%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV489^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 09:41:22 AM UTC 2026
% Result : Theorem 0.24s 1.14s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 124 ( 14 ~; 0 |; 0 &; 92 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 4 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 32 ( 7 ^; 21 !; 4 ?; 32 :)
% 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_12,type,
sK1: sK0 > $o ).
thf(func_def_14,type,
sK3: sK0 ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f31,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
$true != $true,
inference(superposition,[status(thm)],[f18,f29]) ).
thf(f29,plain,
( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ 'const/sets/EMPTY' @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK3 @ 'const/sets/EMPTY' @ sK0 )
=> ( sK1 @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0 )
=> ( sK1 @ Y0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $tType,X1: X0 > $o] :
( $true
!= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0 )
=> ( X1 @ Y0 ) ) ) )
=> ( $true
!= ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0 )
=> ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o] :
( $true
!= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0 )
=> ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( $true
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0 )
=> ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 )
=> ( X1 @ X2 ) )
= $true ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X4: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
=> ( X4 @ X1 ) )
= $true ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X4: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
=> ( X4 @ X1 ) )
= $true ),
file('/export/starexec/sandbox2/tmp/tmp.6vwPKWPdM0/DTF2THF_11568.p','thm/sets/FORALL_IN_CLAUSES_0') ).
thf(f18,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.6vwPKWPdM0/DTF2THF_11568.p','thm/sets/NOT_IN_EMPTY_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV489^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n026.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 12:48:10 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
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEV489^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.44 % Domain : Analysis
% 0.17/0.44 % Problem : FORALL_IN_CLAUSES_
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Kal16]
% 0.17/0.44 % Names : FORALL_IN_CLAUSES_0.p [Kal16]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v7.1.0
% 0.17/0.44 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 0 def)
% 0.17/0.44 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 2 ( 3 avg)
% 0.17/0.44 % Number of connectives : 21 ( 1 ~; 1 |; 0 &; 18 @)
% 0.17/0.44 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 7 ( 5 avg)
% 0.17/0.44 % Number of types : 1 ( 0 usr)
% 0.17/0.44 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 5 ( 3 usr; 1 con; 0-4 aty)
% 0.17/0.44 % Number of variables : 12 ( 0 ^; 9 !; 0 ?; 12 :)
% 0.17/0.44 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.44 % SPC : TH1_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : Exported from core HOL Light.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf('thf_const_const/sets/INSERT',type,
% 0.17/0.44 'const/sets/INSERT':
% 0.17/0.44 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/IN',type,
% 0.17/0.44 'const/sets/IN':
% 0.17/0.44 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thf_const_const/sets/EMPTY',type,
% 0.17/0.44 'const/sets/EMPTY':
% 0.17/0.44 !>[A: $tType] : ( A > $o ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/sets/IN_INSERT_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A,A1: A,A2: A > $o] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
% 0.17/0.44 = ( ( A0 = A1 )
% 0.17/0.44 | ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.17/0.44 ! [A: $tType,A0: A] :
% 0.17/0.44 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.17/0.44
% 0.17/0.44 thf('thm/sets/FORALL_IN_CLAUSES_0',conjecture,
% 0.17/0.44 ! [A: $tType,P: A > $o] :
% 0.17/0.44 ( ( ! [A0: A] :
% 0.17/0.44 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
% 0.17/0.44 => ( P @ A0 ) ) )
% 0.17/0.44 = $true ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 0.24/1.12 ---- Embedded in THF ---
% 0.24/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.24/1.12 %%% Generated on Tue Feb 24 12:48:11 EST 2026
% 0.24/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 0.24/1.12 %%% Logic specification used:
% 0.24/1.12 %%% thf(spec, logic, $$dhol).
