%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET580^5 : 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 09:31:48 AM UTC 2026
% Result : Theorem 1.49s 1.26s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 1 unt; 0 typ; 2 def)
% Number of atoms : 433 ( 176 equ; 0 cnn)
% Maximal formula atoms : 44 ( 16 avg)
% Number of connectives : 477 ( 104 ~; 98 |; 66 &; 194 @)
% ( 13 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 15 !; 15 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a ).
thf(f45,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f41,f42,f43,f44]) ).
thf(f44,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f38,f34]) ).
thf(f34,definition,
( spl3_1
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f38,definition,
( spl3_2
<=> ( ( sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
!= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK1 @ sK2 )
!= $true )
| ( $true
!= ( sK0 @ sK2 ) )
| ( $true
!= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( $true
= ( sK0 @ sK2 ) )
| ( ( ( ( sK1 @ sK2 )
!= $true )
| ( ( ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) )
& ( ( ( sK1 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ) ) )
& ( ( ( sK1 @ sK2 )
= $true )
| ( ( ( sK1 @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) ) ) ) )
& ( ( $true
!= ( sK0 @ sK2 ) )
| ( ( ( ( ( sK1 @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) )
| ( ( sK1 @ sK2 )
!= $true ) )
& ( ( ( sK1 @ sK2 )
= $true )
| ( ( ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) )
& ( ( ( sK1 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: a > $o,X1: a > $o,X2: a] :
( ( ( $true
= ( X0 @ X2 ) )
| ( ( ( $true
!= ( X1 @ X2 ) )
| ( ( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( X0 @ X2 ) ) ) ) )
& ( ( $true
= ( X1 @ X2 ) )
| ( ( $true
!= ( X1 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( $true
!= ( X0 @ X2 ) ) ) ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( ( ( ( $true
!= ( X1 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( $true
!= ( X0 @ X2 ) ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
= ( X1 @ X2 ) )
| ( ( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( X0 @ X2 ) ) ) ) ) ) ) )
=> ( ( ( $true
= ( sK0 @ sK2 ) )
| ( ( ( ( sK1 @ sK2 )
!= $true )
| ( ( ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) )
& ( ( ( sK1 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ) ) )
& ( ( ( sK1 @ sK2 )
= $true )
| ( ( ( sK1 @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) ) ) ) )
& ( ( $true
!= ( sK0 @ sK2 ) )
| ( ( ( ( ( sK1 @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ( sK1 @ sK2 )
= $true )
& ( $true
!= ( sK0 @ sK2 ) ) )
| ( ( sK1 @ sK2 )
!= $true ) )
& ( ( ( sK1 @ sK2 )
= $true )
| ( ( ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) )
& ( ( ( sK1 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a] :
( ( ( $true
= ( X0 @ X2 ) )
| ( ( ( $true
!= ( X1 @ X2 ) )
| ( ( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( X0 @ X2 ) ) ) ) )
& ( ( $true
= ( X1 @ X2 ) )
| ( ( $true
!= ( X1 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( $true
!= ( X0 @ X2 ) ) ) ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( ( ( ( $true
!= ( X1 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( $true
!= ( X0 @ X2 ) ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
= ( X1 @ X2 ) )
| ( ( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( $true
= ( X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( $true
= ( X1 @ X2 ) )
| ( ( ( $true
!= ( X0 @ X2 ) )
| ( ( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( $true
= ( X1 @ X2 ) ) ) ) )
& ( ( $true
= ( X0 @ X2 ) )
| ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) ) ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( ( ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
= ( X0 @ X2 ) )
| ( ( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( $true
= ( X1 @ X2 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( $true
= ( X1 @ X2 ) )
| ( ( ( $true
!= ( X0 @ X2 ) )
| ( ( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( $true
= ( X1 @ X2 ) ) ) ) )
& ( ( $true
= ( X0 @ X2 ) )
| ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) ) ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( ( ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) )
| ( $true
!= ( X0 @ X2 ) ) )
& ( ( $true
= ( X0 @ X2 ) )
| ( ( ( $true
= ( X0 @ X2 ) )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X0 @ X2 ) )
| ( $true
= ( X1 @ X2 ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a] :
( ( ( ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) ) )
<=> ( $true
= ( X0 @ X2 ) ) )
<~> ( $true
!= ( X1 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X2: a,X1: a > $o,X0: a > $o] :
( ( $true
!= ( X1 @ X2 ) )
<=> ( ( ( ( $true
!= ( X0 @ X2 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) ) )
<=> ( $true
= ( X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a] :
( ( $true
!= ( X1 @ X2 ) )
<=> ( ( $true
= ( X0 @ X2 ) )
<=> ( ( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( X1 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( $true
!= ( X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a] :
( ~ ( X1 @ X2 )
<=> ( ( X0 @ X2 )
<=> ( ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a] :
( ~ ( X2 @ X0 )
<=> ( ( X1 @ X0 )
<=> ( ( ( X1 @ X0 )
& ~ ( X2 @ X0 ) )
| ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a] :
( ~ ( X2 @ X0 )
<=> ( ( X1 @ X0 )
<=> ( ( ( X1 @ X0 )
& ~ ( X2 @ X0 ) )
| ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kM14yuaEmv/DTF2THF_23660.p',cBOOL_PROP_23_pme) ).
