%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV446^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:41:15 AM UTC 2026
% Result : Theorem 1.56s 1.37s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 232 ( 69 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 340 ( 41 ~; 43 |; 8 &; 242 @)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 59 ( 0 ^; 50 !; 9 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
sK1: sK0 ).
thf(func_def_7,type,
sK2: sK0 ).
thf(func_def_9,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f45,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f34,f39,f44]) ).
thf(f44,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f42,f21]) ).
thf(f21,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f42,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f41,f32]) ).
thf(f32,plain,
( ( sK1 != sK2 )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl3_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f41,plain,
( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f18,f27]) ).
thf(f27,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_1
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f18,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
!= $true )
| ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( X1 != X2 )
& ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( X1 != X2 )
& ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
!= $true ) ) )
& ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
<=> ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/IN_INSERT_') ).
thf(f39,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(subsumption_resolution,[status(thm)],[f35,f24]) ).
thf(f24,plain,
! [X0: $tType,X2: X0,X3: X0 > $o] :
( $true
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= $true )
| ( X1 != X2 ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f35,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) ) )
| spl3_1
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f28,f31]) ).
thf(f31,plain,
( ( sK1 = sK2 )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f28,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f34,plain,
( spl3_2
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f22,f26,f30]) ).
thf(f22,plain,
( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK1 != sK2 )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) )
& ( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).
thf(f16,plain,
( ? [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
!= $true ) )
& ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true ) ) )
=> ( ( ( sK1 != sK2 )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) )
& ( ( sK1 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
? [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
!= $true ) )
& ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
? [X0: $tType,X1: X0,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true )
<~> ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true )
<=> ( X1 = X2 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/IN_SING_') ).
thf(f33,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f30,f26]) ).
thf(f23,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) ) )
| ( sK1 != sK2 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV446^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n015.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 12:47:16 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SEV446^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.39 % Domain : Analysis
% 0.17/0.39 % Problem : IN_SING
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Kal16]
% 0.17/0.39 % Names : IN_SING_.p [Kal16]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v7.1.0
% 0.17/0.39 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 0 def)
% 0.17/0.39 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 2 ( 4 avg)
% 0.17/0.39 % Number of connectives : 22 ( 1 ~; 1 |; 0 &; 20 @)
% 0.17/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 7 ( 5 avg)
% 0.17/0.39 % Number of types : 1 ( 0 usr)
% 0.17/0.39 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% 0.17/0.39 % Number of variables : 12 ( 0 ^; 9 !; 0 ?; 12 :)
% 0.17/0.39 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.39 % SPC : TH1_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : Exported from core HOL Light.
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf('thf_const_const/sets/INSERT',type,
% 0.17/0.39 'const/sets/INSERT':
% 0.17/0.39 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/IN',type,
% 0.17/0.39 'const/sets/IN':
% 0.17/0.39 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thf_const_const/sets/EMPTY',type,
% 0.17/0.39 'const/sets/EMPTY':
% 0.17/0.39 !>[A: $tType] : ( A > $o ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.17/0.39 ! [A: $tType,A0: A] :
% 0.17/0.39 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/IN_INSERT_',axiom,
% 0.17/0.39 ! [A: $tType,A0: A,A1: A,A2: A > $o] :
% 0.17/0.39 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
% 0.17/0.39 = ( ( A0 = A1 )
% 0.17/0.39 | ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf('thm/sets/IN_SING_',conjecture,
% 0.17/0.39 ! [A: $tType,A0: A,A1: A] :
% 0.17/0.39 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ ( 'const/sets/EMPTY' @ A ) ) )
% 0.17/0.39 = ( A0 = A1 ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.56/1.33 ---- Embedded in THF ---
% 1.56/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.34 %%% Generated on Tue Feb 24 12:47:17 EST 2026
% 1.56/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.34 %%% Logic specification used:
% 1.56/1.34 %%% thf(spec, logic, $$dhol).
