%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV235^5 : 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 : n008.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 09:40:37 AM UTC 2026
% Result : Theorem 1.28s 1.17s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 651 ( 178 equ; 0 cnn)
% Maximal formula atoms : 28 ( 10 avg)
% Number of connectives : 538 ( 129 ~; 132 |; 52 &; 195 @)
% ( 13 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 45 !; 23 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cE: $i > $o ).
thf(func_def_1,type,
cD: $i > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: $i > $o ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f43,f48,f57,f65,f66,f67,f68,f69,f71,f72,f77,f82,f83,f88]) ).
thf(f88,plain,
( spl4_1
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_split_clause,[status(thm)],[f87,f59,f54,f28]) ).
thf(f28,definition,
( spl4_1
<=> ( ( cE @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f54,definition,
( spl4_7
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f59,definition,
( spl4_8
<=> ! [X4: $i] :
( ( ( sK0 @ X4 )
!= $true )
| ( $true
= ( cE @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f87,plain,
( ( ( cE @ sK2 )
= $true )
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( cE @ sK2 )
= $true )
| ( $true != $true )
| ~ spl4_7
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f60,f56]) ).
thf(f56,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f60,plain,
( ! [X4: $i] :
( ( ( sK0 @ X4 )
!= $true )
| ( $true
= ( cE @ X4 ) ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f83,plain,
( spl4_4
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f80,f62,f50,f40]) ).
thf(f40,definition,
( spl4_4
<=> ( $true
= ( cD @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f50,definition,
( spl4_6
<=> ( ( sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f62,definition,
( spl4_9
<=> ! [X6: $i] :
( ( $true
!= ( sK0 @ X6 ) )
| ( ( cD @ X6 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( cD @ sK1 ) )
| ~ spl4_6
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
= ( cD @ sK1 ) )
| ( $true != $true )
| ~ spl4_6
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f63,f52]) ).
thf(f52,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f63,plain,
( ! [X6: $i] :
( ( $true
!= ( sK0 @ X6 ) )
| ( ( cD @ X6 )
= $true ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f82,plain,
( spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_split_clause,[status(thm)],[f81,f59,f50,f36]) ).
thf(f36,definition,
( spl4_3
<=> ( $true
= ( cE @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f81,plain,
( ( $true
= ( cE @ sK1 ) )
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true
= ( cE @ sK1 ) )
| ( $true != $true )
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f60,f52]) ).
thf(f77,plain,
( spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f76,f62,f45,f32]) ).
thf(f32,definition,
( spl4_2
<=> ( ( cD @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f45,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f76,plain,
( ( ( cD @ sK3 )
= $true )
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( cD @ sK3 )
= $true )
| ( $true != $true )
| ~ spl4_5
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f63,f47]) ).
thf(f47,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f72,plain,
( spl4_9
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f17,f62,f62]) ).
thf(f17,plain,
! [X6: $i,X4: $i] :
( ( ( cD @ X6 )
= $true )
| ( $true
!= ( sK0 @ X6 ) )
| ( ( sK0 @ X4 )
!= $true )
| ( $true
= ( cD @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( ( $true
!= ( cD @ sK1 ) )
| ( $true
!= ( cE @ sK1 ) ) )
& ( ( sK0 @ sK1 )
= $true ) )
| ( ( ( cE @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( $true
= ( sK0 @ sK3 ) )
& ( ( cD @ sK3 )
!= $true ) ) )
& ( ! [X4: $i] :
( ( ( $true
= ( cD @ X4 ) )
& ( $true
= ( cE @ X4 ) ) )
| ( ( sK0 @ X4 )
!= $true ) )
| ( ! [X5: $i] :
( ( $true
= ( cE @ X5 ) )
| ( ( sK0 @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
!= ( sK0 @ X6 ) )
| ( ( cD @ X6 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( X0 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( X0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( $true
!= ( cD @ X3 ) ) ) )
& ( ! [X4: $i] :
( ( ( $true
= ( cD @ X4 ) )
& ( $true
= ( cE @ X4 ) ) )