thf(f43,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f38,f34]) ).
thf(f26,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( ( sK1 @ sK2 )
= $true )
| ( $true
!= ( sK0 @ sK2 ) )
| ( $true
!= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f42,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f29,f34,f38]) ).
thf(f29,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( ( sK1 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f41,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f30,f38,f34]) ).
thf(f30,plain,
( ( ( sK1 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
!= $true )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET580^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n019.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 11:59:39 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET580^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPS problem BOOL-PROP-23
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : Trybulec's 23rd Boolean property of sets
% 0.19/0.45
% 0.19/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0292 [Bro09]
% 0.19/0.45 % : BOOL-PROP-23 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.45 % Number of connectives : 14 ( 3 ~; 1 |; 2 &; 6 @)
% 0.19/0.45 % ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.45 % Number of types : 2 ( 1 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.45 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 % : Polymorphic definitions expanded.
% 0.19/0.45 % :
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a_type,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(cBOOL_PROP_23_pme,conjecture,
% 0.19/0.45 ! [Xx: a,X: a > $o,Y: a > $o] :
% 0.19/0.45 ( ( ( ( ( X @ Xx )
% 0.19/0.45 & ~ ( Y @ Xx ) )
% 0.19/0.45 | ( ( Y @ Xx )
% 0.19/0.45 & ~ ( X @ Xx ) ) )
% 0.19/0.45 <=> ( X @ Xx ) )
% 0.19/0.45 <=> ~ ( Y @ Xx ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.49/1.22 ---- Embedded in THF ---
% 1.49/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.22 %%% Generated on Tue Feb 24 11:59:40 EST 2026
% 1.49/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.22 %%% Logic specification used:
% 1.49/1.22 %%% thf(spec, logic, $$dhol).
% 1.49/1.22
% 1.49/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kM14yuaEmv/DTF2DTF23660.p
% See solution above
% 1.49/1.22 ------------------------
% 1.49/1.23 ---- Cleaned THF ---
% 1.49/1.23 thf(a_type,type,
% 1.49/1.23 a: $tType ).
% 1.49/1.23
% 1.49/1.23 thf(cBOOL_PROP_23_pme,conjecture,
% 1.49/1.23 ! [Xx: a,X: a > $o,Y: a > $o] :
% 1.49/1.23 ( ( ( ( ( X @ Xx )
% 1.49/1.23 & ~ ( Y @ Xx ) )
% 1.49/1.23 | ( ( Y @ Xx )
% 1.49/1.23 & ~ ( X @ Xx ) ) )
% 1.49/1.23 <=> ( X @ Xx ) )
% 1.49/1.23 <=> ~ ( Y @ Xx ) ) ).
% 1.49/1.23 ------------------------
% 1.49/1.24 % (23768)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_23660 for (2999ds/4Mi)
% 1.49/1.25 % (23768)Instruction limit reached!
% 1.49/1.25 % (23768)------------------------------
% 1.49/1.25 % (23768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.25 % (23768)Termination reason: Unknown
% 1.49/1.25 % (23768)Termination phase: Saturation
% 1.49/1.25
% 1.49/1.25 % (23768)Memory used [KB]: 5500
% 1.49/1.25 % (23768)Time elapsed: 0.003 s
% 1.49/1.25 % (23768)Instructions burned: 5 (million)
% 1.49/1.25 % (23768)------------------------------
% 1.49/1.25 % (23768)------------------------------
% 1.49/1.25 % (23767)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23660 for (2999ds/183Mi)
% 1.49/1.25 % (23770)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23660 for (2999ds/2Mi)
% 1.49/1.25 % (23771)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_23660 for (2999ds/2Mi)
% 1.49/1.25 % (23772)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_23660 for (2999ds/275Mi)
% 1.49/1.25 % (23769)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_23660 for (2999ds/27Mi)
% 1.49/1.25 % (23770)Instruction limit reached!
