%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET173^5 : 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 : n026.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 09:31:21 AM UTC 2026
% Result : Theorem 1.63s 1.47s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 27 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 103 ( 10 ~; 22 |; 13 &; 57 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 10 ^; 8 !; 4 ?; 22 :)
% 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(func_def_11,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK4: a ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
$true = $false,
inference(superposition,[status(thm)],[f18,f23]) ).
thf(f23,plain,
( $true
= ( sK0 @ sK4 ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ( sK1 @ sK4 )
| ( sK0 @ sK4 ) )
& ( sK0 @ sK4 ) )
= $true )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( sK1 @ sK4 )
| ( sK0 @ sK4 ) )
& ( sK0 @ sK4 ) )
!= ( sK0 @ sK4 ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK0 @ sK4 )
!= ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= sK0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X0 @ Y0 ) ) )
!= X0 )
=> ( ( ^ [Y0: a] :
( ( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X0 @ Y0 ) ) )
!= X0 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X0 @ Y0 ) ) )
= X0 ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) )
= X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) )
= X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.VqtVz6BDac/DTF2THF_17412.p',cBOOL_PROP_68_pme) ).
thf(f18,plain,
( ( sK0 @ sK4 )
= $false ),
inference(duplicate_literal_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( ( sK1 @ sK4 )
| ( sK0 @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( sK1 @ sK4 )
| ( sK0 @ sK4 ) ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( ( ( ( sK1 @ sK4 )
| ( sK0 @ sK4 ) )
& ( sK0 @ sK4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET173^5 : 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
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:54:40 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : SET173^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.49 % Domain : Set Theory
% 0.30/0.49 % Problem : TPS problem BOOL-PROP-68
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English : Trybulec's 68th Boolean property of sets
% 0.30/0.49
% 0.30/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.30/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.49 % Source : [Bro09]
% 0.30/0.49 % Names : tps_0182 [Bro09]
% 0.30/0.49 % : BOOL-PROP-68 [TPS]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % 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, 0.00 v6.1.0, 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
% 0.30/0.49 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.49 % Number of connectives : 5 ( 0 ~; 1 |; 1 &; 3 @)
% 0.30/0.49 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 3 ( 3 avg)
% 0.30/0.49 % Number of types : 2 ( 1 usr)
% 0.30/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.49 % Number of variables : 3 ( 1 ^; 2 !; 0 ?; 3 :)
% 0.30/0.49 % SPC : TH0_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.49 % : Polymorphic definitions expanded.
% 0.30/0.49 % :
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(a_type,type,
% 0.30/0.49 a: $tType ).
% 0.30/0.49
% 0.30/0.49 thf(cBOOL_PROP_68_pme,conjecture,
% 0.30/0.49 ! [X: a > $o,Y: a > $o] :
% 0.30/0.49 ( ( ^ [Xx: a] :
% 0.30/0.49 ( ( X @ Xx )
% 0.30/0.49 & ( ( X @ Xx )
% 0.30/0.49 | ( Y @ Xx ) ) ) )
% 0.30/0.49 = X ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 1.63/1.44 ---- Embedded in THF ---
% 1.63/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.44 %%% Generated on Tue Feb 24 11:54:41 EST 2026
% 1.63/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.44 %%% Logic specification used:
% 1.63/1.44 %%% thf(spec, logic, $$dhol).
% 1.63/1.44
% 1.63/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VqtVz6BDac/DTF2DTF17412.p
% See solution above
% 1.63/1.44 ------------------------
% 1.63/1.45 ---- Cleaned THF ---
% 1.63/1.45 thf(a_type,type,
% 1.63/1.45 a: $tType ).
% 1.63/1.45
% 1.63/1.45 thf(cBOOL_PROP_68_pme,conjecture,
% 1.63/1.45 ! [X: a > $o,Y: a > $o] :
% 1.63/1.45 ( ( ^ [Xx: a] :
% 1.63/1.45 ( ( X @ Xx )
% 1.63/1.45 & ( ( X @ Xx )
% 1.63/1.45 | ( Y @ Xx ) ) ) )
% 1.63/1.45 = X ) ).
