%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET185^5 : 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 09:31:23 AM UTC 2026
% Result : Theorem 1.47s 1.25s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 132 ( 47 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 136 ( 23 ~; 24 |; 12 &; 61 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 22 !; 11 ?; 33 :)
% 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 > $o ).
thf(func_def_6,type,
sK2: a ).
thf(f33,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f22,f23,f32]) ).
thf(f32,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f19,f15]) ).
thf(f15,definition,
( spl3_1
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f19,definition,
( spl3_2
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f30,plain,
( ( ( sK1 @ sK2 )
= $true )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $true != $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f11,f21]) ).
thf(f21,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f11,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( sK1 @ sK2 )
= $true )
| ( ( sK0 @ sK2 )
= $true ) )
& ( ( sK1 @ sK2 )
!= $true )
& ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
& ( ( X1 @ X2 )
!= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) )
=> ( ? [X2: a] :
( ( ( ( sK1 @ X2 )
= $true )
| ( ( sK0 @ X2 )
= $true ) )
& ( ( sK1 @ X2 )
!= $true ) )
& ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X2: a] :
( ( ( ( sK1 @ X2 )
= $true )
| ( ( sK0 @ X2 )
= $true ) )
& ( ( sK1 @ X2 )
!= $true ) )
=> ( ( ( ( sK1 @ sK2 )
= $true )
| ( ( sK0 @ sK2 )
= $true ) )
& ( ( sK1 @ sK2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
& ( ( X1 @ X2 )
!= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o] :
( ? [X3: a] :
( ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) )
& ( ( X0 @ X3 )
!= $true ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
=> ! [X3: a] :
( ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) )
=> ( ( X0 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
=> ( X0 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( ( X0 @ X2 )
| ( X1 @ X2 ) )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( ( X0 @ X2 )
| ( X1 @ X2 ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.E2aTFEYPvl/DTF2THF_26019.p',cBOOL_PROP_35_pme) ).
thf(f23,plain,
~ spl3_1,
inference(avatar_split_clause,[status(thm)],[f12,f15]) ).
thf(f12,plain,
( ( sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f19,f15]) ).
thf(f13,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET185^5 : 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 : n022.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 11:54:36 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
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SET185^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : TPS problem BOOL-PROP-35
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Trybulec's 35th Boolean property of sets
% 0.31/0.47
% 0.31/0.47 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0112 [Bro09]
% 0.31/0.47 % : BOOL-PROP-35 [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.47 % Number of connectives : 9 ( 0 ~; 1 |; 0 &; 5 @)
% 0.31/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 8 ( 8 avg)
% 0.31/0.47 % Number of types : 2 ( 1 usr)
% 0.31/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 % : Polymorphic definitions expanded.
% 0.31/0.47 % :
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(a_type,type,
% 0.31/0.47 a: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(cBOOL_PROP_35_pme,conjecture,
% 0.31/0.47 ! [X: a > $o,Y: a > $o] :
% 0.31/0.47 ( ! [Xx: a] :
% 0.31/0.47 ( ( X @ Xx )
% 0.31/0.47 => ( Y @ Xx ) )
% 0.31/0.47 => ! [Xx: a] :
% 0.31/0.47 ( ( ( X @ Xx )
% 0.31/0.47 | ( Y @ Xx ) )
% 0.31/0.47 => ( Y @ Xx ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.47/1.23 ---- Embedded in THF ---
% 1.47/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.23 %%% Generated on Tue Feb 24 11:54:37 EST 2026
% 1.47/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.23 %%% Logic specification used:
% 1.47/1.23 %%% thf(spec, logic, $$dhol).
% 1.47/1.23
% 1.47/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.E2aTFEYPvl/DTF2DTF26019.p
% See solution above
% 1.47/1.23 ------------------------
% 1.47/1.24 ---- Cleaned THF ---
% 1.47/1.24 thf(a_type,type,
% 1.47/1.24 a: $tType ).
% 1.47/1.24
% 1.47/1.24 thf(cBOOL_PROP_35_pme,conjecture,
% 1.47/1.24 ! [X: a > $o,Y: a > $o] :
% 1.47/1.24 ( ! [Xx: a] :
% 1.47/1.24 ( ( X @ Xx )
% 1.47/1.24 => ( Y @ Xx ) )
% 1.47/1.24 => ! [Xx: a] :
% 1.47/1.24 ( ( ( X @ Xx )
% 1.47/1.24 | ( Y @ Xx ) )
% 1.47/1.24 => ( Y @ Xx ) ) ) ).
% 1.47/1.24 ------------------------
% 1.47/1.25 % (26347)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_26019 for (2999ds/4Mi)
% 1.47/1.25 % (26346)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26019 for (2999ds/183Mi)
% 1.47/1.25 % (26347)First to succeed.
% 1.47/1.25 % (26346)Also succeeded, but the first one will report.
% 1.47/1.25 % (26347)Refutation found. Thanks to Tanya!
% 1.47/1.25 % SZS status Theorem for DTF2THF_26019
% 1.47/1.25 % SZS output start Proof for DTF2THF_26019
% 1.47/1.25 thf(type_def_5, type, a: $tType).
% 1.47/1.25 thf(func_def_0, type, a: $tType).
% 1.47/1.25 thf(func_def_4, type, sK0: a > $o).
% 1.47/1.25 thf(func_def_5, type, sK1: a > $o).
% 1.47/1.25 thf(func_def_6, type, sK2: a).
% 1.47/1.25 thf(f33,plain,(
% 1.47/1.25 $false),
% 1.47/1.25 inference(avatar_sat_refutation,[status(thm)],[f22,f23,f32])).
% 1.47/1.25 thf(f32,plain,(
% 1.47/1.25 spl3_1 | ~spl3_2),
% 1.47/1.25 inference(avatar_split_clause,[status(thm)],[f30,f19,f15])).
