%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET175^5 : 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 : n027.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 09:31:22 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 111 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 124 ( 18 ~; 27 |; 15 &; 61 @)
% ( 2 <=>; 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 : 9 ( 6 usr; 5 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(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f43,f46]) ).
thf(f46,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[status(thm)],[f31,f41]) ).
thf(f41,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_4
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f31,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl2_2
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f43,plain,
spl2_4,
inference(avatar_split_clause,[status(thm)],[f16,f39]) ).
thf(f16,plain,
( ( sK1 @ sK4 )
= $false ),
inference(duplicate_literal_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( ( sK1 @ sK4 )
| ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK1 @ sK4 )
| ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
!= ( sK1 @ sK4 ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sK1 @ sK4 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= sK1 ),
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 ) ) ) )
!= X1 )
=> ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( X1
= ( ^ [X2: a] :
( ( ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( X0
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( X0
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JYRUsP5REV/DTF2THF_18217.p',cBOOL_PROP_69_pme) ).
thf(f33,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f23,f29]) ).
thf(f23,plain,
( ( sK1 @ sK4 )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( sK1 @ sK4 )
| ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET175^5 : 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 : n027.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 11:54:52 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SET175^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPS problem BOOL-PROP-69
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : Trybulec's 69th Boolean property of sets
% 0.28/0.46
% 0.28/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.28/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0181 [Bro09]
% 0.28/0.46 % : BOOL-PROP-69 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.28/0.46 % Number of connectives : 5 ( 0 ~; 1 |; 1 &; 3 @)
% 0.28/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 3 ( 3 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.28/0.46 % Number of variables : 3 ( 1 ^; 2 !; 0 ?; 3 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 % :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(a_type,type,
% 0.28/0.46 a: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(cBOOL_PROP_69_pme,conjecture,
% 0.28/0.46 ! [X: a > $o,Y: a > $o] :
% 0.28/0.46 ( ( ^ [Xz: a] :
% 0.28/0.46 ( ( X @ Xz )
% 0.28/0.46 | ( ( X @ Xz )
% 0.28/0.46 & ( Y @ Xz ) ) ) )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.45/1.28 ---- Embedded in THF ---
% 1.45/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.28 %%% Generated on Tue Feb 24 11:54:53 EST 2026
% 1.45/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.28 %%% Logic specification used:
% 1.45/1.28 %%% thf(spec, logic, $$dhol).
% 1.45/1.28
% 1.45/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JYRUsP5REV/DTF2DTF18217.p
% See solution above
% 1.45/1.28 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(a_type,type,
% 1.45/1.29 a: $tType ).
% 1.45/1.29
% 1.45/1.29 thf(cBOOL_PROP_69_pme,conjecture,
% 1.45/1.29 ! [X: a > $o,Y: a > $o] :
% 1.45/1.29 ( ( ^ [Xz: a] :
% 1.45/1.29 ( ( X @ Xz )
% 1.45/1.29 | ( ( X @ Xz )
% 1.45/1.29 & ( Y @ Xz ) ) ) )
% 1.45/1.29 = X ) ).
% 1.45/1.29 ------------------------
% 1.61/1.31 % (18509)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_18217 for (2999ds/275Mi)
% 1.61/1.31 % (18509)First to succeed.
% 1.61/1.31 % (18509)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_18217
% 1.61/1.31 % SZS output start Proof for DTF2THF_18217
% 1.61/1.31 thf(type_def_5, type, a: $tType).
% 1.61/1.31 thf(func_def_0, type, a: $tType).
% 1.61/1.31 thf(func_def_8, type, sK0: a > $o).
% 1.61/1.31 thf(func_def_9, type, sK1: a > $o).
% 1.61/1.31 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.61/1.31 thf(func_def_12, type, sK4: a).
% 1.61/1.31 thf(f47,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(avatar_sat_refutation,[status(thm)],[f33,f43,f46])).
% 1.61/1.31 thf(f46,plain,(
% 1.61/1.31 ~spl2_2 | ~spl2_4),
% 1.61/1.31 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.61/1.31 thf(f45,plain,(
% 1.61/1.31 $false | (~spl2_2 | ~spl2_4)),
% 1.61/1.31 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.61/1.31 thf(f44,plain,(
% 1.61/1.31 ($true = $false) | (~spl2_2 | ~spl2_4)),
% 1.61/1.31 inference(forward_demodulation,[status(thm)],[f31,f41])).
