%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET043^5 : 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 : n015.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 09:31:03 AM UTC 2026
% Result : Theorem 1.43s 1.29s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 108 ( 23 ~; 11 |; 4 &; 64 @)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 11 !; 7 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cE: $i > $i > $o ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( cE @ X1 @ sK0 )
!= $true )
| ( ( cE @ X1 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i] :
( ( ( ( cE @ X1 @ X1 )
!= $true )
| ( ( cE @ X1 @ sK0 )
!= $true ) )
& ( ( ( cE @ X1 @ sK0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( ( ( cE @ X1 @ X1 )
!= $true )
| ( ( cE @ X1 @ X0 )
!= $true ) )
& ( ( ( cE @ X1 @ X0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) ) )
=> ! [X1: $i] :
( ( ( ( cE @ X1 @ X1 )
!= $true )
| ( ( cE @ X1 @ sK0 )
!= $true ) )
& ( ( ( cE @ X1 @ sK0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i] :
! [X1: $i] :
( ( ( ( cE @ X1 @ X1 )
!= $true )
| ( ( cE @ X1 @ X0 )
!= $true ) )
& ( ( ( cE @ X1 @ X0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i] :
! [X1: $i] :
( ( ( cE @ X1 @ X1 )
!= $true )
<=> ( ( cE @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( ( cE @ X1 @ X0 )
= $true )
<=> ( ( cE @ X1 @ X1 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( cE @ X1 @ X0 )
<=> ~ ( cE @ X1 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( cE @ X1 @ X0 )
<=> ~ ( cE @ X1 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ( cE @ X1 @ X0 )
<=> ~ ( cE @ X1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.gicSBocuNn/DTF2THF_9025.p',cRUSSELL1) ).
thf(f13,plain,
( $true
= ( cE @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( cE @ sK0 @ sK0 ) )
| ( $true != $true ) ),
inference(equality_factoring,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i] :
( ( ( cE @ X1 @ sK0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET043^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:50:31 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : SET043^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPS problem RUSSELL1
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : One form of Russell's Paradox.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0069 [Bro09]
% 0.28/0.46 % : RUSSELL1 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.28/0.46 % Number of connectives : 7 ( 2 ~; 0 |; 0 &; 4 @)
% 0.28/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.28/0.46 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_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 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cE,type,
% 0.28/0.46 cE: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cRUSSELL1,conjecture,
% 0.28/0.46 ~ ? [U: $i] :
% 0.28/0.46 ! [V: $i] :
% 0.28/0.46 ( ( cE @ V @ U )
% 0.28/0.46 <=> ~ ( cE @ V @ V ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.43/1.26 ---- Embedded in THF ---
% 1.43/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.26 %%% Generated on Tue Feb 24 11:50:32 EST 2026
% 1.43/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.26 %%% Logic specification used:
% 1.43/1.26 %%% thf(spec, logic, $$dhol).
% 1.43/1.26
% 1.43/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gicSBocuNn/DTF2DTF9025.p
% See solution above
% 1.43/1.26 ------------------------
% 1.43/1.27 ---- Cleaned THF ---
% 1.43/1.27 thf(cE,type,
% 1.43/1.27 cE: $i > $i > $o ).
% 1.43/1.27
% 1.43/1.27 thf(cRUSSELL1,conjecture,
% 1.43/1.27 ~ ? [U: $i] :
% 1.43/1.27 ! [V: $i] :
% 1.43/1.27 ( ( cE @ V @ U )
% 1.43/1.27 <=> ~ ( cE @ V @ V ) ) ).
% 1.43/1.27 ------------------------
% 1.43/1.29 % (9297)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9025 for (3000ds/183Mi)
% 1.43/1.29 % (9297)First to succeed.
% 1.43/1.29 % (9299)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_9025 for (3000ds/27Mi)
% 1.43/1.29 % (9297)Refutation found. Thanks to Tanya!
% 1.43/1.29 % SZS status Theorem for DTF2THF_9025
% 1.43/1.29 % SZS output start Proof for DTF2THF_9025
% 1.43/1.29 thf(func_def_0, type, cE: $i > $i > $o).
% 1.43/1.29 thf(f14,plain,(
% 1.43/1.29 $false),
% 1.43/1.29 inference(subsumption_resolution,[status(thm)],[f13,f11])).