| ( ( X0 @ X4 )
!= $true ) )
| ( ! [X5: $i] :
( ( $true
= ( cE @ X5 ) )
| ( $true
!= ( X0 @ X5 ) ) )
& ! [X6: $i] :
( ( ( X0 @ X6 )
!= $true )
| ( ( cD @ X6 )
= $true ) ) ) ) )
=> ( ( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( $true
= ( sK0 @ X1 ) ) )
| ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( sK0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( $true
= ( sK0 @ X3 ) )
& ( $true
!= ( cD @ X3 ) ) ) )
& ( ! [X4: $i] :
( ( ( $true
= ( cD @ X4 ) )
& ( $true
= ( cE @ X4 ) ) )
| ( ( sK0 @ X4 )
!= $true ) )
| ( ! [X5: $i] :
( ( $true
= ( cE @ X5 ) )
| ( ( sK0 @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
!= ( sK0 @ X6 ) )
| ( ( cD @ X6 )
= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( $true
= ( sK0 @ X1 ) ) )
=> ( ( ( $true
!= ( cD @ sK1 ) )
| ( $true
!= ( cE @ sK1 ) ) )
& ( ( sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( sK0 @ X2 )
= $true ) )
=> ( ( ( cE @ sK2 )
!= $true )
& ( $true
= ( sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: $i] :
( ( $true
= ( sK0 @ X3 ) )
& ( $true
!= ( cD @ X3 ) ) )
=> ( ( $true
= ( sK0 @ sK3 ) )
& ( ( cD @ sK3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( X0 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( X0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( $true
!= ( cD @ X3 ) ) ) )
& ( ! [X4: $i] :
( ( ( $true
= ( cD @ X4 ) )
& ( $true
= ( cE @ X4 ) ) )
| ( ( X0 @ X4 )
!= $true ) )
| ( ! [X5: $i] :
( ( $true
= ( cE @ X5 ) )
| ( $true
!= ( X0 @ X5 ) ) )
& ! [X6: $i] :
( ( ( X0 @ X6 )
!= $true )
| ( ( cD @ X6 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( X0 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( X0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( $true
!= ( cD @ X3 ) ) ) )
& ( ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) )
| ( ! [X2: $i] :
( ( $true
= ( cE @ X2 ) )
| ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( $true
= ( cD @ X3 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( ( cD @ X1 )
!= $true )
| ( ( cE @ X1 )
!= $true ) )
& ( ( X0 @ X1 )
= $true ) )
| ? [X2: $i] :
( ( $true
!= ( cE @ X2 ) )
& ( ( X0 @ X2 )
= $true ) )
| ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( $true
!= ( cD @ X3 ) ) ) )
& ( ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) )
| ( ! [X2: $i] :
( ( $true
= ( cE @ X2 ) )
| ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( $true
= ( cD @ X3 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i > $o] :
( ( ! [X2: $i] :
( ( $true
= ( cE @ X2 ) )
| ( ( X0 @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( $true
= ( cD @ X3 ) ) ) )
<~> ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
( ( ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( $true
= ( cE @ X2 ) ) )
& ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( $true
= ( cD @ X3 ) ) ) )
<=> ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
<=> ( ! [X2: $i] :
( ( X0 @ X2 )
=> ( cE @ X2 ) )
& ! [X3: $i] :
( ( X0 @ X3 )
=> ( cD @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
<=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) )
<=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O45nUeoAfW/DTF2THF_12331.p',cTHM46A_pme) ).
thf(f71,plain,
( ~ spl4_1
| spl4_6
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f32,f50,f28]) ).
thf(f21,plain,
( ( ( cE @ sK2 )
!= $true )
| ( ( cD @ sK3 )
!= $true )
| ( ( sK0 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f69,plain,
( spl4_6
| spl4_7
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f32,f54,f50]) ).
thf(f19,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( cD @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f68,plain,
( spl4_7
| ~ spl4_3
| ~ spl4_2
| ~ spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f23,f40,f32,f36,f54]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( cD @ sK3 )
!= $true )
| ( $true
!= ( cE @ sK1 ) )
| ( $true
!= ( cD @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f67,plain,
( ~ spl4_3
| spl4_5
| spl4_7
| ~ spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f40,f54,f45,f36]) ).
thf(f24,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
!= ( cE @ sK1 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( cD @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f66,plain,
( spl4_8
| spl4_8 ),
inference(avatar_split_clause,[status(thm)],[f16,f59,f59]) ).
