%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET593^5 : 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 : n006.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 09:31:50 AM UTC 2026
% Result : Theorem 1.47s 1.26s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 352 ( 123 equ; 0 cnn)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 376 ( 87 ~; 59 |; 53 &; 148 @)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 37 !; 24 ?; 61 :)
% 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 > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(f63,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f32,f37,f42,f47,f52,f53,f54,f55,f56,f59,f62]) ).
thf(f62,plain,
( spl5_3
| spl5_1
| ~ spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f61,f49,f25,f34]) ).
thf(f34,definition,
( spl5_3
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f25,definition,
( spl5_1
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f49,definition,
( spl5_6
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f61,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ( $true != $true )
| ( $true
= ( sK0 @ sK4 ) )
| ~ spl5_6 ),
inference(superposition,[status(thm)],[f14,f51]) ).
thf(f51,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f14,plain,
! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) )
| ( $true
= ( sK2 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) )
| ( ( $true
!= ( sK0 @ sK4 ) )
& ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK2 @ sK4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ? [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
& ( $true
= ( X1 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
=> ( ( ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( ( sK2 @ X3 )
!= $true )
& ( $true
= ( sK1 @ X3 ) ) )
| ? [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
& ( $true
= ( sK1 @ X4 ) )
& ( $true
!= ( sK2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
& ( ( sK2 @ X3 )
!= $true )
& ( $true
= ( sK1 @ X3 ) ) )
=> ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
& ( $true
= ( sK1 @ X4 ) )
& ( $true
!= ( sK2 @ X4 ) ) )
=> ( ( $true
!= ( sK0 @ sK4 ) )
& ( $true
= ( sK1 @ sK4 ) )
& ( $true
!= ( sK2 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X0 @ X3 )
!= $true )
& ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ? [X4: a] :
( ( $true
!= ( X0 @ X4 ) )
& ( $true
= ( X1 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
& ( $true
!= ( X2 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
& ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ? [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
& ( $true
!= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
& ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) ) )
=> ( ! [X4: a] :
( ( ( $true
!= ( X1 @ X4 ) )
& ( $true
= ( X0 @ X4 ) ) )
=> ( $true
= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
=> ( $true
= ( X1 @ X5 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) ) )
=> ( ! [X4: a] :
( ( ( $true
= ( X0 @ X4 ) )
& ( $true
!= ( X1 @ X4 ) ) )
=> ( $true
= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
& ( $true
!= ( X2 @ X5 ) ) )
=> ( $true
= ( X1 @ X5 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X1 @ X3 )
| ( X2 @ X3 ) ) )
=> ( ! [X4: a] :
( ( ( X0 @ X4 )
& ~ ( X1 @ X4 ) )
=> ( X2 @ X4 ) )
& ! [X5: a] :
( ( ( X0 @ X5 )
& ~ ( X2 @ X5 ) )
=> ( X1 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X1 @ X3 )
| ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( ( X1 @ X3 )
| ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.a7u7xHexrg/DTF2THF_19248.p',cBOOL_PROP_52_pme) ).
thf(f59,plain,
( spl5_2
| spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f58,f44,f39,f29]) ).
thf(f29,definition,
( spl5_2
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f39,definition,
( spl5_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f44,definition,
( spl5_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f58,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f14,f46]) ).
thf(f46,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f56,plain,
( ~ spl5_4
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f34,f39]) ).
thf(f23,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f55,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f16,f49,f44]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f54,plain,
( ~ spl5_1
| spl5_5 ),
inference(avatar_split_clause,[status(thm)],[f15,f44,f25]) ).
thf(f15,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f53,plain,
( spl5_6
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f29,f49]) ).
thf(f19,plain,
( ( $true
!= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f52,plain,
( ~ spl5_4
| spl5_6 ),
inference(avatar_split_clause,[status(thm)],[f22,f49,f39]) ).
thf(f22,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f47,plain,
( spl5_5
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f17,f34,f44]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f42,plain,
( ~ spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f21,f25,f39]) ).
thf(f21,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f37,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f20,f34,f29]) ).
