%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV445^1 : 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 : n024.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 0.83s 0.89s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 73 ( 10 ~; 2 |; 0 &; 60 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 6 ^; 23 !; 4 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNIV':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
sK1: sK0 ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ^ [Y0: sK0] : $true
@ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: sK0] : $true
@ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f16,f17]) ).
thf(f17,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( $false
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/IN_') ).
thf(f16,plain,
( $true
!= ( 'const/sets/IN' @ sK0 @ sK1
@ ^ [Y0: sK0] : $true ) ),
inference(definition_unfolding,[status(thm)],[f14,f13]) ).
thf(f13,plain,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [Y0: X0] : $true ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [Y0: X0] : $true ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/sets/UNIV'
@ ( X0
= ( ^ [X1: X0] : $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/UNIV_') ).
thf(f14,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
!= $true )
=> ( ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0] : ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/IN_UNIV_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV445^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:46:55 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEV445^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.32 % Domain : Analysis
% 0.07/0.32 % Problem : IN_UNIV
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Kal16]
% 0.07/0.32 % Names : IN_UNIV_.p [Kal16]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.07/0.32 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 1 def)
% 0.07/0.32 % Number of atoms : 7 ( 2 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 2 ( 2 avg)
% 0.07/0.32 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 9 @)
% 0.07/0.32 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 6 ( 4 avg)
% 0.07/0.32 % Number of types : 1 ( 0 usr)
% 0.07/0.32 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 4 ( 2 usr; 1 con; 0-3 aty)
% 0.07/0.32 % Number of variables : 9 ( 1 ^; 6 !; 0 ?; 9 :)
% 0.07/0.32 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.32 % SPC : TH1_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : Exported from core HOL Light.
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf('thf_const_const/sets/UNIV',type,
% 0.07/0.32 'const/sets/UNIV':
% 0.07/0.32 !>[A: $tType] : ( A > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf('thf_const_const/sets/IN',type,
% 0.07/0.32 'const/sets/IN':
% 0.07/0.32 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf('thm/sets/UNIV_',definition,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( 'const/sets/UNIV' @ A )
% 0.07/0.32 = ( ^ [A0: A] : $true ) ) ).
% 0.07/0.32
% 0.07/0.32 thf('thm/sets/IN_',axiom,
% 0.07/0.32 ! [A: $tType,P: A > $o,A0: A] :
% 0.07/0.32 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.07/0.32 = ( P @ A0 ) ) ).
% 0.07/0.32
% 0.07/0.32 thf('thm/sets/IN_UNIV_',conjecture,
% 0.07/0.32 ! [A: $tType,A0: A] : ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.83/0.87 ---- Embedded in THF ---
% 0.83/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.87 %%% Generated on Tue Feb 24 07:46:56 EST 2026
% 0.83/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.87 %%% Logic specification used:
% 0.83/0.87 %%% thf(spec, logic, $$dhol).
% 0.83/0.87
% 0.83/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2DTF23475.p
% See solution above
% 0.83/0.87 ------------------------
% 0.83/0.88 ---- Cleaned THF ---
% 0.83/0.88 thf('thf_const_const/sets/UNIV',type,
% 0.83/0.88 'const/sets/UNIV':
% 0.83/0.88 !>[A: $tType] : ( A > $o ) ).
% 0.83/0.88
% 0.83/0.88 thf('thf_const_const/sets/IN',type,
% 0.83/0.88 'const/sets/IN':
% 0.83/0.88 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.83/0.88
% 0.83/0.88 thf('thm/sets/UNIV_',definition,
% 0.83/0.88 ! [A: $tType] :
% 0.83/0.88 ( ( 'const/sets/UNIV' @ A )
% 0.83/0.88 = ( ^ [A0: A] : $true ) ) ).
% 0.83/0.88
% 0.83/0.88 thf('thm/sets/IN_',axiom,
% 0.83/0.88 ! [A: $tType,P: A > $o,A0: A] :
% 0.83/0.88 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.83/0.88 = ( P @ A0 ) ) ).
% 0.83/0.88
% 0.83/0.88 thf('thm/sets/IN_UNIV_',conjecture,
% 0.83/0.88 ! [A: $tType,A0: A] : ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) ).
% 0.83/0.88 ------------------------
% 0.83/0.89 % (23736)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23475 for (3000ds/183Mi)
% 0.83/0.89 % (23737)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_23475 for (3000ds/4Mi)
% 0.83/0.89 % (23738)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_23475 for (3000ds/27Mi)
% 0.83/0.89 % (23739)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23475 for (3000ds/2Mi)
% 0.83/0.89 % (23740)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_23475 for (3000ds/2Mi)
% 0.83/0.89 % (23741)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_23475 for (3000ds/275Mi)
% 0.83/0.89 % (23742)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23475 for (3000ds/18Mi)
% 0.83/0.89 % Exception at run slice level
% 0.83/0.89 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
% 0.83/0.89 % (23741)Refutation not found, incomplete strategy
% 0.83/0.89 % (23741)------------------------------
% 0.83/0.89 % (23741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (23741)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.89
% 0.83/0.89
% 0.83/0.89 % (23741)Memory used [KB]: 5500
% 0.83/0.89 % (23741)Time elapsed: 0.001 s
% 0.83/0.89 % (23741)Instructions burned: 1 (million)
% 0.83/0.89 % (23741)------------------------------
% 0.83/0.89 % (23741)------------------------------
% 0.83/0.89 % (23739)First to succeed.