thf(f16,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cE @ X5 ) )
| ( $true
= ( cE @ X4 ) )
| ( ( sK0 @ X4 )
!= $true )
| ( ( sK0 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f65,plain,
( spl4_5
| ~ spl4_1
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f22,f50,f28,f45]) ).
thf(f22,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( ( cE @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f57,plain,
( spl4_6
| spl4_7
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f20,f45,f54,f50]) ).
thf(f20,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( sK0 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f48,plain,
( spl4_5
| ~ spl4_1
| ~ spl4_4
| ~ spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f26,f36,f40,f28,f45]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( cD @ sK1 ) )
| ( $true
!= ( cE @ sK1 ) )
| ( ( cE @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f43,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f25,f40,f36,f32,f28]) ).
thf(f25,plain,
( ( $true
!= ( cD @ sK1 ) )
| ( ( cE @ sK2 )
!= $true )
| ( ( cD @ sK3 )
!= $true )
| ( $true
!= ( cE @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV235^5 : TPTP v9.2.1. Released v4.0.0.
% 0.09/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:42:24 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.40 ---- Original DTF file ---
% 0.14/0.40 thf(spec,logic,$$dhol).
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 % File : SEV235^5 : TPTP v9.2.1. Released v4.0.0.
% 0.14/0.40 % Domain : Set Theory (Sets of sets)
% 0.14/0.40 % Problem : TPS problem THM46A
% 0.14/0.40 % Version : Especial.
% 0.14/0.40 % English :
% 0.14/0.40
% 0.14/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.14/0.40 % Source : [Bro09]
% 0.14/0.40 % Names : tps_0459 [Bro09]
% 0.14/0.40 % : THM46A [TPS]
% 0.14/0.40
% 0.14/0.40 % Status : Theorem
% 0.14/0.40 % 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 v6.0.0, 0.00 v4.0.0
% 0.14/0.40 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.14/0.40 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.14/0.40 % Maximal formula atoms : 4 ( 4 avg)
% 0.14/0.40 % Number of connectives : 13 ( 0 ~; 0 |; 2 &; 7 @)
% 0.14/0.40 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.14/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.14/0.40 % Number of types : 2 ( 0 usr)
% 0.14/0.40 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.14/0.40 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.14/0.40 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.14/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.14/0.40
% 0.14/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.14/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.14/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.14/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.14/0.40 % : Polymorphic definitions expanded.
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 thf(cE,type,
% 0.14/0.40 cE: $i > $o ).
% 0.14/0.40
% 0.14/0.40 thf(cD,type,
% 0.14/0.40 cD: $i > $o ).
% 0.14/0.40
% 0.14/0.40 thf(cTHM46A_pme,conjecture,
% 0.14/0.40 ! [Xx: $i > $o] :
% 0.14/0.40 ( ! [Xx0: $i] :
% 0.14/0.40 ( ( Xx @ Xx0 )
% 0.14/0.40 => ( ( cD @ Xx0 )
% 0.14/0.40 & ( cE @ Xx0 ) ) )
% 0.14/0.40 <=> ( ! [Xx0: $i] :
% 0.14/0.40 ( ( Xx @ Xx0 )
% 0.14/0.40 => ( cD @ Xx0 ) )
% 0.14/0.40 & ! [Xx0: $i] :
% 0.14/0.40 ( ( Xx @ Xx0 )
% 0.14/0.40 => ( cE @ Xx0 ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 ------------------------
% 1.28/1.15 ---- Embedded in THF ---
% 1.28/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.28/1.15 %%% Generated on Tue Feb 24 12:42:25 EST 2026
% 1.28/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.28/1.15 %%% Logic specification used:
% 1.28/1.15 %%% thf(spec, logic, $$dhol).
% 1.28/1.15
% 1.28/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.O45nUeoAfW/DTF2DTF12331.p
% See solution above
% 1.28/1.15 ------------------------
% 1.28/1.16 ---- Cleaned THF ---
% 1.28/1.16 thf(cE,type,
% 1.28/1.16 cE: $i > $o ).
% 1.28/1.16
% 1.28/1.16 thf(cD,type,
% 1.28/1.16 cD: $i > $o ).
