%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU575^2 : 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 : n010.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 09:35:22 AM UTC 2026
% Result : Theorem 1.55s 1.32s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 357 ( 113 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 251 ( 48 ~; 35 |; 27 &; 116 @)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 35 !; 12 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(f49,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f48,f26]) ).
thf(f26,plain,
emptyset != sK0,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( setextsub = $true )
& ( emptysetsubset = $true )
& ( $true
= ( subset @ sK0 @ emptyset ) )
& ( emptyset != sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) )
=> ( ( $true
= ( subset @ sK0 @ emptyset ) )
& ( emptyset != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setextsub = $true )
& ( emptysetsubset = $true )
& ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) )
& ( setextsub = $true )
& ( emptysetsubset = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( emptysetsubset = $true )
=> ( ( setextsub = $true )
=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( emptyset = X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',subsetemptysetimpeq) ).
thf(f48,plain,
emptyset = sK0,
inference(subsumption_resolution,[status(thm)],[f47,f42]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( $true != $true )
| ( $true
= ( subset @ emptyset @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f30,f28]) ).
thf(f28,plain,
emptysetsubset = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f30,plain,
! [X1: $i] :
( ( $true
= ( subset @ emptyset @ X1 ) )
| ( emptysetsubset != $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( emptysetsubset = $true )
| ( ( subset @ emptyset @ sK1 )
!= $true ) )
& ( ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) )
| ( emptysetsubset != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f20]) ).
thf(f20,plain,
( ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true )
=> ( ( subset @ emptyset @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) )
| ( emptysetsubset != $true ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true )
| ( emptysetsubset != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( emptysetsubset = $true )
<=> ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( subset @ emptyset @ X0 )
= emptysetsubset ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i] :
( ( subset @ emptyset @ X0 )
= emptysetsubset ),
file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',emptysetsubset) ).
thf(f47,plain,
( ( $true
!= ( subset @ emptyset @ sK0 ) )
| ( emptyset = sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( $true
!= ( subset @ emptyset @ sK0 ) )
| ( $true != $true )
| ( emptyset = sK0 ) ),
inference(superposition,[status(thm)],[f43,f27]) ).
thf(f27,plain,
( $true
= ( subset @ sK0 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f43,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f29]) ).
thf(f29,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( setextsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( setextsub = $true )
| ( ( sK2 != sK3 )
& ( ( subset @ sK2 @ sK3 )
= $true )
& ( ( subset @ sK3 @ sK2 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f23,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( sK2 != sK3 )
& ( ( subset @ sK2 @ sK3 )
= $true )
& ( ( subset @ sK3 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',setextsub) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU575^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n010.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:27:03 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU575^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.18/0.38 % Version : Especial > Reduced > Especial.
% 0.18/0.38 % English : (! A:i.subset A emptyset -> A = emptyset)
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC077l [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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 v4.1.0, 0.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.18/0.38 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.38 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 8 @)
% 0.18/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 7 ( 3 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=479
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(emptyset_type,type,
% 0.18/0.38 emptyset: $i ).
% 0.18/0.38
% 0.18/0.38 thf(subset_type,type,
% 0.18/0.38 subset: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetsubset_type,type,
% 0.18/0.38 emptysetsubset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetsubset,definition,
% 0.18/0.38 ( emptysetsubset
% 0.18/0.38 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setextsub_type,type,
% 0.18/0.38 setextsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setextsub,definition,
% 0.18/0.38 ( setextsub
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( subset @ B @ A )
% 0.18/0.38 => ( A = B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetemptysetimpeq,conjecture,
% 0.18/0.38 ( emptysetsubset
% 0.18/0.38 => ( setextsub
% 0.18/0.38 => ! [A: $i] :
% 0.18/0.38 ( ( subset @ A @ emptyset )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.35/1.29 ---- Embedded in THF ---
% 1.35/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.35/1.29 %%% Generated on Tue Feb 24 12:27:04 EST 2026
% 1.35/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.35/1.29 %%% Logic specification used:
% 1.35/1.29 %%% thf(spec, logic, $$dhol).
% 1.35/1.29
% 1.35/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2DTF28950.p
% See solution above
% 1.35/1.29 ------------------------
% 1.55/1.30 ---- Cleaned THF ---
% 1.55/1.30 thf(emptyset_type,type,
% 1.55/1.30 emptyset: $i ).
% 1.55/1.30
% 1.55/1.30 thf(subset_type,type,
% 1.55/1.30 subset: $i > $i > $o ).