% 1.43/1.29 thf(f11,plain,(
% 1.43/1.29 ( ! [X1 : $i] : (((cE @ X1 @ sK0) != $true) | ((cE @ X1 @ X1) != $true)) )),
% 1.43/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.43/1.29 thf(f9,plain,(
% 1.43/1.29 ! [X1 : $i] : ((((cE @ X1 @ X1) != $true) | ((cE @ X1 @ sK0) != $true)) & (((cE @ X1 @ sK0) = $true) | ((cE @ X1 @ X1) = $true)))),
% 1.43/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.43/1.29 thf(f8,plain,(
% 1.43/1.29 ? [X0 : $i] : ! [X1 : $i] : ((((cE @ X1 @ X1) != $true) | ((cE @ X1 @ X0) != $true)) & (((cE @ X1 @ X0) = $true) | ((cE @ X1 @ X1) = $true))) => ! [X1 : $i] : ((((cE @ X1 @ X1) != $true) | ((cE @ X1 @ sK0) != $true)) & (((cE @ X1 @ sK0) = $true) | ((cE @ X1 @ X1) = $true)))),
% 1.43/1.29 introduced(definition,[],[choice_axiom])).
% 1.43/1.29 thf(f7,plain,(
% 1.43/1.29 ? [X0 : $i] : ! [X1 : $i] : ((((cE @ X1 @ X1) != $true) | ((cE @ X1 @ X0) != $true)) & (((cE @ X1 @ X0) = $true) | ((cE @ X1 @ X1) = $true)))),
% 1.43/1.29 inference(nnf_transformation,[status(thm)],[f6])).
% 1.43/1.29 thf(f6,plain,(
% 1.43/1.29 ? [X0 : $i] : ! [X1 : $i] : (((cE @ X1 @ X1) != $true) <=> ((cE @ X1 @ X0) = $true))),
% 1.43/1.29 inference(flattening,[status(thm)],[f5])).
% 1.43/1.29 thf(f5,plain,(
% 1.43/1.29 ~~? [X0 : $i] : ! [X1 : $i] : (((cE @ X1 @ X0) = $true) <=> ~((cE @ X1 @ X1) = $true))),
% 1.43/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.43/1.29 thf(f4,plain,(
% 1.43/1.29 ~~? [X0 : $i] : ! [X1 : $i] : ((cE @ X1 @ X0) <=> ~(cE @ X1 @ X1))),
% 1.43/1.29 inference(rectify,[status(thm)],[f2])).
% 1.43/1.29 thf(f2,negated_conjecture,(
% 1.43/1.29 ~~? [X0 : $i] : ! [X1 : $i] : ((cE @ X1 @ X0) <=> ~(cE @ X1 @ X1))),
% 1.43/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.43/1.29 thf(f1,conjecture,(
% 1.43/1.29 ~? [X0 : $i] : ! [X1 : $i] : ((cE @ X1 @ X0) <=> ~(cE @ X1 @ X1))),
% 1.43/1.29 file('/export/starexec/sandbox2/tmp/tmp.gicSBocuNn/DTF2THF_9025.p',cRUSSELL1)).
% 1.43/1.29 thf(f13,plain,(
% 1.43/1.29 ($true = (cE @ sK0 @ sK0))),
% 1.43/1.29 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.43/1.29 thf(f12,plain,(
% 1.43/1.29 ($true = (cE @ sK0 @ sK0)) | ($true != $true)),
% 1.43/1.29 inference(equality_factoring,[status(thm)],[f10])).
% 1.43/1.29 thf(f10,plain,(
% 1.43/1.29 ( ! [X1 : $i] : (((cE @ X1 @ sK0) = $true) | ((cE @ X1 @ X1) = $true)) )),
% 1.43/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.43/1.29 % SZS output end Proof for DTF2THF_9025
% 1.43/1.29 % (9297)------------------------------
% 1.43/1.29 % (9297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.29 % (9297)Termination reason: Refutation
% 1.43/1.29
% 1.43/1.29 % (9297)Memory used [KB]: 5500
% 1.43/1.29 % (9297)Time elapsed: 0.002 s
% 1.43/1.29 % (9297)Instructions burned: 2 (million)
% 1.43/1.29 % (9297)------------------------------
% 1.43/1.29 % (9297)------------------------------
% 1.43/1.29 % (9296)Success in time 0.01 s
%------------------------------------------------------------------------------