% 1.28/1.16
% 1.28/1.16 thf(cTHM46A_pme,conjecture,
% 1.28/1.16 ! [Xx: $i > $o] :
% 1.28/1.16 ( ! [Xx0: $i] :
% 1.28/1.16 ( ( Xx @ Xx0 )
% 1.28/1.16 => ( ( cD @ Xx0 )
% 1.28/1.16 & ( cE @ Xx0 ) ) )
% 1.28/1.16 <=> ( ! [Xx0: $i] :
% 1.28/1.16 ( ( Xx @ Xx0 )
% 1.28/1.16 => ( cD @ Xx0 ) )
% 1.28/1.16 & ! [Xx0: $i] :
% 1.28/1.16 ( ( Xx @ Xx0 )
% 1.28/1.16 => ( cE @ Xx0 ) ) ) ) ).
% 1.28/1.16 ------------------------
% 1.28/1.17 % (12447)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_12331 for (3000ds/2Mi)
% 1.28/1.17 % (12448)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_12331 for (3000ds/275Mi)
% 1.28/1.17 % (12446)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12331 for (3000ds/2Mi)
% 1.28/1.17 % (12444)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_12331 for (3000ds/4Mi)
% 1.28/1.17 % (12449)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12331 for (3000ds/18Mi)
% 1.28/1.17 % (12445)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_12331 for (3000ds/27Mi)
% 1.28/1.17 % (12446)Instruction limit reached!
% 1.28/1.17 % (12446)------------------------------
% 1.28/1.17 % (12446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.17 % (12446)Termination reason: Unknown
% 1.28/1.17 % (12446)Termination phase: Property scanning
% 1.28/1.17
% 1.28/1.17 % (12446)Memory used [KB]: 895
% 1.28/1.17 % (12446)Time elapsed: 0.002 s
% 1.28/1.17 % (12446)Instructions burned: 2 (million)
% 1.28/1.17 % (12446)------------------------------
% 1.28/1.17 % (12446)------------------------------
% 1.28/1.17 % (12447)Instruction limit reached!
% 1.28/1.17 % (12447)------------------------------
% 1.28/1.17 % (12447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.17 % (12447)Termination reason: Unknown
% 1.28/1.17 % (12447)Termination phase: Saturation
% 1.28/1.17
% 1.28/1.17 % (12447)Memory used [KB]: 895
% 1.28/1.17 % (12447)Time elapsed: 0.002 s
% 1.28/1.17 % (12447)Instructions burned: 2 (million)
% 1.28/1.17 % (12447)------------------------------
% 1.28/1.17 % (12447)------------------------------
% 1.28/1.17 % (12443)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12331 for (3000ds/183Mi)
% 1.28/1.17 % (12445)First to succeed.
% 1.28/1.17 % (12444)Instruction limit reached!
% 1.28/1.17 % (12444)------------------------------
% 1.28/1.17 % (12444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.17 % (12444)Termination reason: Unknown
% 1.28/1.17 % (12444)Termination phase: Saturation
% 1.28/1.17
% 1.28/1.17 % (12444)Memory used [KB]: 5500
% 1.28/1.17 % (12444)Time elapsed: 0.004 s
% 1.28/1.17 % (12444)Instructions burned: 4 (million)
% 1.28/1.17 % (12444)------------------------------
% 1.28/1.17 % (12444)------------------------------
% 1.28/1.17 % (12448)Also succeeded, but the first one will report.
% 1.28/1.17 % (12445)Refutation found. Thanks to Tanya!
% 1.28/1.17 % SZS status Theorem for DTF2THF_12331
% 1.28/1.17 % SZS output start Proof for DTF2THF_12331
% 1.28/1.17 thf(func_def_0, type, cE: $i > $o).
% 1.28/1.17 thf(func_def_1, type, cD: $i > $o).
% 1.28/1.17 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.28/1.17 thf(func_def_6, type, sK0: $i > $o).
% 1.28/1.17 thf(f89,plain,(
% 1.28/1.17 $false),
% 1.28/1.17 inference(avatar_sat_refutation,[status(thm)],[f43,f48,f57,f65,f66,f67,f68,f69,f71,f72,f77,f82,f83,f88])).
% 1.28/1.17 thf(f88,plain,(
% 1.28/1.17 spl4_1 | ~spl4_7 | ~spl4_8),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f87,f59,f54,f28])).