% 1.55/1.30
% 1.55/1.30 thf(emptysetsubset_type,type,
% 1.55/1.30 emptysetsubset: $o ).
% 1.55/1.30
% 1.55/1.30 thf(emptysetsubset,definition,
% 1.55/1.30 ( emptysetsubset
% 1.55/1.30 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 1.55/1.30
% 1.55/1.30 thf(setextsub_type,type,
% 1.55/1.30 setextsub: $o ).
% 1.55/1.30
% 1.55/1.30 thf(setextsub,definition,
% 1.55/1.30 ( setextsub
% 1.55/1.30 = ( ! [A: $i,B: $i] :
% 1.55/1.30 ( ( subset @ A @ B )
% 1.55/1.30 => ( ( subset @ B @ A )
% 1.55/1.30 => ( A = B ) ) ) ) ) ).
% 1.55/1.30
% 1.55/1.30 thf(subsetemptysetimpeq,conjecture,
% 1.55/1.30 ( emptysetsubset
% 1.55/1.30 => ( setextsub
% 1.55/1.30 => ! [A: $i] :
% 1.55/1.30 ( ( subset @ A @ emptyset )
% 1.55/1.30 => ( A = emptyset ) ) ) ) ).
% 1.55/1.30 ------------------------
% 1.55/1.32 % (29053)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28950 for (2999ds/18Mi)
% 1.55/1.32 % (29047)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28950 for (2999ds/183Mi)
% 1.55/1.32 % (29050)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28950 for (2999ds/2Mi)
% 1.55/1.32 % (29051)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_28950 for (2999ds/2Mi)
% 1.55/1.32 % (29052)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_28950 for (2999ds/275Mi)
% 1.55/1.32 % (29049)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_28950 for (2999ds/27Mi)
% 1.55/1.32 % (29048)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_28950 for (2999ds/4Mi)
% 1.55/1.32 % (29053)First to succeed.
% 1.55/1.32 % (29050)Instruction limit reached!
% 1.55/1.32 % (29050)------------------------------
% 1.55/1.32 % (29050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (29050)Termination reason: Unknown
% 1.55/1.32 % (29050)Termination phase: Saturation
% 1.55/1.32 % (29051)Instruction limit reached!
% 1.55/1.32 % (29051)------------------------------
% 1.55/1.32 % (29051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32
% 1.55/1.32 % (29050)Memory used [KB]: 5500
% 1.55/1.32 % (29050)Time elapsed: 0.003 s
% 1.55/1.32 % (29050)Instructions burned: 3 (million)
% 1.55/1.32 % (29050)------------------------------
% 1.55/1.32 % (29050)------------------------------
% 1.55/1.32 % (29051)Termination reason: Unknown
% 1.55/1.32 % (29051)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (29051)Memory used [KB]: 5500
% 1.55/1.32 % (29051)Time elapsed: 0.003 s
% 1.55/1.32 % (29051)Instructions burned: 3 (million)
% 1.55/1.32 % (29051)------------------------------
% 1.55/1.32 % (29051)------------------------------
% 1.55/1.32 % (29048)Instruction limit reached!
% 1.55/1.32 % (29048)------------------------------
% 1.55/1.32 % (29048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (29048)Termination reason: Unknown
% 1.55/1.32 % (29048)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (29048)Memory used [KB]: 5500
% 1.55/1.32 % (29048)Time elapsed: 0.004 s
% 1.55/1.32 % (29048)Instructions burned: 4 (million)
% 1.55/1.32 % (29048)------------------------------
% 1.55/1.32 % (29048)------------------------------
% 1.55/1.32 % (29052)Also succeeded, but the first one will report.
% 1.55/1.32 % (29047)Also succeeded, but the first one will report.
% 1.55/1.32 % (29053)Refutation found. Thanks to Tanya!
% 1.55/1.32 % SZS status Theorem for DTF2THF_28950
% 1.55/1.32 % SZS output start Proof for DTF2THF_28950
% 1.55/1.32 thf(func_def_1, type, subset: $i > $i > $o).
% 1.55/1.32 thf(f49,plain,(
% 1.55/1.32 $false),
% 1.55/1.32 inference(subsumption_resolution,[status(thm)],[f48,f26])).
% 1.55/1.32 thf(f26,plain,(
% 1.55/1.32 (emptyset != sK0)),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.55/1.32 thf(f17,plain,(
% 1.55/1.32 (setextsub = $true) & (emptysetsubset = $true) & (($true = (subset @ sK0 @ emptyset)) & (emptyset != sK0))),
% 1.55/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f16])).