% 1.56/1.34
% 1.56/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2DTF4301.p
% See solution above
% 1.56/1.34 ------------------------
% 1.56/1.35 ---- Cleaned THF ---
% 1.56/1.35 thf('thf_const_const/sets/INSERT',type,
% 1.56/1.35 'const/sets/INSERT':
% 1.56/1.35 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.56/1.35
% 1.56/1.35 thf('thf_const_const/sets/IN',type,
% 1.56/1.35 'const/sets/IN':
% 1.56/1.35 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.56/1.35
% 1.56/1.35 thf('thf_const_const/sets/EMPTY',type,
% 1.56/1.35 'const/sets/EMPTY':
% 1.56/1.35 !>[A: $tType] : ( A > $o ) ).
% 1.56/1.35
% 1.56/1.35 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 1.56/1.35 ! [A: $tType,A0: A] :
% 1.56/1.35 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 1.56/1.35
% 1.56/1.35 thf('thm/sets/IN_INSERT_',axiom,
% 1.56/1.35 ! [A: $tType,A0: A,A1: A,A2: A > $o] :
% 1.56/1.35 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
% 1.56/1.35 = ( ( A0 = A1 )
% 1.56/1.35 | ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) ).
% 1.56/1.35
% 1.56/1.35 thf('thm/sets/IN_SING_',conjecture,
% 1.56/1.35 ! [A: $tType,A0: A,A1: A] :
% 1.56/1.35 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ ( 'const/sets/EMPTY' @ A ) ) )
% 1.56/1.35 = ( A0 = A1 ) ) ).
% 1.56/1.35 ------------------------
% 1.56/1.37 % (4402)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4301 for (2999ds/2Mi)
% 1.56/1.37 % (4400)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_4301 for (2999ds/4Mi)
% 1.56/1.37 % (4403)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_4301 for (2999ds/2Mi)
% 1.56/1.37 % (4404)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_4301 for (2999ds/275Mi)
% 1.56/1.37 % (4401)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_4301 for (2999ds/27Mi)
% 1.56/1.37 % (4399)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4301 for (2999ds/183Mi)
% 1.56/1.37 % (4405)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4301 for (2999ds/18Mi)
% 1.56/1.37 % Exception at run slice level
% 1.56/1.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.56/1.37 % (4402)Instruction limit reached!
% 1.56/1.37 % (4402)------------------------------
% 1.56/1.37 % (4402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (4402)Termination reason: Unknown
% 1.56/1.37 % (4402)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (4402)Memory used [KB]: 5373
% 1.56/1.37 % (4402)Time elapsed: 0.003 s
% 1.56/1.37 % (4402)Instructions burned: 2 (million)
% 1.56/1.37 % (4402)------------------------------
% 1.56/1.37 % (4402)------------------------------
% 1.56/1.37 % (4404)First to succeed.
% 1.56/1.37 % (4400)Instruction limit reached!
% 1.56/1.37 % (4400)------------------------------
% 1.56/1.37 % (4400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (4400)Termination reason: Unknown
% 1.56/1.37 % (4400)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (4400)Memory used [KB]: 5500
% 1.56/1.37 % (4400)Time elapsed: 0.005 s
% 1.56/1.37 % (4400)Instructions burned: 5 (million)
% 1.56/1.37 % (4400)------------------------------
% 1.56/1.37 % (4400)------------------------------
% 1.56/1.37 % (4404)Refutation found. Thanks to Tanya!
% 1.56/1.37 % SZS status Theorem for DTF2THF_4301
% 1.56/1.37 % SZS output start Proof for DTF2THF_4301
% 1.56/1.37 thf(type_def_6, type, sK0: $tType).
% 1.56/1.37 thf(func_def_0, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.56/1.37 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.56/1.37 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.56/1.37 thf(func_def_6, type, sK1: sK0).
% 1.56/1.37 thf(func_def_7, type, sK2: sK0).
% 1.56/1.37 thf(func_def_9, type, ph4: !>[X0: $tType]:(X0)).
% 1.56/1.37 thf(f45,plain,(
% 1.56/1.37 $false),
% 1.56/1.37 inference(avatar_sat_refutation,[status(thm)],[f33,f34,f39,f44])).