thf(f20,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f32,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f29,f25]) ).
thf(f18,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ( $true
!= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET593^5 : 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
% 0.16/0.33 % Computer : n006.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 11:59:45 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SET593^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : TPS problem BOOL-PROP-52
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : Trybulec's 52nd Boolean property of sets
% 0.18/0.45
% 0.18/0.45 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.45 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0264 [Bro09]
% 0.18/0.45 % : BOOL-PROP-52 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.08 v9.1.0, 0.12 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 v6.2.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.45 % Number of connectives : 19 ( 2 ~; 1 |; 3 &; 9 @)
% 0.18/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.45 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a_type,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(cBOOL_PROP_52_pme,conjecture,
% 0.18/0.45 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.18/0.45 ( ! [Xx: a] :
% 0.18/0.45 ( ( X @ Xx )
% 0.18/0.45 => ( ( Y @ Xx )
% 0.18/0.45 | ( Z @ Xx ) ) )
% 0.18/0.45 => ( ! [Xx: a] :
% 0.18/0.45 ( ( ( X @ Xx )
% 0.18/0.45 & ~ ( Y @ Xx ) )
% 0.18/0.45 => ( Z @ Xx ) )
% 0.18/0.45 & ! [Xx: a] :
% 0.18/0.45 ( ( ( X @ Xx )
% 0.18/0.45 & ~ ( Z @ Xx ) )
% 0.18/0.45 => ( Y @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.47/1.23 ---- Embedded in THF ---
% 1.47/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.24 %%% Generated on Tue Feb 24 11:59:46 EST 2026
% 1.47/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.24 %%% Logic specification used:
% 1.47/1.24 %%% thf(spec, logic, $$dhol).
% 1.47/1.24
% 1.47/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.a7u7xHexrg/DTF2DTF19248.p
% See solution above
% 1.47/1.24 ------------------------
% 1.47/1.24 ---- Cleaned THF ---
% 1.47/1.25 thf(a_type,type,
% 1.47/1.25 a: $tType ).
% 1.47/1.25
% 1.47/1.25 thf(cBOOL_PROP_52_pme,conjecture,
% 1.47/1.25 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.47/1.25 ( ! [Xx: a] :
% 1.47/1.25 ( ( X @ Xx )
% 1.47/1.25 => ( ( Y @ Xx )
% 1.47/1.25 | ( Z @ Xx ) ) )
% 1.47/1.25 => ( ! [Xx: a] :
% 1.47/1.25 ( ( ( X @ Xx )
% 1.47/1.25 & ~ ( Y @ Xx ) )
% 1.47/1.25 => ( Z @ Xx ) )
% 1.47/1.25 & ! [Xx: a] :
% 1.47/1.25 ( ( ( X @ Xx )
% 1.47/1.25 & ~ ( Z @ Xx ) )
% 1.47/1.25 => ( Y @ Xx ) ) ) ) ).
% 1.47/1.25 ------------------------
% 1.47/1.26 % (19576)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_19248 for (2999ds/4Mi)
% 1.47/1.26 % (19577)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_19248 for (2999ds/27Mi)
% 1.47/1.26 % (19577)First to succeed.
% 1.47/1.26 % (19576)Instruction limit reached!
% 1.47/1.26 % (19576)------------------------------
% 1.47/1.26 % (19576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (19576)Termination reason: Unknown
% 1.47/1.26 % (19576)Termination phase: Saturation
% 1.47/1.26
% 1.47/1.26 % (19576)Memory used [KB]: 5500
% 1.47/1.26 % (19576)Time elapsed: 0.004 s
% 1.47/1.26 % (19576)Instructions burned: 6 (million)
% 1.47/1.26 % (19576)------------------------------
% 1.47/1.26 % (19576)------------------------------
% 1.47/1.26 % (19577)Refutation found. Thanks to Tanya!
% 1.47/1.26 % SZS status Theorem for DTF2THF_19248
% 1.47/1.26 % SZS output start Proof for DTF2THF_19248
% 1.47/1.26 thf(type_def_5, type, a: $tType).