% 1.63/1.45 ------------------------
% 1.63/1.47 % (17514)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_17412 for (3000ds/275Mi)
% 1.63/1.47 % (17512)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17412 for (3000ds/2Mi)
% 1.63/1.47 % (17511)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_17412 for (3000ds/27Mi)
% 1.63/1.47 % (17513)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_17412 for (3000ds/2Mi)
% 1.63/1.47 % (17510)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_17412 for (3000ds/4Mi)
% 1.63/1.47 % (17509)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17412 for (3000ds/183Mi)
% 1.63/1.47 % (17515)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17412 for (3000ds/18Mi)
% 1.63/1.47 % (17512)Instruction limit reached!
% 1.63/1.47 % (17512)------------------------------
% 1.63/1.47 % (17512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17512)Termination reason: Unknown
% 1.63/1.47 % (17512)Termination phase: Saturation
% 1.63/1.47 % (17513)Instruction limit reached!
% 1.63/1.47 % (17513)------------------------------
% 1.63/1.47 % (17513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17513)Termination reason: Unknown
% 1.63/1.47 % (17513)Termination phase: Saturation
% 1.63/1.47
% 1.63/1.47 % (17513)Memory used [KB]: 5500
% 1.63/1.47 % (17513)Time elapsed: 0.003 s
% 1.63/1.47 % (17513)Instructions burned: 2 (million)
% 1.63/1.47 % (17513)------------------------------
% 1.63/1.47 % (17513)------------------------------
% 1.63/1.47
% 1.63/1.47 % (17512)Memory used [KB]: 5500
% 1.63/1.47 % (17512)Time elapsed: 0.003 s
% 1.63/1.47 % (17512)Instructions burned: 2 (million)
% 1.63/1.47 % (17512)------------------------------
% 1.63/1.47 % (17512)------------------------------
% 1.63/1.47 % (17509)First to succeed.
% 1.63/1.47 % (17514)Also succeeded, but the first one will report.
% 1.63/1.47 % (17510)Also succeeded, but the first one will report.
% 1.63/1.47 % (17509)Refutation found. Thanks to Tanya!
% 1.63/1.47 % SZS status Theorem for DTF2THF_17412
% 1.63/1.47 % SZS output start Proof for DTF2THF_17412
% 1.63/1.47 thf(type_def_5, type, a: $tType).
% 1.63/1.47 thf(func_def_0, type, a: $tType).
% 1.63/1.47 thf(func_def_8, type, sK0: a > $o).
% 1.63/1.47 thf(func_def_9, type, sK1: a > $o).
% 1.63/1.47 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.47 thf(func_def_12, type, sK4: a).
% 1.63/1.47 thf(f26,plain,(
% 1.63/1.47 $false),
% 1.63/1.47 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.63/1.47 thf(f25,plain,(
% 1.63/1.47 ($true = $false)),
% 1.63/1.47 inference(superposition,[status(thm)],[f18,f23])).
% 1.63/1.47 thf(f23,plain,(
% 1.63/1.47 ($true = (sK0 @ sK4))),
% 1.63/1.47 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.63/1.47 thf(f19,plain,(
% 1.63/1.47 ($true = (sK0 @ sK4)) | ($true = (sK0 @ sK4))),
% 1.63/1.47 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.63/1.47 thf(f12,plain,(
% 1.63/1.47 ((((sK1 @ sK4) | (sK0 @ sK4)) & (sK0 @ sK4)) = $true) | ($true = (sK0 @ sK4))),
% 1.63/1.47 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.63/1.47 thf(f11,plain,(
% 1.63/1.47 ((((sK1 @ sK4) | (sK0 @ sK4)) & (sK0 @ sK4)) != (sK0 @ sK4))),
% 1.63/1.47 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.63/1.47 thf(f10,plain,(
% 1.63/1.47 ((sK0 @ sK4) != ((^[Y0 : a]: (((sK1 @ Y0) | (sK0 @ Y0)) & (sK0 @ Y0))) @ sK4))),
% 1.63/1.47 inference(negative_extensionality,[status(thm)],[f9])).