% 1.55/1.32 thf(f16,plain,(
% 1.55/1.32 ? [X0 : $i] : (((subset @ X0 @ emptyset) = $true) & (emptyset != X0)) => (($true = (subset @ sK0 @ emptyset)) & (emptyset != sK0))),
% 1.55/1.32 introduced(definition,[],[choice_axiom])).
% 1.55/1.32 thf(f13,plain,(
% 1.55/1.32 (setextsub = $true) & (emptysetsubset = $true) & ? [X0 : $i] : (((subset @ X0 @ emptyset) = $true) & (emptyset != X0))),
% 1.55/1.32 inference(flattening,[status(thm)],[f12])).
% 1.55/1.32 thf(f12,plain,(
% 1.55/1.32 (? [X0 : $i] : (((subset @ X0 @ emptyset) = $true) & (emptyset != X0)) & (setextsub = $true)) & (emptysetsubset = $true)),
% 1.55/1.32 inference(ennf_transformation,[status(thm)],[f7])).
% 1.55/1.32 thf(f7,plain,(
% 1.55/1.32 ~((emptysetsubset = $true) => ((setextsub = $true) => ! [X0 : $i] : (((subset @ X0 @ emptyset) = $true) => (emptyset = X0))))),
% 1.55/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.55/1.32 thf(f6,plain,(
% 1.55/1.32 ~(emptysetsubset => (setextsub => ! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0))))),
% 1.55/1.32 inference(rectify,[status(thm)],[f4])).
% 1.55/1.32 thf(f4,negated_conjecture,(
% 1.55/1.32 ~(emptysetsubset => (setextsub => ! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0))))),
% 1.55/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.55/1.32 thf(f3,conjecture,(
% 1.55/1.32 emptysetsubset => (setextsub => ! [X0 : $i] : ((subset @ X0 @ emptyset) => (emptyset = X0)))),
% 1.55/1.32 file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',subsetemptysetimpeq)).
% 1.55/1.32 thf(f48,plain,(
% 1.55/1.32 (emptyset = sK0)),
% 1.55/1.32 inference(subsumption_resolution,[status(thm)],[f47,f42])).
% 1.55/1.32 thf(f42,plain,(
% 1.55/1.32 ( ! [X1 : $i] : (($true = (subset @ emptyset @ X1))) )),
% 1.55/1.32 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.55/1.32 thf(f37,plain,(
% 1.55/1.32 ( ! [X1 : $i] : (($true != $true) | ($true = (subset @ emptyset @ X1))) )),
% 1.55/1.32 inference(definition_unfolding,[status(thm)],[f30,f28])).
% 1.55/1.32 thf(f28,plain,(
% 1.55/1.32 (emptysetsubset = $true)),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.55/1.32 thf(f30,plain,(
% 1.55/1.32 ( ! [X1 : $i] : (($true = (subset @ emptyset @ X1)) | (emptysetsubset != $true)) )),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f21])).
% 1.55/1.32 thf(f21,plain,(
% 1.55/1.32 ((emptysetsubset = $true) | ((subset @ emptyset @ sK1) != $true)) & (! [X1 : $i] : ($true = (subset @ emptyset @ X1)) | (emptysetsubset != $true))),
% 1.55/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f20])).
% 1.55/1.32 thf(f20,plain,(
% 1.55/1.32 ? [X0 : $i] : ((subset @ emptyset @ X0) != $true) => ((subset @ emptyset @ sK1) != $true)),
% 1.55/1.32 introduced(definition,[],[choice_axiom])).
% 1.55/1.32 thf(f19,plain,(
% 1.55/1.32 ((emptysetsubset = $true) | ? [X0 : $i] : ((subset @ emptyset @ X0) != $true)) & (! [X1 : $i] : ($true = (subset @ emptyset @ X1)) | (emptysetsubset != $true))),
% 1.55/1.32 inference(rectify,[status(thm)],[f18])).
% 1.55/1.32 thf(f18,plain,(
% 1.55/1.32 ((emptysetsubset = $true) | ? [X0 : $i] : ((subset @ emptyset @ X0) != $true)) & (! [X0 : $i] : ((subset @ emptyset @ X0) = $true) | (emptysetsubset != $true))),
% 1.55/1.32 inference(nnf_transformation,[status(thm)],[f9])).
% 1.55/1.32 thf(f9,plain,(
% 1.55/1.32 (emptysetsubset = $true) <=> ! [X0 : $i] : ((subset @ emptyset @ X0) = $true)),
% 1.55/1.32 inference(fool_elimination,[status(thm)],[f8])).