% 1.47/1.26 thf(func_def_0, type, a: $tType).
% 1.47/1.26 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.26 thf(func_def_5, type, sK0: a > $o).
% 1.47/1.26 thf(func_def_6, type, sK1: a > $o).
% 1.47/1.26 thf(func_def_7, type, sK2: a > $o).
% 1.47/1.26 thf(func_def_8, type, sK3: a).
% 1.47/1.26 thf(func_def_9, type, sK4: a).
% 1.47/1.26 thf(f63,plain,(
% 1.47/1.26 $false),
% 1.47/1.26 inference(avatar_sat_refutation,[status(thm)],[f32,f37,f42,f47,f52,f53,f54,f55,f56,f59,f62])).
% 1.47/1.26 thf(f62,plain,(
% 1.47/1.26 spl5_3 | spl5_1 | ~spl5_6),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f61,f49,f25,f34])).
% 1.47/1.26 thf(f34,definition,(
% 1.47/1.26 spl5_3 <=> ($true = (sK0 @ sK4))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.47/1.26 thf(f25,definition,(
% 1.47/1.26 spl5_1 <=> ($true = (sK2 @ sK4))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.47/1.26 thf(f49,definition,(
% 1.47/1.26 spl5_6 <=> ($true = (sK1 @ sK4))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.47/1.26 thf(f61,plain,(
% 1.47/1.26 ($true = (sK0 @ sK4)) | ($true = (sK2 @ sK4)) | ~spl5_6),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.47/1.26 thf(f60,plain,(
% 1.47/1.26 ($true = (sK2 @ sK4)) | ($true != $true) | ($true = (sK0 @ sK4)) | ~spl5_6),
% 1.47/1.26 inference(superposition,[status(thm)],[f14,f51])).
% 1.47/1.26 thf(f51,plain,(
% 1.47/1.26 ($true = (sK1 @ sK4)) | ~spl5_6),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.47/1.26 thf(f14,plain,(
% 1.47/1.26 ( ! [X5 : a] : (($true != (sK1 @ X5)) | ($true = (sK0 @ X5)) | ($true = (sK2 @ X5))) )),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f13,plain,(
% 1.47/1.26 ((($true != (sK0 @ sK3)) & ($true != (sK2 @ sK3)) & ($true = (sK1 @ sK3))) | (($true != (sK0 @ sK4)) & ($true = (sK1 @ sK4)) & ($true != (sK2 @ sK4)))) & ! [X5 : a] : (($true = (sK0 @ X5)) | ($true = (sK2 @ X5)) | ($true != (sK1 @ X5)))),
% 1.47/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f12,f11,f10])).
% 1.47/1.26 thf(f10,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) != $true) & ((X2 @ X3) != $true) & ((X1 @ X3) = $true)) | ? [X4 : a] : (($true != (X0 @ X4)) & ($true = (X1 @ X4)) & ($true != (X2 @ X4)))) & ! [X5 : a] : (($true = (X0 @ X5)) | ($true = (X2 @ X5)) | ($true != (X1 @ X5)))) => ((? [X3 : a] : (($true != (sK0 @ X3)) & ((sK2 @ X3) != $true) & ($true = (sK1 @ X3))) | ? [X4 : a] : (($true != (sK0 @ X4)) & ($true = (sK1 @ X4)) & ($true != (sK2 @ X4)))) & ! [X5 : a] : (($true = (sK0 @ X5)) | ($true = (sK2 @ X5)) | ($true != (sK1 @ X5))))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f11,plain,(
% 1.47/1.26 ? [X3 : a] : (($true != (sK0 @ X3)) & ((sK2 @ X3) != $true) & ($true = (sK1 @ X3))) => (($true != (sK0 @ sK3)) & ($true != (sK2 @ sK3)) & ($true = (sK1 @ sK3)))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f12,plain,(
% 1.47/1.26 ? [X4 : a] : (($true != (sK0 @ X4)) & ($true = (sK1 @ X4)) & ($true != (sK2 @ X4))) => (($true != (sK0 @ sK4)) & ($true = (sK1 @ sK4)) & ($true != (sK2 @ sK4)))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f9,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((? [X3 : a] : (((X0 @ X3) != $true) & ((X2 @ X3) != $true) & ((X1 @ X3) = $true)) | ? [X4 : a] : (($true != (X0 @ X4)) & ($true = (X1 @ X4)) & ($true != (X2 @ X4)))) & ! [X5 : a] : (($true = (X0 @ X5)) | ($true = (X2 @ X5)) | ($true != (X1 @ X5))))),
% 1.47/1.26 inference(rectify,[status(thm)],[f8])).