% 1.63/1.47 thf(f9,plain,(
% 1.63/1.47 ((^[Y0 : a]: (((sK1 @ Y0) | (sK0 @ Y0)) & (sK0 @ Y0))) != sK0)),
% 1.63/1.47 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.47 thf(f8,plain,(
% 1.63/1.47 ((^[Y0 : a]: (((sK1 @ Y0) | (sK0 @ Y0)) & (sK0 @ Y0))) != sK0)),
% 1.63/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.63/1.47 thf(f7,plain,(
% 1.63/1.47 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) | (X0 @ Y0)) & (X0 @ Y0))) != X0) => ((^[Y0 : a]: (((sK1 @ Y0) | (sK0 @ Y0)) & (sK0 @ Y0))) != sK0)),
% 1.63/1.47 introduced(definition,[],[choice_axiom])).
% 1.63/1.47 thf(f6,plain,(
% 1.63/1.47 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) | (X0 @ Y0)) & (X0 @ Y0))) != X0)),
% 1.63/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.47 thf(f5,plain,(
% 1.63/1.47 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: (((X1 @ Y0) | (X0 @ Y0)) & (X0 @ Y0))) = X0)),
% 1.63/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.47 thf(f4,plain,(
% 1.63/1.47 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & ((X0 @ X2) | (X1 @ X2)))) = X0)),
% 1.63/1.47 inference(rectify,[status(thm)],[f2])).
% 1.63/1.47 thf(f2,negated_conjecture,(
% 1.63/1.47 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & ((X0 @ X2) | (X1 @ X2)))) = X0)),
% 1.63/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.47 thf(f1,conjecture,(
% 1.63/1.47 ! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & ((X0 @ X2) | (X1 @ X2)))) = X0)),
% 1.63/1.47 file('/export/starexec/sandbox/tmp/tmp.VqtVz6BDac/DTF2THF_17412.p',cBOOL_PROP_68_pme)).
% 1.63/1.47 thf(f18,plain,(
% 1.63/1.47 ((sK0 @ sK4) = $false)),
% 1.63/1.47 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.63/1.47 thf(f16,plain,(
% 1.63/1.47 ((sK0 @ sK4) = $false) | ((sK0 @ sK4) = $false)),
% 1.63/1.47 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.63/1.47 thf(f15,plain,(
% 1.63/1.47 ((sK0 @ sK4) = $false) | ($false = ((sK1 @ sK4) | (sK0 @ sK4)))),
% 1.63/1.47 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.63/1.47 thf(f14,plain,(
% 1.63/1.47 ($false = ((sK1 @ sK4) | (sK0 @ sK4))) | ((sK0 @ sK4) = $false) | ((sK0 @ sK4) = $false)),
% 1.63/1.47 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.63/1.47 thf(f13,plain,(
% 1.63/1.47 ((sK0 @ sK4) = $false) | ((((sK1 @ sK4) | (sK0 @ sK4)) & (sK0 @ sK4)) = $false)),
% 1.63/1.47 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.63/1.47 % SZS output end Proof for DTF2THF_17412
% 1.63/1.47 % (17509)------------------------------
% 1.63/1.47 % (17509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (17509)Termination reason: Refutation
% 1.63/1.47
% 1.63/1.47 % (17509)Memory used [KB]: 5500
% 1.63/1.47 % (17509)Time elapsed: 0.004 s
% 1.63/1.47 % (17509)Instructions burned: 1 (million)
% 1.63/1.47 % (17509)------------------------------
% 1.63/1.47 % (17509)------------------------------
% 1.63/1.47 % (17508)Success in time 0.015 s
%------------------------------------------------------------------------------