1.60/1.31 % (2972)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2679 for (2999ds/18Mi)
% 1.60/1.31 % (2972)Refutation not found, incomplete strategy
% 1.60/1.31 % (2972)------------------------------
% 1.60/1.31 % (2972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2972)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (2972)Memory used [KB]: 5373
% 1.60/1.31 % (2972)Time elapsed: 0.002 s
% 1.60/1.31 % (2972)Instructions burned: 1 (million)
% 1.60/1.31 % (2972)------------------------------
% 1.60/1.31 % (2972)------------------------------
% 1.60/1.31 % (2967)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_2679 for (2999ds/4Mi)
% 1.60/1.31 % (2966)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2679 for (2999ds/183Mi)
% 1.60/1.31 % (2968)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_2679 for (2999ds/27Mi)
% 1.60/1.31 % (2969)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2679 for (2999ds/2Mi)
% 1.60/1.31 % (2970)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_2679 for (2999ds/2Mi)
% 1.60/1.31 % (2967)First to succeed.
% 1.60/1.31 % (2971)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_2679 for (2999ds/275Mi)
% 1.60/1.31 % (2966)Refutation not found, incomplete strategy
% 1.60/1.31 % (2966)------------------------------
% 1.60/1.31 % (2966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2966)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (2966)Memory used [KB]: 5373
% 1.60/1.31 % (2966)Time elapsed: 0.003 s
% 1.60/1.31 % (2966)Instructions burned: 1 (million)
% 1.60/1.31 % (2966)------------------------------
% 1.60/1.31 % (2966)------------------------------
% 1.60/1.31 % (2969)Refutation not found, incomplete strategy
% 1.60/1.31 % (2969)------------------------------
% 1.60/1.31 % (2969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2969)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (2969)Memory used [KB]: 5373
% 1.60/1.31 % (2969)Time elapsed: 0.003 s
% 1.60/1.31 % (2969)Instructions burned: 1 (million)
% 1.60/1.31 % (2968)Refutation not found, incomplete strategy
% 1.60/1.31 % (2968)------------------------------
% 1.60/1.31 % (2968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2969)------------------------------
% 1.60/1.31 % (2969)------------------------------
% 1.60/1.31 % (2968)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (2968)Memory used [KB]: 5500
% 1.60/1.31 % (2968)Time elapsed: 0.003 s
% 1.60/1.31 % (2968)Instructions burned: 1 (million)
% 1.60/1.31 % (2968)------------------------------
% 1.60/1.31 % (2968)------------------------------
% 1.60/1.31 % (2971)Refutation not found, incomplete strategy
% 1.60/1.31 % (2971)------------------------------
% 1.60/1.31 % (2971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2971)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (2971)Memory used [KB]: 5373
% 1.60/1.31 % (2971)Time elapsed: 0.003 s
% 1.60/1.31 % (2971)Instructions burned: 1 (million)
% 1.60/1.31 % (2971)------------------------------
% 1.60/1.31 % (2971)------------------------------
% 1.60/1.31 % (2967)Refutation found. Thanks to Tanya!
% 1.60/1.31 % SZS status Theorem for DTF2THF_2679
% 1.60/1.31 % SZS output start Proof for DTF2THF_2679
% 1.60/1.31 thf(type_def_5, type, a: $tType).
% 1.60/1.31 thf(func_def_0, type, a: $tType).
% 1.60/1.31 thf(func_def_5, type, sK0: a > $o).
% 1.60/1.31 thf(func_def_7, type, ph2: !>[X0: $tType]:(X0)).
% 1.60/1.31 thf(func_def_8, type, sK3: a).
% 1.60/1.31 thf(f20,plain,(
% 1.60/1.31 $false),
% 1.60/1.31 inference(subsumption_resolution,[status(thm)],[f19,f14])).
% 1.60/1.31 thf(f14,plain,(
% 1.60/1.31 ( ! [X1 : a] : (($false = (sK0 @ X1))) )),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.60/1.31 thf(f13,plain,(
% 1.60/1.31 ( ! [X1 : a] : (($true != $true) | ($false = (sK0 @ X1))) )),
% 1.60/1.31 inference(fool_paramodulation,[status(thm)],[f11])).
% 1.60/1.31 thf(f11,plain,(
% 1.60/1.31 ( ! [X1 : a] : (($true != (sK0 @ X1))) )),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.31 thf(f10,plain,(
% 1.60/1.31 ((^[Y0 : a]: ($false)) != sK0) & ! [X1 : a] : ($true != (sK0 @ X1))),
% 1.60/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.60/1.31 thf(f9,plain,(
% 1.60/1.31 ? [X0 : a > $o] : (((^[Y0 : a]: ($false)) != X0) & ! [X1 : a] : ((X0 @ X1) != $true)) => (((^[Y0 : a]: ($false)) != sK0) & ! [X1 : a] : ($true != (sK0 @ X1)))),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f8,plain,(
% 1.60/1.31 ? [X0 : a > $o] : (((^[Y0 : a]: ($false)) != X0) & ! [X1 : a] : ((X0 @ X1) != $true))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f7])).
% 1.60/1.31 thf(f7,plain,(
% 1.60/1.31 ~! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) != $true) => ((^[Y0 : a]: ($false)) = X0))),
% 1.60/1.31 inference(flattening,[status(thm)],[f6])).
% 1.60/1.31 thf(f6,plain,(
% 1.60/1.31 ~! [X0 : a > $o] : (! [X1 : a] : ~((X0 @ X1) = $true) => ((^[Y0 : a]: ($false)) = X0))),
% 1.60/1.31 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.60/1.31 thf(f5,plain,(
% 1.60/1.31 ~! [X0 : a > $o] : (! [X1 : a] : (((X0 @ X1) = $true) => $false) => ((^[Y0 : a]: ($false)) = X0))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.31 thf(f4,plain,(
% 1.60/1.31 ~! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => $false) => (X0 = (^[X2 : a] : ($false))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f2])).
% 1.60/1.31 thf(f2,negated_conjecture,(
% 1.60/1.31 ~! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => $false) => (X0 = (^[X1 : a] : ($false))))),
% 1.60/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.31 thf(f1,conjecture,(
% 1.60/1.31 ! [X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => $false) => (X0 = (^[X1 : a] : ($false))))),
% 1.60/1.31 file('/export/starexec/sandbox2/tmp/tmp.YQAFsEsBvn/DTF2THF_2679.p',cBOOL_PROP_30_pme)).
% 1.60/1.31 thf(f19,plain,(
% 1.60/1.31 ((sK0 @ sK3) != $false)),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.60/1.31 thf(f18,plain,(
% 1.60/1.31 ((sK0 @ sK3) != ((^[Y0 : a]: ($false)) @ sK3))),
% 1.60/1.31 inference(negative_extensionality,[status(thm)],[f12])).
% 1.60/1.31 thf(f12,plain,(
% 1.60/1.31 ((^[Y0 : a]: ($false)) != sK0)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.31 % SZS output end Proof for DTF2THF_2679
% 1.60/1.31 % (2967)------------------------------
% 1.60/1.31 % (2967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (2967)Termination reason: Refutation
% 1.60/1.31
% 1.60/1.31 % (2967)Memory used [KB]: 5500
% 1.60/1.31 % (2967)Time elapsed: 0.003 s
% 1.60/1.31 % (2967)Instructions burned: 1 (million)
% 1.60/1.31 % (2967)------------------------------
% 1.60/1.31 % (2967)------------------------------
% 1.60/1.31 % (2965)Success in time 0.019 s
%------------------------------------------------------------------------------