%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET194^5 : 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 : n019.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 09:31:23 AM UTC 2026
% Result : Theorem 1.63s 1.44s
% Output : Refutation 1.63s
% 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 : 55 ( 23 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 69 ( 16 ~; 4 |; 12 &; 32 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 12 !; 12 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a > $o ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f13]) ).
thf(f13,plain,
( ( sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( sK2 @ sK1 )
!= $true )
& ( $true
!= ( sK0 @ sK1 ) )
& ( ( sK2 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a,X2: a > $o] :
( ( $true
!= ( X2 @ X1 ) )
& ( ( X0 @ X1 )
!= $true )
& ( $true
= ( X2 @ X1 ) ) )
=> ( ( ( sK2 @ sK1 )
!= $true )
& ( $true
!= ( sK0 @ sK1 ) )
& ( ( sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a,X2: a > $o] :
( ( $true
!= ( X2 @ X1 ) )
& ( ( X0 @ X1 )
!= $true )
& ( $true
= ( X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X2: a,X1: a > $o] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( ( X1 @ X2 )
| ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a] :
( ( X0 @ X2 )
=> ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bzNu9hMpQe/DTF2THF_18399.p',cBOOL_PROP_31_pme) ).
thf(f11,plain,
( ( sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET194^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n019.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:22:24 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SET194^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.49 % Domain : Set Theory
% 0.28/0.49 % Problem : TPS problem BOOL-PROP-31
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English : Trybulec's 31st Boolean property of sets
% 0.28/0.49
% 0.28/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.28/0.49 % : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.28/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.49 % Source : [Bro09]
% 0.28/0.49 % Names : tps_0075 [Bro09]
% 0.28/0.49 % : tps_0080 [Bro09]
% 0.28/0.49 % : 18 [Bar92]
% 0.28/0.49 % : GAZING-THM18 [TPS]
% 0.28/0.49 % : BOOL-PROP-31 [TPS]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.28/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.49 % Number of connectives : 5 ( 0 ~; 1 |; 0 &; 3 @)
% 0.28/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.28/0.49 % Number of types : 2 ( 1 usr)
% 0.28/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.49 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.28/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.49 % : Polymorphic definitions expanded.
% 0.28/0.49 % :
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(a_type,type,
% 0.28/0.49 a: $tType ).
% 0.28/0.49
% 0.28/0.49 thf(cBOOL_PROP_31_pme,conjecture,
% 0.28/0.49 ! [X: a > $o,Y: a > $o,Xx: a] :
% 0.28/0.49 ( ( X @ Xx )
% 0.28/0.49 => ( ( X @ Xx )
% 0.28/0.49 | ( Y @ Xx ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.63/1.41 ---- Embedded in THF ---
% 1.63/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.41 %%% Generated on Tue Feb 24 12:22:25 EST 2026
% 1.63/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.41 %%% Logic specification used:
% 1.63/1.41 %%% thf(spec, logic, $$dhol).
% 1.63/1.41
% 1.63/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bzNu9hMpQe/DTF2DTF18399.p
% See solution above
% 1.63/1.41 ------------------------
% 1.63/1.42 ---- Cleaned THF ---
% 1.63/1.42 thf(a_type,type,
% 1.63/1.42 a: $tType ).
% 1.63/1.42
% 1.63/1.42 thf(cBOOL_PROP_31_pme,conjecture,
% 1.63/1.42 ! [X: a > $o,Y: a > $o,Xx: a] :
% 1.63/1.42 ( ( X @ Xx )
% 1.63/1.42 => ( ( X @ Xx )
% 1.63/1.42 | ( Y @ Xx ) ) ) ).
% 1.63/1.42 ------------------------
% 1.63/1.44 % (18499)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_18399 for (3000ds/27Mi)
% 1.63/1.44 % (18497)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18399 for (3000ds/183Mi)
% 1.63/1.44 % (18498)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_18399 for (3000ds/4Mi)
% 1.63/1.44 % (18501)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_18399 for (3000ds/2Mi)
% 1.63/1.44 % (18503)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18399 for (3000ds/18Mi)
% 1.63/1.44 % (18500)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18399 for (3000ds/2Mi)
% 1.63/1.44 % (18502)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_18399 for (3000ds/275Mi)
% 1.63/1.44 % (18500)First to succeed.
% 1.63/1.44 % (18501)Instruction limit reached!
% 1.63/1.44 % (18501)------------------------------
% 1.63/1.44 % (18501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (18501)Termination reason: Unknown
% 1.63/1.44 % (18501)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (18501)Memory used [KB]: 5500
% 1.63/1.44 % (18501)Time elapsed: 0.003 s
% 1.63/1.44 % (18501)Instructions burned: 2 (million)
% 1.63/1.44 % (18501)------------------------------
% 1.63/1.44 % (18501)------------------------------
% 1.63/1.44 % (18497)Also succeeded, but the first one will report.