% 0.24/1.12
% 0.24/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6vwPKWPdM0/DTF2DTF11568.p
% See solution above
% 0.24/1.12 ------------------------
% 0.24/1.13 ---- Cleaned THF ---
% 0.24/1.13 thf('thf_const_const/sets/INSERT',type,
% 0.24/1.13 'const/sets/INSERT':
% 0.24/1.13 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.24/1.13
% 0.24/1.13 thf('thf_const_const/sets/IN',type,
% 0.24/1.13 'const/sets/IN':
% 0.24/1.13 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.24/1.13
% 0.24/1.13 thf('thf_const_const/sets/EMPTY',type,
% 0.24/1.13 'const/sets/EMPTY':
% 0.24/1.13 !>[A: $tType] : ( A > $o ) ).
% 0.24/1.13
% 0.24/1.13 thf('thm/sets/IN_INSERT_',axiom,
% 0.24/1.13 ! [A: $tType,A0: A,A1: A,A2: A > $o] :
% 0.24/1.13 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/INSERT' @ A @ A1 @ A2 ) )
% 0.24/1.13 = ( ( A0 = A1 )
% 0.24/1.13 | ( 'const/sets/IN' @ A @ A0 @ A2 ) ) ) ).
% 0.24/1.13
% 0.24/1.13 thf('thm/sets/NOT_IN_EMPTY_',axiom,
% 0.24/1.13 ! [A: $tType,A0: A] :
% 0.24/1.13 ~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
% 0.24/1.13
% 0.24/1.13 thf('thm/sets/FORALL_IN_CLAUSES_0',conjecture,
% 0.24/1.13 ! [A: $tType,P: A > $o] :
% 0.24/1.13 ( ( ! [A0: A] :
% 0.24/1.13 ( ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) )
% 0.24/1.13 => ( P @ A0 ) ) )
% 0.24/1.13 = $true ) ).
% 0.24/1.13 ------------------------
% 0.24/1.14 % (11669)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11568 for (2999ds/183Mi)
% 0.24/1.14 % (11669)First to succeed.
% 0.24/1.14 % (11669)Refutation found. Thanks to Tanya!
% 0.24/1.14 % SZS status Theorem for DTF2THF_11568
% 0.24/1.14 % SZS output start Proof for DTF2THF_11568
% 0.24/1.14 thf(type_def_6, type, sK0: $tType).
% 0.24/1.14 thf(func_def_0, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 0.24/1.14 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.24/1.14 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 0.24/1.14 thf(func_def_12, type, sK1: sK0 > $o).
% 0.24/1.14 thf(func_def_14, type, sK3: sK0).
% 0.24/1.14 thf(func_def_15, type, ph4: !>[X0: $tType]:(X0)).
% 0.24/1.14 thf(f31,plain,(
% 0.24/1.14 $false),
% 0.24/1.14 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 0.24/1.14 thf(f30,plain,(
% 0.24/1.14 ($true != $true)),
% 0.24/1.14 inference(superposition,[status(thm)],[f18,f29])).
% 0.24/1.14 thf(f29,plain,(
% 0.24/1.14 ($true = ('const/sets/IN' @ sK0 @ sK3 @ 'const/sets/EMPTY' @ sK0))),
% 0.24/1.14 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 0.24/1.14 thf(f27,plain,(
% 0.24/1.14 ((('const/sets/IN' @ sK0 @ sK3 @ 'const/sets/EMPTY' @ sK0) => (sK1 @ sK3)) = $false)),
% 0.24/1.14 inference(beta_eta_normalization,[status(thm)],[f26])).
% 0.24/1.14 thf(f26,plain,(
% 0.24/1.14 ($false = ((^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0) => (sK1 @ Y0))) @ sK3))),
% 0.24/1.14 inference(sigma_clausification,[status(thm)],[f17])).
% 0.24/1.14 thf(f17,plain,(
% 0.24/1.14 ($true != (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0) => (sK1 @ Y0)))))),
% 0.24/1.14 inference(cnf_transformation,[status(thm)],[f15])).