% 1.56/1.37 thf(f44,plain,(
% 1.56/1.37 ~spl3_1 | spl3_2),
% 1.56/1.37 inference(avatar_contradiction_clause,[status(thm)],[f43])).
% 1.56/1.37 thf(f43,plain,(
% 1.56/1.37 $false | (~spl3_1 | spl3_2)),
% 1.56/1.37 inference(subsumption_resolution,[status(thm)],[f42,f21])).
% 1.56/1.37 thf(f21,plain,(
% 1.56/1.37 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)) )),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.56/1.37 thf(f11,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 1.56/1.37 inference(flattening,[status(thm)],[f8])).
% 1.56/1.37 thf(f8,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0] : ~(('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.37 thf(f7,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 1.56/1.37 inference(rectify,[status(thm)],[f1])).
% 1.56/1.37 thf(f1,axiom,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 1.56/1.37 file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/NOT_IN_EMPTY_')).
% 1.56/1.37 thf(f42,plain,(
% 1.56/1.37 ($true = ('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0)) | (~spl3_1 | spl3_2)),
% 1.56/1.37 inference(subsumption_resolution,[status(thm)],[f41,f32])).
% 1.56/1.37 thf(f32,plain,(
% 1.56/1.37 (sK1 != sK2) | spl3_2),
% 1.56/1.37 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.56/1.37 thf(f30,definition,(
% 1.56/1.37 spl3_2 <=> (sK1 = sK2)),
% 1.56/1.37 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.56/1.37 thf(f41,plain,(
% 1.56/1.37 (sK1 = sK2) | ($true = ('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0)) | ~spl3_1),
% 1.56/1.37 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.56/1.37 thf(f40,plain,(
% 1.56/1.37 ($true != $true) | (sK1 = sK2) | ($true = ('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0)) | ~spl3_1),
% 1.56/1.37 inference(superposition,[status(thm)],[f18,f27])).
% 1.56/1.37 thf(f27,plain,(
% 1.56/1.37 ($true = ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0))) | ~spl3_1),
% 1.56/1.37 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.56/1.37 thf(f26,definition,(
% 1.56/1.37 spl3_1 <=> ($true = ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0)))),
% 1.56/1.37 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.56/1.37 thf(f18,plain,(
% 1.56/1.37 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) != $true) | (X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ X3) = $true)) )),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.37 thf(f14,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : (((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) = $true) | ((X1 != X2) & (('const/sets/IN' @ X0 @ X1 @ X3) != $true))) & ((X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ X3) = $true) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) != $true)))),
% 1.56/1.37 inference(flattening,[status(thm)],[f13])).
% 1.56/1.37 thf(f13,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : (((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) = $true) | ((X1 != X2) & (('const/sets/IN' @ X0 @ X1 @ X3) != $true))) & (((X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ X3) = $true)) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) != $true)))),
% 1.56/1.37 inference(nnf_transformation,[status(thm)],[f10])).
% 1.56/1.37 thf(f10,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) = $true) <=> ((X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ X3) = $true)))),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.56/1.37 thf(f9,plain,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((X1 = X2) | ('const/sets/IN' @ X0 @ X1 @ X3) = ('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)))),
% 1.56/1.37 inference(rectify,[status(thm)],[f2])).
% 1.56/1.37 thf(f2,axiom,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((X1 = X2) | ('const/sets/IN' @ X0 @ X1 @ X3) = ('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)))),
% 1.56/1.37 file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/IN_INSERT_')).
% 1.56/1.37 thf(f39,plain,(
% 1.56/1.37 spl3_1 | ~spl3_2),
% 1.56/1.37 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.56/1.37 thf(f38,plain,(
% 1.56/1.37 $false | (spl3_1 | ~spl3_2)),
% 1.56/1.37 inference(subsumption_resolution,[status(thm)],[f35,f24])).
% 1.56/1.37 thf(f24,plain,(
% 1.56/1.37 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o] : (($true = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)))) )),
% 1.56/1.37 inference(equality_resolution,[status(thm)],[f20])).
