%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU562^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 09:35:17 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 159 ( 17 ~; 6 |; 6 &; 105 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 38 ( 15 ^; 19 !; 4 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f37,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f32]) ).
thf(f32,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( ( in @ sK3 @ sK0 )
=> ( in @ sK3 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( in @ Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
@ sK0
@ sK1 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f16,f19]) ).
thf(f19,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
file('/export/starexec/sandbox2/tmp/tmp.zGNxeBVwwQ/DTF2THF_3356.p',subset) ).
thf(f16,plain,
( ( subset @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetI1 = $true )
& ( ( subset @ sK0 @ sK1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
| ( $true
= ( in @ X2 @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) )
=> ( ( ( subset @ sK0 @ sK1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK0 )
!= $true )
| ( $true
= ( in @ X2 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( subsetI1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( subsetI1 = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( subsetI1
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( subsetI1
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zGNxeBVwwQ/DTF2THF_3356.p',subsetI2) ).
thf(f36,plain,
( $true
!= ( in @ sK3 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false = $true )
| ( $true
!= ( in @ sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f15,f31]) ).
thf(f31,plain,
( $false
= ( in @ sK3 @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f15,plain,
! [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
| ( ( in @ X2 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU562^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:26:32 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU562^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! B:i.(! x:i.in x A -> in x B) -> subset A B)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC064l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 2 def)
% 0.30/0.46 % Number of atoms : 13 ( 2 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.30/0.46 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 16 @)
% 0.30/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 9 ( 2 ^; 7 !; 0 ?; 9 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=151
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subset,definition,
% 0.30/0.46 ( subset
% 0.30/0.46 = ( ^ [A: $i,B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2,conjecture,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 => ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 12:26:33 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.zGNxeBVwwQ/DTF2DTF3356.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(in_type,type,
% 1.47/1.28 in: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(subset_type,type,
% 1.47/1.28 subset: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(subset,definition,
% 1.47/1.28 ( subset
% 1.47/1.28 = ( ^ [A: $i,B: $i] :
% 1.47/1.28 ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( in @ Xx @ B ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(subsetI1_type,type,
% 1.47/1.28 subsetI1: $o ).
% 1.47/1.28
% 1.47/1.28 thf(subsetI1,definition,
% 1.47/1.28 ( subsetI1
% 1.47/1.28 = ( ! [A: $i,B: $i] :
% 1.47/1.28 ( ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( in @ Xx @ B ) )
% 1.47/1.28 => ( subset @ A @ B ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(subsetI2,conjecture,
% 1.47/1.28 ( subsetI1
% 1.47/1.28 => ! [A: $i,B: $i] :
% 1.47/1.28 ( ! [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 => ( in @ Xx @ B ) )
% 1.47/1.28 => ( subset @ A @ B ) ) ) ).
% 1.47/1.28 ------------------------
% 1.64/1.30 % (3518)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3356 for (2999ds/183Mi)
% 1.64/1.30 % (3523)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_3356 for (2999ds/275Mi)
% 1.64/1.30 % (3518)First to succeed.
% 1.64/1.30 % (3523)Also succeeded, but the first one will report.
% 1.64/1.30 % (3518)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_3356
% 1.64/1.30 % SZS output start Proof for DTF2THF_3356
% 1.64/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.30 thf(func_def_1, type, subset: $i > $i > $o).
% 1.64/1.30 thf(f37,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(subsumption_resolution,[status(thm)],[f36,f32])).
% 1.64/1.30 thf(f32,plain,(
% 1.64/1.30 ($true = (in @ sK3 @ sK0))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.30 thf(f30,plain,(
% 1.64/1.30 ($false = ((in @ sK3 @ sK0) => (in @ sK3 @ sK1)))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.64/1.30 thf(f29,plain,(
% 1.64/1.30 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1))) @ sK3))),
% 1.64/1.30 inference(sigma_clausification,[status(thm)],[f28])).
% 1.64/1.30 thf(f28,plain,(
% 1.64/1.30 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (in @ Y0 @ sK1)))))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))) @ sK0 @ sK1) != $true)),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f16,f19])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.64/1.30 inference(rectify,[status(thm)],[f1])).
% 1.64/1.30 thf(f1,axiom,(
% 1.64/1.30 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.zGNxeBVwwQ/DTF2THF_3356.p',subset)).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 ((subset @ sK0 @ sK1) != $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 (subsetI1 = $true) & (((subset @ sK0 @ sK1) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) != $true) | ($true = (in @ X2 @ sK1))))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))) => (((subset @ sK0 @ sK1) != $true) & ! [X2 : $i] : (((in @ X2 @ sK0) != $true) | ($true = (in @ X2 @ sK1))))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 (subsetI1 = $true) & ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,plain,(
% 1.64/1.30 ~((subsetI1 = $true) => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.64/1.30 thf(f6,plain,(
% 1.64/1.30 ~(subsetI1 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.64/1.30 inference(rectify,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,negated_conjecture,(
% 1.64/1.30 ~(subsetI1 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.64/1.30 thf(f3,conjecture,(
% 1.64/1.30 subsetI1 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.zGNxeBVwwQ/DTF2THF_3356.p',subsetI2)).
% 1.64/1.30 thf(f36,plain,(
% 1.64/1.30 ($true != (in @ sK3 @ sK0))),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.64/1.30 thf(f34,plain,(
% 1.64/1.30 ($false = $true) | ($true != (in @ sK3 @ sK0))),
% 1.64/1.30 inference(superposition,[status(thm)],[f15,f31])).
% 1.64/1.30 thf(f31,plain,(
% 1.64/1.30 ($false = (in @ sK3 @ sK1))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 ( ! [X2 : $i] : (($true = (in @ X2 @ sK1)) | ((in @ X2 @ sK0) != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_3356
% 1.64/1.30 % (3518)------------------------------
% 1.64/1.30 % (3518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (3518)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (3518)Memory used [KB]: 5500
% 1.64/1.30 % (3518)Time elapsed: 0.003 s
% 1.64/1.30 % (3518)Instructions burned: 2 (million)
% 1.64/1.30 % (3518)------------------------------
% 1.64/1.30 % (3518)------------------------------
% 1.64/1.30 % (3517)Success in time 0.014 s
%------------------------------------------------------------------------------