% 1.49/1.25 % (23770)------------------------------
% 1.49/1.25 % (23770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.25 % (23770)Termination reason: Unknown
% 1.49/1.25 % (23770)Termination phase: Property scanning
% 1.49/1.25
% 1.49/1.25 % (23770)Memory used [KB]: 895
% 1.49/1.25 % (23770)Time elapsed: 0.003 s
% 1.49/1.25 % (23770)Instructions burned: 2 (million)
% 1.49/1.25 % (23770)------------------------------
% 1.49/1.25 % (23770)------------------------------
% 1.49/1.25 % (23771)Instruction limit reached!
% 1.49/1.25 % (23771)------------------------------
% 1.49/1.25 % (23771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.25 % (23771)Termination reason: Unknown
% 1.49/1.25 % (23771)Termination phase: Saturation
% 1.49/1.25
% 1.49/1.25 % (23771)Memory used [KB]: 895
% 1.49/1.25 % (23771)Time elapsed: 0.003 s
% 1.49/1.25 % (23771)Instructions burned: 2 (million)
% 1.49/1.25 % (23771)------------------------------
% 1.49/1.25 % (23771)------------------------------
% 1.49/1.25 % (23769)First to succeed.
% 1.49/1.25 % (23773)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23660 for (2999ds/18Mi)
% 1.49/1.25 % (23767)Also succeeded, but the first one will report.
% 1.49/1.26 % (23772)Also succeeded, but the first one will report.
% 1.49/1.26 % (23769)Refutation found. Thanks to Tanya!
% 1.49/1.26 % SZS status Theorem for DTF2THF_23660
% 1.49/1.26 % SZS output start Proof for DTF2THF_23660
% 1.49/1.26 thf(type_def_5, type, a: $tType).
% 1.49/1.26 thf(func_def_0, type, a: $tType).
% 1.49/1.26 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.26 thf(func_def_5, type, sK0: a > $o).
% 1.49/1.26 thf(func_def_6, type, sK1: a > $o).
% 1.49/1.26 thf(func_def_7, type, sK2: a).
% 1.49/1.26 thf(f45,plain,(
% 1.49/1.26 $false),
% 1.49/1.26 inference(avatar_sat_refutation,[status(thm)],[f41,f42,f43,f44])).
% 1.49/1.26 thf(f44,plain,(
% 1.49/1.26 ~spl3_1 | ~spl3_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f25,f38,f34])).
% 1.49/1.26 thf(f34,definition,(
% 1.49/1.26 spl3_1 <=> ($true = (sK0 @ sK2))),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.49/1.26 thf(f38,definition,(
% 1.49/1.26 spl3_2 <=> ((sK1 @ sK2) = $true)),
% 1.49/1.26 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.49/1.26 thf(f25,plain,(
% 1.49/1.26 ($true != (sK0 @ sK2)) | ((sK1 @ sK2) != $true)),
% 1.49/1.26 inference(duplicate_literal_removal,[status(thm)],[f17])).