% 1.47/1.26 thf(f8,plain,(
% 1.47/1.26 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((? [X4 : a] : (($true != (X1 @ X4)) & ($true != (X2 @ X4)) & ($true = (X0 @ X4))) | ? [X5 : a] : (($true != (X1 @ X5)) & ($true = (X0 @ X5)) & ($true != (X2 @ X5)))) & ! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) = $true) | ((X0 @ X3) != $true)))),
% 1.47/1.26 inference(flattening,[status(thm)],[f7])).
% 1.47/1.26 thf(f7,plain,(
% 1.47/1.26 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((? [X4 : a] : (($true != (X2 @ X4)) & (($true != (X1 @ X4)) & ($true = (X0 @ X4)))) | ? [X5 : a] : (($true != (X1 @ X5)) & (($true = (X0 @ X5)) & ($true != (X2 @ X5))))) & ! [X3 : a] : ((((X1 @ X3) = $true) | ((X2 @ X3) = $true)) | ((X0 @ X3) != $true)))),
% 1.47/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.26 thf(f6,plain,(
% 1.47/1.26 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) => (((X1 @ X3) = $true) | ((X2 @ X3) = $true))) => (! [X4 : a] : ((($true != (X1 @ X4)) & ($true = (X0 @ X4))) => ($true = (X2 @ X4))) & ! [X5 : a] : ((($true = (X0 @ X5)) & ($true != (X2 @ X5))) => ($true = (X1 @ X5)))))),
% 1.47/1.26 inference(flattening,[status(thm)],[f5])).
% 1.47/1.26 thf(f5,plain,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X0 @ X3) = $true) => (((X1 @ X3) = $true) | ((X2 @ X3) = $true))) => (! [X4 : a] : ((($true = (X0 @ X4)) & ~($true = (X1 @ X4))) => ($true = (X2 @ X4))) & ! [X5 : a] : ((($true = (X0 @ X5)) & ~($true = (X2 @ X5))) => ($true = (X1 @ X5)))))),
% 1.47/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.26 thf(f4,plain,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((X0 @ X3) => ((X1 @ X3) | (X2 @ X3))) => (! [X4 : a] : (((X0 @ X4) & ~(X1 @ X4)) => (X2 @ X4)) & ! [X5 : a] : (((X0 @ X5) & ~(X2 @ X5)) => (X1 @ X5))))),
% 1.47/1.26 inference(rectify,[status(thm)],[f2])).
% 1.47/1.26 thf(f2,negated_conjecture,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((X0 @ X3) => ((X1 @ X3) | (X2 @ X3))) => (! [X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) => (X2 @ X3)) & ! [X3 : a] : (((X0 @ X3) & ~(X2 @ X3)) => (X1 @ X3))))),
% 1.47/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.26 thf(f1,conjecture,(
% 1.47/1.26 ! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : ((X0 @ X3) => ((X1 @ X3) | (X2 @ X3))) => (! [X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) => (X2 @ X3)) & ! [X3 : a] : (((X0 @ X3) & ~(X2 @ X3)) => (X1 @ X3))))),
% 1.47/1.26 file('/export/starexec/sandbox/tmp/tmp.a7u7xHexrg/DTF2THF_19248.p',cBOOL_PROP_52_pme)).
% 1.47/1.26 thf(f59,plain,(
% 1.47/1.26 spl5_2 | spl5_4 | ~spl5_5),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f58,f44,f39,f29])).