% 1.28/1.17 thf(f28,definition,(
% 1.28/1.17 spl4_1 <=> ((cE @ sK2) = $true)),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.28/1.17 thf(f54,definition,(
% 1.28/1.17 spl4_7 <=> ($true = (sK0 @ sK2))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.28/1.17 thf(f59,definition,(
% 1.28/1.17 spl4_8 <=> ! [X4 : $i] : (((sK0 @ X4) != $true) | ($true = (cE @ X4)))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.28/1.17 thf(f87,plain,(
% 1.28/1.17 ((cE @ sK2) = $true) | (~spl4_7 | ~spl4_8)),
% 1.28/1.17 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.28/1.17 thf(f85,plain,(
% 1.28/1.17 ((cE @ sK2) = $true) | ($true != $true) | (~spl4_7 | ~spl4_8)),
% 1.28/1.17 inference(superposition,[status(thm)],[f60,f56])).
% 1.28/1.17 thf(f56,plain,(
% 1.28/1.17 ($true = (sK0 @ sK2)) | ~spl4_7),
% 1.28/1.17 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.28/1.17 thf(f60,plain,(
% 1.28/1.17 ( ! [X4 : $i] : (((sK0 @ X4) != $true) | ($true = (cE @ X4))) ) | ~spl4_8),
% 1.28/1.17 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.28/1.17 thf(f83,plain,(
% 1.28/1.17 spl4_4 | ~spl4_6 | ~spl4_9),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f80,f62,f50,f40])).
% 1.28/1.17 thf(f40,definition,(
% 1.28/1.17 spl4_4 <=> ($true = (cD @ sK1))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.28/1.17 thf(f50,definition,(
% 1.28/1.17 spl4_6 <=> ((sK0 @ sK1) = $true)),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.28/1.17 thf(f62,definition,(
% 1.28/1.17 spl4_9 <=> ! [X6 : $i] : (($true != (sK0 @ X6)) | ((cD @ X6) = $true))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.28/1.17 thf(f80,plain,(
% 1.28/1.17 ($true = (cD @ sK1)) | (~spl4_6 | ~spl4_9)),
% 1.28/1.17 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.28/1.17 thf(f78,plain,(
% 1.28/1.17 ($true = (cD @ sK1)) | ($true != $true) | (~spl4_6 | ~spl4_9)),
% 1.28/1.17 inference(superposition,[status(thm)],[f63,f52])).
% 1.28/1.17 thf(f52,plain,(
% 1.28/1.17 ((sK0 @ sK1) = $true) | ~spl4_6),
% 1.28/1.17 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.28/1.17 thf(f63,plain,(
% 1.28/1.17 ( ! [X6 : $i] : (($true != (sK0 @ X6)) | ((cD @ X6) = $true)) ) | ~spl4_9),
% 1.28/1.17 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.28/1.17 thf(f82,plain,(
% 1.28/1.17 spl4_3 | ~spl4_6 | ~spl4_8),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f81,f59,f50,f36])).
% 1.28/1.17 thf(f36,definition,(
% 1.28/1.17 spl4_3 <=> ($true = (cE @ sK1))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.28/1.17 thf(f81,plain,(
% 1.28/1.17 ($true = (cE @ sK1)) | (~spl4_6 | ~spl4_8)),
% 1.28/1.17 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.28/1.17 thf(f79,plain,(
% 1.28/1.17 ($true = (cE @ sK1)) | ($true != $true) | (~spl4_6 | ~spl4_8)),
% 1.28/1.17 inference(superposition,[status(thm)],[f60,f52])).
% 1.28/1.17 thf(f77,plain,(
% 1.28/1.17 spl4_2 | ~spl4_5 | ~spl4_9),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f76,f62,f45,f32])).
% 1.28/1.17 thf(f32,definition,(
% 1.28/1.17 spl4_2 <=> ((cD @ sK3) = $true)),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.28/1.17 thf(f45,definition,(
% 1.28/1.17 spl4_5 <=> ($true = (sK0 @ sK3))),
% 1.28/1.17 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.28/1.17 thf(f76,plain,(
% 1.28/1.17 ((cD @ sK3) = $true) | (~spl4_5 | ~spl4_9)),
% 1.28/1.17 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.28/1.17 thf(f75,plain,(
% 1.28/1.17 ((cD @ sK3) = $true) | ($true != $true) | (~spl4_5 | ~spl4_9)),
% 1.28/1.17 inference(superposition,[status(thm)],[f63,f47])).