% 1.56/1.37 thf(f20,plain,(
% 1.56/1.37 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ X3)) = $true) | (X1 != X2)) )),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.56/1.37 thf(f35,plain,(
% 1.56/1.37 ($true != ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0))) | (spl3_1 | ~spl3_2)),
% 1.56/1.37 inference(superposition,[status(thm)],[f28,f31])).
% 1.56/1.37 thf(f31,plain,(
% 1.56/1.37 (sK1 = sK2) | ~spl3_2),
% 1.56/1.37 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.56/1.37 thf(f28,plain,(
% 1.56/1.37 ($true != ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0))) | spl3_1),
% 1.56/1.37 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.56/1.37 thf(f34,plain,(
% 1.56/1.37 spl3_2 | spl3_1),
% 1.56/1.37 inference(avatar_split_clause,[status(thm)],[f22,f26,f30])).
% 1.56/1.37 thf(f22,plain,(
% 1.56/1.37 (sK1 = sK2) | ($true = ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0)))),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.37 thf(f17,plain,(
% 1.56/1.37 ((sK1 != sK2) | ($true != ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0)))) & ((sK1 = sK2) | ($true = ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0))))),
% 1.56/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16])).
% 1.56/1.37 thf(f16,plain,(
% 1.56/1.37 ? [X0 : $tType,X1 : X0,X2 : X0] : (((X1 != X2) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) != $true)) & ((X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) = $true))) => (((sK1 != sK2) | ($true != ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0)))) & ((sK1 = sK2) | ($true = ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0)))))),
% 1.56/1.37 introduced(definition,[],[choice_axiom])).
% 1.56/1.37 thf(f15,plain,(
% 1.56/1.37 ? [X0 : $tType,X1 : X0,X2 : X0] : (((X1 != X2) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) != $true)) & ((X1 = X2) | (('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) = $true)))),
% 1.56/1.37 inference(nnf_transformation,[status(thm)],[f12])).
% 1.56/1.37 thf(f12,plain,(
% 1.56/1.37 ? [X0 : $tType,X1 : X0,X2 : X0] : ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) = $true) <~> (X1 = X2))),
% 1.56/1.37 inference(ennf_transformation,[status(thm)],[f6])).
% 1.56/1.37 thf(f6,plain,(
% 1.56/1.37 ~! [X0 : $tType,X1 : X0,X2 : X0] : ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)) = $true) <=> (X1 = X2))),
% 1.56/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.37 thf(f4,negated_conjecture,(
% 1.56/1.37 ~! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) = ('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)))),
% 1.56/1.37 inference(negated_conjecture,[status(cth)],[f3])).
% 1.56/1.37 thf(f3,conjecture,(
% 1.56/1.37 ! [X0 : $tType,X1 : X0,X2 : X0] : ((X1 = X2) = ('const/sets/IN' @ X0 @ X1 @ ('const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0)))),
% 1.56/1.37 file('/export/starexec/sandbox/tmp/tmp.fT3XnE4lQW/DTF2THF_4301.p','thm/sets/IN_SING_')).
% 1.56/1.37 thf(f33,plain,(
% 1.56/1.37 ~spl3_1 | ~spl3_2),
% 1.56/1.37 inference(avatar_split_clause,[status(thm)],[f23,f30,f26])).
% 1.56/1.37 thf(f23,plain,(
% 1.56/1.37 ($true != ('const/sets/IN' @ sK0 @ sK1 @ ('const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0))) | (sK1 != sK2)),
% 1.56/1.37 inference(cnf_transformation,[status(thm)],[f17])).
% 1.56/1.37 % SZS output end Proof for DTF2THF_4301
% 1.56/1.37 % (4404)------------------------------
% 1.56/1.37 % (4404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (4404)Termination reason: Refutation
% 1.56/1.37
% 1.56/1.37 % (4404)Memory used [KB]: 5500
% 1.56/1.37 % (4404)Time elapsed: 0.005 s
% 1.56/1.37 % (4404)Instructions burned: 4 (million)
% 1.56/1.37 % (4404)------------------------------
% 1.56/1.37 % (4404)------------------------------
% 1.56/1.37 % (4398)Success in time 0.019 s
%------------------------------------------------------------------------------