% 0.83/0.89 % (23738)Also succeeded, but the first one will report.
% 0.83/0.89 % (23739)Refutation found. Thanks to Tanya!
% 0.83/0.89 % SZS status Theorem for DTF2THF_23475
% 0.83/0.89 % SZS output start Proof for DTF2THF_23475
% 0.83/0.89 thf(type_def_6, type, sK0: $tType).
% 0.83/0.89 thf(func_def_0, type, 'const/sets/UNIV': !>[X0: $tType]:(X0 > $o)).
% 0.83/0.89 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 0.83/0.89 thf(func_def_6, type, sK1: sK0).
% 0.83/0.89 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 0.83/0.89 thf(f22,plain,(
% 0.83/0.89 $false),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 0.83/0.89 thf(f21,plain,(
% 0.83/0.89 ($false = $true)),
% 0.83/0.89 inference(beta_eta_normalization,[status(thm)],[f20])).
% 0.83/0.89 thf(f20,plain,(
% 0.83/0.89 ($false = ((^[Y0 : sK0]: ($true)) @ sK1))),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 0.83/0.89 thf(f19,plain,(
% 0.83/0.89 ($false = ((^[Y0 : sK0]: ($true)) @ sK1)) | ($true != $true)),
% 0.83/0.89 inference(superposition,[status(thm)],[f16,f17])).
% 0.83/0.89 thf(f17,plain,(
% 0.83/0.89 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ($false = (X1 @ X2))) )),
% 0.83/0.89 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 0.83/0.89 thf(f15,plain,(
% 0.83/0.89 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f9])).
% 0.83/0.89 thf(f9,plain,(
% 0.83/0.89 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 0.83/0.89 inference(rectify,[status(thm)],[f2])).
% 0.83/0.89 thf(f2,axiom,(
% 0.83/0.89 ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ X2) = (X2 @ X1))),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/IN_')).
% 0.83/0.89 thf(f16,plain,(
% 0.83/0.89 ($true != ('const/sets/IN' @ sK0 @ sK1 @ (^[Y0 : sK0]: ($true))))),
% 0.83/0.89 inference(definition_unfolding,[status(thm)],[f14,f13])).
% 0.83/0.89 thf(f13,plain,(
% 0.83/0.89 ( ! [X0 : $tType] : (('const/sets/UNIV' @ X0 = (^[Y0 : X0]: ($true)))) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f8])).
% 0.83/0.89 thf(f8,plain,(
% 0.83/0.89 ! [X0 : $tType] : ('const/sets/UNIV' @ X0 = (^[Y0 : X0]: ($true)))),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f1])).
% 0.83/0.89 thf(f1,axiom,(
% 0.83/0.89 ! [X0 : $tType] : ('const/sets/UNIV' @ X0 = (^[X1 : X0] : ($true)))),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/UNIV_')).
% 0.83/0.89 thf(f14,plain,(
% 0.83/0.89 (('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0) != $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f12])).
% 0.83/0.89 thf(f12,plain,(
% 0.83/0.89 (('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0) != $true)),
% 0.83/0.89 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11])).
% 0.83/0.89 thf(f11,plain,(
% 0.83/0.89 ? [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) != $true) => (('const/sets/IN' @ sK0 @ sK1 @ 'const/sets/UNIV' @ sK0) != $true)),
% 0.83/0.89 introduced(definition,[],[choice_axiom])).
% 0.83/0.89 thf(f10,plain,(
% 0.83/0.89 ? [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) != $true)),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f7])).
% 0.83/0.89 thf(f7,plain,(
% 0.83/0.89 ~! [X0 : $tType,X1 : X0] : (('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0) = $true)),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f6])).
% 0.83/0.89 thf(f6,plain,(
% 0.83/0.89 ~! [X0 : $tType,X1 : X0] : ('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 0.83/0.89 inference(rectify,[status(thm)],[f4])).
% 0.83/0.89 thf(f4,negated_conjecture,(
% 0.83/0.89 ~! [X0 : $tType,X1 : X0] : ('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 0.83/0.89 inference(negated_conjecture,[status(cth)],[f3])).
% 0.83/0.89 thf(f3,conjecture,(
% 0.83/0.89 ! [X0 : $tType,X1 : X0] : ('const/sets/IN' @ X0 @ X1 @ 'const/sets/UNIV' @ X0)),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.4bXZYpYHnd/DTF2THF_23475.p','thm/sets/IN_UNIV_')).
% 0.83/0.89 % SZS output end Proof for DTF2THF_23475
% 0.83/0.89 % (23739)------------------------------
% 0.83/0.89 % (23739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (23739)Termination reason: Refutation
% 0.83/0.89
% 0.83/0.89 % (23739)Memory used [KB]: 5500
% 0.83/0.89 % (23739)Time elapsed: 0.002 s
% 0.83/0.89 % (23739)Instructions burned: 1 (million)
% 0.83/0.89 % (23739)------------------------------
% 0.83/0.89 % (23739)------------------------------
% 0.83/0.89 % (23735)Success in time 0.009 s
%------------------------------------------------------------------------------