% 1.28/1.17 thf(f47,plain,(
% 1.28/1.17 ($true = (sK0 @ sK3)) | ~spl4_5),
% 1.28/1.17 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.28/1.17 thf(f72,plain,(
% 1.28/1.17 spl4_9 | spl4_9),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f17,f62,f62])).
% 1.28/1.17 thf(f17,plain,(
% 1.28/1.17 ( ! [X6 : $i,X4 : $i] : (((cD @ X6) = $true) | ($true != (sK0 @ X6)) | ((sK0 @ X4) != $true) | ($true = (cD @ X4))) )),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f14,plain,(
% 1.28/1.17 (((($true != (cD @ sK1)) | ($true != (cE @ sK1))) & ((sK0 @ sK1) = $true)) | (((cE @ sK2) != $true) & ($true = (sK0 @ sK2))) | (($true = (sK0 @ sK3)) & ((cD @ sK3) != $true))) & (! [X4 : $i] : ((($true = (cD @ X4)) & ($true = (cE @ X4))) | ((sK0 @ X4) != $true)) | (! [X5 : $i] : (($true = (cE @ X5)) | ((sK0 @ X5) != $true)) & ! [X6 : $i] : (($true != (sK0 @ X6)) | ((cD @ X6) = $true))))),
% 1.28/1.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f13,f12,f11,f10])).
% 1.28/1.17 thf(f10,plain,(
% 1.28/1.17 ? [X0 : $i > $o] : ((? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ((X0 @ X1) = $true)) | ? [X2 : $i] : (($true != (cE @ X2)) & ((X0 @ X2) = $true)) | ? [X3 : $i] : (((X0 @ X3) = $true) & ($true != (cD @ X3)))) & (! [X4 : $i] : ((($true = (cD @ X4)) & ($true = (cE @ X4))) | ((X0 @ X4) != $true)) | (! [X5 : $i] : (($true = (cE @ X5)) | ($true != (X0 @ X5))) & ! [X6 : $i] : (((X0 @ X6) != $true) | ((cD @ X6) = $true))))) => ((? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ($true = (sK0 @ X1))) | ? [X2 : $i] : (($true != (cE @ X2)) & ((sK0 @ X2) = $true)) | ? [X3 : $i] : (($true = (sK0 @ X3)) & ($true != (cD @ X3)))) & (! [X4 : $i] : ((($true = (cD @ X4)) & ($true = (cE @ X4))) | ((sK0 @ X4) != $true)) | (! [X5 : $i] : (($true = (cE @ X5)) | ((sK0 @ X5) != $true)) & ! [X6 : $i] : (($true != (sK0 @ X6)) | ((cD @ X6) = $true)))))),
% 1.28/1.17 introduced(definition,[],[choice_axiom])).
% 1.28/1.17 thf(f11,plain,(
% 1.28/1.17 ? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ($true = (sK0 @ X1))) => ((($true != (cD @ sK1)) | ($true != (cE @ sK1))) & ((sK0 @ sK1) = $true))),
% 1.28/1.17 introduced(definition,[],[choice_axiom])).
% 1.28/1.17 thf(f12,plain,(
% 1.28/1.17 ? [X2 : $i] : (($true != (cE @ X2)) & ((sK0 @ X2) = $true)) => (((cE @ sK2) != $true) & ($true = (sK0 @ sK2)))),
% 1.28/1.17 introduced(definition,[],[choice_axiom])).
% 1.28/1.17 thf(f13,plain,(
% 1.28/1.17 ? [X3 : $i] : (($true = (sK0 @ X3)) & ($true != (cD @ X3))) => (($true = (sK0 @ sK3)) & ((cD @ sK3) != $true))),
% 1.28/1.17 introduced(definition,[],[choice_axiom])).