% 1.47/1.26 thf(f29,definition,(
% 1.47/1.26 spl5_2 <=> ($true = (sK2 @ sK3))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.47/1.26 thf(f39,definition,(
% 1.47/1.26 spl5_4 <=> ($true = (sK0 @ sK3))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.47/1.26 thf(f44,definition,(
% 1.47/1.26 spl5_5 <=> ($true = (sK1 @ sK3))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.47/1.26 thf(f58,plain,(
% 1.47/1.26 ($true = (sK2 @ sK3)) | ($true = (sK0 @ sK3)) | ~spl5_5),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.47/1.26 thf(f57,plain,(
% 1.47/1.26 ($true != $true) | ($true = (sK0 @ sK3)) | ($true = (sK2 @ sK3)) | ~spl5_5),
% 1.47/1.26 inference(superposition,[status(thm)],[f14,f46])).
% 1.47/1.26 thf(f46,plain,(
% 1.47/1.26 ($true = (sK1 @ sK3)) | ~spl5_5),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.47/1.26 thf(f56,plain,(
% 1.47/1.26 ~spl5_4 | ~spl5_3),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f23,f34,f39])).
% 1.47/1.26 thf(f23,plain,(
% 1.47/1.26 ($true != (sK0 @ sK4)) | ($true != (sK0 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f55,plain,(
% 1.47/1.26 spl5_5 | spl5_6),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f16,f49,f44])).
% 1.47/1.26 thf(f16,plain,(
% 1.47/1.26 ($true = (sK1 @ sK4)) | ($true = (sK1 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f54,plain,(
% 1.47/1.26 ~spl5_1 | spl5_5),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f15,f44,f25])).
% 1.47/1.26 thf(f15,plain,(
% 1.47/1.26 ($true != (sK2 @ sK4)) | ($true = (sK1 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f53,plain,(
% 1.47/1.26 spl5_6 | ~spl5_2),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f19,f29,f49])).
% 1.47/1.26 thf(f19,plain,(
% 1.47/1.26 ($true != (sK2 @ sK3)) | ($true = (sK1 @ sK4))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f52,plain,(
% 1.47/1.26 ~spl5_4 | spl5_6),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f22,f49,f39])).
% 1.47/1.26 thf(f22,plain,(
% 1.47/1.26 ($true = (sK1 @ sK4)) | ($true != (sK0 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f47,plain,(
% 1.47/1.26 spl5_5 | ~spl5_3),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f17,f34,f44])).
% 1.47/1.26 thf(f17,plain,(
% 1.47/1.26 ($true = (sK1 @ sK3)) | ($true != (sK0 @ sK4))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f42,plain,(
% 1.47/1.26 ~spl5_4 | ~spl5_1),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f21,f25,f39])).
% 1.47/1.26 thf(f21,plain,(
% 1.47/1.26 ($true != (sK2 @ sK4)) | ($true != (sK0 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f37,plain,(
% 1.47/1.26 ~spl5_2 | ~spl5_3),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f20,f34,f29])).
% 1.47/1.26 thf(f20,plain,(
% 1.47/1.26 ($true != (sK0 @ sK4)) | ($true != (sK2 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 thf(f32,plain,(
% 1.47/1.26 ~spl5_1 | ~spl5_2),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f18,f29,f25])).
% 1.47/1.26 thf(f18,plain,(
% 1.47/1.26 ($true != (sK2 @ sK4)) | ($true != (sK2 @ sK3))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f13])).
% 1.47/1.26 % SZS output end Proof for DTF2THF_19248
% 1.47/1.26 % (19577)------------------------------
% 1.47/1.26 % (19577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (19577)Termination reason: Refutation
% 1.47/1.26
% 1.47/1.26 % (19577)Memory used [KB]: 5500
% 1.47/1.26 % (19577)Time elapsed: 0.003 s
% 1.47/1.26 % (19577)Instructions burned: 2 (million)
% 1.47/1.26 % (19577)------------------------------
% 1.47/1.26 % (19577)------------------------------
% 1.47/1.26 % (19574)Success in time 0.014 s
%------------------------------------------------------------------------------