% 1.61/1.31 thf(f41,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $false) | ~spl2_4),
% 1.61/1.31 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.61/1.31 thf(f39,definition,(
% 1.61/1.31 spl2_4 <=> ((sK1 @ sK4) = $false)),
% 1.61/1.31 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.61/1.31 thf(f31,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $true) | ~spl2_2),
% 1.61/1.31 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.61/1.31 thf(f29,definition,(
% 1.61/1.31 spl2_2 <=> ((sK1 @ sK4) = $true)),
% 1.61/1.31 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.61/1.31 thf(f43,plain,(
% 1.61/1.31 spl2_4),
% 1.61/1.31 inference(avatar_split_clause,[status(thm)],[f16,f39])).
% 1.61/1.31 thf(f16,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $false)),
% 1.61/1.31 inference(duplicate_literal_removal,[status(thm)],[f15])).
% 1.61/1.31 thf(f15,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $false) | ((sK1 @ sK4) = $false)),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $false) | (((sK1 @ sK4) | ((sK1 @ sK4) & (sK0 @ sK4))) = $false)),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.61/1.31 thf(f11,plain,(
% 1.61/1.31 (((sK1 @ sK4) | ((sK1 @ sK4) & (sK0 @ sK4))) != (sK1 @ sK4))),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.61/1.31 thf(f10,plain,(
% 1.61/1.31 ((sK1 @ sK4) != ((^[Y0 : a]: ((sK1 @ Y0) | ((sK1 @ Y0) & (sK0 @ Y0)))) @ sK4))),
% 1.61/1.31 inference(negative_extensionality,[status(thm)],[f9])).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 ((^[Y0 : a]: ((sK1 @ Y0) | ((sK1 @ Y0) & (sK0 @ Y0)))) != sK1)),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 ((^[Y0 : a]: ((sK1 @ Y0) | ((sK1 @ Y0) & (sK0 @ Y0)))) != sK1)),
% 1.61/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.61/1.31 thf(f7,plain,(
% 1.61/1.31 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) | ((X1 @ Y0) & (X0 @ Y0)))) != X1) => ((^[Y0 : a]: ((sK1 @ Y0) | ((sK1 @ Y0) & (sK0 @ Y0)))) != sK1)),
% 1.61/1.31 introduced(definition,[],[choice_axiom])).
% 1.61/1.31 thf(f6,plain,(
% 1.61/1.31 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) | ((X1 @ Y0) & (X0 @ Y0)))) != X1)),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.31 thf(f5,plain,(
% 1.61/1.31 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X1 @ Y0) | ((X1 @ Y0) & (X0 @ Y0)))) = X1)),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.31 thf(f4,plain,(
% 1.61/1.31 ~! [X0 : a > $o,X1 : a > $o] : (X1 = (^[X2 : a] : (((X0 @ X2) & (X1 @ X2)) | (X1 @ X2))))),
% 1.61/1.31 inference(rectify,[status(thm)],[f2])).
% 1.61/1.31 thf(f2,negated_conjecture,(
% 1.61/1.31 ~! [X1 : a > $o,X0 : a > $o] : (X0 = (^[X2 : a] : (((X1 @ X2) & (X0 @ X2)) | (X0 @ X2))))),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.31 thf(f1,conjecture,(
% 1.61/1.31 ! [X1 : a > $o,X0 : a > $o] : (X0 = (^[X2 : a] : (((X1 @ X2) & (X0 @ X2)) | (X0 @ X2))))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.JYRUsP5REV/DTF2THF_18217.p',cBOOL_PROP_69_pme)).
% 1.61/1.31 thf(f33,plain,(
% 1.61/1.31 spl2_2),
% 1.61/1.31 inference(avatar_split_clause,[status(thm)],[f23,f29])).
% 1.61/1.31 thf(f23,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $true)),
% 1.61/1.31 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.61/1.31 thf(f22,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $true) | ((sK1 @ sK4) = $true)),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.61/1.31 thf(f20,plain,(
% 1.61/1.31 (((sK1 @ sK4) & (sK0 @ sK4)) = $true) | ((sK1 @ sK4) = $true)),
% 1.61/1.31 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 ((sK1 @ sK4) = $true) | (((sK1 @ sK4) & (sK0 @ sK4)) = $true) | ((sK1 @ sK4) = $true)),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.61/1.31 thf(f12,plain,(
% 1.61/1.31 (((sK1 @ sK4) | ((sK1 @ sK4) & (sK0 @ sK4))) = $true) | ((sK1 @ sK4) = $true)),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.61/1.31 % SZS output end Proof for DTF2THF_18217
% 1.61/1.31 % (18509)------------------------------
% 1.61/1.31 % (18509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (18509)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (18509)Memory used [KB]: 5500
% 1.61/1.31 % (18509)Time elapsed: 0.002 s
% 1.61/1.31 % (18509)Instructions burned: 2 (million)
% 1.61/1.31 % (18509)------------------------------
% 1.61/1.31 % (18509)------------------------------
% 1.61/1.31 % (18503)Success in time 0.013 s
%------------------------------------------------------------------------------