% 1.28/1.17 thf(f9,plain,(
% 1.28/1.17 ? [X0 : $i > $o] : ((? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ((X0 @ X1) = $true)) | ? [X2 : $i] : (($true != (cE @ X2)) & ((X0 @ X2) = $true)) | ? [X3 : $i] : (((X0 @ X3) = $true) & ($true != (cD @ X3)))) & (! [X4 : $i] : ((($true = (cD @ X4)) & ($true = (cE @ X4))) | ((X0 @ X4) != $true)) | (! [X5 : $i] : (($true = (cE @ X5)) | ($true != (X0 @ X5))) & ! [X6 : $i] : (((X0 @ X6) != $true) | ((cD @ X6) = $true)))))),
% 1.28/1.17 inference(rectify,[status(thm)],[f8])).
% 1.28/1.17 thf(f8,plain,(
% 1.28/1.17 ? [X0 : $i > $o] : ((? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ((X0 @ X1) = $true)) | ? [X2 : $i] : (($true != (cE @ X2)) & ((X0 @ X2) = $true)) | ? [X3 : $i] : (((X0 @ X3) = $true) & ($true != (cD @ X3)))) & (! [X1 : $i] : ((((cD @ X1) = $true) & ((cE @ X1) = $true)) | ((X0 @ X1) != $true)) | (! [X2 : $i] : (($true = (cE @ X2)) | ((X0 @ X2) != $true)) & ! [X3 : $i] : (((X0 @ X3) != $true) | ($true = (cD @ X3))))))),
% 1.28/1.17 inference(flattening,[status(thm)],[f7])).
% 1.28/1.17 thf(f7,plain,(
% 1.28/1.17 ? [X0 : $i > $o] : ((? [X1 : $i] : ((((cD @ X1) != $true) | ((cE @ X1) != $true)) & ((X0 @ X1) = $true)) | (? [X2 : $i] : (($true != (cE @ X2)) & ((X0 @ X2) = $true)) | ? [X3 : $i] : (((X0 @ X3) = $true) & ($true != (cD @ X3))))) & (! [X1 : $i] : ((((cD @ X1) = $true) & ((cE @ X1) = $true)) | ((X0 @ X1) != $true)) | (! [X2 : $i] : (($true = (cE @ X2)) | ((X0 @ X2) != $true)) & ! [X3 : $i] : (((X0 @ X3) != $true) | ($true = (cD @ X3))))))),
% 1.28/1.17 inference(nnf_transformation,[status(thm)],[f6])).
% 1.28/1.17 thf(f6,plain,(
% 1.28/1.17 ? [X0 : $i > $o] : ((! [X2 : $i] : (($true = (cE @ X2)) | ((X0 @ X2) != $true)) & ! [X3 : $i] : (((X0 @ X3) != $true) | ($true = (cD @ X3)))) <~> ! [X1 : $i] : ((((cD @ X1) = $true) & ((cE @ X1) = $true)) | ((X0 @ X1) != $true)))),
% 1.28/1.17 inference(ennf_transformation,[status(thm)],[f5])).
% 1.28/1.17 thf(f5,plain,(
% 1.28/1.17 ~! [X0 : $i > $o] : ((! [X2 : $i] : (((X0 @ X2) = $true) => ($true = (cE @ X2))) & ! [X3 : $i] : (((X0 @ X3) = $true) => ($true = (cD @ X3)))) <=> ! [X1 : $i] : (((X0 @ X1) = $true) => (((cD @ X1) = $true) & ((cE @ X1) = $true))))),
% 1.28/1.17 inference(fool_elimination,[status(thm)],[f4])).
% 1.28/1.17 thf(f4,plain,(
% 1.28/1.17 ~! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cD @ X1) & (cE @ X1))) <=> (! [X2 : $i] : ((X0 @ X2) => (cE @ X2)) & ! [X3 : $i] : ((X0 @ X3) => (cD @ X3))))),
% 1.28/1.17 inference(rectify,[status(thm)],[f2])).
% 1.28/1.17 thf(f2,negated_conjecture,(
% 1.28/1.17 ~! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cD @ X1) & (cE @ X1))) <=> (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 1.28/1.17 inference(negated_conjecture,[status(cth)],[f1])).
% 1.28/1.17 thf(f1,conjecture,(
% 1.28/1.17 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cD @ X1) & (cE @ X1))) <=> (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 1.28/1.17 file('/export/starexec/sandbox2/tmp/tmp.O45nUeoAfW/DTF2THF_12331.p',cTHM46A_pme)).