% 0.24/1.14 thf(f15,plain,(
% 0.24/1.14 ($true != (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0) => (sK1 @ Y0)))))),
% 0.24/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 0.24/1.14 thf(f14,plain,(
% 0.24/1.14 ? [X0 : $tType,X1 : X0 > $o] : ($true != (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0) => (X1 @ Y0))))) => ($true != (!! @ sK0 @ (^[Y0 : sK0]: (('const/sets/IN' @ sK0 @ Y0 @ 'const/sets/EMPTY' @ sK0) => (sK1 @ Y0)))))),
% 0.24/1.14 introduced(definition,[],[choice_axiom])).
% 0.24/1.14 thf(f13,plain,(
% 0.24/1.14 ? [X0 : $tType,X1 : X0 > $o] : ($true != (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0) => (X1 @ Y0)))))),
% 0.24/1.14 inference(ennf_transformation,[status(thm)],[f7])).
% 0.24/1.14 thf(f7,plain,(
% 0.24/1.14 ~! [X0 : $tType,X1 : X0 > $o] : ($true = (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ 'const/sets/EMPTY' @ X0) => (X1 @ Y0)))))),
% 0.24/1.14 inference(fool_elimination,[status(thm)],[f6])).
% 0.24/1.14 thf(f6,plain,(
% 0.24/1.14 ~! [X0 : $tType,X1 : X0 > $o] : (! [X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0) => (X1 @ X2)) = $true)),
% 0.24/1.14 inference(rectify,[status(thm)],[f4])).
% 0.24/1.14 thf(f4,negated_conjecture,(
% 0.24/1.14 ~! [X0 : $tType,X4 : X0 > $o] : (! [X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) => (X4 @ X1)) = $true)),
% 0.24/1.14 inference(negated_conjecture,[status(cth)],[f3])).
% 0.24/1.14 thf(f3,conjecture,(
% 0.24/1.14 ! [X0 : $tType,X4 : X0 > $o] : (! [X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) => (X4 @ X1)) = $true)),
% 0.24/1.14 file('/export/starexec/sandbox2/tmp/tmp.6vwPKWPdM0/DTF2THF_11568.p','thm/sets/FORALL_IN_CLAUSES_0')).
% 0.24/1.14 thf(f18,plain,(
% 0.24/1.14 ( ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)) )),
% 0.24/1.14 inference(cnf_transformation,[status(thm)],[f12])).
% 0.24/1.14 thf(f12,plain,(
% 0.24/1.14 ! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) != $true)),
% 0.24/1.14 inference(flattening,[status(thm)],[f9])).
% 0.24/1.14 thf(f9,plain,(
% 0.24/1.14 ! [X0 : $tType,X1 : X0] : ~(('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) = $true)),
% 0.24/1.14 inference(fool_elimination,[status(thm)],[f8])).
% 0.24/1.14 thf(f8,plain,(
% 0.24/1.14 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.24/1.14 inference(rectify,[status(thm)],[f2])).
% 0.24/1.14 thf(f2,axiom,(
% 0.24/1.14 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.24/1.14 file('/export/starexec/sandbox2/tmp/tmp.6vwPKWPdM0/DTF2THF_11568.p','thm/sets/NOT_IN_EMPTY_')).
% 0.24/1.14 % SZS output end Proof for DTF2THF_11568
% 0.24/1.14 % (11669)------------------------------
% 0.24/1.14 % (11669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.24/1.14 % (11669)Termination reason: Refutation
% 0.24/1.14
% 0.24/1.14 % (11669)Memory used [KB]: 5500
% 0.24/1.14 % (11669)Time elapsed: 0.003 s
% 0.24/1.14 % (11669)Instructions burned: 2 (million)
% 0.24/1.14 % (11669)------------------------------
% 0.24/1.14 % (11669)------------------------------
% 0.24/1.14 % (11668)Success in time 0.006 s
%------------------------------------------------------------------------------