% 1.55/1.32 thf(f8,plain,(
% 1.55/1.32 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 1.55/1.32 inference(rectify,[status(thm)],[f1])).
% 1.55/1.32 thf(f1,axiom,(
% 1.55/1.32 (! [X0 : $i] : (subset @ emptyset @ X0) = emptysetsubset)),
% 1.55/1.32 file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',emptysetsubset)).
% 1.55/1.32 thf(f47,plain,(
% 1.55/1.32 ($true != (subset @ emptyset @ sK0)) | (emptyset = sK0)),
% 1.55/1.32 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.55/1.32 thf(f44,plain,(
% 1.55/1.32 ($true != (subset @ emptyset @ sK0)) | ($true != $true) | (emptyset = sK0)),
% 1.55/1.32 inference(superposition,[status(thm)],[f43,f27])).
% 1.55/1.32 thf(f27,plain,(
% 1.55/1.32 ($true = (subset @ sK0 @ emptyset))),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.55/1.32 thf(f43,plain,(
% 1.55/1.32 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | (X2 = X3) | ((subset @ X2 @ X3) != $true)) )),
% 1.55/1.32 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.55/1.32 thf(f41,plain,(
% 1.55/1.32 ( ! [X2 : $i,X3 : $i] : (($true != $true) | (X2 = X3) | ((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true)) )),
% 1.55/1.32 inference(definition_unfolding,[status(thm)],[f32,f29])).
% 1.55/1.32 thf(f29,plain,(
% 1.55/1.32 (setextsub = $true)),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f17])).
% 1.55/1.32 thf(f32,plain,(
% 1.55/1.32 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (setextsub != $true)) )),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f25])).
% 1.55/1.32 thf(f25,plain,(
% 1.55/1.32 ((setextsub = $true) | ((sK2 != sK3) & ((subset @ sK2 @ sK3) = $true) & ((subset @ sK3 @ sK2) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true)) | (setextsub != $true))),
% 1.55/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f23,f24])).
% 1.55/1.32 thf(f24,plain,(
% 1.55/1.32 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true)) => ((sK2 != sK3) & ((subset @ sK2 @ sK3) = $true) & ((subset @ sK3 @ sK2) = $true))),
% 1.55/1.32 introduced(definition,[],[choice_axiom])).
% 1.55/1.32 thf(f23,plain,(
% 1.55/1.32 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true)) | (setextsub != $true))),
% 1.55/1.32 inference(rectify,[status(thm)],[f22])).
% 1.55/1.32 thf(f22,plain,(
% 1.55/1.32 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true)) | (setextsub != $true))),
% 1.55/1.32 inference(nnf_transformation,[status(thm)],[f15])).
% 1.55/1.32 thf(f15,plain,(
% 1.55/1.32 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true))),
% 1.55/1.32 inference(flattening,[status(thm)],[f14])).
% 1.55/1.32 thf(f14,plain,(
% 1.55/1.32 (setextsub = $true) <=> ! [X1 : $i,X0 : $i] : (((X0 = X1) | ((subset @ X1 @ X0) != $true)) | ((subset @ X0 @ X1) != $true))),
% 1.55/1.32 inference(ennf_transformation,[status(thm)],[f11])).
% 1.55/1.32 thf(f11,plain,(
% 1.55/1.32 (setextsub = $true) <=> ! [X1 : $i,X0 : $i] : (((subset @ X0 @ X1) = $true) => (((subset @ X1 @ X0) = $true) => (X0 = X1)))),
% 1.55/1.32 inference(fool_elimination,[status(thm)],[f10])).
% 1.55/1.32 thf(f10,plain,(
% 1.55/1.32 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 1.55/1.32 inference(rectify,[status(thm)],[f2])).
% 1.55/1.32 thf(f2,axiom,(
% 1.55/1.32 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 1.55/1.32 file('/export/starexec/sandbox2/tmp/tmp.Abuskv94Tq/DTF2THF_28950.p',setextsub)).
% 1.55/1.32 % SZS output end Proof for DTF2THF_28950
% 1.55/1.32 % (29053)------------------------------
% 1.55/1.32 % (29053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (29053)Termination reason: Refutation
% 1.55/1.32
% 1.55/1.32 % (29053)Memory used [KB]: 5500
% 1.55/1.32 % (29053)Time elapsed: 0.004 s
% 1.55/1.32 % (29053)Instructions burned: 2 (million)
% 1.55/1.32 % (29053)------------------------------
% 1.55/1.32 % (29053)------------------------------
% 1.55/1.32 % (29046)Success in time 0.018 s
%------------------------------------------------------------------------------