% 1.49/1.26 thf(f17,plain,(
% 1.49/1.26 ((sK1 @ sK2) != $true) | ($true != (sK0 @ sK2)) | ($true != (sK0 @ sK2)) | ((sK1 @ sK2) != $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f12,plain,(
% 1.49/1.26 (($true = (sK0 @ sK2)) | ((((sK1 @ sK2) != $true) | ((((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2))) & (((sK1 @ sK2) != $true) | ($true = (sK0 @ sK2))))) & (((sK1 @ sK2) = $true) | (((sK1 @ sK2) != $true) & ($true = (sK0 @ sK2))) | (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2)))))) & (($true != (sK0 @ sK2)) | (((((sK1 @ sK2) != $true) & ($true = (sK0 @ sK2))) | (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2))) | ((sK1 @ sK2) != $true)) & (((sK1 @ sK2) = $true) | ((((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2))) & (((sK1 @ sK2) != $true) | ($true = (sK0 @ sK2)))))))),
% 1.49/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.49/1.26 thf(f11,plain,(
% 1.49/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a] : ((($true = (X0 @ X2)) | ((($true != (X1 @ X2)) | ((($true = (X1 @ X2)) | ($true != (X0 @ X2))) & (($true != (X1 @ X2)) | ($true = (X0 @ X2))))) & (($true = (X1 @ X2)) | (($true != (X1 @ X2)) & ($true = (X0 @ X2))) | (($true = (X1 @ X2)) & ($true != (X0 @ X2)))))) & (($true != (X0 @ X2)) | (((($true != (X1 @ X2)) & ($true = (X0 @ X2))) | (($true = (X1 @ X2)) & ($true != (X0 @ X2))) | ($true != (X1 @ X2))) & (($true = (X1 @ X2)) | ((($true = (X1 @ X2)) | ($true != (X0 @ X2))) & (($true != (X1 @ X2)) | ($true = (X0 @ X2)))))))) => ((($true = (sK0 @ sK2)) | ((((sK1 @ sK2) != $true) | ((((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2))) & (((sK1 @ sK2) != $true) | ($true = (sK0 @ sK2))))) & (((sK1 @ sK2) = $true) | (((sK1 @ sK2) != $true) & ($true = (sK0 @ sK2))) | (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2)))))) & (($true != (sK0 @ sK2)) | (((((sK1 @ sK2) != $true) & ($true = (sK0 @ sK2))) | (((sK1 @ sK2) = $true) & ($true != (sK0 @ sK2))) | ((sK1 @ sK2) != $true)) & (((sK1 @ sK2) = $true) | ((((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2))) & (((sK1 @ sK2) != $true) | ($true = (sK0 @ sK2))))))))),
% 1.49/1.26 introduced(definition,[],[choice_axiom])).
% 1.49/1.26 thf(f10,plain,(
% 1.49/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a] : ((($true = (X0 @ X2)) | ((($true != (X1 @ X2)) | ((($true = (X1 @ X2)) | ($true != (X0 @ X2))) & (($true != (X1 @ X2)) | ($true = (X0 @ X2))))) & (($true = (X1 @ X2)) | (($true != (X1 @ X2)) & ($true = (X0 @ X2))) | (($true = (X1 @ X2)) & ($true != (X0 @ X2)))))) & (($true != (X0 @ X2)) | (((($true != (X1 @ X2)) & ($true = (X0 @ X2))) | (($true = (X1 @ X2)) & ($true != (X0 @ X2))) | ($true != (X1 @ X2))) & (($true = (X1 @ X2)) | ((($true = (X1 @ X2)) | ($true != (X0 @ X2))) & (($true != (X1 @ X2)) | ($true = (X0 @ X2))))))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f9])).
% 1.49/1.26 thf(f9,plain,(
% 1.49/1.26 ? [X1 : a > $o,X0 : a > $o,X2 : a] : ((($true = (X1 @ X2)) | ((($true != (X0 @ X2)) | ((($true = (X0 @ X2)) | ($true != (X1 @ X2))) & (($true != (X0 @ X2)) | ($true = (X1 @ X2))))) & (($true = (X0 @ X2)) | (($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2)))))) & (($true != (X1 @ X2)) | (((($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2))) | ($true != (X0 @ X2))) & (($true = (X0 @ X2)) | ((($true = (X0 @ X2)) | ($true != (X1 @ X2))) & (($true != (X0 @ X2)) | ($true = (X1 @ X2))))))))),
% 1.49/1.26 inference(flattening,[status(thm)],[f8])).
% 1.49/1.26 thf(f8,plain,(
% 1.49/1.26 ? [X1 : a > $o,X0 : a > $o,X2 : a] : ((($true = (X1 @ X2)) | ((($true != (X0 @ X2)) | ((($true = (X0 @ X2)) | ($true != (X1 @ X2))) & (($true != (X0 @ X2)) | ($true = (X1 @ X2))))) & (($true = (X0 @ X2)) | ((($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2))))))) & (($true != (X1 @ X2)) | ((((($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2)))) | ($true != (X0 @ X2))) & (($true = (X0 @ X2)) | ((($true = (X0 @ X2)) | ($true != (X1 @ X2))) & (($true != (X0 @ X2)) | ($true = (X1 @ X2))))))))),
% 1.49/1.26 inference(nnf_transformation,[status(thm)],[f7])).