% 1.47/1.25 thf(f15,definition,(
% 1.47/1.25 spl3_1 <=> ((sK1 @ sK2) = $true)),
% 1.47/1.25 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.47/1.25 thf(f19,definition,(
% 1.47/1.25 spl3_2 <=> ((sK0 @ sK2) = $true)),
% 1.47/1.25 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.47/1.25 thf(f30,plain,(
% 1.47/1.25 ((sK1 @ sK2) = $true) | ~spl3_2),
% 1.47/1.25 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.47/1.25 thf(f29,plain,(
% 1.47/1.25 ((sK1 @ sK2) = $true) | ($true != $true) | ~spl3_2),
% 1.47/1.25 inference(superposition,[status(thm)],[f11,f21])).
% 1.47/1.25 thf(f21,plain,(
% 1.47/1.25 ((sK0 @ sK2) = $true) | ~spl3_2),
% 1.47/1.25 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.47/1.25 thf(f11,plain,(
% 1.47/1.25 ( ! [X3 : a] : (((sK0 @ X3) != $true) | ((sK1 @ X3) = $true)) )),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.25 thf(f10,plain,(
% 1.47/1.25 ((((sK1 @ sK2) = $true) | ((sK0 @ sK2) = $true)) & ((sK1 @ sK2) != $true)) & ! [X3 : a] : (((sK1 @ X3) = $true) | ((sK0 @ X3) != $true))),
% 1.47/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 1.47/1.25 thf(f8,plain,(
% 1.47/1.25 ? [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : ((((X1 @ X2) = $true) | ((X0 @ X2) = $true)) & ((X1 @ X2) != $true)) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X0 @ X3) != $true))) => (? [X2 : a] : ((((sK1 @ X2) = $true) | ((sK0 @ X2) = $true)) & ((sK1 @ X2) != $true)) & ! [X3 : a] : (((sK1 @ X3) = $true) | ((sK0 @ X3) != $true)))),
% 1.47/1.25 introduced(definition,[],[choice_axiom])).
% 1.47/1.25 thf(f9,plain,(
% 1.47/1.25 ? [X2 : a] : ((((sK1 @ X2) = $true) | ((sK0 @ X2) = $true)) & ((sK1 @ X2) != $true)) => ((((sK1 @ sK2) = $true) | ((sK0 @ sK2) = $true)) & ((sK1 @ sK2) != $true))),
% 1.47/1.25 introduced(definition,[],[choice_axiom])).
% 1.47/1.25 thf(f7,plain,(
% 1.47/1.25 ? [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : ((((X1 @ X2) = $true) | ((X0 @ X2) = $true)) & ((X1 @ X2) != $true)) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X0 @ X3) != $true)))),
% 1.47/1.25 inference(rectify,[status(thm)],[f6])).
% 1.47/1.25 thf(f6,plain,(
% 1.47/1.25 ? [X1 : a > $o,X0 : a > $o] : (? [X3 : a] : ((((X0 @ X3) = $true) | ((X1 @ X3) = $true)) & ((X0 @ X3) != $true)) & ! [X2 : a] : (((X0 @ X2) = $true) | ((X1 @ X2) != $true)))),
% 1.47/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.25 thf(f5,plain,(
% 1.47/1.25 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) = $true) => ((X0 @ X2) = $true)) => ! [X3 : a] : ((((X0 @ X3) = $true) | ((X1 @ X3) = $true)) => ((X0 @ X3) = $true)))),
% 1.47/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.25 thf(f4,plain,(
% 1.47/1.25 ~! [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (X0 @ X2)) => ! [X3 : a] : (((X1 @ X3) | (X0 @ X3)) => (X0 @ X3)))),
% 1.47/1.25 inference(rectify,[status(thm)],[f2])).
% 1.47/1.25 thf(f2,negated_conjecture,(
% 1.47/1.25 ~! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : (((X0 @ X2) | (X1 @ X2)) => (X1 @ X2)))),
% 1.47/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.25 thf(f1,conjecture,(
% 1.47/1.25 ! [X1 : a > $o,X0 : a > $o] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : (((X0 @ X2) | (X1 @ X2)) => (X1 @ X2)))),
% 1.47/1.25 file('/export/starexec/sandbox/tmp/tmp.E2aTFEYPvl/DTF2THF_26019.p',cBOOL_PROP_35_pme)).
% 1.47/1.25 thf(f23,plain,(
% 1.47/1.25 ~spl3_1),
% 1.47/1.25 inference(avatar_split_clause,[status(thm)],[f12,f15])).
% 1.47/1.25 thf(f12,plain,(
% 1.47/1.25 ((sK1 @ sK2) != $true)),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.25 thf(f22,plain,(
% 1.47/1.25 spl3_1 | spl3_2),
% 1.47/1.25 inference(avatar_split_clause,[status(thm)],[f13,f19,f15])).
% 1.47/1.25 thf(f13,plain,(
% 1.47/1.25 ((sK0 @ sK2) = $true) | ((sK1 @ sK2) = $true)),
% 1.47/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.25 % SZS output end Proof for DTF2THF_26019
% 1.47/1.25 % (26347)------------------------------
% 1.47/1.25 % (26347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.25 % (26347)Termination reason: Refutation
% 1.47/1.25
% 1.47/1.25 % (26347)Memory used [KB]: 5500
% 1.47/1.25 % (26347)Time elapsed: 0.003 s
% 1.47/1.25 % (26347)Instructions burned: 1 (million)
% 1.47/1.25 % (26347)------------------------------
% 1.47/1.25 % (26347)------------------------------
% 1.47/1.25 % (26345)Success in time 0.012 s
%------------------------------------------------------------------------------