% 1.28/1.17 thf(f71,plain,(
% 1.28/1.17 ~spl4_1 | spl4_6 | ~spl4_2),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f21,f32,f50,f28])).
% 1.28/1.17 thf(f21,plain,(
% 1.28/1.17 ((cE @ sK2) != $true) | ((cD @ sK3) != $true) | ((sK0 @ sK1) = $true)),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f69,plain,(
% 1.28/1.17 spl4_6 | spl4_7 | ~spl4_2),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f19,f32,f54,f50])).
% 1.28/1.17 thf(f19,plain,(
% 1.28/1.17 ((sK0 @ sK1) = $true) | ($true = (sK0 @ sK2)) | ((cD @ sK3) != $true)),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f68,plain,(
% 1.28/1.17 spl4_7 | ~spl4_3 | ~spl4_2 | ~spl4_4),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f23,f40,f32,f36,f54])).
% 1.28/1.17 thf(f23,plain,(
% 1.28/1.17 ($true = (sK0 @ sK2)) | ((cD @ sK3) != $true) | ($true != (cE @ sK1)) | ($true != (cD @ sK1))),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f67,plain,(
% 1.28/1.17 ~spl4_3 | spl4_5 | spl4_7 | ~spl4_4),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f24,f40,f54,f45,f36])).
% 1.28/1.17 thf(f24,plain,(
% 1.28/1.17 ($true = (sK0 @ sK2)) | ($true != (cE @ sK1)) | ($true = (sK0 @ sK3)) | ($true != (cD @ sK1))),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f66,plain,(
% 1.28/1.17 spl4_8 | spl4_8),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f16,f59,f59])).
% 1.28/1.17 thf(f16,plain,(
% 1.28/1.17 ( ! [X4 : $i,X5 : $i] : (($true = (cE @ X5)) | ($true = (cE @ X4)) | ((sK0 @ X4) != $true) | ((sK0 @ X5) != $true)) )),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f65,plain,(
% 1.28/1.17 spl4_5 | ~spl4_1 | spl4_6),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f22,f50,f28,f45])).
% 1.28/1.17 thf(f22,plain,(
% 1.28/1.17 ((sK0 @ sK1) = $true) | ($true = (sK0 @ sK3)) | ((cE @ sK2) != $true)),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f57,plain,(
% 1.28/1.17 spl4_6 | spl4_7 | spl4_5),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f20,f45,f54,f50])).
% 1.28/1.17 thf(f20,plain,(
% 1.28/1.17 ($true = (sK0 @ sK3)) | ($true = (sK0 @ sK2)) | ((sK0 @ sK1) = $true)),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f48,plain,(
% 1.28/1.17 spl4_5 | ~spl4_1 | ~spl4_4 | ~spl4_3),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f26,f36,f40,f28,f45])).
% 1.28/1.17 thf(f26,plain,(
% 1.28/1.17 ($true = (sK0 @ sK3)) | ($true != (cD @ sK1)) | ($true != (cE @ sK1)) | ((cE @ sK2) != $true)),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 thf(f43,plain,(
% 1.28/1.17 ~spl4_1 | ~spl4_2 | ~spl4_3 | ~spl4_4),
% 1.28/1.17 inference(avatar_split_clause,[status(thm)],[f25,f40,f36,f32,f28])).
% 1.28/1.17 thf(f25,plain,(
% 1.28/1.17 ($true != (cD @ sK1)) | ((cE @ sK2) != $true) | ((cD @ sK3) != $true) | ($true != (cE @ sK1))),
% 1.28/1.17 inference(cnf_transformation,[status(thm)],[f14])).
% 1.28/1.17 % SZS output end Proof for DTF2THF_12331
% 1.28/1.17 % (12445)------------------------------
% 1.28/1.17 % (12445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.28/1.17 % (12445)Termination reason: Refutation
% 1.28/1.17
% 1.28/1.17 % (12445)Memory used [KB]: 5500
% 1.28/1.17 % (12445)Time elapsed: 0.004 s
% 1.28/1.17 % (12445)Instructions burned: 3 (million)
% 1.28/1.17 % (12445)------------------------------
% 1.28/1.17 % (12445)------------------------------
% 1.28/1.17 % (12441)Success in time 0.012 s
%------------------------------------------------------------------------------