% 1.49/1.26 thf(f7,plain,(
% 1.49/1.26 ? [X1 : a > $o,X0 : a > $o,X2 : a] : ((((($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2)))) <=> ($true = (X0 @ X2))) <~> ($true != (X1 @ X2)))),
% 1.49/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.26 thf(f6,plain,(
% 1.49/1.26 ~! [X2 : a,X1 : a > $o,X0 : a > $o] : (($true != (X1 @ X2)) <=> (((($true != (X0 @ X2)) & ($true = (X1 @ X2))) | (($true = (X0 @ X2)) & ($true != (X1 @ X2)))) <=> ($true = (X0 @ X2))))),
% 1.49/1.26 inference(flattening,[status(thm)],[f5])).
% 1.49/1.26 thf(f5,plain,(
% 1.49/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a] : (~($true = (X1 @ X2)) <=> (($true = (X0 @ X2)) <=> ((($true = (X0 @ X2)) & ~($true = (X1 @ X2))) | (($true = (X1 @ X2)) & ~($true = (X0 @ X2))))))),
% 1.49/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.26 thf(f4,plain,(
% 1.49/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a] : (~(X1 @ X2) <=> ((X0 @ X2) <=> (((X0 @ X2) & ~(X1 @ X2)) | ((X1 @ X2) & ~(X0 @ X2)))))),
% 1.49/1.26 inference(rectify,[status(thm)],[f2])).
% 1.49/1.26 thf(f2,negated_conjecture,(
% 1.49/1.26 ~! [X1 : a > $o,X2 : a > $o,X0 : a] : (~(X2 @ X0) <=> ((X1 @ X0) <=> (((X1 @ X0) & ~(X2 @ X0)) | ((X2 @ X0) & ~(X1 @ X0)))))),
% 1.49/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.26 thf(f1,conjecture,(
% 1.49/1.26 ! [X1 : a > $o,X2 : a > $o,X0 : a] : (~(X2 @ X0) <=> ((X1 @ X0) <=> (((X1 @ X0) & ~(X2 @ X0)) | ((X2 @ X0) & ~(X1 @ X0)))))),
% 1.49/1.26 file('/export/starexec/sandbox/tmp/tmp.kM14yuaEmv/DTF2THF_23660.p',cBOOL_PROP_23_pme)).
% 1.49/1.26 thf(f43,plain,(
% 1.49/1.26 ~spl3_1 | spl3_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f26,f38,f34])).
% 1.49/1.26 thf(f26,plain,(
% 1.49/1.26 ((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2))),
% 1.49/1.26 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.49/1.26 thf(f14,plain,(
% 1.49/1.26 ((sK1 @ sK2) = $true) | ((sK1 @ sK2) = $true) | ($true != (sK0 @ sK2)) | ($true != (sK0 @ sK2))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f42,plain,(
% 1.49/1.26 spl3_2 | spl3_1),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f29,f34,f38])).
% 1.49/1.26 thf(f29,plain,(
% 1.49/1.26 ((sK1 @ sK2) = $true) | ($true = (sK0 @ sK2))),
% 1.49/1.26 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.49/1.26 thf(f20,plain,(
% 1.49/1.26 ((sK1 @ sK2) = $true) | ((sK1 @ sK2) = $true) | ($true = (sK0 @ sK2)) | ($true = (sK0 @ sK2))),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 thf(f41,plain,(
% 1.49/1.26 spl3_1 | ~spl3_2),
% 1.49/1.26 inference(avatar_split_clause,[status(thm)],[f30,f38,f34])).
% 1.49/1.26 thf(f30,plain,(
% 1.49/1.26 ((sK1 @ sK2) != $true) | ($true = (sK0 @ sK2))),
% 1.49/1.26 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.49/1.26 thf(f23,plain,(
% 1.49/1.26 ($true = (sK0 @ sK2)) | ($true = (sK0 @ sK2)) | ((sK1 @ sK2) != $true) | ((sK1 @ sK2) != $true)),
% 1.49/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.26 % SZS output end Proof for DTF2THF_23660
% 1.49/1.26 % (23769)------------------------------
% 1.49/1.26 % (23769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (23769)Termination reason: Refutation
% 1.49/1.26
% 1.49/1.26 % (23769)Memory used [KB]: 5500
% 1.49/1.26 % (23769)Time elapsed: 0.004 s
% 1.49/1.26 % (23769)Instructions burned: 1 (million)
% 1.49/1.26 % (23769)------------------------------
% 1.49/1.26 % (23769)------------------------------
% 1.49/1.26 % (23766)Success in time 0.021 s
%------------------------------------------------------------------------------