% 1.63/1.44 % (18502)Also succeeded, but the first one will report.
% 1.63/1.44 % (18500)Refutation found. Thanks to Tanya!
% 1.63/1.44 % SZS status Theorem for DTF2THF_18399
% 1.63/1.44 % SZS output start Proof for DTF2THF_18399
% 1.63/1.44 thf(type_def_5, type, a: $tType).
% 1.63/1.44 thf(func_def_0, type, a: $tType).
% 1.63/1.44 thf(func_def_4, type, sK0: a > $o).
% 1.63/1.44 thf(func_def_5, type, sK1: a).
% 1.63/1.44 thf(func_def_6, type, sK2: a > $o).
% 1.63/1.44 thf(f14,plain,(
% 1.63/1.44 $false),
% 1.63/1.44 inference(subsumption_resolution,[status(thm)],[f11,f13])).
% 1.63/1.44 thf(f13,plain,(
% 1.63/1.44 ((sK2 @ sK1) != $true)),
% 1.63/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.44 thf(f10,plain,(
% 1.63/1.44 ((sK2 @ sK1) != $true) & ($true != (sK0 @ sK1)) & ((sK2 @ sK1) = $true)),
% 1.63/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.63/1.44 thf(f9,plain,(
% 1.63/1.44 ? [X0 : a > $o,X1 : a,X2 : a > $o] : (($true != (X2 @ X1)) & ((X0 @ X1) != $true) & ($true = (X2 @ X1))) => (((sK2 @ sK1) != $true) & ($true != (sK0 @ sK1)) & ((sK2 @ sK1) = $true))),
% 1.63/1.44 introduced(definition,[],[choice_axiom])).
% 1.63/1.44 thf(f8,plain,(
% 1.63/1.44 ? [X0 : a > $o,X1 : a,X2 : a > $o] : (($true != (X2 @ X1)) & ((X0 @ X1) != $true) & ($true = (X2 @ X1)))),
% 1.63/1.44 inference(rectify,[status(thm)],[f7])).
% 1.63/1.44 thf(f7,plain,(
% 1.63/1.44 ? [X0 : a > $o,X2 : a,X1 : a > $o] : (((X1 @ X2) != $true) & ((X0 @ X2) != $true) & ((X1 @ X2) = $true))),
% 1.63/1.44 inference(flattening,[status(thm)],[f6])).
% 1.63/1.44 thf(f6,plain,(
% 1.63/1.44 ? [X1 : a > $o,X0 : a > $o,X2 : a] : ((((X1 @ X2) != $true) & ((X0 @ X2) != $true)) & ((X1 @ X2) = $true))),
% 1.63/1.44 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.44 thf(f5,plain,(
% 1.63/1.44 ~! [X1 : a > $o,X0 : a > $o,X2 : a] : (((X1 @ X2) = $true) => (((X1 @ X2) = $true) | ((X0 @ X2) = $true)))),
% 1.63/1.44 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.44 thf(f4,plain,(
% 1.63/1.44 ~! [X0 : a > $o,X1 : a > $o,X2 : a] : ((X1 @ X2) => ((X1 @ X2) | (X0 @ X2)))),
% 1.63/1.44 inference(rectify,[status(thm)],[f2])).
% 1.63/1.44 thf(f2,negated_conjecture,(
% 1.63/1.44 ~! [X1 : a > $o,X0 : a > $o,X2 : a] : ((X0 @ X2) => ((X0 @ X2) | (X1 @ X2)))),
% 1.63/1.44 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.44 thf(f1,conjecture,(
% 1.63/1.44 ! [X1 : a > $o,X0 : a > $o,X2 : a] : ((X0 @ X2) => ((X0 @ X2) | (X1 @ X2)))),
% 1.63/1.44 file('/export/starexec/sandbox/tmp/tmp.bzNu9hMpQe/DTF2THF_18399.p',cBOOL_PROP_31_pme)).
% 1.63/1.44 thf(f11,plain,(
% 1.63/1.44 ((sK2 @ sK1) = $true)),
% 1.63/1.44 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.44 % SZS output end Proof for DTF2THF_18399
% 1.63/1.44 % (18500)------------------------------
% 1.63/1.44 % (18500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (18500)Termination reason: Refutation
% 1.63/1.44
% 1.63/1.44 % (18500)Memory used [KB]: 5373
% 1.63/1.44 % (18500)Time elapsed: 0.003 s
% 1.63/1.44 % (18500)Instructions burned: 1 (million)
% 1.63/1.44 % (18500)------------------------------
% 1.63/1.44 % (18500)------------------------------
% 1.63/1.44 % (18496)Success in time 0.017 s
%------------------------------------------------------------------------------